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+Provided by The Internet Classics Archive.
+See bottom for copyright. Available online at
+    http://classics.mit.edu//Aristotle/posterior.html
+
+Posterior Analytics
+By Aristotle
+
+Translated by G. R. G. Mure
+
+----------------------------------------------------------------------
+
+BOOK I
+
+Part 1 
+
+All instruction given or received by way of argument proceeds from
+pre-existent knowledge. This becomes evident upon a survey of all
+the species of such instruction. The mathematical sciences and all
+other speculative disciplines are acquired in this way, and so are
+the two forms of dialectical reasoning, syllogistic and inductive;
+for each of these latter make use of old knowledge to impart new,
+the syllogism assuming an audience that accepts its premisses, induction
+exhibiting the universal as implicit in the clearly known particular.
+Again, the persuasion exerted by rhetorical arguments is in principle
+the same, since they use either example, a kind of induction, or enthymeme,
+a form of syllogism. 
+
+The pre-existent knowledge required is of two kinds. In some cases
+admission of the fact must be assumed, in others comprehension of
+the meaning of the term used, and sometimes both assumptions are essential.
+Thus, we assume that every predicate can be either truly affirmed
+or truly denied of any subject, and that 'triangle' means so and so;
+as regards 'unit' we have to make the double assumption of the meaning
+of the word and the existence of the thing. The reason is that these
+several objects are not equally obvious to us. Recognition of a truth
+may in some cases contain as factors both previous knowledge and also
+knowledge acquired simultaneously with that recognition-knowledge,
+this latter, of the particulars actually falling under the universal
+and therein already virtually known. For example, the student knew
+beforehand that the angles of every triangle are equal to two right
+angles; but it was only at the actual moment at which he was being
+led on to recognize this as true in the instance before him that he
+came to know 'this figure inscribed in the semicircle' to be a triangle.
+For some things (viz. the singulars finally reached which are not
+predicable of anything else as subject) are only learnt in this way,
+i.e. there is here no recognition through a middle of a minor term
+as subject to a major. Before he was led on to recognition or before
+he actually drew a conclusion, we should perhaps say that in a manner
+he knew, in a manner not. 
+
+If he did not in an unqualified sense of the term know the existence
+of this triangle, how could he know without qualification that its
+angles were equal to two right angles? No: clearly he knows not without
+qualification but only in the sense that he knows universally. If
+this distinction is not drawn, we are faced with the dilemma in the
+Meno: either a man will learn nothing or what he already knows; for
+we cannot accept the solution which some people offer. A man is asked,
+'Do you, or do you not, know that every pair is even?' He says he
+does know it. The questioner then produces a particular pair, of the
+existence, and so a fortiori of the evenness, of which he was unaware.
+The solution which some people offer is to assert that they do not
+know that every pair is even, but only that everything which they
+know to be a pair is even: yet what they know to be even is that of
+which they have demonstrated evenness, i.e. what they made the subject
+of their premiss, viz. not merely every triangle or number which they
+know to be such, but any and every number or triangle without reservation.
+For no premiss is ever couched in the form 'every number which you
+know to be such', or 'every rectilinear figure which you know to be
+such': the predicate is always construed as applicable to any and
+every instance of the thing. On the other hand, I imagine there is
+nothing to prevent a man in one sense knowing what he is learning,
+in another not knowing it. The strange thing would be, not if in some
+sense he knew what he was learning, but if he were to know it in that
+precise sense and manner in which he was learning it. 
+
+Part 2
+
+We suppose ourselves to possess unqualified scientific knowledge of
+a thing, as opposed to knowing it in the accidental way in which the
+sophist knows, when we think that we know the cause on which the fact
+depends, as the cause of that fact and of no other, and, further,
+that the fact could not be other than it is. Now that scientific knowing
+is something of this sort is evident-witness both those who falsely
+claim it and those who actually possess it, since the former merely
+imagine themselves to be, while the latter are also actually, in the
+condition described. Consequently the proper object of unqualified
+scientific knowledge is something which cannot be other than it is.
+
+There may be another manner of knowing as well-that will be discussed
+later. What I now assert is that at all events we do know by demonstration.
+By demonstration I mean a syllogism productive of scientific knowledge,
+a syllogism, that is, the grasp of which is eo ipso such knowledge.
+Assuming then that my thesis as to the nature of scientific knowing
+is correct, the premisses of demonstrated knowledge must be true,
+primary, immediate, better known than and prior to the conclusion,
+which is further related to them as effect to cause. Unless these
+conditions are satisfied, the basic truths will not be 'appropriate'
+to the conclusion. Syllogism there may indeed be without these conditions,
+but such syllogism, not being productive of scientific knowledge,
+will not be demonstration. The premisses must be true: for that which
+is non-existent cannot be known-we cannot know, e.g. that the diagonal
+of a square is commensurate with its side. The premisses must be primary
+and indemonstrable; otherwise they will require demonstration in order
+to be known, since to have knowledge, if it be not accidental knowledge,
+of things which are demonstrable, means precisely to have a demonstration
+of them. The premisses must be the causes of the conclusion, better
+known than it, and prior to it; its causes, since we possess scientific
+knowledge of a thing only when we know its cause; prior, in order
+to be causes; antecedently known, this antecedent knowledge being
+not our mere understanding of the meaning, but knowledge of the fact
+as well. Now 'prior' and 'better known' are ambiguous terms, for there
+is a difference between what is prior and better known in the order
+of being and what is prior and better known to man. I mean that objects
+nearer to sense are prior and better known to man; objects without
+qualification prior and better known are those further from sense.
+Now the most universal causes are furthest from sense and particular
+causes are nearest to sense, and they are thus exactly opposed to
+one another. In saying that the premisses of demonstrated knowledge
+must be primary, I mean that they must be the 'appropriate' basic
+truths, for I identify primary premiss and basic truth. A 'basic truth'
+in a demonstration is an immediate proposition. An immediate proposition
+is one which has no other proposition prior to it. A proposition is
+either part of an enunciation, i.e. it predicates a single attribute
+of a single subject. If a proposition is dialectical, it assumes either
+part indifferently; if it is demonstrative, it lays down one part
+to the definite exclusion of the other because that part is true.
+The term 'enunciation' denotes either part of a contradiction indifferently.
+A contradiction is an opposition which of its own nature excludes
+a middle. The part of a contradiction which conjoins a predicate with
+a subject is an affirmation; the part disjoining them is a negation.
+I call an immediate basic truth of syllogism a 'thesis' when, though
+it is not susceptible of proof by the teacher, yet ignorance of it
+does not constitute a total bar to progress on the part of the pupil:
+one which the pupil must know if he is to learn anything whatever
+is an axiom. I call it an axiom because there are such truths and
+we give them the name of axioms par excellence. If a thesis assumes
+one part or the other of an enunciation, i.e. asserts either the existence
+or the non-existence of a subject, it is a hypothesis; if it does
+not so assert, it is a definition. Definition is a 'thesis' or a 'laying
+something down', since the arithmetician lays it down that to be a
+unit is to be quantitatively indivisible; but it is not a hypothesis,
+for to define what a unit is is not the same as to affirm its existence.
+
+Now since the required ground of our knowledge-i.e. of our conviction-of
+a fact is the possession of such a syllogism as we call demonstration,
+and the ground of the syllogism is the facts constituting its premisses,
+we must not only know the primary premisses-some if not all of them-beforehand,
+but know them better than the conclusion: for the cause of an attribute's
+inherence in a subject always itself inheres in the subject more firmly
+than that attribute; e.g. the cause of our loving anything is dearer
+to us than the object of our love. So since the primary premisses
+are the cause of our knowledge-i.e. of our conviction-it follows that
+we know them better-that is, are more convinced of them-than their
+consequences, precisely because of our knowledge of the latter is
+the effect of our knowledge of the premisses. Now a man cannot believe
+in anything more than in the things he knows, unless he has either
+actual knowledge of it or something better than actual knowledge.
+But we are faced with this paradox if a student whose belief rests
+on demonstration has not prior knowledge; a man must believe in some,
+if not in all, of the basic truths more than in the conclusion. Moreover,
+if a man sets out to acquire the scientific knowledge that comes through
+demonstration, he must not only have a better knowledge of the basic
+truths and a firmer conviction of them than of the connexion which
+is being demonstrated: more than this, nothing must be more certain
+or better known to him than these basic truths in their character
+as contradicting the fundamental premisses which lead to the opposed
+and erroneous conclusion. For indeed the conviction of pure science
+must be unshakable. 
+
+Part 3
+
+Some hold that, owing to the necessity of knowing the primary premisses,
+there is no scientific knowledge. Others think there is, but that
+all truths are demonstrable. Neither doctrine is either true or a
+necessary deduction from the premisses. The first school, assuming
+that there is no way of knowing other than by demonstration, maintain
+that an infinite regress is involved, on the ground that if behind
+the prior stands no primary, we could not know the posterior through
+the prior (wherein they are right, for one cannot traverse an infinite
+series): if on the other hand-they say-the series terminates and there
+are primary premisses, yet these are unknowable because incapable
+of demonstration, which according to them is the only form of knowledge.
+And since thus one cannot know the primary premisses, knowledge of
+the conclusions which follow from them is not pure scientific knowledge
+nor properly knowing at all, but rests on the mere supposition that
+the premisses are true. The other party agree with them as regards
+knowing, holding that it is only possible by demonstration, but they
+see no difficulty in holding that all truths are demonstrated, on
+the ground that demonstration may be circular and reciprocal.
+
+Our own doctrine is that not all knowledge is demonstrative: on the
+contrary, knowledge of the immediate premisses is independent of demonstration.
+(The necessity of this is obvious; for since we must know the prior
+premisses from which the demonstration is drawn, and since the regress
+must end in immediate truths, those truths must be indemonstrable.)
+Such, then, is our doctrine, and in addition we maintain that besides
+scientific knowledge there is its originative source which enables
+us to recognize the definitions. 
+
+Now demonstration must be based on premisses prior to and better known
+than the conclusion; and the same things cannot simultaneously be
+both prior and posterior to one another: so circular demonstration
+is clearly not possible in the unqualified sense of 'demonstration',
+but only possible if 'demonstration' be extended to include that other
+method of argument which rests on a distinction between truths prior
+to us and truths without qualification prior, i.e. the method by which
+induction produces knowledge. But if we accept this extension of its
+meaning, our definition of unqualified knowledge will prove faulty;
+for there seem to be two kinds of it. Perhaps, however, the second
+form of demonstration, that which proceeds from truths better known
+to us, is not demonstration in the unqualified sense of the term.
+
+The advocates of circular demonstration are not only faced with the
+difficulty we have just stated: in addition their theory reduces to
+the mere statement that if a thing exists, then it does exist-an easy
+way of proving anything. That this is so can be clearly shown by taking
+three terms, for to constitute the circle it makes no difference whether
+many terms or few or even only two are taken. Thus by direct proof,
+if A is, B must be; if B is, C must be; therefore if A is, C must
+be. Since then-by the circular proof-if A is, B must be, and if B
+is, A must be, A may be substituted for C above. Then 'if B is, A
+must be'='if B is, C must be', which above gave the conclusion 'if
+A is, C must be': but C and A have been identified. Consequently the
+upholders of circular demonstration are in the position of saying
+that if A is, A must be-a simple way of proving anything. Moreover,
+even such circular demonstration is impossible except in the case
+of attributes that imply one another, viz. 'peculiar' properties.
+
+Now, it has been shown that the positing of one thing-be it one term
+or one premiss-never involves a necessary consequent: two premisses
+constitute the first and smallest foundation for drawing a conclusion
+at all and therefore a fortiori for the demonstrative syllogism of
+science. If, then, A is implied in B and C, and B and C are reciprocally
+implied in one another and in A, it is possible, as has been shown
+in my writings on the syllogism, to prove all the assumptions on which
+the original conclusion rested, by circular demonstration in the first
+figure. But it has also been shown that in the other figures either
+no conclusion is possible, or at least none which proves both the
+original premisses. Propositions the terms of which are not convertible
+cannot be circularly demonstrated at all, and since convertible terms
+occur rarely in actual demonstrations, it is clearly frivolous and
+impossible to say that demonstration is reciprocal and that therefore
+everything can be demonstrated. 
+
+Part 4
+
+Since the object of pure scientific knowledge cannot be other than
+it is, the truth obtained by demonstrative knowledge will be necessary.
+And since demonstrative knowledge is only present when we have a demonstration,
+it follows that demonstration is an inference from necessary premisses.
+So we must consider what are the premisses of demonstration-i.e. what
+is their character: and as a preliminary, let us define what we mean
+by an attribute 'true in every instance of its subject', an 'essential'
+attribute, and a 'commensurate and universal' attribute. I call 'true
+in every instance' what is truly predicable of all instances-not of
+one to the exclusion of others-and at all times, not at this or that
+time only; e.g. if animal is truly predicable of every instance of
+man, then if it be true to say 'this is a man', 'this is an animal'
+is also true, and if the one be true now the other is true now. A
+corresponding account holds if point is in every instance predicable
+as contained in line. There is evidence for this in the fact that
+the objection we raise against a proposition put to us as true in
+every instance is either an instance in which, or an occasion on which,
+it is not true. Essential attributes are (1) such as belong to their
+subject as elements in its essential nature (e.g. line thus belongs
+to triangle, point to line; for the very being or 'substance' of triangle
+and line is composed of these elements, which are contained in the
+formulae defining triangle and line): (2) such that, while they belong
+to certain subjects, the subjects to which they belong are contained
+in the attribute's own defining formula. Thus straight and curved
+belong to line, odd and even, prime and compound, square and oblong,
+to number; and also the formula defining any one of these attributes
+contains its subject-e.g. line or number as the case may be.
+
+Extending this classification to all other attributes, I distinguish
+those that answer the above description as belonging essentially to
+their respective subjects; whereas attributes related in neither of
+these two ways to their subjects I call accidents or 'coincidents';
+e.g. musical or white is a 'coincident' of animal. 
+
+Further (a) that is essential which is not predicated of a subject
+other than itself: e.g. 'the walking [thing]' walks and is white in
+virtue of being something else besides; whereas substance, in the
+sense of whatever signifies a 'this somewhat', is not what it is in
+virtue of being something else besides. Things, then, not predicated
+of a subject I call essential; things predicated of a subject I call
+accidental or 'coincidental'. 
+
+In another sense again (b) a thing consequentially connected with
+anything is essential; one not so connected is 'coincidental'. An
+example of the latter is 'While he was walking it lightened': the
+lightning was not due to his walking; it was, we should say, a coincidence.
+If, on the other hand, there is a consequential connexion, the predication
+is essential; e.g. if a beast dies when its throat is being cut, then
+its death is also essentially connected with the cutting, because
+the cutting was the cause of death, not death a 'coincident' of the
+cutting. 
+
+So far then as concerns the sphere of connexions scientifically known
+in the unqualified sense of that term, all attributes which (within
+that sphere) are essential either in the sense that their subjects
+are contained in them, or in the sense that they are contained in
+their subjects, are necessary as well as consequentially connected
+with their subjects. For it is impossible for them not to inhere in
+their subjects either simply or in the qualified sense that one or
+other of a pair of opposites must inhere in the subject; e.g. in line
+must be either straightness or curvature, in number either oddness
+or evenness. For within a single identical genus the contrary of a
+given attribute is either its privative or its contradictory; e.g.
+within number what is not odd is even, inasmuch as within this sphere
+even is a necessary consequent of not-odd. So, since any given predicate
+must be either affirmed or denied of any subject, essential attributes
+must inhere in their subjects of necessity. 
+
+Thus, then, we have established the distinction between the attribute
+which is 'true in every instance' and the 'essential' attribute.
+
+I term 'commensurately universal' an attribute which belongs to every
+instance of its subject, and to every instance essentially and as
+such; from which it clearly follows that all commensurate universals
+inhere necessarily in their subjects. The essential attribute, and
+the attribute that belongs to its subject as such, are identical.
+E.g. point and straight belong to line essentially, for they belong
+to line as such; and triangle as such has two right angles, for it
+is essentially equal to two right angles. 
+
+An attribute belongs commensurately and universally to a subject when
+it can be shown to belong to any random instance of that subject and
+when the subject is the first thing to which it can be shown to belong.
+Thus, e.g. (1) the equality of its angles to two right angles is not
+a commensurately universal attribute of figure. For though it is possible
+to show that a figure has its angles equal to two right angles, this
+attribute cannot be demonstrated of any figure selected at haphazard,
+nor in demonstrating does one take a figure at random-a square is
+a figure but its angles are not equal to two right angles. On the
+other hand, any isosceles triangle has its angles equal to two right
+angles, yet isosceles triangle is not the primary subject of this
+attribute but triangle is prior. So whatever can be shown to have
+its angles equal to two right angles, or to possess any other attribute,
+in any random instance of itself and primarily-that is the first subject
+to which the predicate in question belongs commensurately and universally,
+and the demonstration, in the essential sense, of any predicate is
+the proof of it as belonging to this first subject commensurately
+and universally: while the proof of it as belonging to the other subjects
+to which it attaches is demonstration only in a secondary and unessential
+sense. Nor again (2) is equality to two right angles a commensurately
+universal attribute of isosceles; it is of wider application.
+
+Part 5
+
+We must not fail to observe that we often fall into error because
+our conclusion is not in fact primary and commensurately universal
+in the sense in which we think we prove it so. We make this mistake
+(1) when the subject is an individual or individuals above which there
+is no universal to be found: (2) when the subjects belong to different
+species and there is a higher universal, but it has no name: (3) when
+the subject which the demonstrator takes as a whole is really only
+a part of a larger whole; for then the demonstration will be true
+of the individual instances within the part and will hold in every
+instance of it, yet the demonstration will not be true of this subject
+primarily and commensurately and universally. When a demonstration
+is true of a subject primarily and commensurately and universally,
+that is to be taken to mean that it is true of a given subject primarily
+and as such. Case (3) may be thus exemplified. If a proof were given
+that perpendiculars to the same line are parallel, it might be supposed
+that lines thus perpendicular were the proper subject of the demonstration
+because being parallel is true of every instance of them. But it is
+not so, for the parallelism depends not on these angles being equal
+to one another because each is a right angle, but simply on their
+being equal to one another. An example of (1) would be as follows:
+if isosceles were the only triangle, it would be thought to have its
+angles equal to two right angles qua isosceles. An instance of (2)
+would be the law that proportionals alternate. Alternation used to
+be demonstrated separately of numbers, lines, solids, and durations,
+though it could have been proved of them all by a single demonstration.
+Because there was no single name to denote that in which numbers,
+lengths, durations, and solids are identical, and because they differed
+specifically from one another, this property was proved of each of
+them separately. To-day, however, the proof is commensurately universal,
+for they do not possess this attribute qua lines or qua numbers, but
+qua manifesting this generic character which they are postulated as
+possessing universally. Hence, even if one prove of each kind of triangle
+that its angles are equal to two right angles, whether by means of
+the same or different proofs; still, as long as one treats separately
+equilateral, scalene, and isosceles, one does not yet know, except
+sophistically, that triangle has its angles equal to two right angles,
+nor does one yet know that triangle has this property commensurately
+and universally, even if there is no other species of triangle but
+these. For one does not know that triangle as such has this property,
+nor even that 'all' triangles have it-unless 'all' means 'each taken
+singly': if 'all' means 'as a whole class', then, though there be
+none in which one does not recognize this property, one does not know
+it of 'all triangles'. 
+
+When, then, does our knowledge fail of commensurate universality,
+and when it is unqualified knowledge? If triangle be identical in
+essence with equilateral, i.e. with each or all equilaterals, then
+clearly we have unqualified knowledge: if on the other hand it be
+not, and the attribute belongs to equilateral qua triangle; then our
+knowledge fails of commensurate universality. 'But', it will be asked,
+'does this attribute belong to the subject of which it has been demonstrated
+qua triangle or qua isosceles? What is the point at which the subject.
+to which it belongs is primary? (i.e. to what subject can it be demonstrated
+as belonging commensurately and universally?)' Clearly this point
+is the first term in which it is found to inhere as the elimination
+of inferior differentiae proceeds. Thus the angles of a brazen isosceles
+triangle are equal to two right angles: but eliminate brazen and isosceles
+and the attribute remains. 'But'-you may say-'eliminate figure or
+limit, and the attribute vanishes.' True, but figure and limit are
+not the first differentiae whose elimination destroys the attribute.
+'Then what is the first?' If it is triangle, it will be in virtue
+of triangle that the attribute belongs to all the other subjects of
+which it is predicable, and triangle is the subject to which it can
+be demonstrated as belonging commensurately and universally.
+
+Part 6
+
+Demonstrative knowledge must rest on necessary basic truths; for the
+object of scientific knowledge cannot be other than it is. Now attributes
+attaching essentially to their subjects attach necessarily to them:
+for essential attributes are either elements in the essential nature
+of their subjects, or contain their subjects as elements in their
+own essential nature. (The pairs of opposites which the latter class
+includes are necessary because one member or the other necessarily
+inheres.) It follows from this that premisses of the demonstrative
+syllogism must be connexions essential in the sense explained: for
+all attributes must inhere essentially or else be accidental, and
+accidental attributes are not necessary to their subjects.
+
+We must either state the case thus, or else premise that the conclusion
+of demonstration is necessary and that a demonstrated conclusion cannot
+be other than it is, and then infer that the conclusion must be developed
+from necessary premisses. For though you may reason from true premisses
+without demonstrating, yet if your premisses are necessary you will
+assuredly demonstrate-in such necessity you have at once a distinctive
+character of demonstration. That demonstration proceeds from necessary
+premisses is also indicated by the fact that the objection we raise
+against a professed demonstration is that a premiss of it is not a
+necessary truth-whether we think it altogether devoid of necessity,
+or at any rate so far as our opponent's previous argument goes. This
+shows how naive it is to suppose one's basic truths rightly chosen
+if one starts with a proposition which is (1) popularly accepted and
+(2) true, such as the sophists' assumption that to know is the same
+as to possess knowledge. For (1) popular acceptance or rejection is
+no criterion of a basic truth, which can only be the primary law of
+the genus constituting the subject matter of the demonstration; and
+(2) not all truth is 'appropriate'. 
+
+A further proof that the conclusion must be the development of necessary
+premisses is as follows. Where demonstration is possible, one who
+can give no account which includes the cause has no scientific knowledge.
+If, then, we suppose a syllogism in which, though A necessarily inheres
+in C, yet B, the middle term of the demonstration, is not necessarily
+connected with A and C, then the man who argues thus has no reasoned
+knowledge of the conclusion, since this conclusion does not owe its
+necessity to the middle term; for though the conclusion is necessary,
+the mediating link is a contingent fact. Or again, if a man is without
+knowledge now, though he still retains the steps of the argument,
+though there is no change in himself or in the fact and no lapse of
+memory on his part; then neither had he knowledge previously. But
+the mediating link, not being necessary, may have perished in the
+interval; and if so, though there be no change in him nor in the fact,
+and though he will still retain the steps of the argument, yet he
+has not knowledge, and therefore had not knowledge before. Even if
+the link has not actually perished but is liable to perish, this situation
+is possible and might occur. But such a condition cannot be knowledge.
+
+When the conclusion is necessary, the middle through which it was
+proved may yet quite easily be non-necessary. You can in fact infer
+the necessary even from a non-necessary premiss, just as you can infer
+the true from the not true. On the other hand, when the middle is
+necessary the conclusion must be necessary; just as true premisses
+always give a true conclusion. Thus, if A is necessarily predicated
+of B and B of C, then A is necessarily predicated of C. But when the
+conclusion is nonnecessary the middle cannot be necessary either.
+Thus: let A be predicated non-necessarily of C but necessarily of
+B, and let B be a necessary predicate of C; then A too will be a necessary
+predicate of C, which by hypothesis it is not. 
+
+To sum up, then: demonstrative knowledge must be knowledge of a necessary
+nexus, and therefore must clearly be obtained through a necessary
+middle term; otherwise its possessor will know neither the cause nor
+the fact that his conclusion is a necessary connexion. Either he will
+mistake the non-necessary for the necessary and believe the necessity
+of the conclusion without knowing it, or else he will not even believe
+it-in which case he will be equally ignorant, whether he actually
+infers the mere fact through middle terms or the reasoned fact and
+from immediate premisses. 
+
+Of accidents that are not essential according to our definition of
+essential there is no demonstrative knowledge; for since an accident,
+in the sense in which I here speak of it, may also not inhere, it
+is impossible to prove its inherence as a necessary conclusion. A
+difficulty, however, might be raised as to why in dialectic, if the
+conclusion is not a necessary connexion, such and such determinate
+premisses should be proposed in order to deal with such and such determinate
+problems. Would not the result be the same if one asked any questions
+whatever and then merely stated one's conclusion? The solution is
+that determinate questions have to be put, not because the replies
+to them affirm facts which necessitate facts affirmed by the conclusion,
+but because these answers are propositions which if the answerer affirm,
+he must affirm the conclusion and affirm it with truth if they are
+true. 
+
+Since it is just those attributes within every genus which are essential
+and possessed by their respective subjects as such that are necessary
+it is clear that both the conclusions and the premisses of demonstrations
+which produce scientific knowledge are essential. For accidents are
+not necessary: and, further, since accidents are not necessary one
+does not necessarily have reasoned knowledge of a conclusion drawn
+from them (this is so even if the accidental premisses are invariable
+but not essential, as in proofs through signs; for though the conclusion
+be actually essential, one will not know it as essential nor know
+its reason); but to have reasoned knowledge of a conclusion is to
+know it through its cause. We may conclude that the middle must be
+consequentially connected with the minor, and the major with the middle.
+
+Part 7
+
+It follows that we cannot in demonstrating pass from one genus to
+another. We cannot, for instance, prove geometrical truths by arithmetic.
+For there are three elements in demonstration: (1) what is proved,
+the conclusion-an attribute inhering essentially in a genus; (2) the
+axioms, i.e. axioms which are premisses of demonstration; (3) the
+subject-genus whose attributes, i.e. essential properties, are revealed
+by the demonstration. The axioms which are premisses of demonstration
+may be identical in two or more sciences: but in the case of two different
+genera such as arithmetic and geometry you cannot apply arithmetical
+demonstration to the properties of magnitudes unless the magnitudes
+in question are numbers. How in certain cases transference is possible
+I will explain later. 
+
+Arithmetical demonstration and the other sciences likewise possess,
+each of them, their own genera; so that if the demonstration is to
+pass from one sphere to another, the genus must be either absolutely
+or to some extent the same. If this is not so, transference is clearly
+impossible, because the extreme and the middle terms must be drawn
+from the same genus: otherwise, as predicated, they will not be essential
+and will thus be accidents. That is why it cannot be proved by geometry
+that opposites fall under one science, nor even that the product of
+two cubes is a cube. Nor can the theorem of any one science be demonstrated
+by means of another science, unless these theorems are related as
+subordinate to superior (e.g. as optical theorems to geometry or harmonic
+theorems to arithmetic). Geometry again cannot prove of lines any
+property which they do not possess qua lines, i.e. in virtue of the
+fundamental truths of their peculiar genus: it cannot show, for example,
+that the straight line is the most beautiful of lines or the contrary
+of the circle; for these qualities do not belong to lines in virtue
+of their peculiar genus, but through some property which it shares
+with other genera. 
+
+Part 8
+
+It is also clear that if the premisses from which the syllogism proceeds
+are commensurately universal, the conclusion of such i.e. in the unqualified
+sense-must also be eternal. Therefore no attribute can be demonstrated
+nor known by strictly scientific knowledge to inhere in perishable
+things. The proof can only be accidental, because the attribute's
+connexion with its perishable subject is not commensurately universal
+but temporary and special. If such a demonstration is made, one premiss
+must be perishable and not commensurately universal (perishable because
+only if it is perishable will the conclusion be perishable; not commensurately
+universal, because the predicate will be predicable of some instances
+of the subject and not of others); so that the conclusion can only
+be that a fact is true at the moment-not commensurately and universally.
+The same is true of definitions, since a definition is either a primary
+premiss or a conclusion of a demonstration, or else only differs from
+a demonstration in the order of its terms. Demonstration and science
+of merely frequent occurrences-e.g. of eclipse as happening to the
+moon-are, as such, clearly eternal: whereas so far as they are not
+eternal they are not fully commensurate. Other subjects too have properties
+attaching to them in the same way as eclipse attaches to the moon.
+
+Part 9
+
+It is clear that if the conclusion is to show an attribute inhering
+as such, nothing can be demonstrated except from its 'appropriate'
+basic truths. Consequently a proof even from true, indemonstrable,
+and immediate premisses does not constitute knowledge. Such proofs
+are like Bryson's method of squaring the circle; for they operate
+by taking as their middle a common character-a character, therefore,
+which the subject may share with another-and consequently they apply
+equally to subjects different in kind. They therefore afford knowledge
+of an attribute only as inhering accidentally, not as belonging to
+its subject as such: otherwise they would not have been applicable
+to another genus. 
+
+Our knowledge of any attribute's connexion with a subject is accidental
+unless we know that connexion through the middle term in virtue of
+which it inheres, and as an inference from basic premisses essential
+and 'appropriate' to the subject-unless we know, e.g. the property
+of possessing angles equal to two right angles as belonging to that
+subject in which it inheres essentially, and as inferred from basic
+premisses essential and 'appropriate' to that subject: so that if
+that middle term also belongs essentially to the minor, the middle
+must belong to the same kind as the major and minor terms. The only
+exceptions to this rule are such cases as theorems in harmonics which
+are demonstrable by arithmetic. Such theorems are proved by the same
+middle terms as arithmetical properties, but with a qualification-the
+fact falls under a separate science (for the subject genus is separate),
+but the reasoned fact concerns the superior science, to which the
+attributes essentially belong. Thus, even these apparent exceptions
+show that no attribute is strictly demonstrable except from its 'appropriate'
+basic truths, which, however, in the case of these sciences have the
+requisite identity of character. 
+
+It is no less evident that the peculiar basic truths of each inhering
+attribute are indemonstrable; for basic truths from which they might
+be deduced would be basic truths of all that is, and the science to
+which they belonged would possess universal sovereignty. This is so
+because he knows better whose knowledge is deduced from higher causes,
+for his knowledge is from prior premisses when it derives from causes
+themselves uncaused: hence, if he knows better than others or best
+of all, his knowledge would be science in a higher or the highest
+degree. But, as things are, demonstration is not transferable to another
+genus, with such exceptions as we have mentioned of the application
+of geometrical demonstrations to theorems in mechanics or optics,
+or of arithmetical demonstrations to those of harmonics.
+
+It is hard to be sure whether one knows or not; for it is hard to
+be sure whether one's knowledge is based on the basic truths appropriate
+to each attribute-the differentia of true knowledge. We think we have
+scientific knowledge if we have reasoned from true and primary premisses.
+But that is not so: the conclusion must be homogeneous with the basic
+facts of the science. 
+
+Part 10
+
+I call the basic truths of every genus those clements in it the existence
+of which cannot be proved. As regards both these primary truths and
+the attributes dependent on them the meaning of the name is assumed.
+The fact of their existence as regards the primary truths must be
+assumed; but it has to be proved of the remainder, the attributes.
+Thus we assume the meaning alike of unity, straight, and triangular;
+but while as regards unity and magnitude we assume also the fact of
+their existence, in the case of the remainder proof is required.
+
+Of the basic truths used in the demonstrative sciences some are peculiar
+to each science, and some are common, but common only in the sense
+of analogous, being of use only in so far as they fall within the
+genus constituting the province of the science in question.
+
+Peculiar truths are, e.g. the definitions of line and straight; common
+truths are such as 'take equals from equals and equals remain'. Only
+so much of these common truths is required as falls within the genus
+in question: for a truth of this kind will have the same force even
+if not used generally but applied by the geometer only to magnitudes,
+or by the arithmetician only to numbers. Also peculiar to a science
+are the subjects the existence as well as the meaning of which it
+assumes, and the essential attributes of which it investigates, e.g.
+in arithmetic units, in geometry points and lines. Both the existence
+and the meaning of the subjects are assumed by these sciences; but
+of their essential attributes only the meaning is assumed. For example
+arithmetic assumes the meaning of odd and even, square and cube, geometry
+that of incommensurable, or of deflection or verging of lines, whereas
+the existence of these attributes is demonstrated by means of the
+axioms and from previous conclusions as premisses. Astronomy too proceeds
+in the same way. For indeed every demonstrative science has three
+elements: (1) that which it posits, the subject genus whose essential
+attributes it examines; (2) the so-called axioms, which are primary
+premisses of its demonstration; (3) the attributes, the meaning of
+which it assumes. Yet some sciences may very well pass over some of
+these elements; e.g. we might not expressly posit the existence of
+the genus if its existence were obvious (for instance, the existence
+of hot and cold is more evident than that of number); or we might
+omit to assume expressly the meaning of the attributes if it were
+well understood. In the way the meaning of axioms, such as 'Take equals
+from equals and equals remain', is well known and so not expressly
+assumed. Nevertheless in the nature of the case the essential elements
+of demonstration are three: the subject, the attributes, and the basic
+premisses. 
+
+That which expresses necessary self-grounded fact, and which we must
+necessarily believe, is distinct both from the hypotheses of a science
+and from illegitimate postulate-I say 'must believe', because all
+syllogism, and therefore a fortiori demonstration, is addressed not
+to the spoken word, but to the discourse within the soul, and though
+we can always raise objections to the spoken word, to the inward discourse
+we cannot always object. That which is capable of proof but assumed
+by the teacher without proof is, if the pupil believes and accepts
+it, hypothesis, though only in a limited sense hypothesis-that is,
+relatively to the pupil; if the pupil has no opinion or a contrary
+opinion on the matter, the same assumption is an illegitimate postulate.
+Therein lies the distinction between hypothesis and illegitimate postulate:
+the latter is the contrary of the pupil's opinion, demonstrable, but
+assumed and used without demonstration. 
+
+The definition-viz. those which are not expressed as statements that
+anything is or is not-are not hypotheses: but it is in the premisses
+of a science that its hypotheses are contained. Definitions require
+only to be understood, and this is not hypothesis-unless it be contended
+that the pupil's hearing is also an hypothesis required by the teacher.
+Hypotheses, on the contrary, postulate facts on the being of which
+depends the being of the fact inferred. Nor are the geometer's hypotheses
+false, as some have held, urging that one must not employ falsehood
+and that the geometer is uttering falsehood in stating that the line
+which he draws is a foot long or straight, when it is actually neither.
+The truth is that the geometer does not draw any conclusion from the
+being of the particular line of which he speaks, but from what his
+diagrams symbolize. A further distinction is that all hypotheses and
+illegitimate postulates are either universal or particular, whereas
+a definition is neither. 
+
+Part 11
+
+So demonstration does not necessarily imply the being of Forms nor
+a One beside a Many, but it does necessarily imply the possibility
+of truly predicating one of many; since without this possibility we
+cannot save the universal, and if the universal goes, the middle term
+goes witb. it, and so demonstration becomes impossible. We conclude,
+then, that there must be a single identical term unequivocally predicable
+of a number of individuals. 
+
+The law that it is impossible to affirm and deny simultaneously the
+same predicate of the same subject is not expressly posited by any
+demonstration except when the conclusion also has to be expressed
+in that form; in which case the proof lays down as its major premiss
+that the major is truly affirmed of the middle but falsely denied.
+It makes no difference, however, if we add to the middle, or again
+to the minor term, the corresponding negative. For grant a minor term
+of which it is true to predicate man-even if it be also true to predicate
+not-man of it--still grant simply that man is animal and not not-animal,
+and the conclusion follows: for it will still be true to say that
+Callias--even if it be also true to say that not-Callias--is animal
+and not not-animal. The reason is that the major term is predicable
+not only of the middle, but of something other than the middle as
+well, being of wider application; so that the conclusion is not affected
+even if the middle is extended to cover the original middle term and
+also what is not the original middle term. 
+
+The law that every predicate can be either truly affirmed or truly
+denied of every subject is posited by such demonstration as uses reductio
+ad impossibile, and then not always universally, but so far as it
+is requisite; within the limits, that is, of the genus-the genus,
+I mean (as I have already explained), to which the man of science
+applies his demonstrations. In virtue of the common elements of demonstration-I
+mean the common axioms which are used as premisses of demonstration,
+not the subjects nor the attributes demonstrated as belonging to them-all
+the sciences have communion with one another, and in communion with
+them all is dialectic and any science which might attempt a universal
+proof of axioms such as the law of excluded middle, the law that the
+subtraction of equals from equals leaves equal remainders, or other
+axioms of the same kind. Dialectic has no definite sphere of this
+kind, not being confined to a single genus. Otherwise its method would
+not be interrogative; for the interrogative method is barred to the
+demonstrator, who cannot use the opposite facts to prove the same
+nexus. This was shown in my work on the syllogism. 
+
+Part 12
+
+If a syllogistic question is equivalent to a proposition embodying
+one of the two sides of a contradiction, and if each science has its
+peculiar propositions from which its peculiar conclusion is developed,
+then there is such a thing as a distinctively scientific question,
+and it is the interrogative form of the premisses from which the 'appropriate'
+conclusion of each science is developed. Hence it is clear that not
+every question will be relevant to geometry, nor to medicine, nor
+to any other science: only those questions will be geometrical which
+form premisses for the proof of the theorems of geometry or of any
+other science, such as optics, which uses the same basic truths as
+geometry. Of the other sciences the like is true. Of these questions
+the geometer is bound to give his account, using the basic truths
+of geometry in conjunction with his previous conclusions; of the basic
+truths the geometer, as such, is not bound to give any account. The
+like is true of the other sciences. There is a limit, then, to the
+questions which we may put to each man of science; nor is each man
+of science bound to answer all inquiries on each several subject,
+but only such as fall within the defined field of his own science.
+If, then, in controversy with a geometer qua geometer the disputant
+confines himself to geometry and proves anything from geometrical
+premisses, he is clearly to be applauded; if he goes outside these
+he will be at fault, and obviously cannot even refute the geometer
+except accidentally. One should therefore not discuss geometry among
+those who are not geometers, for in such a company an unsound argument
+will pass unnoticed. This is correspondingly true in the other sciences.
+
+Since there are 'geometrical' questions, does it follow that there
+are also distinctively 'ungeometrical' questions? Further, in each
+special science-geometry for instance-what kind of error is it that
+may vitiate questions, and yet not exclude them from that science?
+Again, is the erroneous conclusion one constructed from premisses
+opposite to the true premisses, or is it formal fallacy though drawn
+from geometrical premisses? Or, perhaps, the erroneous conclusion
+is due to the drawing of premisses from another science; e.g. in a
+geometrical controversy a musical question is distinctively ungeometrical,
+whereas the notion that parallels meet is in one sense geometrical,
+being ungeometrical in a different fashion: the reason being that
+'ungeometrical', like 'unrhythmical', is equivocal, meaning in the
+one case not geometry at all, in the other bad geometry? It is this
+error, i.e. error based on premisses of this kind-'of' the science
+but false-that is the contrary of science. In mathematics the formal
+fallacy is not so common, because it is the middle term in which the
+ambiguity lies, since the major is predicated of the whole of the
+middle and the middle of the whole of the minor (the predicate of
+course never has the prefix 'all'); and in mathematics one can, so
+to speak, see these middle terms with an intellectual vision, while
+in dialectic the ambiguity may escape detection. E.g. 'Is every circle
+a figure?' A diagram shows that this is so, but the minor premiss
+'Are epics circles?' is shown by the diagram to be false.
+
+If a proof has an inductive minor premiss, one should not bring an
+'objection' against it. For since every premiss must be applicable
+to a number of cases (otherwise it will not be true in every instance,
+which, since the syllogism proceeds from universals, it must be),
+then assuredly the same is true of an 'objection'; since premisses
+and 'objections' are so far the same that anything which can be validly
+advanced as an 'objection' must be such that it could take the form
+of a premiss, either demonstrative or dialectical. On the other hand,
+arguments formally illogical do sometimes occur through taking as
+middles mere attributes of the major and minor terms. An instance
+of this is Caeneus' proof that fire increases in geometrical proportion:
+'Fire', he argues, 'increases rapidly, and so does geometrical proportion'.
+There is no syllogism so, but there is a syllogism if the most rapidly
+increasing proportion is geometrical and the most rapidly increasing
+proportion is attributable to fire in its motion. Sometimes, no doubt,
+it is impossible to reason from premisses predicating mere attributes:
+but sometimes it is possible, though the possibility is overlooked.
+If false premisses could never give true conclusions 'resolution'
+would be easy, for premisses and conclusion would in that case inevitably
+reciprocate. I might then argue thus: let A be an existing fact; let
+the existence of A imply such and such facts actually known to me
+to exist, which we may call B. I can now, since they reciprocate,
+infer A from B. 
+
+Reciprocation of premisses and conclusion is more frequent in mathematics,
+because mathematics takes definitions, but never an accident, for
+its premisses-a second characteristic distinguishing mathematical
+reasoning from dialectical disputations. 
+
+A science expands not by the interposition of fresh middle terms,
+but by the apposition of fresh extreme terms. E.g. A is predicated
+of B, B of C, C of D, and so indefinitely. Or the expansion may be
+lateral: e.g. one major A, may be proved of two minors, C and E. Thus
+let A represent number-a number or number taken indeterminately; B
+determinate odd number; C any particular odd number. We can then predicate
+A of C. Next let D represent determinate even number, and E even number.
+Then A is predicable of E. 
+
+Part 13
+
+Knowledge of the fact differs from knowledge of the reasoned fact.
+To begin with, they differ within the same science and in two ways:
+(1) when the premisses of the syllogism are not immediate (for then
+the proximate cause is not contained in them-a necessary condition
+of knowledge of the reasoned fact): (2) when the premisses are immediate,
+but instead of the cause the better known of the two reciprocals is
+taken as the middle; for of two reciprocally predicable terms the
+one which is not the cause may quite easily be the better known and
+so become the middle term of the demonstration. Thus (2, a) you might
+prove as follows that the planets are near because they do not twinkle:
+let C be the planets, B not twinkling, A proximity. Then B is predicable
+of C; for the planets do not twinkle. But A is also predicable of
+B, since that which does not twinkle is near--we must take this truth
+as having been reached by induction or sense-perception. Therefore
+A is a necessary predicate of C; so that we have demonstrated that
+the planets are near. This syllogism, then, proves not the reasoned
+fact but only the fact; since they are not near because they do not
+twinkle, but, because they are near, do not twinkle. The major and
+middle of the proof, however, may be reversed, and then the demonstration
+will be of the reasoned fact. Thus: let C be the planets, B proximity,
+A not twinkling. Then B is an attribute of C, and A-not twinkling-of
+B. Consequently A is predicable of C, and the syllogism proves the
+reasoned fact, since its middle term is the proximate cause. Another
+example is the inference that the moon is spherical from its manner
+of waxing. Thus: since that which so waxes is spherical, and since
+the moon so waxes, clearly the moon is spherical. Put in this form,
+the syllogism turns out to be proof of the fact, but if the middle
+and major be reversed it is proof of the reasoned fact; since the
+moon is not spherical because it waxes in a certain manner, but waxes
+in such a manner because it is spherical. (Let C be the moon, B spherical,
+and A waxing.) Again (b), in cases where the cause and the effect
+are not reciprocal and the effect is the better known, the fact is
+demonstrated but not the reasoned fact. This also occurs (1) when
+the middle falls outside the major and minor, for here too the strict
+cause is not given, and so the demonstration is of the fact, not of
+the reasoned fact. For example, the question 'Why does not a wall
+breathe?' might be answered, 'Because it is not an animal'; but that
+answer would not give the strict cause, because if not being an animal
+causes the absence of respiration, then being an animal should be
+the cause of respiration, according to the rule that if the negation
+of causes the non-inherence of y, the affirmation of x causes the
+inherence of y; e.g. if the disproportion of the hot and cold elements
+is the cause of ill health, their proportion is the cause of health;
+and conversely, if the assertion of x causes the inherence of y, the
+negation of x must cause y's non-inherence. But in the case given
+this consequence does not result; for not every animal breathes. A
+syllogism with this kind of cause takes place in the second figure.
+Thus: let A be animal, B respiration, C wall. Then A is predicable
+of all B (for all that breathes is animal), but of no C; and consequently
+B is predicable of no C; that is, the wall does not breathe. Such
+causes are like far-fetched explanations, which precisely consist
+in making the cause too remote, as in Anacharsis' account of why the
+Scythians have no flute-players; namely because they have no vines.
+
+Thus, then, do the syllogism of the fact and the syllogism of the
+reasoned fact differ within one science and according to the position
+of the middle terms. But there is another way too in which the fact
+and the reasoned fact differ, and that is when they are investigated
+respectively by different sciences. This occurs in the case of problems
+related to one another as subordinate and superior, as when optical
+problems are subordinated to geometry, mechanical problems to stereometry,
+harmonic problems to arithmetic, the data of observation to astronomy.
+(Some of these sciences bear almost the same name; e.g. mathematical
+and nautical astronomy, mathematical and acoustical harmonics.) Here
+it is the business of the empirical observers to know the fact, of
+the mathematicians to know the reasoned fact; for the latter are in
+possession of the demonstrations giving the causes, and are often
+ignorant of the fact: just as we have often a clear insight into a
+universal, but through lack of observation are ignorant of some of
+its particular instances. These connexions have a perceptible existence
+though they are manifestations of forms. For the mathematical sciences
+concern forms: they do not demonstrate properties of a substratum,
+since, even though the geometrical subjects are predicable as properties
+of a perceptible substratum, it is not as thus predicable that the
+mathematician demonstrates properties of them. As optics is related
+to geometry, so another science is related to optics, namely the theory
+of the rainbow. Here knowledge of the fact is within the province
+of the natural philosopher, knowledge of the reasoned fact within
+that of the optician, either qua optician or qua mathematical optician.
+Many sciences not standing in this mutual relation enter into it at
+points; e.g. medicine and geometry: it is the physician's business
+to know that circular wounds heal more slowly, the geometer's to know
+the reason why. 
+
+Part 14
+
+Of all the figures the most scientific is the first. Thus, it is the
+vehicle of the demonstrations of all the mathematical sciences, such
+as arithmetic, geometry, and optics, and practically all of all sciences
+that investigate causes: for the syllogism of the reasoned fact is
+either exclusively or generally speaking and in most cases in this
+figure-a second proof that this figure is the most scientific; for
+grasp of a reasoned conclusion is the primary condition of knowledge.
+Thirdly, the first is the only figure which enables us to pursue knowledge
+of the essence of a thing. In the second figure no affirmative conclusion
+is possible, and knowledge of a thing's essence must be affirmative;
+while in the third figure the conclusion can be affirmative, but cannot
+be universal, and essence must have a universal character: e.g. man
+is not two-footed animal in any qualified sense, but universally.
+Finally, the first figure has no need of the others, while it is by
+means of the first that the other two figures are developed, and have
+their intervals closepacked until immediate premisses are reached.
+
+Clearly, therefore, the first figure is the primary condition of knowledge.
+
+Part 15
+
+Just as an attribute A may (as we saw) be atomically connected with
+a subject B, so its disconnexion may be atomic. I call 'atomic' connexions
+or disconnexions which involve no intermediate term; since in that
+case the connexion or disconnexion will not be mediated by something
+other than the terms themselves. It follows that if either A or B,
+or both A and B, have a genus, their disconnexion cannot be primary.
+Thus: let C be the genus of A. Then, if C is not the genus of B-for
+A may well have a genus which is not the genus of B-there will be
+a syllogism proving A's disconnexion from B thus: 
+
+all A is C, no B is C, therefore no B is A. Or if it is B which has
+a genus D, we have 
+
+all B is D, no D is A, therefore no B is A, by syllogism; and the
+proof will be similar if both A and B have a genus. That the genus
+of A need not be the genus of B and vice versa, is shown by the existence
+of mutually exclusive coordinate series of predication. If no term
+in the series ACD...is predicable of any term in the series BEF...,and
+if G-a term in the former series-is the genus of A, clearly G will
+not be the genus of B; since, if it were, the series would not be
+mutually exclusive. So also if B has a genus, it will not be the genus
+of A. If, on the other hand, neither A nor B has a genus and A does
+not inhere in B, this disconnexion must be atomic. If there be a middle
+term, one or other of them is bound to have a genus, for the syllogism
+will be either in the first or the second figure. If it is in the
+first, B will have a genus-for the premiss containing it must be affirmative:
+if in the second, either A or B indifferently, since syllogism is
+possible if either is contained in a negative premiss, but not if
+both premisses are negative. 
+
+Hence it is clear that one thing may be atomically disconnected from
+another, and we have stated when and how this is possible.
+
+Part 16
+
+Ignorance-defined not as the negation of knowledge but as a positive
+state of mind-is error produced by inference. 
+
+(1) Let us first consider propositions asserting a predicate's immediate
+connexion with or disconnexion from a subject. Here, it is true, positive
+error may befall one in alternative ways; for it may arise where one
+directly believes a connexion or disconnexion as well as where one's
+belief is acquired by inference. The error, however, that consists
+in a direct belief is without complication; but the error resulting
+from inference-which here concerns us-takes many forms. Thus, let
+A be atomically disconnected from all B: then the conclusion inferred
+through a middle term C, that all B is A, will be a case of error
+produced by syllogism. Now, two cases are possible. Either (a) both
+premisses, or (b) one premiss only, may be false. (a) If neither A
+is an attribute of any C nor C of any B, whereas the contrary was
+posited in both cases, both premisses will be false. (C may quite
+well be so related to A and B that C is neither subordinate to A nor
+a universal attribute of B: for B, since A was said to be primarily
+disconnected from B, cannot have a genus, and A need not necessarily
+be a universal attribute of all things. Consequently both premisses
+may be false.) On the other hand, (b) one of the premisses may be
+true, though not either indifferently but only the major A-C since,
+B having no genus, the premiss C-B will always be false, while A-C
+may be true. This is the case if, for example, A is related atomically
+to both C and B; because when the same term is related atomically
+to more terms than one, neither of those terms will belong to the
+other. It is, of course, equally the case if A-C is not atomic.
+
+Error of attribution, then, occurs through these causes and in this
+form only-for we found that no syllogism of universal attribution
+was possible in any figure but the first. On the other hand, an error
+of non-attribution may occur either in the first or in the second
+figure. Let us therefore first explain the various forms it takes
+in the first figure and the character of the premisses in each case.
+
+(c) It may occur when both premisses are false; e.g. supposing A atomically
+connected with both C and B, if it be then assumed that no C is and
+all B is C, both premisses are false. 
+
+(d) It is also possible when one is false. This may be either premiss
+indifferently. A-C may be true, C-B false-A-C true because A is not
+an attribute of all things, C-B false because C, which never has the
+attribute A, cannot be an attribute of B; for if C-B were true, the
+premiss A-C would no longer be true, and besides if both premisses
+were true, the conclusion would be true. Or again, C-B may be true
+and A-C false; e.g. if both C and A contain B as genera, one of them
+must be subordinate to the other, so that if the premiss takes the
+form No C is A, it will be false. This makes it clear that whether
+either or both premisses are false, the conclusion will equally be
+false. 
+
+In the second figure the premisses cannot both be wholly false; for
+if all B is A, no middle term can be with truth universally affirmed
+of one extreme and universally denied of the other: but premisses
+in which the middle is affirmed of one extreme and denied of the other
+are the necessary condition if one is to get a valid inference at
+all. Therefore if, taken in this way, they are wholly false, their
+contraries conversely should be wholly true. But this is impossible.
+On the other hand, there is nothing to prevent both premisses being
+partially false; e.g. if actually some A is C and some B is C, then
+if it is premised that all A is C and no B is C, both premisses are
+false, yet partially, not wholly, false. The same is true if the major
+is made negative instead of the minor. Or one premiss may be wholly
+false, and it may be either of them. Thus, supposing that actually
+an attribute of all A must also be an attribute of all B, then if
+C is yet taken to be a universal attribute of all but universally
+non-attributable to B, C-A will be true but C-B false. Again, actually
+that which is an attribute of no B will not be an attribute of all
+A either; for if it be an attribute of all A, it will also be an attribute
+of all B, which is contrary to supposition; but if C be nevertheless
+assumed to be a universal attribute of A, but an attribute of no B,
+then the premiss C-B is true but the major is false. The case is similar
+if the major is made the negative premiss. For in fact what is an
+attribute of no A will not be an attribute of any B either; and if
+it be yet assumed that C is universally non-attributable to A, but
+a universal attribute of B, the premiss C-A is true but the minor
+wholly false. Again, in fact it is false to assume that that which
+is an attribute of all B is an attribute of no A, for if it be an
+attribute of all B, it must be an attribute of some A. If then C is
+nevertheless assumed to be an attribute of all B but of no A, C-B
+will be true but C-A false. 
+
+It is thus clear that in the case of atomic propositions erroneous
+inference will be possible not only when both premisses are false
+but also when only one is false. 
+
+Part 17
+
+In the case of attributes not atomically connected with or disconnected
+from their subjects, (a, i) as long as the false conclusion is inferred
+through the 'appropriate' middle, only the major and not both premisses
+can be false. By 'appropriate middle' I mean the middle term through
+which the contradictory-i.e. the true-conclusion is inferrible. Thus,
+let A be attributable to B through a middle term C: then, since to
+produce a conclusion the premiss C-B must be taken affirmatively,
+it is clear that this premiss must always be true, for its quality
+is not changed. But the major A-C is false, for it is by a change
+in the quality of A-C that the conclusion becomes its contradictory-i.e.
+true. Similarly (ii) if the middle is taken from another series of
+predication; e.g. suppose D to be not only contained within A as a
+part within its whole but also predicable of all B. Then the premiss
+D-B must remain unchanged, but the quality of A-D must be changed;
+so that D-B is always true, A-D always false. Such error is practically
+identical with that which is inferred through the 'appropriate' middle.
+On the other hand, (b) if the conclusion is not inferred through the
+'appropriate' middle-(i) when the middle is subordinate to A but is
+predicable of no B, both premisses must be false, because if there
+is to be a conclusion both must be posited as asserting the contrary
+of what is actually the fact, and so posited both become false: e.g.
+suppose that actually all D is A but no B is D; then if these premisses
+are changed in quality, a conclusion will follow and both of the new
+premisses will be false. When, however, (ii) the middle D is not subordinate
+to A, A-D will be true, D-B false-A-D true because A was not subordinate
+to D, D-B false because if it had been true, the conclusion too would
+have been true; but it is ex hypothesi false. 
+
+When the erroneous inference is in the second figure, both premisses
+cannot be entirely false; since if B is subordinate to A, there can
+be no middle predicable of all of one extreme and of none of the other,
+as was stated before. One premiss, however, may be false, and it may
+be either of them. Thus, if C is actually an attribute of both A and
+B, but is assumed to be an attribute of A only and not of B, C-A will
+be true, C-B false: or again if C be assumed to be attributable to
+B but to no A, C-B will be true, C-A false. 
+
+We have stated when and through what kinds of premisses error will
+result in cases where the erroneous conclusion is negative. If the
+conclusion is affirmative, (a, i) it may be inferred through the
+'appropriate' middle term. In this case both premisses cannot be false
+since, as we said before, C-B must remain unchanged if there is to
+be a conclusion, and consequently A-C, the quality of which is changed,
+will always be false. This is equally true if (ii) the middle is taken
+from another series of predication, as was stated to be the case also
+with regard to negative error; for D-B must remain unchanged, while
+the quality of A-D must be converted, and the type of error is the
+same as before. 
+
+(b) The middle may be inappropriate. Then (i) if D is subordinate
+to A, A-D will be true, but D-B false; since A may quite well be predicable
+of several terms no one of which can be subordinated to another. If,
+however, (ii) D is not subordinate to A, obviously A-D, since it is
+affirmed, will always be false, while D-B may be either true or false;
+for A may very well be an attribute of no D, whereas all B is D, e.g.
+no science is animal, all music is science. Equally well A may be
+an attribute of no D, and D of no B. It emerges, then, that if the
+middle term is not subordinate to the major, not only both premisses
+but either singly may be false. 
+
+Thus we have made it clear how many varieties of erroneous inference
+are liable to happen and through what kinds of premisses they occur,
+in the case both of immediate and of demonstrable truths.
+
+Part 18
+
+It is also clear that the loss of any one of the senses entails the
+loss of a corresponding portion of knowledge, and that, since we learn
+either by induction or by demonstration, this knowledge cannot be
+acquired. Thus demonstration develops from universals, induction from
+particulars; but since it is possible to familiarize the pupil with
+even the so-called mathematical abstractions only through induction-i.e.
+only because each subject genus possesses, in virtue of a determinate
+mathematical character, certain properties which can be treated as
+separate even though they do not exist in isolation-it is consequently
+impossible to come to grasp universals except through induction. But
+induction is impossible for those who have not sense-perception. For
+it is sense-perception alone which is adequate for grasping the particulars:
+they cannot be objects of scientific knowledge, because neither can
+universals give us knowledge of them without induction, nor can we
+get it through induction without sense-perception. 
+
+Part 19
+
+Every syllogism is effected by means of three terms. One kind of syllogism
+serves to prove that A inheres in C by showing that A inheres in B
+and B in C; the other is negative and one of its premisses asserts
+one term of another, while the other denies one term of another. It
+is clear, then, that these are the fundamentals and so-called hypotheses
+of syllogism. Assume them as they have been stated, and proof is bound
+to follow-proof that A inheres in C through B, and again that A inheres
+in B through some other middle term, and similarly that B inheres
+in C. If our reasoning aims at gaining credence and so is merely dialectical,
+it is obvious that we have only to see that our inference is based
+on premisses as credible as possible: so that if a middle term between
+A and B is credible though not real, one can reason through it and
+complete a dialectical syllogism. If, however, one is aiming at truth,
+one must be guided by the real connexions of subjects and attributes.
+Thus: since there are attributes which are predicated of a subject
+essentially or naturally and not coincidentally-not, that is, in the
+sense in which we say 'That white (thing) is a man', which is not
+the same mode of predication as when we say 'The man is white': the
+man is white not because he is something else but because he is man,
+but the white is man because 'being white' coincides with 'humanity'
+within one substratum-therefore there are terms such as are naturally
+subjects of predicates. Suppose, then, C such a term not itself attributable
+to anything else as to a subject, but the proximate subject of the
+attribute B--i.e. so that B-C is immediate; suppose further E related
+immediately to F, and F to B. The first question is, must this series
+terminate, or can it proceed to infinity? The second question is as
+follows: Suppose nothing is essentially predicated of A, but A is
+predicated primarily of H and of no intermediate prior term, and suppose
+H similarly related to G and G to B; then must this series also terminate,
+or can it too proceed to infinity? There is this much difference between
+the questions: the first is, is it possible to start from that which
+is not itself attributable to anything else but is the subject of
+attributes, and ascend to infinity? The second is the problem whether
+one can start from that which is a predicate but not itself a subject
+of predicates, and descend to infinity? A third question is, if the
+extreme terms are fixed, can there be an infinity of middles? I mean
+this: suppose for example that A inheres in C and B is intermediate
+between them, but between B and A there are other middles, and between
+these again fresh middles; can these proceed to infinity or can they
+not? This is the equivalent of inquiring, do demonstrations proceed
+to infinity, i.e. is everything demonstrable? Or do ultimate subject
+and primary attribute limit one another? 
+
+I hold that the same questions arise with regard to negative conclusions
+and premisses: viz. if A is attributable to no B, then either this
+predication will be primary, or there will be an intermediate term
+prior to B to which a is not attributable-G, let us say, which is
+attributable to all B-and there may still be another term H prior
+to G, which is attributable to all G. The same questions arise, I
+say, because in these cases too either the series of prior terms to
+which a is not attributable is infinite or it terminates.
+
+One cannot ask the same questions in the case of reciprocating terms,
+since when subject and predicate are convertible there is neither
+primary nor ultimate subject, seeing that all the reciprocals qua
+subjects stand in the same relation to one another, whether we say
+that the subject has an infinity of attributes or that both subjects
+and attributes-and we raised the question in both cases-are infinite
+in number. These questions then cannot be asked-unless, indeed, the
+terms can reciprocate by two different modes, by accidental predication
+in one relation and natural predication in the other. 
+
+Part 20
+
+Now, it is clear that if the predications terminate in both the upward
+and the downward direction (by 'upward' I mean the ascent to the more
+universal, by 'downward' the descent to the more particular), the
+middle terms cannot be infinite in number. For suppose that A is predicated
+of F, and that the intermediates-call them BB'B"...-are infinite,
+then clearly you might descend from and find one term predicated of
+another ad infinitum, since you have an infinity of terms between
+you and F; and equally, if you ascend from F, there are infinite terms
+between you and A. It follows that if these processes are impossible
+there cannot be an infinity of intermediates between A and F. Nor
+is it of any effect to urge that some terms of the series AB...F are
+contiguous so as to exclude intermediates, while others cannot be
+taken into the argument at all: whichever terms of the series B...I
+take, the number of intermediates in the direction either of A or
+of F must be finite or infinite: where the infinite series starts,
+whether from the first term or from a later one, is of no moment,
+for the succeeding terms in any case are infinite in number.
+
+Part 21
+
+Further, if in affirmative demonstration the series terminates in
+both directions, clearly it will terminate too in negative demonstration.
+Let us assume that we cannot proceed to infinity either by ascending
+from the ultimate term (by 'ultimate term' I mean a term such as was,
+not itself attributable to a subject but itself the subject of attributes),
+or by descending towards an ultimate from the primary term (by 'primary
+term' I mean a term predicable of a subject but not itself a subject).
+If this assumption is justified, the series will also terminate in
+the case of negation. For a negative conclusion can be proved in all
+three figures. In the first figure it is proved thus: no B is A, all
+C is B. In packing the interval B-C we must reach immediate propositions--as
+is always the case with the minor premiss--since B-C is affirmative.
+As regards the other premiss it is plain that if the major term is
+denied of a term D prior to B, D will have to be predicable of all
+B, and if the major is denied of yet another term prior to D, this
+term must be predicable of all D. Consequently, since the ascending
+series is finite, the descent will also terminate and there will be
+a subject of which A is primarily non-predicable. In the second figure
+the syllogism is, all A is B, no C is B,..no C is A. If proof of this
+is required, plainly it may be shown either in the first figure as
+above, in the second as here, or in the third. The first figure has
+been discussed, and we will proceed to display the second, proof by
+which will be as follows: all B is D, no C is D..., since it is required
+that B should be a subject of which a predicate is affirmed. Next,
+since D is to be proved not to belong to C, then D has a further predicate
+which is denied of C. Therefore, since the succession of predicates
+affirmed of an ever higher universal terminates, the succession of
+predicates denied terminates too. 
+
+The third figure shows it as follows: all B is A, some B is not C.
+Therefore some A is not C. This premiss, i.e. C-B, will be proved
+either in the same figure or in one of the two figures discussed above.
+In the first and second figures the series terminates. If we use the
+third figure, we shall take as premisses, all E is B, some E is not
+C, and this premiss again will be proved by a similar prosyllogism.
+But since it is assumed that the series of descending subjects also
+terminates, plainly the series of more universal non-predicables will
+terminate also. Even supposing that the proof is not confined to one
+method, but employs them all and is now in the first figure, now in
+the second or third-even so the regress will terminate, for the methods
+are finite in number, and if finite things are combined in a finite
+number of ways, the result must be finite. 
+
+Thus it is plain that the regress of middles terminates in the case
+of negative demonstration, if it does so also in the case of affirmative
+demonstration. That in fact the regress terminates in both these cases
+may be made clear by the following dialectical considerations.
+
+Part 22
+
+In the case of predicates constituting the essential nature of a thing,
+it clearly terminates, seeing that if definition is possible, or in
+other words, if essential form is knowable, and an infinite series
+cannot be traversed, predicates constituting a thing's essential nature
+must be finite in number. But as regards predicates generally we have
+the following prefatory remarks to make. (1) We can affirm without
+falsehood 'the white (thing) is walking', and that big (thing) is
+a log'; or again, 'the log is big', and 'the man walks'. But the affirmation
+differs in the two cases. When I affirm 'the white is a log', I mean
+that something which happens to be white is a log-not that white is
+the substratum in which log inheres, for it was not qua white or qua
+a species of white that the white (thing) came to be a log, and the
+white (thing) is consequently not a log except incidentally. On the
+other hand, when I affirm 'the log is white', I do not mean that something
+else, which happens also to be a log, is white (as I should if I said
+'the musician is white,' which would mean 'the man who happens also
+to be a musician is white'); on the contrary, log is here the substratum-the
+substratum which actually came to be white, and did so qua wood or
+qua a species of wood and qua nothing else. 
+
+If we must lay down a rule, let us entitle the latter kind of statement
+predication, and the former not predication at all, or not strict
+but accidental predication. 'White' and 'log' will thus serve as types
+respectively of predicate and subject. 
+
+We shall assume, then, that the predicate is invariably predicated
+strictly and not accidentally of the subject, for on such predication
+demonstrations depend for their force. It follows from this that when
+a single attribute is predicated of a single subject, the predicate
+must affirm of the subject either some element constituting its essential
+nature, or that it is in some way qualified, quantified, essentially
+related, active, passive, placed, or dated. 
+
+(2) Predicates which signify substance signify that the subject is
+identical with the predicate or with a species of the predicate. Predicates
+not signifying substance which are predicated of a subject not identical
+with themselves or with a species of themselves are accidental or
+coincidental; e.g. white is a coincident of man, seeing that man is
+not identical with white or a species of white, but rather with animal,
+since man is identical with a species of animal. These predicates
+which do not signify substance must be predicates of some other subject,
+and nothing can be white which is not also other than white. The Forms
+we can dispense with, for they are mere sound without sense; and even
+if there are such things, they are not relevant to our discussion,
+since demonstrations are concerned with predicates such as we have
+defined. 
+
+(3) If A is a quality of B, B cannot be a quality of A-a quality of
+a quality. Therefore A and B cannot be predicated reciprocally of
+one another in strict predication: they can be affirmed without falsehood
+of one another, but not genuinely predicated of each other. For one
+alternative is that they should be substantially predicated of one
+another, i.e. B would become the genus or differentia of A-the predicate
+now become subject. But it has been shown that in these substantial
+predications neither the ascending predicates nor the descending subjects
+form an infinite series; e.g. neither the series, man is biped, biped
+is animal, &c., nor the series predicating animal of man, man of Callias,
+Callias of a further. subject as an element of its essential nature,
+is infinite. For all such substance is definable, and an infinite
+series cannot be traversed in thought: consequently neither the ascent
+nor the descent is infinite, since a substance whose predicates were
+infinite would not be definable. Hence they will not be predicated
+each as the genus of the other; for this would equate a genus with
+one of its own species. Nor (the other alternative) can a quale be
+reciprocally predicated of a quale, nor any term belonging to an adjectival
+category of another such term, except by accidental predication; for
+all such predicates are coincidents and are predicated of substances.
+On the other hand-in proof of the impossibility of an infinite ascending
+series-every predication displays the subject as somehow qualified
+or quantified or as characterized under one of the other adjectival
+categories, or else is an element in its substantial nature: these
+latter are limited in number, and the number of the widest kinds under
+which predications fall is also limited, for every predication must
+exhibit its subject as somehow qualified, quantified, essentially
+related, acting or suffering, or in some place or at some time.
+
+I assume first that predication implies a single subject and a single
+attribute, and secondly that predicates which are not substantial
+are not predicated of one another. We assume this because such predicates
+are all coincidents, and though some are essential coincidents, others
+of a different type, yet we maintain that all of them alike are predicated
+of some substratum and that a coincident is never a substratum-since
+we do not class as a coincident anything which does not owe its designation
+to its being something other than itself, but always hold that any
+coincident is predicated of some substratum other than itself, and
+that another group of coincidents may have a different substratum.
+Subject to these assumptions then, neither the ascending nor the descending
+series of predication in which a single attribute is predicated of
+a single subject is infinite. For the subjects of which coincidents
+are predicated are as many as the constitutive elements of each individual
+substance, and these we have seen are not infinite in number, while
+in the ascending series are contained those constitutive elements
+with their coincidents-both of which are finite. We conclude that
+there is a given subject (D) of which some attribute (C) is primarily
+predicable; that there must be an attribute (B) primarily predicable
+of the first attribute, and that the series must end with a term (A)
+not predicable of any term prior to the last subject of which it was
+predicated (B), and of which no term prior to it is predicable.
+
+The argument we have given is one of the so-called proofs; an alternative
+proof follows. Predicates so related to their subjects that there
+are other predicates prior to them predicable of those subjects are
+demonstrable; but of demonstrable propositions one cannot have something
+better than knowledge, nor can one know them without demonstration.
+Secondly, if a consequent is only known through an antecedent (viz.
+premisses prior to it) and we neither know this antecedent nor have
+something better than knowledge of it, then we shall not have scientific
+knowledge of the consequent. Therefore, if it is possible through
+demonstration to know anything without qualification and not merely
+as dependent on the acceptance of certain premisses-i.e. hypothetically-the
+series of intermediate predications must terminate. If it does not
+terminate, and beyond any predicate taken as higher than another there
+remains another still higher, then every predicate is demonstrable.
+Consequently, since these demonstrable predicates are infinite in
+number and therefore cannot be traversed, we shall not know them by
+demonstration. If, therefore, we have not something better than knowledge
+of them, we cannot through demonstration have unqualified but only
+hypothetical science of anything. 
+
+As dialectical proofs of our contention these may carry conviction,
+but an analytic process will show more briefly that neither the ascent
+nor the descent of predication can be infinite in the demonstrative
+sciences which are the object of our investigation. Demonstration
+proves the inherence of essential attributes in things. Now attributes
+may be essential for two reasons: either because they are elements
+in the essential nature of their subjects, or because their subjects
+are elements in their essential nature. An example of the latter is
+odd as an attribute of number-though it is number's attribute, yet
+number itself is an element in the definition of odd; of the former,
+multiplicity or the indivisible, which are elements in the definition
+of number. In neither kind of attribution can the terms be infinite.
+They are not infinite where each is related to the term below it as
+odd is to number, for this would mean the inherence in odd of another
+attribute of odd in whose nature odd was an essential element: but
+then number will be an ultimate subject of the whole infinite chain
+of attributes, and be an element in the definition of each of them.
+Hence, since an infinity of attributes such as contain their subject
+in their definition cannot inhere in a single thing, the ascending
+series is equally finite. Note, moreover, that all such attributes
+must so inhere in the ultimate subject-e.g. its attributes in number
+and number in them-as to be commensurate with the subject and not
+of wider extent. Attributes which are essential elements in the nature
+of their subjects are equally finite: otherwise definition would be
+impossible. Hence, if all the attributes predicated are essential
+and these cannot be infinite, the ascending series will terminate,
+and consequently the descending series too. 
+
+If this is so, it follows that the intermediates between any two terms
+are also always limited in number. An immediately obvious consequence
+of this is that demonstrations necessarily involve basic truths, and
+that the contention of some-referred to at the outset-that all truths
+are demonstrable is mistaken. For if there are basic truths, (a) not
+all truths are demonstrable, and (b) an infinite regress is impossible;
+since if either (a) or (b) were not a fact, it would mean that no
+interval was immediate and indivisible, but that all intervals were
+divisible. This is true because a conclusion is demonstrated by the
+interposition, not the apposition, of a fresh term. If such interposition
+could continue to infinity there might be an infinite number of terms
+between any two terms; but this is impossible if both the ascending
+and descending series of predication terminate; and of this fact,
+which before was shown dialectically, analytic proof has now been
+given. 
+
+Part 23
+
+It is an evident corollary of these conclusions that if the same attribute
+A inheres in two terms C and D predicable either not at all, or not
+of all instances, of one another, it does not always belong to them
+in virtue of a common middle term. Isosceles and scalene possess the
+attribute of having their angles equal to two right angles in virtue
+of a common middle; for they possess it in so far as they are both
+a certain kind of figure, and not in so far as they differ from one
+another. But this is not always the case: for, were it so, if we take
+B as the common middle in virtue of which A inheres in C and D, clearly
+B would inhere in C and D through a second common middle, and this
+in turn would inhere in C and D through a third, so that between two
+terms an infinity of intermediates would fall-an impossibility. Thus
+it need not always be in virtue of a common middle term that a single
+attribute inheres in several subjects, since there must be immediate
+intervals. Yet if the attribute to be proved common to two subjects
+is to be one of their essential attributes, the middle terms involved
+must be within one subject genus and be derived from the same group
+of immediate premisses; for we have seen that processes of proof cannot
+pass from one genus to another. 
+
+It is also clear that when A inheres in B, this can be demonstrated
+if there is a middle term. Further, the 'elements' of such a conclusion
+are the premisses containing the middle in question, and they are
+identical in number with the middle terms, seeing that the immediate
+propositions-or at least such immediate propositions as are universal-are
+the 'elements'. If, on the other hand, there is no middle term, demonstration
+ceases to be possible: we are on the way to the basic truths. Similarly
+if A does not inhere in B, this can be demonstrated if there is a
+middle term or a term prior to B in which A does not inhere: otherwise
+there is no demonstration and a basic truth is reached. There are,
+moreover, as many 'elements' of the demonstrated conclusion as there
+are middle terms, since it is propositions containing these middle
+terms that are the basic premisses on which the demonstration rests;
+and as there are some indemonstrable basic truths asserting that 'this
+is that' or that 'this inheres in that', so there are others denying
+that 'this is that' or that 'this inheres in that'-in fact some basic
+truths will affirm and some will deny being. 
+
+When we are to prove a conclusion, we must take a primary essential
+predicate-suppose it C-of the subject B, and then suppose A similarly
+predicable of C. If we proceed in this manner, no proposition or attribute
+which falls beyond A is admitted in the proof: the interval is constantly
+condensed until subject and predicate become indivisible, i.e. one.
+We have our unit when the premiss becomes immediate, since the immediate
+premiss alone is a single premiss in the unqualified sense of 'single'.
+And as in other spheres the basic element is simple but not identical
+in all-in a system of weight it is the mina, in music the quarter-tone,
+and so on--so in syllogism the unit is an immediate premiss, and in
+the knowledge that demonstration gives it is an intuition. In syllogisms,
+then, which prove the inherence of an attribute, nothing falls outside
+the major term. In the case of negative syllogisms on the other hand,
+(1) in the first figure nothing falls outside the major term whose
+inherence is in question; e.g. to prove through a middle C that A
+does not inhere in B the premisses required are, all B is C, no C
+is A. Then if it has to be proved that no C is A, a middle must be
+found between and C; and this procedure will never vary.
+
+(2) If we have to show that E is not D by means of the premisses,
+all D is C; no E, or not all E, is C; then the middle will never fall
+beyond E, and E is the subject of which D is to be denied in the conclusion.
+
+(3) In the third figure the middle will never fall beyond the limits
+of the subject and the attribute denied of it. 
+
+Part 24
+
+Since demonstrations may be either commensurately universal or particular,
+and either affirmative or negative; the question arises, which form
+is the better? And the same question may be put in regard to so-called
+'direct' demonstration and reductio ad impossibile. Let us first examine
+the commensurately universal and the particular forms, and when we
+have cleared up this problem proceed to discuss 'direct' demonstration
+and reductio ad impossibile. 
+
+The following considerations might lead some minds to prefer particular
+demonstration. 
+
+(1) The superior demonstration is the demonstration which gives us
+greater knowledge (for this is the ideal of demonstration), and we
+have greater knowledge of a particular individual when we know it
+in itself than when we know it through something else; e.g. we know
+Coriscus the musician better when we know that Coriscus is musical
+than when we know only that man is musical, and a like argument holds
+in all other cases. But commensurately universal demonstration, instead
+of proving that the subject itself actually is x, proves only that
+something else is x- e.g. in attempting to prove that isosceles is
+x, it proves not that isosceles but only that triangle is x- whereas
+particular demonstration proves that the subject itself is x. The
+demonstration, then, that a subject, as such, possesses an attribute
+is superior. If this is so, and if the particular rather than the
+commensurately universal forms demonstrates, particular demonstration
+is superior. 
+
+(2) The universal has not a separate being over against groups of
+singulars. Demonstration nevertheless creates the opinion that its
+function is conditioned by something like this-some separate entity
+belonging to the real world; that, for instance, of triangle or of
+figure or number, over against particular triangles, figures, and
+numbers. But demonstration which touches the real and will not mislead
+is superior to that which moves among unrealities and is delusory.
+Now commensurately universal demonstration is of the latter kind:
+if we engage in it we find ourselves reasoning after a fashion well
+illustrated by the argument that the proportionate is what answers
+to the definition of some entity which is neither line, number, solid,
+nor plane, but a proportionate apart from all these. Since, then,
+such a proof is characteristically commensurate and universal, and
+less touches reality than does particular demonstration, and creates
+a false opinion, it will follow that commensurate and universal is
+inferior to particular demonstration. 
+
+We may retort thus. (1) The first argument applies no more to commensurate
+and universal than to particular demonstration. If equality to two
+right angles is attributable to its subject not qua isosceles but
+qua triangle, he who knows that isosceles possesses that attribute
+knows the subject as qua itself possessing the attribute, to a less
+degree than he who knows that triangle has that attribute. To sum
+up the whole matter: if a subject is proved to possess qua triangle
+an attribute which it does not in fact possess qua triangle, that
+is not demonstration: but if it does possess it qua triangle the rule
+applies that the greater knowledge is his who knows the subject as
+possessing its attribute qua that in virtue of which it actually does
+possess it. Since, then, triangle is the wider term, and there is
+one identical definition of triangle-i.e. the term is not equivocal-and
+since equality to two right angles belongs to all triangles, it is
+isosceles qua triangle and not triangle qua isosceles which has its
+angles so related. It follows that he who knows a connexion universally
+has greater knowledge of it as it in fact is than he who knows the
+particular; and the inference is that commensurate and universal is
+superior to particular demonstration. 
+
+(2) If there is a single identical definition i.e. if the commensurate
+universal is unequivocal-then the universal will possess being not
+less but more than some of the particulars, inasmuch as it is universals
+which comprise the imperishable, particulars that tend to perish.
+
+(3) Because the universal has a single meaning, we are not therefore
+compelled to suppose that in these examples it has being as a substance
+apart from its particulars-any more than we need make a similar supposition
+in the other cases of unequivocal universal predication, viz. where
+the predicate signifies not substance but quality, essential relatedness,
+or action. If such a supposition is entertained, the blame rests not
+with the demonstration but with the hearer. 
+
+(4) Demonstration is syllogism that proves the cause, i.e. the reasoned
+fact, and it is rather the commensurate universal than the particular
+which is causative (as may be shown thus: that which possesses an
+attribute through its own essential nature is itself the cause of
+the inherence, and the commensurate universal is primary; hence the
+commensurate universal is the cause). Consequently commensurately
+universal demonstration is superior as more especially proving the
+cause, that is the reasoned fact. 
+
+(5) Our search for the reason ceases, and we think that we know, when
+the coming to be or existence of the fact before us is not due to
+the coming to be or existence of some other fact, for the last step
+of a search thus conducted is eo ipso the end and limit of the problem.
+Thus: 'Why did he come?' 'To get the money-wherewith to pay a debt-that
+he might thereby do what was right.' When in this regress we can no
+longer find an efficient or final cause, we regard the last step of
+it as the end of the coming-or being or coming to be-and we regard
+ourselves as then only having full knowledge of the reason why he
+came. 
+
+If, then, all causes and reasons are alike in this respect, and if
+this is the means to full knowledge in the case of final causes such
+as we have exemplified, it follows that in the case of the other causes
+also full knowledge is attained when an attribute no longer inheres
+because of something else. Thus, when we learn that exterior angles
+are equal to four right angles because they are the exterior angles
+of an isosceles, there still remains the question 'Why has isosceles
+this attribute?' and its answer 'Because it is a triangle, and a triangle
+has it because a triangle is a rectilinear figure.' If rectilinear
+figure possesses the property for no further reason, at this point
+we have full knowledge-but at this point our knowledge has become
+commensurately universal, and so we conclude that commensurately universal
+demonstration is superior. 
+
+(6) The more demonstration becomes particular the more it sinks into
+an indeterminate manifold, while universal demonstration tends to
+the simple and determinate. But objects so far as they are an indeterminate
+manifold are unintelligible, so far as they are determinate, intelligible:
+they are therefore intelligible rather in so far as they are universal
+than in so far as they are particular. From this it follows that universals
+are more demonstrable: but since relative and correlative increase
+concomitantly, of the more demonstrable there will be fuller demonstration.
+Hence the commensurate and universal form, being more truly demonstration,
+is the superior. 
+
+(7) Demonstration which teaches two things is preferable to demonstration
+which teaches only one. He who possesses commensurately universal
+demonstration knows the particular as well, but he who possesses particular
+demonstration does not know the universal. So that this is an additional
+reason for preferring commensurately universal demonstration. And
+there is yet this further argument: 
+
+(8) Proof becomes more and more proof of the commensurate universal
+as its middle term approaches nearer to the basic truth, and nothing
+is so near as the immediate premiss which is itself the basic truth.
+If, then, proof from the basic truth is more accurate than proof not
+so derived, demonstration which depends more closely on it is more
+accurate than demonstration which is less closely dependent. But commensurately
+universal demonstration is characterized by this closer dependence,
+and is therefore superior. Thus, if A had to be proved to inhere in
+D, and the middles were B and C, B being the higher term would render
+the demonstration which it mediated the more universal. 
+
+Some of these arguments, however, are dialectical. The clearest indication
+of the precedence of commensurately universal demonstration is as
+follows: if of two propositions, a prior and a posterior, we have
+a grasp of the prior, we have a kind of knowledge-a potential grasp-of
+the posterior as well. For example, if one knows that the angles of
+all triangles are equal to two right angles, one knows in a sense-potentially-that
+the isosceles' angles also are equal to two right angles, even if
+one does not know that the isosceles is a triangle; but to grasp this
+posterior proposition is by no means to know the commensurate universal
+either potentially or actually. Moreover, commensurately universal
+demonstration is through and through intelligible; particular demonstration
+issues in sense-perception. 
+
+Part 25
+
+The preceding arguments constitute our defence of the superiority
+of commensurately universal to particular demonstration. That affirmative
+demonstration excels negative may be shown as follows. 
+
+(1) We may assume the superiority ceteris paribus of the demonstration
+which derives from fewer postulates or hypotheses-in short from fewer
+premisses; for, given that all these are equally well known, where
+they are fewer knowledge will be more speedily acquired, and that
+is a desideratum. The argument implied in our contention that demonstration
+from fewer assumptions is superior may be set out in universal form
+as follows. Assuming that in both cases alike the middle terms are
+known, and that middles which are prior are better known than such
+as are posterior, we may suppose two demonstrations of the inherence
+of A in E, the one proving it through the middles B, C and D, the
+other through F and G. Then A-D is known to the same degree as A-E
+(in the second proof), but A-D is better known than and prior to A-E
+(in the first proof); since A-E is proved through A-D, and the ground
+is more certain than the conclusion. 
+
+Hence demonstration by fewer premisses is ceteris paribus superior.
+Now both affirmative and negative demonstration operate through three
+terms and two premisses, but whereas the former assumes only that
+something is, the latter assumes both that something is and that something
+else is not, and thus operating through more kinds of premiss is inferior.
+
+(2) It has been proved that no conclusion follows if both premisses
+are negative, but that one must be negative, the other affirmative.
+So we are compelled to lay down the following additional rule: as
+the demonstration expands, the affirmative premisses must increase
+in number, but there cannot be more than one negative premiss in each
+complete proof. Thus, suppose no B is A, and all C is B. Then if both
+the premisses are to be again expanded, a middle must be interposed.
+Let us interpose D between A and B, and E between B and C. Then clearly
+E is affirmatively related to B and C, while D is affirmatively related
+to B but negatively to A; for all B is D, but there must be no D which
+is A. Thus there proves to be a single negative premiss, A-D. In the
+further prosyllogisms too it is the same, because in the terms of
+an affirmative syllogism the middle is always related affirmatively
+to both extremes; in a negative syllogism it must be negatively related
+only to one of them, and so this negation comes to be a single negative
+premiss, the other premisses being affirmative. If, then, that through
+which a truth is proved is a better known and more certain truth,
+and if the negative proposition is proved through the affirmative
+and not vice versa, affirmative demonstration, being prior and better
+known and more certain, will be superior. 
+
+(3) The basic truth of demonstrative syllogism is the universal immediate
+premiss, and the universal premiss asserts in affirmative demonstration
+and in negative denies: and the affirmative proposition is prior to
+and better known than the negative (since affirmation explains denial
+and is prior to denial, just as being is prior to not-being). It follows
+that the basic premiss of affirmative demonstration is superior to
+that of negative demonstration, and the demonstration which uses superior
+basic premisses is superior. 
+
+(4) Affirmative demonstration is more of the nature of a basic form
+of proof, because it is a sine qua non of negative demonstration.
+
+Part 26
+
+Since affirmative demonstration is superior to negative, it is clearly
+superior also to reductio ad impossibile. We must first make certain
+what is the difference between negative demonstration and reductio
+ad impossibile. Let us suppose that no B is A, and that all C is B:
+the conclusion necessarily follows that no C is A. If these premisses
+are assumed, therefore, the negative demonstration that no C is A
+is direct. Reductio ad impossibile, on the other hand, proceeds as
+follows. Supposing we are to prove that does not inhere in B, we have
+to assume that it does inhere, and further that B inheres in C, with
+the resulting inference that A inheres in C. This we have to suppose
+a known and admitted impossibility; and we then infer that A cannot
+inhere in B. Thus if the inherence of B in C is not questioned, A's
+inherence in B is impossible. 
+
+The order of the terms is the same in both proofs: they differ according
+to which of the negative propositions is the better known, the one
+denying A of B or the one denying A of C. When the falsity of the
+conclusion is the better known, we use reductio ad impossible; when
+the major premiss of the syllogism is the more obvious, we use direct
+demonstration. All the same the proposition denying A of B is, in
+the order of being, prior to that denying A of C; for premisses are
+prior to the conclusion which follows from them, and 'no C is A' is
+the conclusion, 'no B is A' one of its premisses. For the destructive
+result of reductio ad impossibile is not a proper conclusion, nor
+are its antecedents proper premisses. On the contrary: the constituents
+of syllogism are premisses related to one another as whole to part
+or part to whole, whereas the premisses A-C and A-B are not thus related
+to one another. Now the superior demonstration is that which proceeds
+from better known and prior premisses, and while both these forms
+depend for credence on the not-being of something, yet the source
+of the one is prior to that of the other. Therefore negative demonstration
+will have an unqualified superiority to reductio ad impossibile, and
+affirmative demonstration, being superior to negative, will consequently
+be superior also to reductio ad impossibile. 
+
+Part 27
+
+The science which is knowledge at once of the fact and of the reasoned
+fact, not of the fact by itself without the reasoned fact, is the
+more exact and the prior science. 
+
+A science such as arithmetic, which is not a science of properties
+qua inhering in a substratum, is more exact than and prior to a science
+like harmonics, which is a science of pr,operties inhering in a substratum;
+and similarly a science like arithmetic, which is constituted of fewer
+basic elements, is more exact than and prior to geometry, which requires
+additional elements. What I mean by 'additional elements' is this:
+a unit is substance without position, while a point is substance with
+position; the latter contains an additional element. 
+
+Part 28
+
+A single science is one whose domain is a single genus, viz. all the
+subjects constituted out of the primary entities of the genus-i.e.
+the parts of this total subject-and their essential properties.
+
+One science differs from another when their basic truths have neither
+a common source nor are derived those of the one science from those
+the other. This is verified when we reach the indemonstrable premisses
+of a science, for they must be within one genus with its conclusions:
+and this again is verified if the conclusions proved by means of them
+fall within one genus-i.e. are homogeneous. 
+
+Part 29
+
+One can have several demonstrations of the same connexion not only
+by taking from the same series of predication middles which are other
+than the immediately cohering term e.g. by taking C, D, and F severally
+to prove A-B--but also by taking a middle from another series. Thus
+let A be change, D alteration of a property, B feeling pleasure, and
+G relaxation. We can then without falsehood predicate D of B and A
+of D, for he who is pleased suffers alteration of a property, and
+that which alters a property changes. Again, we can predicate A of
+G without falsehood, and G of B; for to feel pleasure is to relax,
+and to relax is to change. So the conclusion can be drawn through
+middles which are different, i.e. not in the same series-yet not so
+that neither of these middles is predicable of the other, for they
+must both be attributable to some one subject. 
+
+A further point worth investigating is how many ways of proving the
+same conclusion can be obtained by varying the figure, 
+
+Part 30
+
+There is no knowledge by demonstration of chance conjunctions; for
+chance conjunctions exist neither by necessity nor as general connexions
+but comprise what comes to be as something distinct from these. Now
+demonstration is concerned only with one or other of these two; for
+all reasoning proceeds from necessary or general premisses, the conclusion
+being necessary if the premisses are necessary and general if the
+premisses are general. Consequently, if chance conjunctions are neither
+general nor necessary, they are not demonstrable. 
+
+Part 31
+
+Scientific knowledge is not possible through the act of perception.
+Even if perception as a faculty is of 'the such' and not merely of
+a 'this somewhat', yet one must at any rate actually perceive a 'this
+somewhat', and at a definite present place and time: but that which
+is commensurately universal and true in all cases one cannot perceive,
+since it is not 'this' and it is not 'now'; if it were, it would not
+be commensurately universal-the term we apply to what is always and
+everywhere. Seeing, therefore, that demonstrations are commensurately
+universal and universals imperceptible, we clearly cannot obtain scientific
+knowledge by the act of perception: nay, it is obvious that even if
+it were possible to perceive that a triangle has its angles equal
+to two right angles, we should still be looking for a demonstration-we
+should not (as some say) possess knowledge of it; for perception must
+be of a particular, whereas scientific knowledge involves the recognition
+of the commensurate universal. So if we were on the moon, and saw
+the earth shutting out the sun's light, we should not know the cause
+of the eclipse: we should perceive the present fact of the eclipse,
+but not the reasoned fact at all, since the act of perception is not
+of the commensurate universal. I do not, of course, deny that by watching
+the frequent recurrence of this event we might, after tracking the
+commensurate universal, possess a demonstration, for the commensurate
+universal is elicited from the several groups of singulars.
+
+The commensurate universal is precious because it makes clear the
+cause; so that in the case of facts like these which have a cause
+other than themselves universal knowledge is more precious than sense-perceptions
+and than intuition. (As regards primary truths there is of course
+a different account to be given.) Hence it is clear that knowledge
+of things demonstrable cannot be acquired by perception, unless the
+term perception is applied to the possession of scientific knowledge
+through demonstration. Nevertheless certain points do arise with regard
+to connexions to be proved which are referred for their explanation
+to a failure in sense-perception: there are cases when an act of vision
+would terminate our inquiry, not because in seeing we should be knowing,
+but because we should have elicited the universal from seeing; if,
+for example, we saw the pores in the glass and the light passing through,
+the reason of the kindling would be clear to us because we should
+at the same time see it in each instance and intuit that it must be
+so in all instances. 
+
+Part 32
+
+All syllogisms cannot have the same basic truths. This may be shown
+first of all by the following dialectical considerations. (1) Some
+syllogisms are true and some false: for though a true inference is
+possible from false premisses, yet this occurs once only-I mean if
+A for instance, is truly predicable of C, but B, the middle, is false,
+both A-B and B-C being false; nevertheless, if middles are taken to
+prove these premisses, they will be false because every conclusion
+which is a falsehood has false premisses, while true conclusions have
+true premisses, and false and true differ in kind. Then again, (2)
+falsehoods are not all derived from a single identical set of principles:
+there are falsehoods which are the contraries of one another and cannot
+coexist, e.g. 'justice is injustice', and 'justice is cowardice';
+'man is horse', and 'man is ox'; 'the equal is greater', and 'the
+equal is less.' From established principles we may argue the case
+as follows, confining-ourselves therefore to true conclusions. Not
+even all these are inferred from the same basic truths; many of them
+in fact have basic truths which differ generically and are not transferable;
+units, for instance, which are without position, cannot take the place
+of points, which have position. The transferred terms could only fit
+in as middle terms or as major or minor terms, or else have some of
+the other terms between them, others outside them. 
+
+Nor can any of the common axioms-such, I mean, as the law of excluded
+middle-serve as premisses for the proof of all conclusions. For the
+kinds of being are different, and some attributes attach to quanta
+and some to qualia only; and proof is achieved by means of the common
+axioms taken in conjunction with these several kinds and their attributes.
+
+Again, it is not true that the basic truths are much fewer than the
+conclusions, for the basic truths are the premisses, and the premisses
+are formed by the apposition of a fresh extreme term or the interposition
+of a fresh middle. Moreover, the number of conclusions is indefinite,
+though the number of middle terms is finite; and lastly some of the
+basic truths are necessary, others variable. 
+
+Looking at it in this way we see that, since the number of conclusions
+is indefinite, the basic truths cannot be identical or limited in
+number. If, on the other hand, identity is used in another sense,
+and it is said, e.g. 'these and no other are the fundamental truths
+of geometry, these the fundamentals of calculation, these again of
+medicine'; would the statement mean anything except that the sciences
+have basic truths? To call them identical because they are self-identical
+is absurd, since everything can be identified with everything in that
+sense of identity. Nor again can the contention that all conclusions
+have the same basic truths mean that from the mass of all possible
+premisses any conclusion may be drawn. That would be exceedingly naive,
+for it is not the case in the clearly evident mathematical sciences,
+nor is it possible in analysis, since it is the immediate premisses
+which are the basic truths, and a fresh conclusion is only formed
+by the addition of a new immediate premiss: but if it be admitted
+that it is these primary immediate premisses which are basic truths,
+each subject-genus will provide one basic truth. If, however, it is
+not argued that from the mass of all possible premisses any conclusion
+may be proved, nor yet admitted that basic truths differ so as to
+be generically different for each science, it remains to consider
+the possibility that, while the basic truths of all knowledge are
+within one genus, special premisses are required to prove special
+conclusions. But that this cannot be the case has been shown by our
+proof that the basic truths of things generically different themselves
+differ generically. For fundamental truths are of two kinds, those
+which are premisses of demonstration and the subject-genus; and though
+the former are common, the latter-number, for instance, and magnitude-are
+peculiar. 
+
+Part 33
+
+Scientific knowledge and its object differ from opinion and the object
+of opinion in that scientific knowledge is commensurately universal
+and proceeds by necessary connexions, and that which is necessary
+cannot be otherwise. So though there are things which are true and
+real and yet can be otherwise, scientific knowledge clearly does not
+concern them: if it did, things which can be otherwise would be incapable
+of being otherwise. Nor are they any concern of rational intuition-by
+rational intuition I mean an originative source of scientific knowledge-nor
+of indemonstrable knowledge, which is the grasping of the immediate
+premiss. Since then rational intuition, science, and opinion, and
+what is revealed by these terms, are the only things that can be 'true',
+it follows that it is opinion that is concerned with that which may
+be true or false, and can be otherwise: opinion in fact is the grasp
+of a premiss which is immediate but not necessary. This view also
+fits the observed facts, for opinion is unstable, and so is the kind
+of being we have described as its object. Besides, when a man thinks
+a truth incapable of being otherwise he always thinks that he knows
+it, never that he opines it. He thinks that he opines when he thinks
+that a connexion, though actually so, may quite easily be otherwise;
+for he believes that such is the proper object of opinion, while the
+necessary is the object of knowledge. 
+
+In what sense, then, can the same thing be the object of both opinion
+and knowledge? And if any one chooses to maintain that all that he
+knows he can also opine, why should not opinion be knowledge? For
+he that knows and he that opines will follow the same train of thought
+through the same middle terms until the immediate premisses are reached;
+because it is possible to opine not only the fact but also the reasoned
+fact, and the reason is the middle term; so that, since the former
+knows, he that opines also has knowledge. 
+
+The truth perhaps is that if a man grasp truths that cannot be other
+than they are, in the way in which he grasps the definitions through
+which demonstrations take place, he will have not opinion but knowledge:
+if on the other hand he apprehends these attributes as inhering in
+their subjects, but not in virtue of the subjects' substance and essential
+nature possesses opinion and not genuine knowledge; and his opinion,
+if obtained through immediate premisses, will be both of the fact
+and of the reasoned fact; if not so obtained, of the fact alone. The
+object of opinion and knowledge is not quite identical; it is only
+in a sense identical, just as the object of true and false opinion
+is in a sense identical. The sense in which some maintain that true
+and false opinion can have the same object leads them to embrace many
+strange doctrines, particularly the doctrine that what a man opines
+falsely he does not opine at all. There are really many senses of
+'identical', and in one sense the object of true and false opinion
+can be the same, in another it cannot. Thus, to have a true opinion
+that the diagonal is commensurate with the side would be absurd: but
+because the diagonal with which they are both concerned is the same,
+the two opinions have objects so far the same: on the other hand,
+as regards their essential definable nature these objects differ.
+The identity of the objects of knowledge and opinion is similar. Knowledge
+is the apprehension of, e.g. the attribute 'animal' as incapable of
+being otherwise, opinion the apprehension of 'animal' as capable of
+being otherwise-e.g. the apprehension that animal is an element in
+the essential nature of man is knowledge; the apprehension of animal
+as predicable of man but not as an element in man's essential nature
+is opinion: man is the subject in both judgements, but the mode of
+inherence differs. 
+
+This also shows that one cannot opine and know the same thing simultaneously;
+for then one would apprehend the same thing as both capable and incapable
+of being otherwise-an impossibility. Knowledge and opinion of the
+same thing can co-exist in two different people in the sense we have
+explained, but not simultaneously in the same person. That would involve
+a man's simultaneously apprehending, e.g. (1) that man is essentially
+animal-i.e. cannot be other than animal-and (2) that man is not essentially
+animal, that is, we may assume, may be other than animal.
+
+Further consideration of modes of thinking and their distribution
+under the heads of discursive thought, intuition, science, art, practical
+wisdom, and metaphysical thinking, belongs rather partly to natural
+science, partly to moral philosophy. 
+
+Part 34
+
+Quick wit is a faculty of hitting upon the middle term instantaneously.
+It would be exemplified by a man who saw that the moon has her bright
+side always turned towards the sun, and quickly grasped the cause
+of this, namely that she borrows her light from him; or observed somebody
+in conversation with a man of wealth and divined that he was borrowing
+money, or that the friendship of these people sprang from a common
+enmity. In all these instances he has seen the major and minor terms
+and then grasped the causes, the middle terms. 
+
+Let A represent 'bright side turned sunward', B 'lighted from the
+sun', C the moon. Then B, 'lighted from the sun' is predicable of
+C, the moon, and A, 'having her bright side towards the source of
+her light', is predicable of B. So A is predicable of C through B.
+
+----------------------------------------------------------------------
+
+BOOK II
+
+Part 1 
+
+The kinds of question we ask are as many as the kinds of things which
+we know. They are in fact four:-(1) whether the connexion of an attribute
+with a thing is a fact, (2) what is the reason of the connexion, (3)
+whether a thing exists, (4) What is the nature of the thing. Thus,
+when our question concerns a complex of thing and attribute and we
+ask whether the thing is thus or otherwise qualified-whether, e.g.
+the sun suffers eclipse or not-then we are asking as to the fact of
+a connexion. That our inquiry ceases with the discovery that the sun
+does suffer eclipse is an indication of this; and if we know from
+the start that the sun suffers eclipse, we do not inquire whether
+it does so or not. On the other hand, when we know the fact we ask
+the reason; as, for example, when we know that the sun is being eclipsed
+and that an earthquake is in progress, it is the reason of eclipse
+or earthquake into which we inquire. 
+
+Where a complex is concerned, then, those are the two questions we
+ask; but for some objects of inquiry we have a different kind of question
+to ask, such as whether there is or is not a centaur or a God. (By
+'is or is not' I mean 'is or is not, without further qualification';
+as opposed to 'is or is not [e.g.] white'.) On the other hand, when
+we have ascertained the thing's existence, we inquire as to its nature,
+asking, for instance, 'what, then, is God?' or 'what is man?'.
+
+Part 2
+
+These, then, are the four kinds of question we ask, and it is in the
+answers to these questions that our knowledge consists. 
+
+Now when we ask whether a connexion is a fact, or whether a thing
+without qualification is, we are really asking whether the connexion
+or the thing has a 'middle'; and when we have ascertained either that
+the connexion is a fact or that the thing is-i.e. ascertained either
+the partial or the unqualified being of the thing-and are proceeding
+to ask the reason of the connexion or the nature of the thing, then
+we are asking what the 'middle' is. 
+
+(By distinguishing the fact of the connexion and the existence of
+the thing as respectively the partial and the unqualified being of
+the thing, I mean that if we ask 'does the moon suffer eclipse?',
+or 'does the moon wax?', the question concerns a part of the thing's
+being; for what we are asking in such questions is whether a thing
+is this or that, i.e. has or has not this or that attribute: whereas,
+if we ask whether the moon or night exists, the question concerns
+the unqualified being of a thing.) 
+
+We conclude that in all our inquiries we are asking either whether
+there is a 'middle' or what the 'middle' is: for the 'middle' here
+is precisely the cause, and it is the cause that we seek in all our
+inquiries. Thus, 'Does the moon suffer eclipse?' means 'Is there or
+is there not a cause producing eclipse of the moon?', and when we
+have learnt that there is, our next question is, 'What, then, is this
+cause? for the cause through which a thing is-not is this or that,
+i.e. has this or that attribute, but without qualification is-and
+the cause through which it is-not is without qualification, but is
+this or that as having some essential attribute or some accident-are
+both alike the middle'. By that which is without qualification I mean
+the subject, e.g. moon or earth or sun or triangle; by that which
+a subject is (in the partial sense) I mean a property, e.g. eclipse,
+equality or inequality, interposition or non-interposition. For in
+all these examples it is clear that the nature of the thing and the
+reason of the fact are identical: the question 'What is eclipse?'
+and its answer 'The privation of the moon's light by the interposition
+of the earth' are identical with the question 'What is the reason
+of eclipse?' or 'Why does the moon suffer eclipse?' and the reply
+'Because of the failure of light through the earth's shutting it out'.
+Again, for 'What is a concord? A commensurate numerical ratio of a
+high and a low note', we may substitute 'What ratio makes a high and
+a low note concordant? Their relation according to a commensurate
+numerical ratio.' 'Are the high and the low note concordant?' is equivalent
+to 'Is their ratio commensurate?'; and when we find that it is commensurate,
+we ask 'What, then, is their ratio?'. 
+
+Cases in which the 'middle' is sensible show that the object of our
+inquiry is always the 'middle': we inquire, because we have not perceived
+it, whether there is or is not a 'middle' causing, e.g. an eclipse.
+On the other hand, if we were on the moon we should not be inquiring
+either as to the fact or the reason, but both fact and reason would
+be obvious simultaneously. For the act of perception would have enabled
+us to know the universal too; since, the present fact of an eclipse
+being evident, perception would then at the same time give us the
+present fact of the earth's screening the sun's light, and from this
+would arise the universal. 
+
+Thus, as we maintain, to know a thing's nature is to know the reason
+why it is; and this is equally true of things in so far as they are
+said without qualification to he as opposed to being possessed of
+some attribute, and in so far as they are said to be possessed of
+some attribute such as equal to right angles, or greater or less.
+
+Part 3
+
+It is clear, then, that all questions are a search for a 'middle'.
+Let us now state how essential nature is revealed and in what way
+it can be reduced to demonstration; what definition is, and what things
+are definable. And let us first discuss certain difficulties which
+these questions raise, beginning what we have to say with a point
+most intimately connected with our immediately preceding remarks,
+namely the doubt that might be felt as to whether or not it is possible
+to know the same thing in the same relation, both by definition and
+by demonstration. It might, I mean, be urged that definition is held
+to concern essential nature and is in every case universal and affirmative;
+whereas, on the other hand, some conclusions are negative and some
+are not universal; e.g. all in the second figure are negative, none
+in the third are universal. And again, not even all affirmative conclusions
+in the first figure are definable, e.g. 'every triangle has its angles
+equal to two right angles'. An argument proving this difference between
+demonstration and definition is that to have scientific knowledge
+of the demonstrable is identical with possessing a demonstration of
+it: hence if demonstration of such conclusions as these is possible,
+there clearly cannot also be definition of them. If there could, one
+might know such a conclusion also in virtue of its definition without
+possessing the demonstration of it; for there is nothing to stop our
+having the one without the other. 
+
+Induction too will sufficiently convince us of this difference; for
+never yet by defining anything-essential attribute or accident-did
+we get knowledge of it. Again, if to define is to acquire knowledge
+of a substance, at any rate such attributes are not substances.
+
+It is evident, then, that not everything demonstrable can be defined.
+What then? Can everything definable be demonstrated, or not? There
+is one of our previous arguments which covers this too. Of a single
+thing qua single there is a single scientific knowledge. Hence, since
+to know the demonstrable scientifically is to possess the demonstration
+of it, an impossible consequence will follow:-possession of its definition
+without its demonstration will give knowledge of the demonstrable.
+
+Moreover, the basic premisses of demonstrations are definitions, and
+it has already been shown that these will be found indemonstrable;
+either the basic premisses will be demonstrable and will depend on
+prior premisses, and the regress will be endless; or the primary truths
+will be indemonstrable definitions. 
+
+But if the definable and the demonstrable are not wholly the same,
+may they yet be partially the same? Or is that impossible, because
+there can be no demonstration of the definable? There can be none,
+because definition is of the essential nature or being of something,
+and all demonstrations evidently posit and assume the essential nature-mathematical
+demonstrations, for example, the nature of unity and the odd, and
+all the other sciences likewise. Moreover, every demonstration proves
+a predicate of a subject as attaching or as not attaching to it, but
+in definition one thing is not predicated of another; we do not, e.g.
+predicate animal of biped nor biped of animal, nor yet figure of plane-plane
+not being figure nor figure plane. Again, to prove essential nature
+is not the same as to prove the fact of a connexion. Now definition
+reveals essential nature, demonstration reveals that a given attribute
+attaches or does not attach to a given subject; but different things
+require different demonstrations-unless the one demonstration is related
+to the other as part to whole. I add this because if all triangles
+have been proved to possess angles equal to two right angles, then
+this attribute has been proved to attach to isosceles; for isosceles
+is a part of which all triangles constitute the whole. But in the
+case before us the fact and the essential nature are not so related
+to one another, since the one is not a part of the other.
+
+So it emerges that not all the definable is demonstrable nor all the
+demonstrable definable; and we may draw the general conclusion that
+there is no identical object of which it is possible to possess both
+a definition and a demonstration. It follows obviously that definition
+and demonstration are neither identical nor contained either within
+the other: if they were, their objects would be related either as
+identical or as whole and part. 
+
+Part 4
+
+So much, then, for the first stage of our problem. The next step is
+to raise the question whether syllogism-i.e. demonstration-of the
+definable nature is possible or, as our recent argument assumed, impossible.
+
+We might argue it impossible on the following grounds:-(a) syllogism
+proves an attribute of a subject through the middle term; on the other
+hand (b) its definable nature is both 'peculiar' to a subject and
+predicated of it as belonging to its essence. But in that case (1)
+the subject, its definition, and the middle term connecting them must
+be reciprocally predicable of one another; for if A is to C, obviously
+A is 'peculiar' to B and B to C-in fact all three terms are 'peculiar'
+to one another: and further (2) if A inheres in the essence of all
+B and B is predicated universally of all C as belonging to C's essence,
+A also must be predicated of C as belonging to its essence.
+
+If one does not take this relation as thus duplicated-if, that is,
+A is predicated as being of the essence of B, but B is not of the
+essence of the subjects of which it is predicated-A will not necessarily
+be predicated of C as belonging to its essence. So both premisses
+will predicate essence, and consequently B also will be predicated
+of C as its essence. Since, therefore, both premisses do predicate
+essence-i.e. definable form-C's definable form will appear in the
+middle term before the conclusion is drawn. 
+
+We may generalize by supposing that it is possible to prove the essential
+nature of man. Let C be man, A man's essential nature--two-footed
+animal, or aught else it may be. Then, if we are to syllogize, A must
+be predicated of all B. But this premiss will be mediated by a fresh
+definition, which consequently will also be the essential nature of
+man. Therefore the argument assumes what it has to prove, since B
+too is the essential nature of man. It is, however, the case in which
+there are only the two premisses-i.e. in which the premisses are primary
+and immediate-which we ought to investigate, because it best illustrates
+the point under discussion. 
+
+Thus they who prove the essential nature of soul or man or anything
+else through reciprocating terms beg the question. It would be begging
+the question, for example, to contend that the soul is that which
+causes its own life, and that what causes its own life is a self-moving
+number; for one would have to postulate that the soul is a self-moving
+number in the sense of being identical with it. For if A is predicable
+as a mere consequent of B and B of C, A will not on that account be
+the definable form of C: A will merely be what it was true to say
+of C. Even if A is predicated of all B inasmuch as B is identical
+with a species of A, still it will not follow: being an animal is
+predicated of being a man-since it is true that in all instances to
+be human is to be animal, just as it is also true that every man is
+an animal-but not as identical with being man. 
+
+We conclude, then, that unless one takes both the premisses as predicating
+essence, one cannot infer that A is the definable form and essence
+of C: but if one does so take them, in assuming B one will have assumed,
+before drawing the conclusion, what the definable form of C is; so
+that there has been no inference, for one has begged the question.
+
+Part 5
+
+Nor, as was said in my formal logic, is the method of division a process
+of inference at all, since at no point does the characterization of
+the subject follow necessarily from the premising of certain other
+facts: division demonstrates as little as does induction. For in a
+genuine demonstration the conclusion must not be put as a question
+nor depend on a concession, but must follow necessarily from its premisses,
+even if the respondent deny it. The definer asks 'Is man animal or
+inanimate?' and then assumes-he has not inferred-that man is animal.
+Next, when presented with an exhaustive division of animal into terrestrial
+and aquatic, he assumes that man is terrestrial. Moreover, that man
+is the complete formula, terrestrial-animal, does not follow necessarily
+from the premisses: this too is an assumption, and equally an assumption
+whether the division comprises many differentiae or few. (Indeed as
+this method of division is used by those who proceed by it, even truths
+that can be inferred actually fail to appear as such.) For why should
+not the whole of this formula be true of man, and yet not exhibit
+his essential nature or definable form? Again, what guarantee is there
+against an unessential addition, or against the omission of the final
+or of an intermediate determinant of the substantial being?
+
+The champion of division might here urge that though these lapses
+do occur, yet we can solve that difficulty if all the attributes we
+assume are constituents of the definable form, and if, postulating
+the genus, we produce by division the requisite uninterrupted sequence
+of terms, and omit nothing; and that indeed we cannot fail to fulfil
+these conditions if what is to be divided falls whole into the division
+at each stage, and none of it is omitted; and that this-the dividendum-must
+without further question be (ultimately) incapable of fresh specific
+division. Nevertheless, we reply, division does not involve inference;
+if it gives knowledge, it gives it in another way. Nor is there any
+absurdity in this: induction, perhaps, is not demonstration any more
+than is division, et it does make evident some truth. Yet to state
+a definition reached by division is not to state a conclusion: as,
+when conclusions are drawn without their appropriate middles, the
+alleged necessity by which the inference follows from the premisses
+is open to a question as to the reason for it, so definitions reached
+by division invite the same question. 
+
+Thus to the question 'What is the essential nature of man?' the divider
+replies 'Animal, mortal, footed, biped, wingless'; and when at each
+step he is asked 'Why?', he will say, and, as he thinks, proves by
+division, that all animal is mortal or immortal: but such a formula
+taken in its entirety is not definition; so that even if division
+does demonstrate its formula, definition at any rate does not turn
+out to be a conclusion of inference. 
+
+Part 6
+
+Can we nevertheless actually demonstrate what a thing essentially
+and substantially is, but hypothetically, i.e. by premising (1) that
+its definable form is constituted by the 'peculiar' attributes of
+its essential nature; (2) that such and such are the only attributes
+of its essential nature, and that the complete synthesis of them is
+peculiar to the thing; and thus-since in this synthesis consists the
+being of the thing-obtaining our conclusion? Or is the truth that,
+since proof must be through the middle term, the definable form is
+once more assumed in this minor premiss too? 
+
+Further, just as in syllogizing we do not premise what syllogistic
+inference is (since the premisses from which we conclude must be related
+as whole and part), so the definable form must not fall within the
+syllogism but remain outside the premisses posited. It is only against
+a doubt as to its having been a syllogistic inference at all that
+we have to defend our argument as conforming to the definition of
+syllogism. It is only when some one doubts whether the conclusion
+proved is the definable form that we have to defend it as conforming
+to the definition of definable form which we assumed. Hence syllogistic
+inference must be possible even without the express statement of what
+syllogism is or what definable form is. 
+
+The following type of hypothetical proof also begs the question. If
+evil is definable as the divisible, and the definition of a thing's
+contrary-if it has one the contrary of the thing's definition; then,
+if good is the contrary of evil and the indivisible of the divisible,
+we conclude that to be good is essentially to be indivisible. The
+question is begged because definable form is assumed as a premiss,
+and as a premiss which is to prove definable form. 'But not the same
+definable form', you may object. That I admit, for in demonstrations
+also we premise that 'this' is predicable of 'that'; but in this premiss
+the term we assert of the minor is neither the major itself nor a
+term identical in definition, or convertible, with the major.
+
+Again, both proof by division and the syllogism just described are
+open to the question why man should be animal-biped-terrestrial and
+not merely animal and terrestrial, since what they premise does not
+ensure that the predicates shall constitute a genuine unity and not
+merely belong to a single subject as do musical and grammatical when
+predicated of the same man. 
+
+Part 7
+
+How then by definition shall we prove substance or essential nature?
+We cannot show it as a fresh fact necessarily following from the assumption
+of premisses admitted to be facts-the method of demonstration: we
+may not proceed as by induction to establish a universal on the evidence
+of groups of particulars which offer no exception, because induction
+proves not what the essential nature of a thing is but that it has
+or has not some attribute. Therefore, since presumably one cannot
+prove essential nature by an appeal to sense perception or by pointing
+with the finger, what other method remains? 
+
+To put it another way: how shall we by definition prove essential
+nature? He who knows what human-or any other-nature is, must know
+also that man exists; for no one knows the nature of what does not
+exist-one can know the meaning of the phrase or name 'goat-stag' but
+not what the essential nature of a goat-stag is. But further, if definition
+can prove what is the essential nature of a thing, can it also prove
+that it exists? And how will it prove them both by the same process,
+since definition exhibits one single thing and demonstration another
+single thing, and what human nature is and the fact that man exists
+are not the same thing? Then too we hold that it is by demonstration
+that the being of everything must be proved-unless indeed to be were
+its essence; and, since being is not a genus, it is not the essence
+of anything. Hence the being of anything as fact is matter for demonstration;
+and this is the actual procedure of the sciences, for the geometer
+assumes the meaning of the word triangle, but that it is possessed
+of some attribute he proves. What is it, then, that we shall prove
+in defining essential nature? Triangle? In that case a man will know
+by definition what a thing's nature is without knowing whether it
+exists. But that is impossible. 
+
+Moreover it is clear, if we consider the methods of defining actually
+in use, that definition does not prove that the thing defined exists:
+since even if there does actually exist something which is equidistant
+from a centre, yet why should the thing named in the definition exist?
+Why, in other words, should this be the formula defining circle? One
+might equally well call it the definition of mountain copper. For
+definitions do not carry a further guarantee that the thing defined
+can exist or that it is what they claim to define: one can always
+ask why. 
+
+Since, therefore, to define is to prove either a thing's essential
+nature or the meaning of its name, we may conclude that definition,
+if it in no sense proves essential nature, is a set of words signifying
+precisely what a name signifies. But that were a strange consequence;
+for (1) both what is not substance and what does not exist at all
+would be definable, since even non-existents can be signified by a
+name: (2) all sets of words or sentences would be definitions, since
+any kind of sentence could be given a name; so that we should all
+be talking in definitions, and even the Iliad would be a definition:
+(3) no demonstration can prove that any particular name means any
+particular thing: neither, therefore, do definitions, in addition
+to revealing the meaning of a name, also reveal that the name has
+this meaning. It appears then from these considerations that neither
+definition and syllogism nor their objects are identical, and further
+that definition neither demonstrates nor proves anything, and that
+knowledge of essential nature is not to be obtained either by definition
+or by demonstration. 
+
+Part 8
+
+We must now start afresh and consider which of these conclusions are
+sound and which are not, and what is the nature of definition, and
+whether essential nature is in any sense demonstrable and definable
+or in none. 
+
+Now to know its essential nature is, as we said, the same as to know
+the cause of a thing's existence, and the proof of this depends on
+the fact that a thing must have a cause. Moreover, this cause is either
+identical with the essential nature of the thing or distinct from
+it; and if its cause is distinct from it, the essential nature of
+the thing is either demonstrable or indemonstrable. Consequently,
+if the cause is distinct from the thing's essential nature and demonstration
+is possible, the cause must be the middle term, and, the conclusion
+proved being universal and affirmative, the proof is in the first
+figure. So the method just examined of proving it through another
+essential nature would be one way of proving essential nature, because
+a conclusion containing essential nature must be inferred through
+a middle which is an essential nature just as a 'peculiar' property
+must be inferred through a middle which is a 'peculiar' property;
+so that of the two definable natures of a single thing this method
+will prove one and not the other. 
+
+Now it was said before that this method could not amount to demonstration
+of essential nature-it is actually a dialectical proof of it-so let
+us begin again and explain by what method it can be demonstrated.
+When we are aware of a fact we seek its reason, and though sometimes
+the fact and the reason dawn on us simultaneously, yet we cannot apprehend
+the reason a moment sooner than the fact; and clearly in just the
+same way we cannot apprehend a thing's definable form without apprehending
+that it exists, since while we are ignorant whether it exists we cannot
+know its essential nature. Moreover we are aware whether a thing exists
+or not sometimes through apprehending an element in its character,
+and sometimes accidentally, as, for example, when we are aware of
+thunder as a noise in the clouds, of eclipse as a privation of light,
+or of man as some species of animal, or of the soul as a self-moving
+thing. As often as we have accidental knowledge that the thing exists,
+we must be in a wholly negative state as regards awareness of its
+essential nature; for we have not got genuine knowledge even of its
+existence, and to search for a thing's essential nature when we are
+unaware that it exists is to search for nothing. On the other hand,
+whenever we apprehend an element in the thing's character there is
+less difficulty. Thus it follows that the degree of our knowledge
+of a thing's essential nature is determined by the sense in which
+we are aware that it exists. Let us then take the following as our
+first instance of being aware of an element in the essential nature.
+Let A be eclipse, C the moon, B the earth's acting as a screen. Now
+to ask whether the moon is eclipsed or not is to ask whether or not
+B has occurred. But that is precisely the same as asking whether A
+has a defining condition; and if this condition actually exists, we
+assert that A also actually exists. Or again we may ask which side
+of a contradiction the defining condition necessitates: does it make
+the angles of a triangle equal or not equal to two right angles? When
+we have found the answer, if the premisses are immediate, we know
+fact and reason together; if they are not immediate, we know the fact
+without the reason, as in the following example: let C be the moon,
+A eclipse, B the fact that the moon fails to produce shadows though
+she is full and though no visible body intervenes between us and her.
+Then if B, failure to produce shadows in spite of the absence of an
+intervening body, is attributable A to C, and eclipse, is attributable
+to B, it is clear that the moon is eclipsed, but the reason why is
+not yet clear, and we know that eclipse exists, but we do not know
+what its essential nature is. But when it is clear that A is attributable
+to C and we proceed to ask the reason of this fact, we are inquiring
+what is the nature of B: is it the earth's acting as a screen, or
+the moon's rotation or her extinction? But B is the definition of
+the other term, viz. in these examples, of the major term A; for eclipse
+is constituted by the earth acting as a screen. Thus, (1) 'What is
+thunder?' 'The quenching of fire in cloud', and (2) 'Why does it thunder?'
+'Because fire is quenched in the cloud', are equivalent. Let C be
+cloud, A thunder, B the quenching of fire. Then B is attributable
+to C, cloud, since fire is quenched in it; and A, noise, is attributable
+to B; and B is assuredly the definition of the major term A. If there
+be a further mediating cause of B, it will be one of the remaining
+partial definitions of A. 
+
+We have stated then how essential nature is discovered and becomes
+known, and we see that, while there is no syllogism-i.e. no demonstrative
+syllogism-of essential nature, yet it is through syllogism, viz. demonstrative
+syllogism, that essential nature is exhibited. So we conclude that
+neither can the essential nature of anything which has a cause distinct
+from itself be known without demonstration, nor can it be demonstrated;
+and this is what we contended in our preliminary discussions.
+
+Part 9
+
+Now while some things have a cause distinct from themselves, others
+have not. Hence it is evident that there are essential natures which
+are immediate, that is are basic premisses; and of these not only
+that they are but also what they are must be assumed or revealed in
+some other way. This too is the actual procedure of the arithmetician,
+who assumes both the nature and the existence of unit. On the other
+hand, it is possible (in the manner explained) to exhibit through
+demonstration the essential nature of things which have a 'middle',
+i.e. a cause of their substantial being other than that being itself;
+but we do not thereby demonstrate it. 
+
+Part 10
+
+Since definition is said to be the statement of a thing's nature,
+obviously one kind of definition will be a statement of the meaning
+of the name, or of an equivalent nominal formula. A definition in
+this sense tells you, e.g. the meaning of the phrase 'triangular character'.
+When we are aware that triangle exists, we inquire the reason why
+it exists. But it is difficult thus to learn the definition of things
+the existence of which we do not genuinely know-the cause of this
+difficulty being, as we said before, that we only know accidentally
+whether or not the thing exists. Moreover, a statement may be a unity
+in either of two ways, by conjunction, like the Iliad, or because
+it exhibits a single predicate as inhering not accidentally in a single
+subject. 
+
+That then is one way of defining definition. Another kind of definition
+is a formula exhibiting the cause of a thing's existence. Thus the
+former signifies without proving, but the latter will clearly be a
+quasi-demonstration of essential nature, differing from demonstration
+in the arrangement of its terms. For there is a difference between
+stating why it thunders, and stating what is the essential nature
+of thunder; since the first statement will be 'Because fire is quenched
+in the clouds', while the statement of what the nature of thunder
+is will be 'The noise of fire being quenched in the clouds'. Thus
+the same statement takes a different form: in one form it is continuous
+demonstration, in the other definition. Again, thunder can be defined
+as noise in the clouds, which is the conclusion of the demonstration
+embodying essential nature. On the other hand the definition of immediates
+is an indemonstrable positing of essential nature. 
+
+We conclude then that definition is (a) an indemonstrable statement
+of essential nature, or (b) a syllogism of essential nature differing
+from demonstration in grammatical form, or (c) the conclusion of a
+demonstration giving essential nature. 
+
+Our discussion has therefore made plain (1) in what sense and of what
+things the essential nature is demonstrable, and in what sense and
+of what things it is not; (2) what are the various meanings of the
+term definition, and in what sense and of what things it proves the
+essential nature, and in what sense and of what things it does not;
+(3) what is the relation of definition to demonstration, and how far
+the same thing is both definable and demonstrable and how far it is
+not. 
+
+Part 11
+
+We think we have scientific knowledge when we know the cause, and
+there are four causes: (1) the definable form, (2) an antecedent which
+necessitates a consequent, (3) the efficient cause, (4) the final
+cause. Hence each of these can be the middle term of a proof, for
+(a) though the inference from antecedent to necessary consequent does
+not hold if only one premiss is assumed-two is the minimum-still when
+there are two it holds on condition that they have a single common
+middle term. So it is from the assumption of this single middle term
+that the conclusion follows necessarily. The following example will
+also show this. Why is the angle in a semicircle a right angle?-or
+from what assumption does it follow that it is a right angle? Thus,
+let A be right angle, B the half of two right angles, C the angle
+in a semicircle. Then B is the cause in virtue of which A, right angle,
+is attributable to C, the angle in a semicircle, since B=A and the
+other, viz. C,=B, for C is half of two right angles. Therefore it
+is the assumption of B, the half of two right angles, from which it
+follows that A is attributable to C, i.e. that the angle in a semicircle
+is a right angle. Moreover, B is identical with (b) the defining form
+of A, since it is what A's definition signifies. Moreover, the formal
+cause has already been shown to be the middle. (c) 'Why did the Athenians
+become involved in the Persian war?' means 'What cause originated
+the waging of war against the Athenians?' and the answer is, 'Because
+they raided Sardis with the Eretrians', since this originated the
+war. Let A be war, B unprovoked raiding, C the Athenians. Then B,
+unprovoked raiding, is true of C, the Athenians, and A is true of
+B, since men make war on the unjust aggressor. So A, having war waged
+upon them, is true of B, the initial aggressors, and B is true of
+C, the Athenians, who were the aggressors. Hence here too the cause-in
+this case the efficient cause-is the middle term. (d) This is no less
+true where the cause is the final cause. E.g. why does one take a
+walk after supper? For the sake of one's health. Why does a house
+exist? For the preservation of one's goods. The end in view is in
+the one case health, in the other preservation. To ask the reason
+why one must walk after supper is precisely to ask to what end one
+must do it. Let C be walking after supper, B the non-regurgitation
+of food, A health. Then let walking after supper possess the property
+of preventing food from rising to the orifice of the stomach, and
+let this condition be healthy; since it seems that B, the non-regurgitation
+of food, is attributable to C, taking a walk, and that A, health,
+is attributable to B. What, then, is the cause through which A, the
+final cause, inheres in C? It is B, the non-regurgitation of food;
+but B is a kind of definition of A, for A will be explained by it.
+Why is B the cause of A's belonging to C? Because to be in a condition
+such as B is to be in health. The definitions must be transposed,
+and then the detail will become clearer. Incidentally, here the order
+of coming to be is the reverse of what it is in proof through the
+efficient cause: in the efficient order the middle term must come
+to be first, whereas in the teleological order the minor, C, must
+first take place, and the end in view comes last in time.
+
+The same thing may exist for an end and be necessitated as well. For
+example, light shines through a lantern (1) because that which consists
+of relatively small particles necessarily passes through pores larger
+than those particles-assuming that light does issue by penetration-
+and (2) for an end, namely to save us from stumbling. If then, a thing
+can exist through two causes, can it come to be through two causes-as
+for instance if thunder be a hiss and a roar necessarily produced
+by the quenching of fire, and also designed, as the Pythagoreans say,
+for a threat to terrify those that lie in Tartarus? Indeed, there
+are very many such cases, mostly among the processes and products
+of the natural world; for nature, in different senses of the term
+'nature', produces now for an end, now by necessity. 
+
+Necessity too is of two kinds. It may work in accordance with a thing's
+natural tendency, or by constraint and in opposition to it; as, for
+instance, by necessity a stone is borne both upwards and downwards,
+but not by the same necessity. 
+
+Of the products of man's intelligence some are never due to chance
+or necessity but always to an end, as for example a house or a statue;
+others, such as health or safety, may result from chance as well.
+
+It is mostly in cases where the issue is indeterminate (though only
+where the production does not originate in chance, and the end is
+consequently good), that a result is due to an end, and this is true
+alike in nature or in art. By chance, on the other hand, nothing comes
+to be for an end. 
+
+Part 12 The effect may be still coming to be, or its occurrence may
+be past or future, yet the cause will be the same as when it is actually
+existent-for it is the middle which is the cause-except that if the
+effect actually exists the cause is actually existent, if it is coming
+to be so is the cause, if its occurrence is past the cause is past,
+if future the cause is future. For example, the moon was eclipsed
+because the earth intervened, is becoming eclipsed because the earth
+is in process of intervening, will be eclipsed because the earth will
+intervene, is eclipsed because the earth intervenes. 
+
+To take a second example: assuming that the definition of ice is solidified
+water, let C be water, A solidified, B the middle, which is the cause,
+namely total failure of heat. Then B is attributed to C, and A, solidification,
+to B: ice when B is occurring, has formed when B has occurred, and
+will form when B shall occur. 
+
+This sort of cause, then, and its effect come to be simultaneously
+when they are in process of becoming, and exist simultaneously when
+they actually exist; and the same holds good when they are past and
+when they are future. But what of cases where they are not simultaneous?
+Can causes and effects different from one another form, as they seem
+to us to form, a continuous succession, a past effect resulting from
+a past cause different from itself, a future effect from a future
+cause different from it, and an effect which is coming-to-be from
+a cause different from and prior to it? Now on this theory it is from
+the posterior event that we reason (and this though these later events
+actually have their source of origin in previous events--a fact which
+shows that also when the effect is coming-to-be we still reason from
+the posterior event), and from the event we cannot reason (we cannot
+argue that because an event A has occurred, therefore an event B has
+occurred subsequently to A but still in the past-and the same holds
+good if the occurrence is future)-cannot reason because, be the time
+interval definite or indefinite, it will never be possible to infer
+that because it is true to say that A occurred, therefore it is true
+to say that B, the subsequent event, occurred; for in the interval
+between the events, though A has already occurred, the latter statement
+will be false. And the same argument applies also to future events;
+i.e. one cannot infer from an event which occurred in the past that
+a future event will occur. The reason of this is that the middle must
+be homogeneous, past when the extremes are past, future when they
+are future, coming to be when they are coming-to-be, actually existent
+when they are actually existent; and there cannot be a middle term
+homogeneous with extremes respectively past and future. And it is
+a further difficulty in this theory that the time interval can be
+neither indefinite nor definite, since during it the inference will
+be false. We have also to inquire what it is that holds events together
+so that the coming-to-be now occurring in actual things follows upon
+a past event. It is evident, we may suggest, that a past event and
+a present process cannot be 'contiguous', for not even two past events
+can be 'contiguous'. For past events are limits and atomic; so just
+as points are not 'contiguous' neither are past events, since both
+are indivisible. For the same reason a past event and a present process
+cannot be 'contiguous', for the process is divisible, the event indivisible.
+Thus the relation of present process to past event is analogous to
+that of line to point, since a process contains an infinity of past
+events. These questions, however, must receive a more explicit treatment
+in our general theory of change. 
+
+The following must suffice as an account of the manner in which the
+middle would be identical with the cause on the supposition that coming-to-be
+is a series of consecutive events: for in the terms of such a series
+too the middle and major terms must form an immediate premiss; e.g.
+we argue that, since C has occurred, therefore A occurred: and C's
+occurrence was posterior, A's prior; but C is the source of the inference
+because it is nearer to the present moment, and the starting-point
+of time is the present. We next argue that, since D has occurred,
+therefore C occurred. Then we conclude that, since D has occurred,
+therefore A must have occurred; and the cause is C, for since D has
+occurred C must have occurred, and since C has occurred A must previously
+have occurred. 
+
+If we get our middle term in this way, will the series terminate in
+an immediate premiss, or since, as we said, no two events are 'contiguous',
+will a fresh middle term always intervene because there is an infinity
+of middles? No: though no two events are 'contiguous', yet we must
+start from a premiss consisting of a middle and the present event
+as major. The like is true of future events too, since if it is true
+to say that D will exist, it must be a prior truth to say that A will
+exist, and the cause of this conclusion is C; for if D will exist,
+C will exist prior to D, and if C will exist, A will exist prior to
+it. And here too the same infinite divisibility might be urged, since
+future events are not 'contiguous'. But here too an immediate basic
+premiss must be assumed. And in the world of fact this is so: if a
+house has been built, then blocks must have been quarried and shaped.
+The reason is that a house having been built necessitates a foundation
+having been laid, and if a foundation has been laid blocks must have
+been shaped beforehand. Again, if a house will be built, blocks will
+similarly be shaped beforehand; and proof is through the middle in
+the same way, for the foundation will exist before the house.
+
+Now we observe in Nature a certain kind of circular process of coming-to-be;
+and this is possible only if the middle and extreme terms are reciprocal,
+since conversion is conditioned by reciprocity in the terms of the
+proof. This-the convertibility of conclusions and premisses-has been
+proved in our early chapters, and the circular process is an instance
+of this. In actual fact it is exemplified thus: when the earth had
+been moistened an exhalation was bound to rise, and when an exhalation
+had risen cloud was bound to form, and from the formation of cloud
+rain necessarily resulted and by the fall of rain the earth was necessarily
+moistened: but this was the starting-point, so that a circle is completed;
+for posit any one of the terms and another follows from it, and from
+that another, and from that again the first. 
+
+Some occurrences are universal (for they are, or come-to-be what they
+are, always and in ever case); others again are not always what they
+are but only as a general rule: for instance, not every man can grow
+a beard, but it is the general rule. In the case of such connexions
+the middle term too must be a general rule. For if A is predicated
+universally of B and B of C, A too must be predicated always and in
+every instance of C, since to hold in every instance and always is
+of the nature of the universal. But we have assumed a connexion which
+is a general rule; consequently the middle term B must also be a general
+rule. So connexions which embody a general rule-i.e. which exist or
+come to be as a general rule-will also derive from immediate basic
+premisses. 
+
+Part 13
+
+We have already explained how essential nature is set out in the terms
+of a demonstration, and the sense in which it is or is not demonstrable
+or definable; so let us now discuss the method to be adopted in tracing
+the elements predicated as constituting the definable form.
+
+Now of the attributes which inhere always in each several thing there
+are some which are wider in extent than it but not wider than its
+genus (by attributes of wider extent mean all such as are universal
+attributes of each several subject, but in their application are not
+confined to that subject). while an attribute may inhere in every
+triad, yet also in a subject not a triad-as being inheres in triad
+but also in subjects not numbers at all-odd on the other hand is an
+attribute inhering in every triad and of wider application (inhering
+as it does also in pentad), but which does not extend beyond the genus
+of triad; for pentad is a number, but nothing outside number is odd.
+It is such attributes which we have to select, up to the exact point
+at which they are severally of wider extent than the subject but collectively
+coextensive with it; for this synthesis must be the substance of the
+thing. For example every triad possesses the attributes number, odd,
+and prime in both senses, i.e. not only as possessing no divisors,
+but also as not being a sum of numbers. This, then, is precisely what
+triad is, viz. a number, odd, and prime in the former and also the
+latter sense of the term: for these attributes taken severally apply,
+the first two to all odd numbers, the last to the dyad also as well
+as to the triad, but, taken collectively, to no other subject. Now
+since we have shown above' that attributes predicated as belonging
+to the essential nature are necessary and that universals are necessary,
+and since the attributes which we select as inhering in triad, or
+in any other subject whose attributes we select in this way, are predicated
+as belonging to its essential nature, triad will thus possess these
+attributes necessarily. Further, that the synthesis of them constitutes
+the substance of triad is shown by the following argument. If it is
+not identical with the being of triad, it must be related to triad
+as a genus named or nameless. It will then be of wider extent than
+triad-assuming that wider potential extent is the character of a genus.
+If on the other hand this synthesis is applicable to no subject other
+than the individual triads, it will be identical with the being of
+triad, because we make the further assumption that the substance of
+each subject is the predication of elements in its essential nature
+down to the last differentia characterizing the individuals. It follows
+that any other synthesis thus exhibited will likewise be identical
+with the being of the subject. 
+
+The author of a hand-book on a subject that is a generic whole should
+divide the genus into its first infimae species-number e.g. into triad
+and dyad-and then endeavour to seize their definitions by the method
+we have described-the definition, for example, of straight line or
+circle or right angle. After that, having established what the category
+is to which the subaltern genus belongs-quantity or quality, for instance-he
+should examine the properties 'peculiar' to the species, working through
+the proximate common differentiae. He should proceed thus because
+the attributes of the genera compounded of the infimae species will
+be clearly given by the definitions of the species; since the basic
+element of them all is the definition, i.e. the simple infirma species,
+and the attributes inhere essentially in the simple infimae species,
+in the genera only in virtue of these. 
+
+Divisions according to differentiae are a useful accessory to this
+method. What force they have as proofs we did, indeed, explain above,
+but that merely towards collecting the essential nature they may be
+of use we will proceed to show. They might, indeed, seem to be of
+no use at all, but rather to assume everything at the start and to
+be no better than an initial assumption made without division. But,
+in fact, the order in which the attributes are predicated does make
+a difference--it matters whether we say animal-tame-biped, or biped-animal-tame.
+For if every definable thing consists of two elements and 'animal-tame'
+forms a unity, and again out of this and the further differentia man
+(or whatever else is the unity under construction) is constituted,
+then the elements we assume have necessarily been reached by division.
+Again, division is the only possible method of avoiding the omission
+of any element of the essential nature. Thus, if the primary genus
+is assumed and we then take one of the lower divisions, the dividendum
+will not fall whole into this division: e.g. it is not all animal
+which is either whole-winged or split-winged but all winged animal,
+for it is winged animal to which this differentiation belongs. The
+primary differentiation of animal is that within which all animal
+falls. The like is true of every other genus, whether outside animal
+or a subaltern genus of animal; e.g. the primary differentiation of
+bird is that within which falls every bird, of fish that within which
+falls every fish. So, if we proceed in this way, we can be sure that
+nothing has been omitted: by any other method one is bound to omit
+something without knowing it. 
+
+To define and divide one need not know the whole of existence. Yet
+some hold it impossible to know the differentiae distinguishing each
+thing from every single other thing without knowing every single other
+thing; and one cannot, they say, know each thing without knowing its
+differentiae, since everything is identical with that from which it
+does not differ, and other than that from which it differs. Now first
+of all this is a fallacy: not every differentia precludes identity,
+since many differentiae inhere in things specifically identical, though
+not in the substance of these nor essentially. Secondly, when one
+has taken one's differing pair of opposites and assumed that the two
+sides exhaust the genus, and that the subject one seeks to define
+is present in one or other of them, and one has further verified its
+presence in one of them; then it does not matter whether or not one
+knows all the other subjects of which the differentiae are also predicated.
+For it is obvious that when by this process one reaches subjects incapable
+of further differentiation one will possess the formula defining the
+substance. Moreover, to postulate that the division exhausts the genus
+is not illegitimate if the opposites exclude a middle; since if it
+is the differentia of that genus, anything contained in the genus
+must lie on one of the two sides. 
+
+In establishing a definition by division one should keep three objects
+in view: (1) the admission only of elements in the definable form,
+(2) the arrangement of these in the right order, (3) the omission
+of no such elements. The first is feasible because one can establish
+genus and differentia through the topic of the genus, just as one
+can conclude the inherence of an accident through the topic of the
+accident. The right order will be achieved if the right term is assumed
+as primary, and this will be ensured if the term selected is predicable
+of all the others but not all they of it; since there must be one
+such term. Having assumed this we at once proceed in the same way
+with the lower terms; for our second term will be the first of the
+remainder, our third the first of those which follow the second in
+a 'contiguous' series, since when the higher term is excluded, that
+term of the remainder which is 'contiguous' to it will be primary,
+and so on. Our procedure makes it clear that no elements in the definable
+form have been omitted: we have taken the differentia that comes first
+in the order of division, pointing out that animal, e.g. is divisible
+exhaustively into A and B, and that the subject accepts one of the
+two as its predicate. Next we have taken the differentia of the whole
+thus reached, and shown that the whole we finally reach is not further
+divisible-i.e. that as soon as we have taken the last differentia
+to form the concrete totality, this totality admits of no division
+into species. For it is clear that there is no superfluous addition,
+since all these terms we have selected are elements in the definable
+form; and nothing lacking, since any omission would have to be a genus
+or a differentia. Now the primary term is a genus, and this term taken
+in conjunction with its differentiae is a genus: moreover the differentiae
+are all included, because there is now no further differentia; if
+there were, the final concrete would admit of division into species,
+which, we said, is not the case. 
+
+To resume our account of the right method of investigation: We must
+start by observing a set of similar-i.e. specifically identical-individuals,
+and consider what element they have in common. We must then apply
+the same process to another set of individuals which belong to one
+species and are generically but not specifically identical with the
+former set. When we have established what the common element is in
+all members of this second species, and likewise in members of further
+species, we should again consider whether the results established
+possess any identity, and persevere until we reach a single formula,
+since this will be the definition of the thing. But if we reach not
+one formula but two or more, evidently the definiendum cannot be one
+thing but must be more than one. I may illustrate my meaning as follows.
+If we were inquiring what the essential nature of pride is, we should
+examine instances of proud men we know of to see what, as such, they
+have in common; e.g. if Alcibiades was proud, or Achilles and Ajax
+were proud, we should find on inquiring what they all had in common,
+that it was intolerance of insult; it was this which drove Alcibiades
+to war, Achilles wrath, and Ajax to suicide. We should next examine
+other cases, Lysander, for example, or Socrates, and then if these
+have in common indifference alike to good and ill fortune, I take
+these two results and inquire what common element have equanimity
+amid the vicissitudes of life and impatience of dishonour. If they
+have none, there will be two genera of pride. Besides, every definition
+is always universal and commensurate: the physician does not prescribe
+what is healthy for a single eye, but for all eyes or for a determinate
+species of eye. It is also easier by this method to define the single
+species than the universal, and that is why our procedure should be
+from the several species to the universal genera-this for the further
+reason too that equivocation is less readily detected in genera than
+in infimae species. Indeed, perspicuity is essential in definitions,
+just as inferential movement is the minimum required in demonstrations;
+and we shall attain perspicuity if we can collect separately the definition
+of each species through the group of singulars which we have established
+e.g. the definition of similarity not unqualified but restricted to
+colours and to figures; the definition of acuteness, but only of sound-and
+so proceed to the common universal with a careful avoidance of equivocation.
+We may add that if dialectical disputation must not employ metaphors,
+clearly metaphors and metaphorical expressions are precluded in definition:
+otherwise dialectic would involve metaphors. 
+
+Part 14
+
+In order to formulate the connexions we wish to prove we have to select
+our analyses and divisions. The method of selection consists in laying
+down the common genus of all our subjects of investigation-if e.g.
+they are animals, we lay down what the properties are which inhere
+in every animal. These established, we next lay down the properties
+essentially connected with the first of the remaining classes-e.g.
+if this first subgenus is bird, the essential properties of every
+bird-and so on, always characterizing the proximate subgenus. This
+will clearly at once enable us to say in virtue of what character
+the subgenera-man, e.g. or horse-possess their properties. Let A be
+animal, B the properties of every animal, C D E various species of
+animal. Then it is clear in virtue of what character B inheres in
+D-namely A-and that it inheres in C and E for the same reason: and
+throughout the remaining subgenera always the same rule applies.
+
+We are now taking our examples from the traditional class-names, but
+we must not confine ourselves to considering these. We must collect
+any other common character which we observe, and then consider with
+what species it is connected and what.properties belong to it. For
+example, as the common properties of horned animals we collect the
+possession of a third stomach and only one row of teeth. Then since
+it is clear in virtue of what character they possess these attributes-namely
+their horned character-the next question is, to what species does
+the possession of horns attach? 
+
+Yet a further method of selection is by analogy: for we cannot find
+a single identical name to give to a squid's pounce, a fish's spine,
+and an animal's bone, although these too possess common properties
+as if there were a single osseous nature. 
+
+Part 15
+
+Some connexions that require proof are identical in that they possess
+an identical 'middle' e.g. a whole group might be proved through 'reciprocal
+replacement'-and of these one class are identical in genus, namely
+all those whose difference consists in their concerning different
+subjects or in their mode of manifestation. This latter class may
+be exemplified by the questions as to the causes respectively of echo,
+of reflection, and of the rainbow: the connexions to be proved which
+these questions embody are identical generically, because all three
+are forms of repercussion; but specifically they are different.
+
+Other connexions that require proof only differ in that the 'middle'
+of the one is subordinate to the 'middle' of the other. For example:
+Why does the Nile rise towards the end of the month? Because towards
+its close the month is more stormy. Why is the month more stormy towards
+its close? Because the moon is waning. Here the one cause is subordinate
+to the other. 
+
+Part 16
+
+The question might be raised with regard to cause and effect whether
+when the effect is present the cause also is present; whether, for
+instance, if a plant sheds its leaves or the moon is eclipsed, there
+is present also the cause of the eclipse or of the fall of the leaves-the
+possession of broad leaves, let us say, in the latter case, in the
+former the earth's interposition. For, one might argue, if this cause
+is not present, these phenomena will have some other cause: if it
+is present, its effect will be at once implied by it-the eclipse by
+the earth's interposition, the fall of the leaves by the possession
+of broad leaves; but if so, they will be logically coincident and
+each capable of proof through the other. Let me illustrate: Let A
+be deciduous character, B the possession of broad leaves, C vine.
+Now if A inheres in B (for every broad-leaved plant is deciduous),
+and B in C (every vine possessing broad leaves); then A inheres in
+C (every vine is deciduous), and the middle term B is the cause. But
+we can also demonstrate that the vine has broad leaves because it
+is deciduous. Thus, let D be broad-leaved, E deciduous, F vine. Then
+E inheres in F (since every vine is deciduous), and D in E (for every
+deciduous plant has broad leaves): therefore every vine has broad
+leaves, and the cause is its deciduous character. If, however, they
+cannot each be the cause of the other (for cause is prior to effect,
+and the earth's interposition is the cause of the moon's eclipse and
+not the eclipse of the interposition)-if, then, demonstration through
+the cause is of the reasoned fact and demonstration not through the
+cause is of the bare fact, one who knows it through the eclipse knows
+the fact of the earth's interposition but not the reasoned fact. Moreover,
+that the eclipse is not the cause of the interposition, but the interposition
+of the eclipse, is obvious because the interposition is an element
+in the definition of eclipse, which shows that the eclipse is known
+through the interposition and not vice versa. 
+
+On the other hand, can a single effect have more than one cause? One
+might argue as follows: if the same attribute is predicable of more
+than one thing as its primary subject, let B be a primary subject
+in which A inheres, and C another primary subject of A, and D and
+E primary subjects of B and C respectively. A will then inhere in
+D and E, and B will be the cause of A's inherence in D, C of A's inherence
+in E. The presence of the cause thus necessitates that of the effect,
+but the presence of the effect necessitates the presence not of all
+that may cause it but only of a cause which yet need not be the whole
+cause. We may, however, suggest that if the connexion to be proved
+is always universal and commensurate, not only will the cause be a
+whole but also the effect will be universal and commensurate. For
+instance, deciduous character will belong exclusively to a subject
+which is a whole, and, if this whole has species, universally and
+commensurately to those species-i.e. either to all species of plant
+or to a single species. So in these universal and commensurate connexions
+the 'middle' and its effect must reciprocate, i.e. be convertible.
+Supposing, for example, that the reason why trees are deciduous is
+the coagulation of sap, then if a tree is deciduous, coagulation must
+be present, and if coagulation is present-not in any subject but in
+a tree-then that tree must be deciduous. 
+
+Part 17
+
+Can the cause of an identical effect be not identical in every instance
+of the effect but different? Or is that impossible? Perhaps it is
+impossible if the effect is demonstrated as essential and not as inhering
+in virtue of a symptom or an accident-because the middle is then the
+definition of the major term-though possible if the demonstration
+is not essential. Now it is possible to consider the effect and its
+subject as an accidental conjunction, though such conjunctions would
+not be regarded as connexions demanding scientific proof. But if they
+are accepted as such, the middle will correspond to the extremes,
+and be equivocal if they are equivocal, generically one if they are
+generically one. Take the question why proportionals alternate. The
+cause when they are lines, and when they are numbers, is both different
+and identical; different in so far as lines are lines and not numbers,
+identical as involving a given determinate increment. In all proportionals
+this is so. Again, the cause of likeness between colour and colour
+is other than that between figure and figure; for likeness here is
+equivocal, meaning perhaps in the latter case equality of the ratios
+of the sides and equality of the angles, in the case of colours identity
+of the act of perceiving them, or something else of the sort. Again,
+connexions requiring proof which are identical by analogy middles
+also analogous. 
+
+The truth is that cause, effect, and subject are reciprocally predicable
+in the following way. If the species are taken severally, the effect
+is wider than the subject (e.g. the possession of external angles
+equal to four right angles is an attribute wider than triangle or
+are), but it is coextensive with the species taken collectively (in
+this instance with all figures whose external angles are equal to
+four right angles). And the middle likewise reciprocates, for the
+middle is a definition of the major; which is incidentally the reason
+why all the sciences are built up through definition. 
+
+We may illustrate as follows. Deciduous is a universal attribute of
+vine, and is at the same time of wider extent than vine; and of fig,
+and is of wider extent than fig: but it is not wider than but coextensive
+with the totality of the species. Then if you take the middle which
+is proximate, it is a definition of deciduous. I say that, because
+you will first reach a middle next the subject, and a premiss asserting
+it of the whole subject, and after that a middle-the coagulation of
+sap or something of the sort-proving the connexion of the first middle
+with the major: but it is the coagulation of sap at the junction of
+leaf-stalk and stem which defines deciduous. 
+
+If an explanation in formal terms of the inter-relation of cause and
+effect is demanded, we shall offer the following. Let A be an attribute
+of all B, and B of every species of D, but so that both A and B are
+wider than their respective subjects. Then B will be a universal attribute
+of each species of D (since I call such an attribute universal even
+if it is not commensurate, and I call an attribute primary universal
+if it is commensurate, not with each species severally but with their
+totality), and it extends beyond each of them taken separately.
+
+Thus, B is the cause of A's inherence in the species of D: consequently
+A must be of wider extent than B; otherwise why should B be the cause
+of A's inherence in D any more than A the cause of B's inherence in
+D? Now if A is an attribute of all the species of E, all the species
+of E will be united by possessing some common cause other than B:
+otherwise how shall we be able to say that A is predicable of all
+of which E is predicable, while E is not predicable of all of which
+A can be predicated? I mean how can there fail to be some special
+cause of A's inherence in E, as there was of A's inherence in all
+the species of D? Then are the species of E, too, united by possessing
+some common cause? This cause we must look for. Let us call it C.
+
+We conclude, then, that the same effect may have more than one cause,
+but not in subjects specifically identical. For instance, the cause
+of longevity in quadrupeds is lack of bile, in birds a dry constitution-or
+certainly something different. 
+
+Part 18
+
+If immediate premisses are not reached at once, and there is not merely
+one middle but several middles, i.e. several causes; is the cause
+of the property's inherence in the several species the middle which
+is proximate to the primary universal, or the middle which is proximate
+to the species? Clearly the cause is that nearest to each species
+severally in which it is manifested, for that is the cause of the
+subject's falling under the universal. To illustrate formally: C is
+the cause of B's inherence in D; hence C is the cause of A's inherence
+in D, B of A's inherence in C, while the cause of A's inherence in
+B is B itself. 
+
+Part 19
+
+As regards syllogism and demonstration, the definition of, and the
+conditions required to produce each of them, are now clear, and with
+that also the definition of, and the conditions required to produce,
+demonstrative knowledge, since it is the same as demonstration. As
+to the basic premisses, how they become known and what is the developed
+state of knowledge of them is made clear by raising some preliminary
+problems. 
+
+We have already said that scientific knowledge through demonstration
+is impossible unless a man knows the primary immediate premisses.
+But there are questions which might be raised in respect of the apprehension
+of these immediate premisses: one might not only ask whether it is
+of the same kind as the apprehension of the conclusions, but also
+whether there is or is not scientific knowledge of both; or scientific
+knowledge of the latter, and of the former a different kind of knowledge;
+and, further, whether the developed states of knowledge are not innate
+but come to be in us, or are innate but at first unnoticed. Now it
+is strange if we possess them from birth; for it means that we possess
+apprehensions more accurate than demonstration and fail to notice
+them. If on the other hand we acquire them and do not previously possess
+them, how could we apprehend and learn without a basis of pre-existent
+knowledge? For that is impossible, as we used to find in the case
+of demonstration. So it emerges that neither can we possess them from
+birth, nor can they come to be in us if we are without knowledge of
+them to the extent of having no such developed state at all. Therefore
+we must possess a capacity of some sort, but not such as to rank higher
+in accuracy than these developed states. And this at least is an obvious
+characteristic of all animals, for they possess a congenital discriminative
+capacity which is called sense-perception. But though sense-perception
+is innate in all animals, in some the sense-impression comes to persist,
+in others it does not. So animals in which this persistence does not
+come to be have either no knowledge at all outside the act of perceiving,
+or no knowledge of objects of which no impression persists; animals
+in which it does come into being have perception and can continue
+to retain the sense-impression in the soul: and when such persistence
+is frequently repeated a further distinction at once arises between
+those which out of the persistence of such sense-impressions develop
+a power of systematizing them and those which do not. So out of sense-perception
+comes to be what we call memory, and out of frequently repeated memories
+of the same thing develops experience; for a number of memories constitute
+a single experience. From experience again-i.e. from the universal
+now stabilized in its entirety within the soul, the one beside the
+many which is a single identity within them all-originate the skill
+of the craftsman and the knowledge of the man of science, skill in
+the sphere of coming to be and science in the sphere of being.
+
+We conclude that these states of knowledge are neither innate in a
+determinate form, nor developed from other higher states of knowledge,
+but from sense-perception. It is like a rout in battle stopped by
+first one man making a stand and then another, until the original
+formation has been restored. The soul is so constituted as to be capable
+of this process. 
+
+Let us now restate the account given already, though with insufficient
+clearness. When one of a number of logically indiscriminable particulars
+has made a stand, the earliest universal is present in the soul: for
+though the act of sense-perception is of the particular, its content
+is universal-is man, for example, not the man Callias. A fresh stand
+is made among these rudimentary universals, and the process does not
+cease until the indivisible concepts, the true universals, are established:
+e.g. such and such a species of animal is a step towards the genus
+animal, which by the same process is a step towards a further generalization.
+
+Thus it is clear that we must get to know the primary premisses by
+induction; for the method by which even sense-perception implants
+the universal is inductive. Now of the thinking states by which we
+grasp truth, some are unfailingly true, others admit of error-opinion,
+for instance, and calculation, whereas scientific knowing and intuition
+are always true: further, no other kind of thought except intuition
+is more accurate than scientific knowledge, whereas primary premisses
+are more knowable than demonstrations, and all scientific knowledge
+is discursive. From these considerations it follows that there will
+be no scientific knowledge of the primary premisses, and since except
+intuition nothing can be truer than scientific knowledge, it will
+be intuition that apprehends the primary premisses-a result which
+also follows from the fact that demonstration cannot be the originative
+source of demonstration, nor, consequently, scientific knowledge of
+scientific knowledge.If, therefore, it is the only other kind of true
+thinking except scientific knowing, intuition will be the originative
+source of scientific knowledge. And the originative source of science
+grasps the original basic premiss, while science as a whole is similarly
+related as originative source to the whole body of fact.
+
+THE END
+
+----------------------------------------------------------------------
+
+Copyright statement:
+The Internet Classics Archive by Daniel C. Stevenson, Web Atomics.
+World Wide Web presentation is copyright (C) 1994-2000, Daniel
+C. Stevenson, Web Atomics.
+All rights reserved under international and pan-American copyright
+conventions, including the right of reproduction in whole or in part
+in any form. Direct permission requests to classics@classics.mit.edu.
+Translation of "The Deeds of the Divine Augustus" by Augustus is
+copyright (C) Thomas Bushnell, BSG.
\ No newline at end of file