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of justice and injustice; for the one is a virtue and the other a vice of the soul: 'of the soul', therefore, is the differentia in both cases, seeing that the body as well has its virtue and vice. But this much at least is true, that the differentiae of contraries are either contrary or else the same. If, then, the co... |
Moreover, look at it from the point of view of its inflexions and coordinates. For genera and definitions are bound to correspond in either case. Thus if forgetfulness be the loss of knowledge, to forget is to lose knowledge, and to have forgotten is to have lost knowledge. If, then, any one whatever of these is agreed... |
Moreover, look at it from the point of view of things that stand in relations that are like each other. For if 'healthy' means 'productive of health', 'vigorous' too will mean 'productive of vigour', and 'useful' will mean 'productive of good.' For each of these things is related in like manner to its own peculiar end,... |
Moreover, look at it from the point of and like degrees, in all the ways in which it is possible to establish a result by comparing two and two together. Thus if A defines a better than B defines and B is a definition of so too is A of a. Further, if A's claim to define a is like B's to define B, and B defines B, then ... |
Part 4 The most handy of all the commonplace arguments are those just mentioned and those from co-ordinates and inflexions, and these therefore are those which it is most important to master and to have ready to hand: for they are the most useful on the greatest number of occasions. Of the rest, too, the most important... |
Part 5 That it is more difficult to establish than to overthrow a definition, is obvious from considerations presently to be urged. For to see for oneself, and to secure from those whom one is questioning, an admission of premisses of this sort is no simple matter, e.g. that of the elements of the definition rendered t... |
Further, even supposing it should be necessary to overthrow something by a universal proposition, not even so is there any need to prove the converse of the proposition in the process of overthrowing the definition. For merely to show that the definition fails to be predicated of every one of the things of which the te... |
The case stands likewise in regard to the property and genus of a term also. For in both cases it is easier to overthrow than to establish. As regards the property this is clear from what has been said: for as a rule the property is rendered in a complex phrase, so that to overthrow it, it is only necessary to demolish... |
In the case of an accidental attribute the universal proposition is easier to overthrow than to establish; for to establish it, one has to show that it belongs in every case, whereas to overthrow it, it is enough to show that it does not belong in one single case. The particular proposition is, on the contrary, easier ... |
It is clear also that the easiest thing of all is to overthrow a definition. For on account of the number of statements involved we are presented in the definition with the greatest number of points for attack, and the more plentiful the material, the quicker an argument comes: for there is more likelihood of a mistake... |
Of the rest, the property is most nearly of this kind: for it is easier to demolish, because as a rule it contains several terms; while it is the hardest to establish, both because of the number of things that people must be brought to accept, and, besides this, because it belongs to its subject alone and is predicated... |
The easiest thing of all to establish is an accidental predicate: for in other cases one has to show not only that the predicate belongs, but also that it belongs in such and such a particular way: whereas in the case of the accident it is enough to show merely that it belongs. On the other hand, an accidental predicat... |
The commonplace arguments through which we shall be well supplied with lines of argument with regard to our several problems have now been enumerated at about sufficient length. |
BOOK VIII Part 1 Next there fall to be discussed the problems of arrangement and method in pitting questions. Any one who intends to frame questions must, first of all, select the ground from which he should make his attack; secondly, he must frame them and arrange them one by one to himself; thirdly and lastly, he mus... |
The sources from which one's commonplace arguments should be drawn have already been described:' we have now to discuss the arrangement and formation of questions and first to distinguish the premisses, other than the necessary premisses, which have to be adopted. By necessary premisses are meant those through which th... |
The necessary premisses through which the reasoning is effected, ought not to be propounded directly in so many words. Rather one should soar as far aloof from them as possible. Thus if one desires to secure an admission that the knowledge of contraries is one, one should ask him to admit it not of contraries, but of o... |
Speaking generally, a man who desires to get information by a concealed method should so put his questions that when he has put his whole argument and has stated the conclusion, people still ask 'Well, but why is that?' This result will be secured best of all by the method above described: for if one states only the fi... |
It is a useful rule, too, not to secure the admissions claimed as the bases of the syllogisms in their proper order, but alternately those that conduce to one conclusion and those that conduce to another; for, if those which go together are set side by side, the conclusion that will result from them is more obvious in ... |
One should also, wherever possible, secure the universal premiss by a definition relating not to the precise terms themselves but to their co-ordinates; for people deceive themselves, whenever the definition is taken in regard to a co-ordinate, into thinking that they are not making the admission universally. An instan... |
Moreover, formulate your proposition as though you did so not for its own sake, but in order to get at something else: for people are shy of granting what an opponent's case really requires. Speaking generally, a questioner should leave it as far as possible doubtful whether he wishes to secure an admission of his prop... |
Moreover, try to secure admissions by means of likeness: for such admissions are plausible, and the universal involved is less patent; e.g. make the other person admit that as knowledge and ignorance of contraries is the same, so too perception of contraries is the same; or vice versa, that since the perception is the ... |
It is a good rule also, occasionally to bring an objection against oneself: for answerers are put off their guard against those who appear to be arguing impartially. It is useful too, to add that 'So and so is generally held or commonly said'; for people are shy of upsetting the received opinion unless they have some p... |
Moreover, it is well to expand the argument and insert things that it does not require at all, as do those who draw false geometrical figures: for in the multitude of details the whereabouts of the fallacy is obscured. For this reason also a questioner sometimes evades observation as he adds in a corner what, if he for... |
For concealment, then, the rules which should be followed are the above. Ornament is attained by induction and distinction of things closely akin. What sort of process induction is obvious: as for distinction, an instance of the kind of thing meant is the distinction of one form of knowledge as better than another by b... |
For clearness, examples and comparisons should be adduced, and let the illustrations be relevant and drawn from things that we know, as in Homer and not as in Choerilus; for then the proposition is likely to become clearer. |
Part 2 In dialectics, syllogism should be employed in reasoning against dialecticians rather than against the crowd: induction, on the other hand, is most useful against the crowd. This point has been treated previously as well.' In induction, it is possible in some cases to ask the question in its universal form, but ... |
If one has made an induction on the strength of several cases and yet the answerer refuses to grant the universal proposition, then it is fair to demand his objection. But until one has oneself stated in what cases it is so, it is not fair to demand that he shall say in what cases it is not so: for one should make the ... |
One should similarly treat those who object to the statement that 'the greater the good, the greater the evil that is its opposite': for they allege that health, which is a less good thing than vigour, has a greater evil as its opposite: for disease is a greater evil than debility. In this case too, therefore, we have ... |
Whenever it is possible to reason to the same conclusion either through or without a reduction per impossibile, if one is demonstrating and not arguing dialectically it makes no difference which method of reasoning be adopted, but in argument with another reasoning per impossibile should be avoided. For where one has r... |
One should put forward all propositions that hold true of several cases, and to which either no objection whatever appears or at least not any on the surface: for when people cannot see any case in which it is not so, they admit it for true. |
The conclusion should not be put in the form of a question; if it be, and the man shakes his head, it looks as if the reasoning had failed. For often, even if it be not put as a question but advanced as a consequence, people deny it, and then those who do not see that it follows upon the previous admissions do not real... |
Not every universal question can form a dialectical proposition as ordinarily understood, e.g. 'What is man?' or 'How many meanings has "the good"?' For a dialectical premiss must be of a form to which it is possible to reply 'Yes' or 'No', whereas to the aforesaid it is not possible. For this reason questions of this ... |
Any one who keeps on asking one thing for a long time is a bad inquirer. For if he does so though the person questioned keeps on answering the questions, clearly he asks a large number of questions, or else asks the same question a large number of times: in the one case he merely babbles, in the other he fails to reaso... |
Part 3 There are certain hypotheses upon which it is at once difficult to bring, and easy to stand up to, an argument. Such (e.g.) are those things which stand first and those which stand last in the order of nature. For the former require definition, while the latter have to be arrived at through many steps if one wis... |
In general, it is safe to suppose that, whenever any problem proves intractable, it either needs definition or else bears either several senses, or a metaphorical sense, or it is not far removed from the first principles; or else the reason is that we have yet to discover in the first place just this-in which of the af... |
It often happens that a difficulty is found in discussing or arguing a given position because the definition has not been correctly rendered: e.g. 'Has one thing one contrary or many?': here when the term 'contraries' has been properly defined, it is easy to bring people to see whether it is possible for the same thing... |
One may be sure then, whenever a position is hard to discuss, that one or other of the aforesaid things has happened to it. Whenever, on the other hand, it is a harder task to argue to the point claimed, i.e. the premiss, than to the resulting position, a doubt may arise whether such claims should be admitted or not: f... |
Part 4 As to the formulation, then, and arrangement of one's questions, about enough has been said. With regard to the giving of answers, we must first define what is the business of a good answerer, as of a good questioner. The business of the questioner is so to develop the argument as to make the answerer utter the ... |
Part 5 Inasmuch as no rules are laid down for those who argue for the sake of training and of examination:-and the aim of those engaged in teaching or learning is quite different from that of those engaged in a competition; as is the latter from that of those who discuss things together in the spirit of inquiry: for a ... |
The thesis laid down by the answerer before facing the questioner's argument is bound of necessity to be one that is either generally accepted or generally rejected or else is neither: and moreover is so accepted or rejected either absolutely or else with a restriction, e.g. by some given person, by the speaker or by s... |
(2) If, on the other hand, the statement laid down by the answerer be generally accepted without qualification, clearly the conclusion sought by the questioner will be one generally rejected without qualification. Accordingly, the answerer should admit all views that are generally accepted and, of those that are not ge... |
Part 6 It is clear, then, what the aims of the answerer should be, whether the position he lays down be a view generally accepted without qualification or accepted by some definite person. Now every question asked is bound to involve some view that is either generally held or generally rejected or neither, and is also ... |
Part 7 The questioner should be met in a like manner also in the case of terms used obscurely, i.e. in several senses. For the answerer, if he does not understand, is always permitted to say 'I do not understand': he is not compelled to reply 'Yes' or 'No' to a question which may mean different things. Clearly, then, i... |
Part 8 A premiss in reasoning always either is one of the constituent elements in the reasoning, or else goes to establish one of these: (and you can always tell when it is secured in order to establish something else by the fact of a number of similar questions being put: for as a rule people secure their universal by... |
Part 9 Before maintaining either a thesis or a definition the answerer should try his hand at attacking it by himself; for clearly his business is to oppose those positions from which questioners demolish what he has laid down. |
He should beware of maintaining a hypothesis that is generally rejected: and this it may be in two ways: for it may be one which results in absurd statements, e.g. suppose any one were to say that everything is in motion or that nothing is; and also there are all those which only a bad character would choose, and which... |
Part 10 Of all arguments that reason to a false conclusion the right solution is to demolish the point on which the fallacy that occurs depends: for the demolition of any random point is no solution, even though the point demolished be false. For the argument may contain many falsehoods, e.g. suppose some one to secure... |
There are four possible ways of preventing a man from working his argument to a conclusion. It can be done either by demolishing the point on which the falsehood that comes about depends, or by stating an objection directed against the questioner: for often when a solution has not as a matter of fact been brought, yet ... |
There are then, as we said, four ways of making objections: but of them the first alone is a solution: the others are just hindrances and stumbling-blocks to prevent the conclusions. |
Part 11 Adverse criticism of an argument on its own merits, and of it when presented in the form of questions, are two different things. For often the failure to carry through the argument correctly in discussion is due to the person questioned, because he will not grant the steps of which a correct argument might have... |
The principle that a man who hinders the common business is a bad partner, clearly applies to an argument as well; for in arguments as well there is a common aim in view, except with mere contestants, for these cannot both reach the same goal; for more than one cannot possibly win. It makes no difference whether he eff... |
Inasmuch as it is indeterminate when people are claiming the admission of contrary things, and when they are claiming what originally they set out to prove-for often when they are talking by themselves they say contrary things, and admit afterwards what they have previously denied; for which reason they often assent, w... |
In itself an argument is liable to five kinds of adverse criticism: (1) The first is when neither the proposed conclusion nor indeed any conclusion at all is drawn from the questions asked, and when most, if not all, of the premisses on which the conclusion rests are false or generally rejected, when, moreover, neither... |
(2) The second is, supposing the reasoning, though constructed from the premisses, and in the manner, described above, were to be irrelevant to the original position. |
(3) The third is, supposing certain additions would bring an inference about but yet these additions were to be weaker than those that were put as questions and less generally held than the conclusion. |
(4) Again, supposing certain withdrawals could effect the same: for sometimes people secure more premisses than are necessary, so that it is not through them that the inference comes about. |
(5) Moreover, suppose the premisses be less generally held and less credible than the conclusion, or if, though true, they require more trouble to prove than the proposed view. |
One must not claim that the reasoning to a proposed view shall in every case equally be a view generally accepted and convincing: for it is a direct result of the nature of things that some subjects of inquiry shall be easier and some harder, so that if a man brings people to accept his point from opinions that are as ... |
Whenever by the argument stated something is demonstrated, but that something is other than what is wanted and has no bearing whatever on the conclusion, then no inference as to the latter can be drawn from it: and if there appears to be, it will be a sophism, not a proof. A philosopheme is a demonstrative inference: a... |
If something were to be shown from premisses, both of which are views generally accepted, but not accepted with like conviction, it may very well be that the conclusion shown is something held more strongly than either. If, on the other hand, general opinion be for the one and neither for nor against the other, or if i... |
It is also a fault in reasoning when a man shows something through a long chain of steps, when he might employ fewer steps and those already included in his argument: suppose him to be showing (e.g.) that one opinion is more properly so called than another, and suppose him to make his postulates as follows: 'x-in-itsel... |
Part 12 An argument is clear in one, and that the most ordinary, sense, if it be so brought to a conclusion as to make no further questions necessary: in another sense, and this is the type most usually advanced, when the propositions secured are such as compel the conclusion, and the argument is concluded through prem... |
An argument is called fallacious in four senses: (1) when it appears to be brought to a conclusion, and is not really so-what is called 'contentious' reasoning: (2) when it comes to a conclusion but not to the conclusion proposed-which happens principally in the case of reductiones ad impossibile: (3) when it comes to ... |
Fallacy in argument is due to a mistake of the arguer rather than of the argument: yet it is not always the fault of the arguer either, but only when he is not aware of it: for we often accept on its merits in preference to many true ones an argument which demolishes some true proposition if it does so from premisses a... |
Part 13 Of the ways in which a questioner may beg the original question and also beg contraries the true account has been given in the Analytics:' but an account on the level of general opinion must be given now. |
People appear to beg their original question in five ways: the first and most obvious being if any one begs the actual point requiring to be shown: this is easily detected when put in so many words; but it is more apt to escape detection in the case of different terms, or a term and an expression, that mean the same th... |
The ways in which people assume contraries are equal in number to those in which they beg their original question. For it would happen, firstly, if any one were to beg an opposite affirmation and negation; secondly, if he were to beg the contrary terms of an antithesis, e.g. that the same thing is good and evil; thirdl... |
Part 14 The best way to secure training and practice in arguments of this kind is in the first place to get into the habit of converting the arguments. For in this way we shall be better equipped for dealing with the proposition stated, and after a few attempts we shall know several arguments by heart. For by 'conversi... |
It is best to know by heart arguments upon those questions which are of most frequent occurrence, and particularly in regard to those propositions which are ultimate: for in discussing these answerers frequently give up in despair. Moreover, get a good stock of definitions: and have those of familiar and primary ideas ... |
Moreover, you should get into the habit of turning one argument into several, and conceal your procedure as darkly as you can: this kind of effect is best produced by keeping as far as possible away from topics akin to the subject of the argument. This can be done with arguments that are entirely universal, e.g. the st... |
Records of discussions should be made in a universal form, even though one has argued only some particular case: for this will enable one to turn a single rule into several. A like rule applies in Rhetoric as well to enthymemes. For yourself, however, you should as far as possible avoid universalizing your reasonings. ... |
You should display your training in inductive reasoning against a young man, in deductive against an expert. You should try, moreover, to secure from those skilled in deduction their premisses, from inductive reasoners their parallel cases; for this is the thing in which they are respectively trained. In general, too, ... |
Do not argue with every one, nor practise upon the man in the street: for there are some people with whom any argument is bound to degenerate. For against any one who is ready to try all means in order to seem not to be beaten, it is indeed fair to try all means of bringing about one's conclusion: but it is not good fo... |
It is best also to have ready-made arguments relating to those questions in which a very small stock will furnish us with arguments serviceable on a very large number of occasions. These are those that are universal, and those in regard to which it is rather difficult to produce points for ourselves from matters of eve... |
# Source: arxiv 0704.2686 # Title: Self-organization processes in laser system with nonlinear absorber and external force influence # Sections: all # Downloaded: 2026-03-03T01:58:46.177610+00:00 |
Self-organization processes in laser system with nonlinear absorber and external force influence Abstract We discuss mechanisms of self-organization processes in two-level solid-state class-B laser system. The model is considered under assumptions of influence of nonlinear absorber and external force, separately. It wa... |
pacs: 05.45.-a, 42.65.-k, 89.75.Fb, 02.30.Oz Introduction The most intriguing phenomena in systems with nonlinear dynamics is a transition to the regime with dissipative structures formation. A related problem of such effects investigation in systems with large numbers of freedom degrees attracts an increasing attentio... |
Laser theory shows that corresponding dissipative structures define formation of pulse or modulated signals in homogeneous systems or spirals in spatially extended ones zigzag . In practice a formation of stable periodic radiation can be induced by introducing an additional medium with nonlinear properties which are re... |
Khanin1 Khanin2 or nonlinear dependence of refractive exponent Hercher Hercher2 physrevlet76 b716 , composite material can be used to introduce different type of such nonlinearity |
sdarticle4 citation2 citation3 citation4 citation5 citation6 . A coherent dynamics of two-level laser systems in the presence of dispersive and absorptive effects was observed theoretically and experimentally |
exp2003 numeric2002 . Statistical properties of self-organization effects of such type systems was discussed in condmat1 . Regimes of optical parametric oscillation in a semiconductor microcavity are studied in |
condmat2 . It was found that stationary behaviour of polarization can be described by the formalism of non-equilibrium transitions, where bistability is observed (see physrevlet76 PhysRevA78 ). It was shown that an oscillating lasing is realized inside a bounded domain of the system parameters. Another (active) way to ... |
Gardiner86 Gardiner2000 Risken84 Horstshemke In this Paper, we are aimed to investigate the dynamics of the solid-state class-B laser systems which are simple in realization and are wide used in physical applications. We consider deterministic models only. According to the theoretical approach, based on Floquet analysi... |
The paper is organized in the following manner. In Section II we present a model of our system where we introduce theoretical constructions to model an influence of both an absorber and external force. Section III is devoted to development of the analytical approach to study process of dissipative structures formation.... |
II Model Considering a prototype model for a two-level laser system, one deals with dimensionless variables such as: an electric field amplitude [MATH] , polarization |
[MATH] and [MATH] to be a population inversion. A standard technique usage Khanin1 allows to reproduce evolution equations for these three macroscopic freedom degrees from both the Maxwell-type equation for electro-magnetic field and density matrix evolution equation. It leads to the system of Maxwell-Bloch type that i... |
[EQUATION] For the single mode laser system a relaxation of electric field amplitude [MATH] is addressed to losses in a bulk of the medium and characterized by the velocity [MATH] , where [MATH] is a life-time of a photon in a cavity. [MATH] is a relaxation velocity of nondiagonal elements of density matrix which is re... |
[MATH] defined by both transition probability between two energy levels and a corresponding frequency. [MATH] controls the pump intensity, as usual. The model ( ) shows a linear combination of the amplitude [MATH] and polarization [MATH] , despite the evolution of both [MATH] and the pump intensity [MATH] |
are nonlinear. It is principally that the positive feedback of [MATH] and [MATH] leads to instability in the polarization that induces a self-organization. According to the Le-Shatelier principle such positive feedback is compensated through negative one in third equation (the last term). |
To make an analysis we pass to dimensionless variables [MATH] [MATH] and [MATH] . Hence, the system ( ) takes the form [EQUATION] |
Assuming different combinations between relaxation scales [MATH] and [MATH] one can describe three possible classes of laser systems. At [MATH] |
we arrive at the laser models of class-A (organic dye lasers) with one-dimensional phase space, where systems states are represented by fixed points only. Here self-organization effects are described by a formalism of non-equilibrium phase transitions. Class-B (solid-state lasers) is characterized by a condition [MATH]... |
Assuming conditions [MATH] , one can use the adiabatic elimination procedure which yields the relation [MATH] . As a result, instead of the system ( ) we obtain a two-component model in the form |
[EQUATION] The model ( ) can not show the stable oscillating regime of the electric field [MATH] , itself. It was shown experimentally and theoretically |
Hercher Khanin1 Khanin2 that stable oscillations can be realized if an additional nonlinear medium is introduced into the cavity. The first way to get the periodic lasing is to use a passive modulating medium (nonlinear material) to absorb a weak radiation and transmit signal with large amplitude. Such a type of absorb... |
PismavGETF GETF71 . To describe action of the absorber it was proposed to introduce a nonlinear damping into evolution equation for the electric field |
Haken80 [EQUATION] here [MATH] is the saturation amplitude. The second way is to use an additional medium with nonlinear refractive exponent [MATH] |
Hercher Hercher2 sdarticle4 physrevlet76 . Such type of modulator can be used to increase the Q-factor of laser. We will model action of such an effective medium by the external force [MATH] assumed in the form |
[EQUATION] that correspond to action of a bare potential [MATH] , where coefficients [MATH] [MATH] controls photon processes in the modulator. We use an general construction ( ) in order to investigate an influence of parameters |
[MATH] and [MATH] on lasing. In physical applications one can associate [MATH] as incident field amplitude, [MATH] can control nonlinear properties of the refractive index [MATH] . One of the simplest situations is considered in |
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