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500 | "Logos"
Logos ( UK: / ˈ l oʊ ɡ ɒ s, ˈ l ɒ ɡ ɒ s /, US: / ˈ l oʊ ɡ oʊ s /; Ancient Greek: λόγος, romanized: lógos; from λέγω, légō, lit. ''I say'') is a term in Western philosophy, psychology, rhetoric, and religion derived from a Greek word variously meaning "ground", "plea", "opinion", "expectation", "word", "speech",... |
501 | "Logos"
Today, many people may discuss the logos qualities of a text to refer to how strong the logic or reasoning of the text is. But logos more closely refers to the structure and content of the text itself. In this resource, logos means “text.”” [3] Logos became a technical term in Western philosophy beginning with ... |
502 | "Logos"
[6] Pyrrhonist philosophers used the term to refer to dogmatic accounts of non-evident matters. The Stoics spoke of the logos spermatikos (the generative principle of the Universe) which foreshadows related concepts in Neoplatonism. [7] Within Hellenistic Judaism, Philo ( c. 20 BC – c. 50 AD ) integrated the te... |
503 | "Logos"
Early translators of the Greek New Testament, such as Jerome (in the 4th century AD), were frustrated by the inadequacy of any single Latin word to convey the meaning of the word logos as used to describe Jesus Christ in the Gospel of John. The Vulgate Bible usage of in principio erat verbum was thus constraine... |
504 | "Logos"
[11] The term is also used in Sufism, and the analytical psychology of Carl Jung. Despite the conventional translation as "word", logos is not used for a word in the grammatical sense—for that, the term lexis ( λέξις, léxis ) was used. [12] However, both logos and lexis derive from the same verb légō ( λέγω ), ... |
505 | "Logos"
[15] For Heraclitus, logos provided the link between rational discourse and the world's rational structure. [16] This logos holds always but humans always prove unable to ever understand it, both before hearing it and when they have first heard it. For though all things come to be in accordance with this logos,... |
506 | "Logos"
For this reason it is necessary to follow what is common. But although the logos is common, most people live as if they had their own private understanding. Listening not to me but to the logos it is wise to agree that all things are one. What logos means here is not certain; it may mean "reason" or "explanatio... |
507 | "Logos"
The other two modes are pathos ( πᾰ́θος, páthos ), which refers to persuasion by means of emotional appeal, "putting the hearer into a certain frame of mind"; [20] and ethos ( ἦθος, êthos ), persuasion through convincing listeners of one's "moral character". [20] According to Aristotle, logos relates to "the sp... |
508 | "Logos"
[5] Logos, pathos, and ethos can all be appropriate at different times. [22] Arguments from reason (logical arguments) have some advantages, namely that data are (ostensibly) difficult to manipulate, so it is harder to argue against such an argument; and such arguments make the speaker look prepared and knowled... |
509 | "Logos"
[24] Aristotle comments on the three modes by stating: Of the modes of persuasion furnished by the spoken word there are three kinds. The first kind depends on the personal character of the speaker; the second on putting the audience into a certain frame of mind; the third on the proof, or apparent proof, provi... |
510 | "Logos"
[26] Stoic philosophy began with Zeno of Citium c. 300 BC, in which the logos was the active reason pervading and animating the Universe. It was conceived as material and is usually identified with God or Nature. The Stoics also referred to the seminal logos (" logos spermatikos "), or the law of generation in ... |
511 | "Logos"
[28] In his Introduction to the 1964 edition of Marcus Aurelius ' Meditations, the Anglican priest Maxwell Staniforth wrote that " Logos... had long been one of the leading terms of Stoicism, chosen originally for the purpose of explaining how deity came into relation with the universe". [29] Public discourse o... |
512 | "Logos"
[30] He was concerned with establishing the "common good" of Athenian citizens, which he believed could be achieved through the pursuit of philosophy and the application of logos. [30] Philo ( c. 20 BC – c. 50 AD ), a Hellenized Jew, used the term logos to mean an intermediary divine being or demiurge. [8] Phil... |
513 | "Logos"
[31] Philo also wrote that "the Logos of the living God is the bond of everything, holding all things together and binding all the parts, and prevents them from being dissolved and separated". [32] Plato's Theory of Forms was located within the logos, but the logos also acted on behalf of God in the physical wo... |
514 | "Logos"
[33] In Christology, the Logos ( Greek: Λόγος, lit. 'word, discourse, or reason') [2] is a name or title of Jesus Christ, seen as the pre-existent second person of the Trinity. The concept derives from John 1:1, which in the Douay–Rheims, King James, New International, and other versions of the Bible, reads: In... |
515 | "Logos"
[38] The logos was a key element in the meditations of Plotinus [39] regarded as the first neoplatonist. Plotinus referred back to Heraclitus and as far back as Thales [40] in interpreting logos as the principle of meditation, existing as the interrelationship between the hypostases —the soul, the intellect ( n... |
516 | "Logos"
[43] Plotinus relied heavily on the concept of logos, but no explicit references to Christian thought can be found in his works, although there are significant traces of them in his doctrine. [ citation needed ] Plotinus specifically avoided using the term logos to refer to the second person of his trinity. [44... |
517 | "Logos"
[48] A young Augustine experimented with, but failed to achieve ecstasy using the meditations of Plotinus. [49] In his Confessions, Augustine described logos as the Divine Eternal Word, [50] by which he, in part, was able to motivate the early Christian thought throughout the Hellenized world (of which the Lati... |
518 | "Logos"
[53] [54] In Sunni Islam, the concept of the logos has been given many different names by the denomination's metaphysicians, mystics, and philosophers, including ʿaql ("Intellect"), al-insān al-kāmil ("Universal Man"), kalimat Allāh ("Word of God"), haqīqa muḥammadiyya ("The Muhammadan Reality"), and nūr muḥamm... |
519 | "Logos"
1037), [54] the idea of the ʿaql was presented in a manner that both resembled "the late Greek doctrine" and, likewise, "corresponded in many respects to the Logos Christology." [54] The concept of logos in Sufism is used to relate the "Uncreated" (God) to the "Created" (humanity). In Sufism, for the Deist, no ... |
520 | "Logos"
[55] [56] One of the boldest and most radical attempts to reformulate the neoplatonic concepts into Sufism arose with the philosopher Ibn Arabi, who traveled widely in Spain and North Africa. His concepts were expressed in two major works The Ringstones of Wisdom ( Fusus al-Hikam ) and The Meccan Illuminations ... |
521 | "Logos"
[57] Ibn Arabi seems to have adopted his version of the logos concept from neoplatonic and Christian sources, [58] although (writing in Arabic rather than Greek) he used more than twenty different terms when discussing it. [59] For Ibn Arabi, the logos or "Universal Man" was a mediating link between individual ... |
522 | "Logos"
[62] In Ottoman Sufism, Şeyh Gâlib (d. 1799) articulates Sühan ( logos - Kalima ) in his Hüsn ü Aşk ( Beauty and Love ) in parallel to Ibn Arabi's Kalima. In the romance, Sühan appears as an embodiment of Kalima as a reference to the Word of God, the Perfect Man, and the Reality of Muhammad. [63] [ relevant? ] ... |
523 | "Logos"
[65] For Jung, logos represented the masculine principle of rationality, in contrast to its feminine counterpart, eros: Woman’s psychology is founded on the principle of Eros, the great binder and loosener, whereas from ancient times the ruling principle ascribed to man is Logos. The concept of Eros could be ex... |
524 | "Logos"
[67] Jung often proceeded to analyze situations in terms of "paired opposites", e.g. by using the analogy with the eastern yin and yang [68] and was also influenced by the neoplatonists. [69] In his book Mysterium Coniunctionis Jung made some important final remarks about anima and animus: In so far as the spir... |
525 | "Logos"
[70] Author and professor Jeanne Fahnestock describes logos as a "premise". She states that, to find the reason behind a rhetor 's backing of a certain position or stance, one must acknowledge the different "premises" that the rhetor applies via his or her chosen diction. [71] The rhetor's success, she argues, ... |
526 | "Logos"
[72] Furthermore, one can appeal to this sense of logic in two ways. The first is through inductive reasoning, providing the audience with relevant examples and using them to point back to the overall statement. [73] The second is through deductive enthymeme, providing the audience with general scenarios and th... |
527 | "Logos"
[76] [77] [78] Some modern usage in Christian theology distinguishes rhema from logos (which here refers to the written scriptures) while rhema refers to the revelation received by the reader from the Holy Spirit when the Word ( logos ) is read, [79] [80] [81] [82] although this distinction has been criticized.... |
528 | "Inference"
Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word infer means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that in Europe dates at least to Aristotle (300s BCE). Deduction is inference... |
529 | "Inference"
Human inference (i.e. how humans draw conclusions) is traditionally studied within the fields of logic, argumentation studies, and cognitive psychology; artificial intelligence researchers develop automated inference systems to emulate human inference. Statistical inference uses mathematics to draw conclusi... |
530 | "Inference"
Conclusions inferred from multiple observations may be tested by additional observations. This definition is disputable (due to its lack of clarity. Ref: Oxford English dictionary: "induction... 3. Logic the inference of a general law from particular instances." [ clarification needed ] ) The definition giv... |
531 | "Inference"
The validity of an inference depends on the form of the inference. That is, the word "valid" does not refer to the truth of the premises or the conclusion, but rather to the form of the inference. An inference can be valid even if the parts are false, and can be invalid even if some parts are true. But a va... |
532 | "Inference"
To show that this form is invalid, we demonstrate how it can lead from true premises to a false conclusion. A valid argument with a false premise may lead to a false conclusion, (this and the following examples do not follow the Greek syllogism): When a valid argument is used to derive a false conclusion fr... |
533 | "Inference"
Evidence: It is the early 1950s and you are an American stationed in the Soviet Union. You read in the Moscow newspaper that a soccer team from a small city in Siberia starts winning game after game. The team even defeats the Moscow team. Inference: The small city in Siberia is not a small city anymore. The... |
534 | "Inference"
Explanation: In a command economy, people and material are moved where they are needed. Large cities might field good teams due to the greater availability of high quality players; and teams that can practice longer (weather, facilities) can reasonably be expected to be better. In addition, you put your bes... |
535 | "Inference"
Why would you put a large city of your best and brightest in the middle of nowhere? To hide them, of course. An incorrect inference is known as a fallacy. Philosophers who study informal logic have compiled large lists of them, and cognitive psychologists have documented many biases in human reasoning that ... |
536 | "Inference"
An inference system's job is to extend a knowledge base automatically. The knowledge base (KB) is a set of propositions that represent what the system knows about the world. Several techniques can be used by that system to extend KB by means of valid inferences. An additional requirement is that the conclus... |
537 | "Inference"
Let us return to our Socrates syllogism. We enter into our Knowledge Base the following piece of code: ( Here:- can be read as "if". Generally, if P → {\displaystyle \to } Q (if P then Q) then in Prolog we would code Q:- P (Q if P).) This states that all men are mortal and that Socrates is a man. Now we can... |
538 | "Inference"
This is because Prolog does not know anything about Plato, and hence defaults to any property about Plato being false (the so-called closed world assumption ). Finally?- mortal(X) (Is anything mortal) would result in "Yes" (and in some implementations: "Yes": X=socrates) Prolog can be used for vastly more c... |
539 | "Inference"
The Bayesian view has a number of desirable features—one of them is that it embeds deductive (certain) logic as a subset (this prompts some writers to call Bayesian probability "probability logic", following E. T. Jaynes ). Bayesians identify probabilities with degrees of beliefs, with certainly true propos... |
540 | "Inference"
A central rule of Bayesian inference is Bayes' theorem. [1] A relation of inference is monotonic if the addition of premises does not undermine previously reached conclusions; otherwise the relation is non-monotonic. Deductive inference is monotonic: if a conclusion is reached on the basis of a certain set ... |
541 | "Inference"
Various kinds of defeasible but remarkably successful inference have traditionally captured the attention of philosophers (theories of induction, Peirce's theory of abduction, inference to the best explanation, etc.). More recently logicians have begun to approach the phenomenon from a formal point of view.... |
542 | "Demonstration (proof)"
A mathematical proof is an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certa... |
543 | "Demonstration (proof)"
A proposition that has not been proved but is believed to be true is known as a conjecture, or a hypothesis if frequently used as an assumption for further mathematical work. Proofs employ logic expressed in mathematical symbols, along with natural language which usually admits some ambiguity. I... |
544 | "Demonstration (proof)"
The philosophy of mathematics is concerned with the role of language and logic in proofs, and mathematics as a language. The word "proof" comes from the Latin probare (to test). Related modern words are English "probe", "probation", and "probability", Spanish probar (to smell or taste, or someti... |
545 | "Demonstration (proof)"
[8] The development of mathematical proof is primarily the product of ancient Greek mathematics, and one of its greatest achievements. [9] Thales (624–546 BCE) and Hippocrates of Chios (c. 470–410 BCE) gave some of the first known proofs of theorems in geometry. Eudoxus (408–355 BCE) and Theaete... |
546 | "Demonstration (proof)"
From this basis, the method proves theorems using deductive logic. Euclid's book, the Elements, was read by anyone who was considered educated in the West until the middle of the 20th century. [10] In addition to theorems of geometry, such as the Pythagorean theorem, the Elements also covers num... |
547 | "Demonstration (proof)"
In the 10th century CE, the Iraqi mathematician Al-Hashimi worked with numbers as such, called "lines" but not necessarily considered as measurements of geometric objects, to prove algebraic propositions concerning multiplication, division, etc., including the existence of irrational numbers. [1... |
548 | "Demonstration (proof)"
This allows parallel mathematical theories as formal models of a given intuitive concept, based on alternate sets of axioms, for example Axiomatic set theory and Non-Euclidean geometry. As practiced, a proof is expressed in natural language and is a rigorous argument intended to convince the aud... |
549 | "Demonstration (proof)"
[13] A formal proof is written in a formal language instead of natural language. A formal proof is a sequence of formulas in a formal language, starting with an assumption, and with each subsequent formula a logical consequence of the preceding ones. This definition makes the concept of proof am... |
550 | "Demonstration (proof)"
The soundness of this definition amounts to the belief that a published proof can, in principle, be converted into a formal proof. However, outside the field of automated proof assistants, this is rarely done in practice. A classic question in philosophy asks whether mathematical proofs are anal... |
551 | "Demonstration (proof)"
The book Proofs from THE BOOK, published in 2003, is devoted to presenting 32 proofs its editors find particularly pleasing. In direct proof, the conclusion is established by logically combining the axioms, definitions, and earlier theorems. [15] For example, direct proof can be used to prove th... |
552 | "Demonstration (proof)"
Since in principle the induction rule can be applied repeatedly (starting from the proved base case), it follows that all (usually infinitely many) cases are provable. [16] This avoids having to prove each case individually. A variant of mathematical induction is proof by infinite descent, which... |
553 | "Demonstration (proof)"
Let P ( n ) represent " 2 n − 1 is odd": The shorter phrase "proof by induction" is often used instead of "proof by mathematical induction". [18] Proof by contraposition infers the statement "if p then q " by establishing the logically equivalent contrapositive statement: "if not q then not p ".... |
554 | "Demonstration (proof)"
A famous example involves the proof that 2 {\displaystyle {\sqrt {2}}} is an irrational number: To paraphrase: if one could write 2 {\displaystyle {\sqrt {2}}} as a fraction, this fraction could never be written in lowest terms, since 2 could always be factored from numerator and denominator. Pr... |
555 | "Demonstration (proof)"
In proof by exhaustion, the conclusion is established by dividing it into a finite number of cases and proving each one separately. The number of cases sometimes can become very large. For example, the first proof of the four color theorem was a proof by exhaustion with 1,936 cases. This proof w... |
556 | "Demonstration (proof)"
Probabilistic proof, like proof by construction, is one of many ways to prove existence theorems. In the probabilistic method, one seeks an object having a given property, starting with a large set of candidates. One assigns a certain probability for each candidate to be chosen, and then proves ... |
557 | "Demonstration (proof)"
The work on the Collatz conjecture shows how far plausibility is from genuine proof. While most mathematicians do not think that probabilistic evidence for the properties of a given object counts as a genuine mathematical proof, a few mathematicians and philosophers have argued that at least som... |
558 | "Demonstration (proof)"
Alternatively, a double counting argument provides two different expressions for the size of a single set, again showing that the two expressions are equal. A nonconstructive proof establishes that a mathematical object with a certain property exists—without explaining how such an object can be ... |
559 | "Demonstration (proof)"
[22] [23] [24] It is less commonly used to refer to a mathematical proof in the branch of mathematics known as mathematical statistics. See also the " Statistical proof using data " section below. Until the twentieth century it was assumed that any proof could, in principle, be checked by a comp... |
560 | "Demonstration (proof)"
Some mathematicians are concerned that the possibility of an error in a computer program or a run-time error in its calculations calls the validity of such computer-assisted proofs into question. In practice, the chances of an error invalidating a computer-assisted proof can be reduced by incorp... |
561 | "Demonstration (proof)"
One example is the parallel postulate, which is neither provable nor refutable from the remaining axioms of Euclidean geometry. Mathematicians have shown there are many statements that are neither provable nor disprovable in Zermelo–Fraenkel set theory with the axiom of choice (ZFC), the standar... |
562 | "Demonstration (proof)"
[25] With the increase in computing power in the 1960s, significant work began to be done investigating mathematical objects outside of the proof-theorem framework, [26] in experimental mathematics. Early pioneers of these methods intended the work ultimately to be embedded in a classical proof-... |
563 | "Demonstration (proof)"
Visual proof for the (3,4,5) triangle as in the Zhoubi Suanjing 500–200 BCE. Animated visual proof for the Pythagorean theorem by rearrangement. A second animated proof of the Pythagorean theorem. Some illusory visual proofs, such as the missing square puzzle, can be constructed in a way which a... |
564 | "Demonstration (proof)"
More specifically, the term is used in number theory to refer to proofs that make no use of complex analysis. For some time it was thought that certain theorems, like the prime number theorem, could only be proved using "higher" mathematics. However, over time, many of these results have been re... |
565 | "Demonstration (proof)"
The left-hand column is typically headed "Statements" and the right-hand column is typically headed "Reasons". [29] The expression "mathematical proof" is used by lay people to refer to using mathematical methods or arguing with mathematical objects, such as numbers, to demonstrate something abo... |
566 | "Demonstration (proof)"
In physics, in addition to statistical methods, "statistical proof" can refer to the specialized mathematical methods of physics applied to analyze data in a particle physics experiment or observational study in physical cosmology. "Statistical proof" may also refer to raw data or a convincing d... |
567 | "Demonstration (proof)"
Bayesian analysis uses Bayes' theorem to update a person's assessment of likelihoods of hypotheses when new evidence or information is acquired. Psychologism views mathematical proofs as psychological or mental objects. Mathematician philosophers, such as Leibniz, Frege, and Carnap have variousl... |
568 | "Demonstration (proof)"
Other mathematician-philosophers have tried to use standards of mathematical proof and reason, without empiricism, to arrive at statements outside of mathematics, but having the certainty of propositions deduced in a mathematical proof, such as Descartes ' cogito argument. Sometimes, the abbrevi... |
569 | "Formal science"
Formal science is a branch of science studying disciplines concerned with formal systems, such as logic, mathematics, statistics, theoretical computer science, artificial intelligence, information theory, game theory, systems theory, decision theory, and theoretical linguistics. Whereas the natural sci... |
570 | "Formal science"
[1] Going even further back to 1819, a German-language textbook on logic was published by Wilhelm Esser, elucidating the significance of the designation formal science ( Formalwissenschaft ) as applied to logic; [2] an English-language translation of it is provided in William Hamilton's lecture: Logic ... |
571 | "Formal science"
From then on different cultures such as the Greek, Arab and Persian made major contributions to mathematics, while the Chinese and Japanese, independently of more distant cultures, developed their own mathematical tradition. [ citation needed ] Besides mathematics, logic is another example of one of ol... |
572 | "Formal science"
The Indian tradition also continued into the early modern period. The native Chinese tradition did not survive beyond antiquity, though Indian logic was later adopted in medieval China. [ citation needed ] As a number of other disciplines of formal science rely heavily on mathematics, they did not exis... |
573 | "Formal science"
Mathematical statistics was recognized as a mathematical discipline in the early 20th century. [ citation needed ] In the mid-20th century, mathematics was broadened and enriched by the rise of new mathematical sciences and engineering disciplines such as operations research and systems engineering. Th... |
574 | "Formal science"
One reason why mathematics enjoys special esteem, above all other sciences, is that its laws are absolutely certain and indisputable, while those of other sciences are to some extent debatable and in constant danger of being overthrown by newly discovered facts. As opposed to empirical sciences (natura... |
575 | "Formal science"
It is a formal logical system with its content targeted at components of experiential reality, such as information and thoughts. As Francis Bacon pointed out in the 17th century, experimental verification of the propositions must be carried out rigorously and cannot take logic itself as the way to draw... |
576 | "Formal science"
That is why formal sciences are applicable in all domains and useful in all empirical sciences. [ citation needed ] Because of their non-empirical nature, formal sciences are construed by outlining a set of axioms and definitions from which other statements ( theorems ) are deduced. For this reason, in... |
577 | "Formal system"
A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A formal system is essentially an " axiomatic system ". [1] In ... |
578 | "Formal system"
Each formal system is described by primitive symbols (which collectively form an alphabet ) to finitely construct a formal language from a set of axioms through inferential rules of formation. The system thus consists of valid formulas built up through finite combinations of the primitive symbols—combin... |
579 | "Formal system"
Often the formal system will be the basis for or even identified with a larger theory or field (e.g. Euclidean geometry ) consistent with the usage in modern mathematics such as model theory. [ clarification needed ] A formal language is a language that is defined by a formal system. Like languages in l... |
580 | "Formal system"
The two main categories of formal grammar are that of generative grammars, which are sets of rules for how strings in a language can be generated, and that of analytic grammars (or reductive grammar, [4] [5] ) which are sets of rules for how a string can be analyzed to determine whether it is a member o... |
581 | "Formal system"
Logical systems are defined by both a deductive system and natural language. Deductive systems in turn are only defined by natural language (see below). A deductive system, also called a deductive apparatus or a logic, consists of the axioms (or axiom schemata ) and rules of inference that can be used t... |
582 | "Formal system"
The aim is to ensure that each line of a derivation is merely a syntactic consequence of the lines that precede it. There should be no element of any interpretation of the language that gets involved with the deductive nature of the system. An example of deductive system is first order predicate logic. ... |
583 | "Formal system"
A structure that satisfies all the axioms of the formal system is known as a model of the logical system. A logical system is sound if each well-formed formula that can be inferred from the axioms is satisfied by every model of the logical system. Conversely, a logic system is (semantically) complete if... |
584 | "Formal system"
[7] There are also non-standard models of arithmetic. Early logic systems includes Indian logic of Pāṇini, syllogistic logic of Aristotle, propositional logic of Stoicism, and Chinese logic of Gongsun Long (c. 325–250 BCE). In more recent times, contributors include George Boole, Augustus De Morgan, and... |
585 | "Formal system"
Formal proofs are sequences of well-formed formulas (or wff for short). For a wff to qualify as part of a proof, it might either be an axiom or be the product of applying an inference rule on previous wffs in the proof sequence. The last wff in the sequence is recognized as a theorem. The point of view ... |
586 | "Formal system"
Once a formal system is given, one can define the set of theorems which can be proved inside the formal system. This set consists of all wffs for which there is a proof. Thus all axioms are considered theorems. Unlike the grammar for wffs, there is no guarantee that there will be a decision procedure fo... |
587 | "Fallacies"
A fallacy is the use of invalid or otherwise faulty reasoning, or "wrong moves," [1] in the construction of an argument, [2] [3] which may appear stronger than it really is if the fallacy is not spotted. The term was in the Western intellectual tradition introduced in the Aristotelian De Sophisticis Elenchi... |
588 | "Fallacies"
[5] Fallacies are commonly divided into "formal" and "informal." A formal fallacy is a flaw in the structure of a deductive argument which renders the argument invalid, while an informal fallacy originates in an error in reasoning other than an improper logical form. [6] Arguments containing informal fallac... |
589 | "Fallacies"
Fallacious arguments are very common and can be persuasive in common use. They may be even "unsubstantiated assertions that are often delivered with a conviction that makes them sound as though they are proven facts." [7] Informal fallacies in particular are found frequently in mass media such as television... |
590 | "Fallacies"
[9] Moreover, whether a specific argument is fallacious often depends on the content rather than the form of the argument. An example is a probabilistically valid instance of the formally invalid argument form of denying the antecedent or affirming the consequent. [10] Thus, "[f]allacious arguments usually ... |
591 | "Fallacies"
Informal fallacies may also exploit the emotional, intellectual, or psychological weaknesses of the audience. Recognizing fallacies can develop reasoning skills to expose the weaker links between premises and conclusions to better discern between what appears to be true and what is true. Argumentation theor... |
592 | "Fallacies"
Fallacies are used in place of valid reasoning to communicate a point with the intention to persuade. Examples in the mass media today include but are not limited to propaganda, advertisements, politics, newspaper editorials and opinion-based news shows. Because of their variety of structure and application... |
593 | "Fallacies"
In turn, material fallacies may be placed into the more general category of informal fallacies. Verbal fallacies may be placed in either formal or informal classifications: Compare equivocation, which is a word- or phrase-based ambiguity, to the fallacy of composition, which is premise- and inference-based ... |
594 | "Fallacies"
[15]: 2 Aristotle's " Sophistical Refutations " ( De Sophisticis Elenchis ) identifies thirteen fallacies. He divided them up into two major types, linguistic fallacies and non-linguistic fallacies, some which depend on language and others that do not. [16] [17] These fallacies are called verbal fallacies a... |
595 | "Fallacies"
[15]: 3 A language-independent fallacy is for example: Indian logicians took great pains to identify fallacies in an argument. An influential collection of texts on logic and reason, the Nyāya Sūtras, attributed to Aksapada Gautama, variously estimated to have been composed between 6th-century BCE and 2nd-c... |
596 | "Fallacies"
[15]: 8 Whately divided fallacies into two groups: logical and material. According to Whately, logical fallacies are arguments where the conclusion does not follow from the premises. Material fallacies are not logical errors because the conclusion does follow from the premises. He then divided the logical g... |
597 | "Fallacies"
divided fallacies into four Idola (Idols, i.e. False Appearances), which summarize the various kinds of mistakes to which the human intellect is prone. J. S. Mill discussed the subject in book five of his Logic, and Jeremy Bentham 's Book of Fallacies (1824) contains valuable remarks. A formal fallacy, dedu... |
598 | "Fallacies"
Both may actually be true, or may even be more probable as a result of the argument, but the deductive argument is still invalid because the conclusion does not follow from the premises in the manner described. Even non-deductive arguments can be said to be fallacious: for example, an inductive argument tha... |
599 | "Fallacies"
However, formal logic makes no such guarantee if any premise is false; the conclusion can be either true or false. Any formal error or logical fallacy similarly invalidates the deductive guarantee. Both the argument and all its premises must be true for a conclusion to be true. The term logical fallacy is i... |
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