Aristotelian logic, after a great and early triumph, consolidated its position of influence to rule over the philosophical world throughout the Middle Ages up until the 19 th Century. All that changed in a hurry when modern logicians embraced a new kind of mathematical logic and pushed out what they regarded as the antiquated and clunky method of syllogisms. It provides an alternative way of approaching logic and continues to provide critical insights into contemporary issues and concerns. Before getting down to business, it is important to point out that Aristotle is a synoptic thinker with an over-arching theory that ties together all aspects and fields of philosophy.

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It did not always hold this position: in the Hellenistic period, Stoic logic, and in particular the work of Chrysippus, took pride of place. Kant thought that Aristotle had discovered everything there was to know about logic, and the historian of logic Prantl drew the corollary that any logician after Aristotle who said anything new was confused, stupid, or perverse. During the rise of modern formal logic following Frege and Peirce, adherents of Traditional Logic seen as the descendant of Aristotelian Logic and the new mathematical logic tended to see one another as rivals, with incompatible notions of logic.

This article is written from the latter perspective. At the same time, scholars trained in modern formal techniques have come to view Aristotle with new respect, not so much for the correctness of his results as for the remarkable similarity in spirit between much of his work and modern logic. Aristotle himself never uses this term, nor does he give much indication that these particular treatises form some kind of group, though there are frequent cross-references between the Topics and the Analytics.

On the other hand, Aristotle treats the Prior and Posterior Analytics as one work, and On Sophistical Refutations is a final section, or an appendix, to the Topics. To these works should be added the Rhetoric , which explicitly declares its reliance on the Topics. A thorough explanation of what a deduction is, and what they are composed of, will necessarily lead us through the whole of his theory.

What, then, is a deduction? Aristotle says:. Deductions are one of two species of argument recognized by Aristotle. However, induction or something very much like it plays a crucial role in the theory of scientific knowledge in the Posterior Analytics : it is induction, or at any rate a cognitive process that moves from particulars to their generalizations, that is the basis of knowledge of the indemonstrable first principles of sciences.

Some of the differences may have important consequences:. Of these three possible restrictions, the most interesting would be the third. This could be and has been interpreted as committing Aristotle to something like a relevance logic. In fact, there are passages that appear to confirm this.

However, this is too complex a matter to discuss here. However the definition is interpreted, it is clear that Aristotle does not mean to restrict it only to a subset of the valid arguments. Moreover, modern usage distinguishes between valid syllogisms the conclusions of which follow from their premises and invalid syllogisms the conclusions of which do not follow from their premises. The first is also at least highly misleading, since Aristotle does not appear to think that the sullogismoi are simply an interesting subset of the valid arguments.

According to Aristotle, every such sentence must have the same structure: it must contain a subject hupokeimenon and a predicate and must either affirm or deny the predicate of the subject. Thus, every assertion is either the affirmation kataphasis or the denial apophasis of a single predicate of a single subject.

In On Interpretation , Aristotle argues that a single assertion must always either affirm or deny a single predicate of a single subject. Thus, he does not recognize sentential compounds, such as conjunctions and disjunctions, as single assertions. This appears to be a deliberate choice on his part: he argues, for instance, that a conjunction is simply a collection of assertions, with no more intrinsic unity than the sequence of sentences in a lengthy account e.

Since he also treats denials as one of the two basic species of assertion, he does not view negations as sentential compounds. His treatment of conditional sentences and disjunctions is more difficult to appraise, but it is at any rate clear that Aristotle made no efforts to develop a sentential logic.

Some of the consequences of this for his theory of demonstration are important. Subjects and predicates of assertions are terms. A term horos can be either individual, e. Socrates , Plato or universal, e. Subjects may be either individual or universal, but predicates can only be universals: Socrates is human , Plato is not a horse , horses are animals , humans are not horses.

The word universal katholou appears to be an Aristotelian coinage. Universal terms are those which can properly serve as predicates, while particular terms are those which cannot. This distinction is not simply a matter of grammatical function. Aristotle, however, does not consider this a genuine predication.

Consequently, predication for Aristotle is as much a matter of metaphysics as a matter of grammar. The reason that the term Socrates is an individual term and not a universal is that the entity which it designates is an individual, not a universal. What makes white and human universal terms is that they designate universals. Aristotle takes some pains in On Interpretation to argue that to every affirmation there corresponds exactly one denial such that that denial denies exactly what that affirmation affirms.

The pair consisting of an affirmation and its corresponding denial is a contradiction antiphasis. In general, Aristotle holds, exactly one member of any contradiction is true and one false: they cannot both be true, and they cannot both be false. However, he appears to make an exception for propositions about future events, though interpreters have debated extensively what this exception might be see further discussion below.

However, he notes that when the subject is a universal, predication takes on two forms: it can be either universal or particular. These expressions are parallel to those with which Aristotle distinguishes universal and particular terms, and Aristotle is aware of that, explicitly distinguishing between a term being a universal and a term being universally predicated of another. In On Interpretation , Aristotle spells out the relationships of contradiction for sentences with universal subjects as follows:.

Simple as it appears, this table raises important difficulties of interpretation for a thorough discussion, see the entry on the square of opposition. This should really be regarded as a technical expression. For clarity and brevity, I will use the following semi-traditional abbreviations for Aristotelian categorical sentences note that the predicate term comes first and the subject term second :. That theory is in fact the theory of inferences of a very specific sort: inferences with two premises, each of which is a categorical sentence, having exactly one term in common, and having as conclusion a categorical sentence the terms of which are just those two terms not shared by the premises.

Aristotle calls the term shared by the premises the middle term meson and each of the other two terms in the premises an extreme akron. The middle term must be either subject or predicate of each premise, and this can occur in three ways: the middle term can be the subject of one premise and the predicate of the other, the predicate of both premises, or the subject of both premises.

Aristotle calls the term which is the predicate of the conclusion the major term and the term which is the subject of the conclusion the minor term. The premise containing the major term is the major premise , and the premise containing the minor term is the minor premise. Aristotle then systematically investigates all possible combinations of two premises in each of the three figures.

For each combination, he either demonstrates that some conclusion necessarily follows or demonstrates that no conclusion follows. The results he states are correct. The precise interpretation of this distinction is debatable, but it is at any rate clear that Aristotle regards the perfect deductions as not in need of proof in some sense.

For imperfect deductions, Aristotle does give proofs, which invariably depend on the perfect deductions. Thus, with some reservations, we might compare the perfect deductions to the axioms or primitive rules of a deductive system. A direct deduction is a series of steps leading from the premises to the conclusion, each of which is either a conversion of a previous step or an inference from two previous steps relying on a first-figure deduction.

Conversion, in turn, is inferring from a proposition another which has the subject and predicate interchanged. Specifically, Aristotle argues that three such conversions are sound:. He undertakes to justify these in An. From a modern standpoint, the third is sometimes regarded with suspicion. Using it we can get Some monsters are chimeras from the apparently true All chimeras are monsters ; but the former is often construed as implying in turn There is something which is a monster and a chimera , and thus that there are monsters and there are chimeras.

For further discussion of this point, see the entry on the square of opposition. He says:. An example is his proof of Baroco in 27a36—b Aristotle proves invalidity by constructing counterexamples. This is very much in the spirit of modern logical theory: all that it takes to show that a certain form is invalid is a single instance of that form with true premises and a false conclusion. In Prior Analytics I. Having established which deductions in the figures are possible, Aristotle draws a number of metatheoretical conclusions, including:.

His proof of this is elegant. First, he shows that the two particular deductions of the first figure can be reduced, by proof through impossibility, to the universal deductions in the second figure:. He then observes that since he has already shown how to reduce all the particular deductions in the other figures except Baroco and Bocardo to Darii and Ferio , these deductions can thus be reduced to Barbara and Celarent.

This proof is strikingly similar both in structure and in subject to modern proofs of the redundancy of axioms in a system. Many more metatheoretical results, some of them quite sophisticated, are proved in Prior Analytics I. In contrast to the syllogistic itself or, as commentators like to call it, the assertoric syllogistic , this modal syllogistic appears to be much less satisfactory and is certainly far more difficult to interpret. Aristotle gives these same equivalences in On Interpretation.

However, in Prior Analytics , he makes a distinction between two notions of possibility. He then acknowledges an alternative definition of possibility according to the modern equivalence, but this plays only a secondary role in his system.

Aristotle builds his treatment of modal syllogisms on his account of non-modal assertoric syllogisms: he works his way through the syllogisms he has already proved and considers the consequences of adding a modal qualification to one or both premises. A premise can have one of three modalities: it can be necessary, possible, or assertoric. Aristotle works through the combinations of these in order:. Though he generally considers only premise combinations which syllogize in their assertoric forms, he does sometimes extend this; similarly, he sometimes considers conclusions in addition to those which would follow from purely assertoric premises.

As in the case of assertoric syllogisms, Aristotle makes use of conversion rules to prove validity. The conversion rules for necessary premises are exactly analogous to those for assertoric premises:. Possible premises behave differently, however. Aristotle generalizes this to the case of categorical sentences as follows:. This leads to a further complication. Such propositions do occur in his system, but only in exactly this way, i.

Such propositions appear only as premises, never as conclusions. He does not treat this as a trivial consequence but instead offers proofs; in all but two cases, these are parallel to those offered for the assertoric case.

Malink , however, offers a reconstruction that reproduces everything Aristotle says, although the resulting model introduces a high degree of complexity. This subject quickly becomes too complex for summarizing in this brief article. From a modern perspective, we might think that this subject moves outside of logic to epistemology. However, readers should not be misled by the use of that word.

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## Aristotle: Logic

It did not always hold this position: in the Hellenistic period, Stoic logic, and in particular the work of Chrysippus, took pride of place. Kant thought that Aristotle had discovered everything there was to know about logic, and the historian of logic Prantl drew the corollary that any logician after Aristotle who said anything new was confused, stupid, or perverse. During the rise of modern formal logic following Frege and Peirce, adherents of Traditional Logic seen as the descendant of Aristotelian Logic and the new mathematical logic tended to see one another as rivals, with incompatible notions of logic. This article is written from the latter perspective. At the same time, scholars trained in modern formal techniques have come to view Aristotle with new respect, not so much for the correctness of his results as for the remarkable similarity in spirit between much of his work and modern logic. Aristotle himself never uses this term, nor does he give much indication that these particular treatises form some kind of group, though there are frequent cross-references between the Topics and the Analytics.

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## Aristotle’s Logic

The name Organon was given by Aristotle's followers, the Peripatetics. They are as follows:. The order of the works is not chronological which is now hard to determine but was deliberately chosen by Theophrastus to constitute a well-structured system. Indeed, parts of them seem to be a scheme of a lecture on logic. The arrangement of the works was made by Andronicus of Rhodes around 40 BC.

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## Aristotle's Organon: Definition, Philosophy & Summary

SparkNotes is here for you with everything you need to ace or teach! Find out more. These six works have a common interest not primarily in saying what is true but in investigating the structure of truth and the structure of the things that we can say such that they can be true. Broadly speaking, the Organon provides a series of guidelines on how to make sense of things. Our discussion of the Organon is divided into two parts. A syllogism is a three-step argument containing three different terms.