[1.3.9] Ontological Structure of Aristotelian Logic

The most influential classical logical system (see also [2.7] Stoic Logic) was elaborated by Aristotle (384-322 BC) in his work Organon. This system

  • is centered around the concept of syllogism (deduction),
  • is term logic, because analyses the relation, categorization of terms
  • focuses on universal terms, thus reflecting the basic principle of Aristotle’s philosophy, that of knowledge is about universals (see also [1.3.8], [1.3.10]).

Aristotle’s assertoric (non-modal) syllogistic, represented in the OntoUML diagram below, operates with the following main classes and relationships:

Ontological structure of Aristotle’s logic
SyllogismA syllogism is an “inference with two premises, each of which is a categorical sentence, having exactly one term in common, and having as a conclusion a categorical sentence the terms of which are just those two terms not shared by the premises”.
Not all the triplets of two premises and one conclusion of the required structure are syllogisms, only just those who lead to a valid inference, listed in the moods.
E.g. P1: All man are mortal. P2: Socrates is man, C: Socrates is mortal.
Syllogism relates 2 Premises with 1 Conclusion
PremiseA possible role of an Assertion, relative to a Syllogism is Premise (protasis).
E.g. P1: All man are mortal. P2: Socrates is a man.
role of Assertion; relates to Conclusion with deduction; has Extreme and MiddleTerm
ConclusionA possible role of an Assertion, relative to a Syllogism is Conclusion (sumperasma).
E.g. C: Socrates is mortal.
role of Assertion
AssertionAssertions (apophanseis) are sentences with a specific structure: “every such sentence must have the same structure: it must contain a subject and a predicate and must either affirm or deny the predicate of the subject.”Subject and Predicate are components of an Assertion
Affirmation; DenialAn Assertion can be Affirmation or Denialsubkinds of Assertion
SubjectA Subject (hupokeimenon) is an essential part of an Assertion.
E.g: All man; Socrates in P1, P2, C.
is a component of an Assertion; subkind of Term
PredicateA Predicate (katêgorein) is an essential part of Assertion.
E.g: are mortal; is man; is mortal in P1, P2, C.
is a component of an Assertion; subkind of Term
TermSubjects and predicates of assertions are terms (horos) which can be either individual, e.g. Socrates, or universal, e.g. human. Subjects may be individual or universal, but predicates can only be universals.
MiddleTerm“Aristotle calls the term shared by the premises the middle term (meson)…”
E.g: man in P1, P2
role of Term
Extreme“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).”
E.g: Socrates; are mortal in P1, P2.
role of Term
Figure “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 refers to these term arrangements as figures (schêmata)”. There are 3 Figures.mediates Extreme and MiddleTerm; has Moods
Mood“In Prior Analytics I.4–6, Aristotle shows that the premise combinations given in the following table yield deductions and that all other premise combinations fail to yield a deduction. In the terminology traditional since the middle ages, each of these combinations is known as a mood Latin modus, “way”, which in turn is a translation of Greek tropos). Aristotle, however, does not use this expression and instead refers to “the arguments in the figures”.
There are 14 Moods: 4 for the First figure, 4 for the Second figure, and 6 for the Third figure.
Mood characterizes Syllogism; has Proof
ProofFor each Mood there is a logical Proof provided by Aristotle.

The source of all citations and more about the topic in: Smith, Robin, “Aristotle’s Logic“, The Stanford Encyclopedia of Philosophy (Winter 2018 Edition), Edward N. Zalta (ed.)

First published: 25/4/2019
Updated: 7/2/2021 – changed Mood
Updated: 7/12/2021

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