[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:

Main concepts in Aristotle’s assertoric syllogistic
ClassDescriptionRelations
Syllogism“inference 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”.
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 man.
Assertion is super-type for Premise
ConclusionA possible role of an Assertion, relative to an Syllogism is Conclusion (sumperasma).
E.g. C: Socrates is mortal.
Assertion is super-type for Conclusion
Assertion
Assertions (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; Assertion is super-type for Affirmation and Denial.
SubjectA Subject (hupokeimenon) is an essential part of an Assertion.
E.g: All man; Socrates in P1, P2, C.
Subject is a component of an Assertion; Term is a super -type for it.
PredicateA Predicate (katêgorein) is an essential part of Assertion.
E.g: are mortal; is man; is mortal in P1, P2, C.
Predicate is a component of an Assertion; Term is a super -type for it.
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.Term is super-type for Subject and Predicate.
Middle Term“Aristotle calls the term shared by the premises the middle term (meson)…”
E.g: man in P1, P2
Term is a super-type for Middle term, for which Middle term is a role relative to Premise.
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.

Term is a super-type for Extreme, for which Extreme is a role relative to Premise.
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.
MoodA Mood is a meta-syllogism, prooved with a Proof. There are 14 Moods, 4 for the First figure, 4 for the Second figure, and 6 fot the Third figure.Mood is a super-type for Syllogism.
ProofFor each Mood there is a logical Proof provided by Aristotle.There is a 1:1 relation for Mood:Proof.

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: 25/04/2019

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