Year: 2019

[1.3.9] Ontological Structure of Aristotelian Logic

A. L. Komáromi14 Comments

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
ClassDescriptionRelations
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

[1.3.8] Aristotle’s Knowledge/Science Generating Process

A. L. Komáromi6 Comments

In this UML Activity Diagram, I propose a reconstruction of the scientific “business” process using the following Aristotelian (384-322 BC) concepts elaborated in the works Physics, Metaphysics, Posterior Analytics, related to psychology (see [1.3.6]), logic (see [1.3.9]), and scientific inquiry:

  • sense perception
  • observation
  • memory
  • induction (epagôgê)
  • generalization
  • intuition
  • first things (archai) or priori, premise, hipothesis
  • deduction, syllogism (sullogismos ) (see [1.3.9])
  • causation (aition); four causes (material, efficient, formal, final) (see [1.3.4])
  • knowledge (which is about universal, necessary things with identified causes) (epistemê)
Aristotle’s knowledge/science generating process
Activity Action/Description
Start
Careful OBSERVATION• Sense-perception of object
• Store & Recollect the facts
Inference using INDUCTION“it is induction (epagôgê), 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 science.” (R. Smith)

• Organize the facts
• Sort out irrelevant facts
• Generalization
• Use bottom-up syllogism: “there is an induction as a kind of syllogism. We can describe it as a bottom-up syllogism. Induction in this sense means finding out an appropriate middle term where both extreme terms are given” (R. Smith)
• Identify first things (archai; a priori; premise; hypothesis) with the help of intuition
Inference using DEDUCTION“A deduction is speech (logos) in which, certain things having been supposed, something different from those supposed results of necessity because of their being so. Each of the “things supposed” is a premise (protasis) of the argument, and what “results of necessity” is the conclusion (sumperasma).” (R. Smith)
In Aristotle’s model, there is no observational/experimental verification of the knowledge (loop back to the beginning of the process).

• Generate new knowledge using dialectical syllogism
• Identify the Four Causes with demonstrative syllogism (apodeixis): “The demonstrative syllogism, (apódixis) which produces genuine knowledge, science or epistemé, does not aim to lead from premises to a conclusion up to then unknown. On the contrary, in the demonstrative syllogism, also, the conclusion is an observed fact previously known. The scientific explanation, the reason why, the (dióti), or “cause”, will when found form the premise from which that observed fact can be demonstrated as a conclusion. Thus the scientific syllogism derives facts already known through observation, from reasons why, or archai. It is not a logic of the discovery of new facts, but a logic of proof, of formalizing or systematizing facts already known.” (S. Sfekas)
• Record Scientific knowledge (episteme)
End

NOTE: This is the first UML Activity Diagram I present on this blog. For modelling business processes there is an alternative standard also in use: BPMN, (Business Process Model and Notation) managed also by OMG.

Sources:

  • Andersen, Hanne and Hepburn, Brian, “Scientific Method“, The Stanford Encyclopedia of Philosophy (Summer 2016 Edition), Edward N. Zalta (ed.)
  • Galik, Dusan. “Induction in Aristotle’s System of Scientific Knowledge”. Organon F. 13. 495-505., 2006
  • S. Sfekas: Aristotelian Fundamentals of the Practice of Knowledge and Information, conference paper, 2017
  • Shields, Christopher, “Aristotle’s Psychology“, The Stanford Encyclopedia of Philosophy (Winter 2016 Edition), Edward N. Zalta (ed.)
  • Smith, Robin, “Aristotle’s Logic“, The Stanford Encyclopedia of Philosophy (Winter 2018 Edition), Edward N. Zalta (ed.)

First published: 18/04/2019