Ontology

[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

[1.3.5] Aristotle on Hylomorphism

A. L. Komáromi28 Comments

“Central to Aristotle’s (384-322 BC) four-causal account of explanatory adequacy are the notions of matter (hulê) and form (eidos or morphê). Together, they constitute one of his most fundamental philosophical commitments, to hylomorphism:

Hylomorphism =df ordinary objects are composites of matter and form.
Aristotle’s hylomorphism was formulated originally to handle various puzzles about change…”

The following OntoUML diagram shows the main classes in the hylomorphic model:

Aristotle on hylomorphism
ClassDescriptionRelations
Object“‘ordinary objects’ … as a first approximation, it serves to rely on the sorts of examples Aristotle himself employs when motivating hylomorphism: statues and houses, horses and humans.”
Form“form [in Aristotelian sense] =df that which makes some matter which is potentially F actually F“
Acts, forms FormedMatter.		characterizes Object; acts on FormedMatter
Matter“matter [in Aristotelian sense] =df that which persists and which is, for some range of Fs, potentially F”
FormedMatterFormed matter is contained in an Object (not used by Aristotle).is phase of Matter; contained in Object
PrimeMatterPrime matter is usually described as pure potentiality, unformed. is subkind of Matter
PotentialityPotentiality is “possibility” that a thing can have.relates Matter with Object
ActualityActuality is change what realizes fulfillment of a possibility. relates Form with Object

“In general, argues Aristotle, in whatever category a change occurs, something is lost and something gained within that category, even while something else, a substance, remains in existence, as the subject of that change. Of course, substances can come into or go out of existence, in cases of generation or destruction; and these are changes in the category of substance. Evidently even in cases of change in this category, however, something persists. To take an example favourable to Aristotle, in the case of the generation of a statue, the bronze persists, but it comes to acquire a new form, a substantial rather than accidental form. In all cases, whether substantial or accidental, the two-factor analysis obtains: something remains the same and something is gained or lost.
In its most rudimentary formulation, hylomorphism simply labels each of the two factors: what remains is matter and what is gained is form…

Importantly, matter and form come to be paired with another fundamental distinction, that between potentiality and actuality. Again in the case of the generation of a statue, we may say that the bronze is potentially a statue, but that it is an actual statue when and only when it is informed with the form of a statue. Of course, before being made into a statue, the bronze was also in potentiality a fair number of other artefacts—a cannon, a steam-engine, or a goal on a football pitch. Still, it was not in potentiality butter or a beach ball. This shows that potentiality is not the same as possibility: to say that x is potentially F is to say that x already has actual features in virtue of which it might be made to be F by the imposition of a F form upon it. So, given these various connections, it becomes possible to define form and matter generically a

OBSERVATIONS:

  • Since the Aristotelian Form is a part of the Object, when the Object is destroyed, the Form is destroyed. Hence we have a ComponentOf OntoUML (similar to Composition in UML) relation between Object and Form.
  • Object is a Primary Substance in Aristotle’s four-fold categorization system [1.3.1]
  • The same hylomorphic structure can be observed in the previous post [1.3.4] about Causality, Potentiality, Actuality, Teleology:

Sources

  • The source of all citations: Shields, Christopher, “Aristotle“, The Stanford Encyclopedia of Philosophy (Winter 2016 Edition), Edward N. Zalta (ed.)
  • Ainsworth, Thomas, “Form vs. Matter“, The Stanford Encyclopedia of Philosophy (Spring 2016 Edition), Edward N. Zalta (ed.)

First published: 4/4/2019
Updated: 9/4/2019: Added Potentiality, Actuality
Updated: 6/9/2019: Added PrimeMatter
Updated: 9/2/2021: Added Form, FormedMatter
Updated: 7/12/2021