Ontology

[1.3.1] Aristotle’s Categories: the Four-Fold Division

Image A. L. Komáromi14 Comments

“In the Pre-Predicamenta, Aristotle (384-322 BC) discusses a number of semantic relations (1a1–16), gives a division of beings (τἃ ὄντα), into four kinds.
By focusing on Aristotle’s illustrations, most scholars conclude that beings that are said-of others are universals, while those that are not said-of others are particulars. Beings that are present-in others are accidental, while those that are not present-in others are non-accidental. Now, non-accidental beings that are universals are most naturally described as essential, while non-accidental beings that are particulars are best described simply as non-accidental.”

The OntoUML diagram below presents the main entities of Aristotle’s four-fold division:

Aristotle’s categories 4 fold division
ClassDescriptionRelations
BeingBeing (τὰ ὄντα) can be:
particulars:
EssentialParticular-PrimarySubstance; AccidentalParticular-NonSubstantialParticular
and universals:
EssentialUniversal-SecondarySubstance; AccidentalUniversal 		generalizes
EssentialParticular-PrimarySubstance; AccidentalParticular-NonSubstantialParticular;
EssentialUniversal-SecondarySubstance; AccidentalUniversal
EssentialUniversal
-SecondarySubstance		“in addition to primary substances, which are particulars, there are secondary substances, which are [essential] universals. His example of such an entity is man, which, […] is a universal in the category of substance… we should interpret secondary substances as essential characteristics of primary substances”
Example: Man		essential characteristic, component of at least one EssentialParticular
-PrimarySubstance
EssentialParticular
-PrimarySubstance		“The pride of place in this classificatory scheme, according to Aristotle, goes to those entities that are neither said-of nor present-in anything. Such entities, Aristotle says, are primary substances [or essential particulars…]
His favorite examples are an individual man and a horse […]
So, it is natural to interpret him as thinking that among primary substances are concrete particulars that are members of natural kinds.”
Example: Socrates		is in material relation with at least one AccidentalUniversal
AccidentalParticular
-NonSubstantialParticular		“a non-substantial [accidental] particular is a dependent entity, individuated only by reference to primary substance that it is present in. Hence, Socrates’ whiteness cannot exist without Socrates.”
Example: Socrates’s whiteness		role of AccidentalUniversal
AccidentalUniversal“being is both said-of and present-in a primary substance if it is an accidental universal… The universal whiteness is said-of many primary substances but is only accidental to them.”
Example: whiteness, as color

Related posts in theory of Universals: [1.2.2], [1.3.1], [1.3.2], [2.5], [2.7.3], [4.3.1], [4.3.2], [4.4.1], [4.5.2], [4.9.8], [4.11], [4.15.6], [4.18.8]

The source of all citations and more about the topic in: Studtmann, Paul, “Aristotle’s Categories“, The Stanford Encyclopedia of Philosophy (Fall 2018 Edition), Edward N. Zalta (ed.)

First published: 07/02/2019
Updated: 3/1/2020 Diagram modified to OntoUML standard
Updated: 7/12/2021

[1.2.1] Plato: Theory of Forms

A. L. Komáromi15 Comments

“What many things have in common, or a feature they share, is a universal or, in Plato’s terms, a Form. Of course there seems to be a huge number of properties. Many different things are white. Many different things are animals. Each (shared) property is a universal—a ‘one over many instances,’ whiteness over the many white things, roundness over the many round things, and so on. Thus, for Plato, Roundness and Whiteness are Forms.”
This theory is the first known theory of Universals.

The following OntoUML  Class Diagram shows the main elements of Plato’s (429?-347 BC) theory of forms:

Plato’s theory of forms
ClassDescriptionRelations
Form“What many things have in common, or a feature they share, is a universal or, in Plato’s terms, a Form. Of course there seems to be a huge number of properties. Many different things are white. Many different things are animals. Each (shared) property is a universal—a ‘one over many instances,’ whiteness over the many white things, roundness over the many round things, and so on. Thus, for Plato, Roundness and Whiteness are Forms. […] Forms are immaterial, non-spatial and atemporal […] Forms are […] perfect and what particulars strive to be like but fall short of . […] Forms are simple or incomposite, of one form (monoeidetic). Forms are the objects of knowledge, grasped by the intellect through definitions. […] Forms are pure, simple or uniform (monoeidetic , hen).is being Essence; componentOf Particular
Good“[…] all Forms are related to the Good. […] each Form is good, that is, that each Form is a good thing or is characterized by goodness.” characterizes Form
Essence“Each Form is its essence (ousia), which is to say that the relation of Being links the essence of beauty to the subject, Beauty itself. Being, then, is a primitive ontological relation designed exclusively to capture the special tie between that which possesses an essence and the essence possessed.”
Being“Being, then, is a primitive ontological relation designed exclusively to capture the special tie between that which possesses an essence and the essence possessed.” relates Essence with Form
Particular“Particulars are dependent on Forms whereas Forms are not dependent on them. Particulars strive to be such as the Forms are and thus in comparison to Forms are imperfect or deficient treat Partaking as a relation between material particulars and Forms, the result of which is that the particular is characterized by the Form of which it partakes […].” partakes in Form

Related posts in theory of Universals: [1.2.2], [1.3.1], [1.3.2], [2.5], [2.7.3], [4.3.1], [4.3.2], [4.4.1], [4.5.2], [4.9.8], [4.11], [4.15.6], [4.18.8]

The source of all citations and more about the topic in: Silverman, Allan, “Plato’s Middle Period Metaphysics and Epistemology“, The Stanford Encyclopedia of Philosophy (Fall 2014 Edition), Edward N. Zalta (ed.)

First published: 9/1/2019

Updated: 6/2/2019: changed relationship type of Form-Particular
Updated: 18/9/2021: added being, and OntoUML notation