“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

Class Description Relations Being Being (τὰ ὄντα) can be:

-particulars : EssentialParticular_PrimarySubstance; AccidentalParticular

_Non-SubstantialParticular

– and universals: EssentialUniversal

_SecondarySubstance; AccidentalUniversal EssentialUniversal

_SecondarySubstance “in addition to primary substances, which are particulars, there are secondary substances, which are 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 inherits from Being; essential characteristic of least 1 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…

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 inherits from Being; is in material relation with ar least 1 AccidentalUniversal AccidentalParticular

_Non-SubstantialParticular “a non-substantial 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 inherits from Being; mediates between EssentialParticular

_PrimarySubstance and 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 inherits from Being

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]

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: 03/01/2020 Diagram modified to OntoUML standard.