[2.2.5] Stoic Ontology, Genus, Categories

“An examination of Stoic ontology might profitably begin with a passage from Plato’s Sophist. There, Plato asks for a mark or indication of what is real or what has being. One answer which is mooted is that the capacity to act or be acted upon is the distinctive mark of real existence or ‘that which is.’ The Stoics accept this criterion and add the rider that only bodies can act or be acted upon. Thus, only bodies exist. So there is a sense in which the Stoics are materialists or – perhaps more accurately, given their understanding of matter as the passive principle (see below) – ‘corporealists’. However, they also hold that there are other ways of appearing in the complete inventory of the world than by virtue of existing. Incorporeal things like time, place or sayables (lekta, see below) are ‘subsistent’ – as are imaginary things like centaurs.”

In this diagram I used OntoUML notation to present the main concepts of Stoic ontology:

Stoic categories based on Long, A. A. & Sedley, D. N. (1987). The Hellenistic Philosophers, Vol. 1 (p. 163). Cambridge: Cambridge University Press.
Comment texts from Stoic Ontology from Peter Wyss.
ClassDescriptionRelations
Something“This is the highest ontological genus: to be something (τί, ti) is to be some particular thing. Notably, this excludes Platonic Forms, or universals: they are not-somethings (outina), and thus ontological outcasts.” can be: Incorporeal; Body; Neither
Incorporeal“These do not exist, but subsist (ὑφεστάναι, hyphestanai); yet they are real (ὑπάρχειν, hyparchein). We can think of them as conditions ‘without which the interaction of bodies in the world would neither be analysable nor intelligible” can be: Sayable; Void; Place; Time
Body“Only bodies (σώματα, sômata) have being, or exist. Slogan: to exist is to have causal powers. Plato in the Sophist (247d–e): ‘Now, I say that what has some power to make something else into something, or to suffer the slightest, even once, this has real being. For I define being as nothing but power (δύναμις).’ The Stoic conception of existence is thus dynamic. Matter as such is passive, but bodies are not, since they are also infused by logos, which is active… only bodies can act or be acted upon ”
Neither can be: fictional entities (e.g. unicorns); limits can be: fictional entities; limits
Object_Substrate“A dog as merely an object, something ‘out there’, a discrete portion of matter: a substance (οὐσία, ousia). As object, a dog is merely the potential bearer of qualities” part of a Body
DisposedA dog as a further differentiated qualified thing: as running, barking, brave. associated with Body, one to zero or many multiplicity
Qualified“A dog as an object with certain qualities: bad breath, soft fur, dotted; can be qualified commonly as ‘dog’ or ‘furry’, or peculiarly as ‘Fido’.”associated with Body, one to zero or many multiplicity
RelativelyDisposed“A dog as an object in relation to other objects as owned by Jack, Rexs’ father winner at Crufts”associated with Body, one to zero or many multiplicity
OtherBodythe reference body of relatively disposed, e.g. Jack; father associated with RelativelyDisposed

Sources:

  • All citations from: Baltzly, Dirk, “Stoicism“, The Stanford Encyclopedia of Philosophy (Spring 2019 Edition), Edward N. Zalta (ed.)
  • Peter Wyss, “Stoic Ontology
  • Long, A. A. & Sedley, D. N. (1987). “The Hellenistic Philosophers”, Vol. 1 (p. 163). Cambridge: Cambridge University Press.

First published: 06/03/2019

[2.2.4] Ontological Structure of Stoic Logic

Stoic logic, elaborated by Chrysippus (297-206 BC), is one of the two major systems of logic (the other one is Aristotelian logic) in the classical world and can be characterized by:

  • It is propositional logic (unlike the Aristotelian [1.3.9], which is term logic), because analyses the relations and truth values of assertibles (or propositions). Here logical variables are propositions, while in Aristotelian logic terms.
  • It is concerned more with particulars (unlike the Aristotelian logic, which is analyzing categorization and universals) reflecting thus the stoic view that only particulars are real existents (see also [2.2.5]).

The stoic logic, represented in the OntoUML diagram below, operates with the following main classes and relationships:

Stoic logic
ClassDescriptionRelations
SayableSayable (lekta) (see also in [2.2.2]): “are the underlying meanings in everything we say and think, but… also subsist independently of us. They are distinguished from spoken and written linguistic expressions: what we utter are those expressions, but what we say are the sayables.”
AssertibleAssertibles (axiômata) are sayables having a truth value: at any one time they are either true or false. So truth is temporal and assertibles may change their truth-value. They can never be true and false at the same time (law of non-contradiction) and they must be at least true or false (law of excluded middle).is a Sayable
TruthValueTruth value of an Assertible might change over time, so each value is valid from the startTime to endTime.each Assertible has at least 1 truthValue
SimpleAssertibleSimple Assertibles include propositions like: “it is cold”; “it is raining this morning” and “no one is running.” is an Assertible
Non-simpleAssertibleNon-simple Assertibles are compound of simple assertibles linked with logical connectives, like: if.. than, and, either.. or, since, because. E.g. “if it is winter than it is cold”; “either it is day or night”; and “I am moving since I am working”.Non-SimpleAssertible is Assertible; it is a part-hole relationship with the SimpleAssertible
PremisePremise is an Assertible, e.g. “it is winter”; “if it is winter than it is cold”.
ConclusionConclusion is an Assertible, e.g. “it is cold”.
ArgumentArguments relates two (or more) Premises to a Conclusion as cause and effect. At least one Premise has to be a Non-simpleAssertible. E.g.
Premise1: “if it is winter than it is cold”; if P than Q
Premise2: “it is winter”; P
Conclusion: “it is cold”; therefore Q
Argument mediates between Premises and Conclusion
StoicSyllogismStoicSyllogism “is best understood as a… natural-deduction system that consists of five kinds of axiomatic arguments (the indemonstrables) and four inference rules, called themata. An argument is a syllogism precisely if it either is an indemonstrable or can be reduced to one by means of the themata. Thus syllogisms are certain kinds of formally valid arguments. The Stoics explicitly acknowledged that there are valid arguments that are not syllogisms; but assumed that these could be somehow transformed into syllogisms.”if the Argument is valid, it relates to Syllogism;
IndemonstrableThe five indemonstrables are:
1/ Modus ponens: If p, then q.  p. Therefore, q.
2/ Modus tollens: If p, then q. Not q. Therefore, not p.
3/ Not both p and q.  p. Therefore, not q.
4/ Modus tollendo ponens: Either p or q. Not p. Therefore, q.
5/ Modus ponendo tollens: Either p or q.  p. Therefore, not q.
part of StoicSyllogism
ThemataComplex syllogisms could be reduced to the indemonstrables through the use of four ground rules or themata. Of these four, only two have survived.
E.g. when from two assertibles a third follows, then from either of them together with the contradictory of the conclusion the contradictory of the other follows.
part of StoicSyllogism

Sources

  • All citations from: Bobzien, Susanne, “Ancient LogicThe Stanford Encyclopedia of Philosophy (Winter 2016 Edition), Edward N. Zalta (ed.)
  • Bobzien, Suzanne, Stoic Logic, Cambridge Companions Online © Cambridge University Press, 2006

First published: 13/06/2019