1 Jun 2017

Luhtala ( On the Origin of Syntactical Description in Stoic Logic, “Simple Propositions”, summary


by Corry Shores


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[The following is summary. It redoes this entry. All boldface, underlining, and bracketed commentary are my own. Paragraph enumerations are also my own, but they follow the paragraph breaks in the text. Please forgive my distracting typos, as proofreading is incomplete.]




Summary of


Anneli Luhtala


On the Origin of Syntactical Description in Stoic Logic


Ch.5 The Stoics


5.5 Stoic Logic



The Component of Meaning (Σημαινόμενα)

Simple Propositions





Brief summary:

The Stoics discussed simple propositions using intransitive sentence forms with neuter predicates. In other words, instead of using transitive forms that indicate how one subject acts upon another, they instead used intransitive forms that state the properties or accidents of some subject. (Some example predicates are “sitting” and “walking”.) What is crucial and interesting in this discussion is the way this analysis of syntax relates to their metaphysics and correspondence theory of truth. They use the same term ὑπάρχειν to mean that something exists (or that something is the case) and also to mean that a proposition is true. Situations in the world (that are relevant to these intransitive constructions) are the case (exist) when to some subject properly belongs certain attributes. And, a proposition is true when the predicate holds for the subject. This is determined when in reality the stated thing indeed does bear the attributes indicated in the proposition’s predicate.






[Propositions are either simple or non-simple. Simple propositions are classified as either negation, denial, privation, affirmation, the definite and the indefinite. We concern ourselves with definite and indefinite, because they involve important issues regarding referentiality in Stoic logic.]


Luhtala notes that Chrysippus, “Like many other Stoic philosophers [...] divided propositions into simple and non-simple,” and he defines simple in the following way.

Simple are those that consist of one or more propositions which are not ambiguous, as ‘It is day’, (...) and are classified into negation, denial, privation, affirmation, the definite and the indefinite. (Diog. Laert. VII,68-69)186


186. ἁπλᾶ μὲν οὖν ἐστι τὰ συνεστῶτα ἐξ ἀξιώματος μὴ διαφορουμένου (ἢ ἐξ ἀξιωμάτων), οἷον τὸ “ἡμέρα ἐστίν” ... Ἐν δὲ τοῖς ἁπλοῖς ἀξιώμασίν ἐστι τὸ ἀποφατικὸν καὶ τὸ ἀρνητικὸν καὶ τὸ στερητικὸν καὶ τὸ κατηγορικὸν καὶ τὸ καταγορευτικὸν καὶ τὸ ἀόριστον.

(111, text copied from Perseus)

Luhtala says we will only be concerned with definite and indefinite simple propositions, because they “reveal the crucial part that referentiality played in Stoic logic (see Kneale/Kneale 1962: 146; Pinborg 1975: 94; Goulet 1978: 171 ff.)” (111). [Luhtala then mentions higher and lower degrees of referentiality, but I do not know what they are. But it is on the basis of that distinction that simple affirmative propositions are divided into three types. She then quotes Diogenes Laertius, but it seems she unpacks it in the following paragraphs. The quotation will make the following distinctions. It will distinguish: assertoric, demonstrative, and indefinite. I am not sure, but I perhaps assertoric and demonstrative are both definite. Assertoric seem to simply state a situation, where the subject is a nominative like a name. In demonstrative propositions, the subject is a demonstrative phrase like ‘this one’. And in indefinite propositions, the subject is of course indefinite, like ‘someone’ or ‘that one.’ (I am not sure why ‘that one’ is not demonstrative, however. The Greek words are quite different looking, οὗτος and ἐκεῖνος, but I do not know Greek, so I cannot comment further.)]

According to the higher or lower degree of referentiality of the subject, the Stoics divided simple affirmative propositions into three types. I will follow closely the report given by Diogenes Laertius:

An assertoric proposition consists of a nominative case and a predicate, e.g. ‘Dion is walking’. A demonstrative proposition consists of a nominative demonstrative case and a predicate, e.g. ‘This one (οὗτος) is walking’. An indefinite proposition consists of one or more indefinite parts and a predicate, e.g. ‘Someone (τὶς) is walking’; ‘that one (ἐκεῖνος) is moving’. (Diog. Laert. VII,70, tr. Long/Sedley 1987: 205)187


187. κατηγορικὸν δέ ἐστι τὸ συνεστὸς ἐκ πτώσεως ὀρθῆς καὶ κατηγορήματος, οἷον “Δίων περιπατει”: καταγορευτικὸν δέ ἐστι τὸ συνεστὸς ἐκ πτώσεως ὀρθῆς δεικτικῆς καὶ κατηγορήματος, οἷον “οὗτος περιπατεῖ”: ἀόριστον δέ ἐστι τὸ συνεστὸς ἐξ ἀορίστου μορίου ἢ ἀορίστων μορίων καὶ κατηγορήματος, οἷον “τὶς περιπατεῖ,” “ἐκεῖνος κινεῖται.”

(111, text copied from Perseus)

[The definite pronoun makes the most specific reference. The Stoics’ examples for simple propositions do not have active or passive predicates and are thus not matters of transitive states of affairs.]


Luhtala says that the the definite pronoun, as in οὗτος or ‘that man’ most adequately represents the subject “because of its immediately obvious reference” (111). [Note, in the above quotation, οὗτος came beside ‘this one’. Here is seems a bit more specific, because it designates the type of thing being referred to.] What makes the definite pronouns so important for reference is that they pick out specific things: “The importance of the definite pronoun lies in its being the linguistic equivalent of a gesture point to an object which is present (Long/Sedley 1987: 206-207)” (111). The Stoics’ examples of simple propositions have neuter predicates like ‘sitting’ and ‘walking’, which means they were  not concerned in these cases with active and passive predicates and thus with “transitive states of affairs” (111-112).

[Sextus Empiricus’ account of the simple proposition is not a Stoic sort, like what is given by Diogenes’ Laertius.]


Sextus Empiricus’ account of these matters is probably not about the Stoics’ theory but instead about the Megarian Dialecticians, Philo and Diodorus. Luhtala notes some differences between Sextus’ account and Diogenes Laertius’ more properly Stoic account of propositions. In Sextus’ Megarian account, common nouns that refer to universals play a role in indeterminate propositions, but in Diogenes’ account, common nouns “are absent” (112). In fact, “In Stoic logic propositions were generally made about individuals rather than universals” (112). [This is perhaps important when considering the correspondence theory of truth, below.) Luhtala adds one more distinction. While in Stoic accounts the simple proposition receives a linguistic description, “analyzing it into predicate and case,” in Sextus’ account it is treated “in purely non-linguistic terms” (112). [This perhaps emphasizes the importance of linguistic matters in Stoic philosophy, with regard to issues of truth and reality.]

[There is an important Peripatetic notion that probably made its way into Stoic logic, namely, συμβεβηκότα (‘accidents’ / ‘attributes’). The importance of this concept is that it is tied to the notion ὑπάρχειν, which can mean either that an object exists or that a proposition is true. And the statement is true when the predicate holds for the subject (is properly attributed to it) which is also the case when the thing referred to also has the attributes mentioned. (In other words, something exists or ‘is the case’ when in reality there exists such a thing with its proper attributes, and a statement expressing that situation is true if the stated predicate holds for the subject, as they are in reality.)]


Luhtala notes Sextus Empiricus using “the term συμβεβηκότα (‘accidents’ / ‘attributes’)” when describing definite propositions (112).

the definite proposition such as ‘this one is sitting’ or ‘this one is walking’ is said by them (the dialecticians) to be true (ὑπάρχειν) whenever the predicate, such as ‘sitting’ or ‘walking’, belongs (συμβεβήκε) to the thing which falls under the demonstrative reference (δεῖξιν). (Adv. math. VIII,100 = SVF 2.205, tr. Long/Sedley 1987: 204)192


192. καὶ δὴ τὸ ὡρισμένον τοῦτο ἀξίωμα, τὸ “οὗτος κάθηται” ἢ “οὗτος περιπατεῖ”, τότε φασὶν ἀληθὲς ὑπάρχειν, ὅταν τῷ ὑπὸ τὴν δεῖξιν πίπτοντι συμβεβήκῃ κατηγόρημα, οἷον τὸ καθῆσθαι ἢ τὸ περιπατεῖν.

(112, text copied from Ancient Philosophy Source. Note a discrepancy. Above what Luhtala has as “συμβεβήκε” in the online source has as “συμβεβήκῃ”, and the Opera text might have as  “συμβεβήκοι”



Although Sextus is referring to the Dialecticians, Luhtala cites sources providing “evidence of genuinely Stoic usage of this terminology,” (namely, Duhot 1990: 94-96 and Long 1971: 88ff). So it is possible that “Peripatetic terminology” survived “in Stoic usage” (112). There is other evidence, like how Stobaeus attributes a usage of κατηγόρημα (‘predicate’) and συμβεβηκόσ (‘attribute’) to Chrysippus.

Only the present exists (ὑπάρχειν); the past and the future subsist (ὑφεστάναι); in the same way, as attributes (συμβεβηκότα), only the accidents are said to be the case (ὑπάρχειν); for example walking (τὸ περιπατεῖν) is true of me (ὑπάρχειν), when I walk; but when I sit or when I lie down, it is not true. (SVF 2.509)194


194. [taken from  the SVF pdf, with Luhtala continuing after:]

Stobaeus exist and true ambiguous SVF 2.509

It is noteworthy that the attributes are expressed by an infinitive rather than an abstract noun.


Also, “Seneca associates the notion of accident with the feature of the predicate of being incorporeal and being an attribute of something else, ‘accedens alteri’ ”(113). We also here see the survival of Aristotle’s notion of ὑπάρχειν (it was seen in the Stobaeus passage above). [This notion seems very important for understanding the way that statements correspond with reality. The same word ὑπάρχειν is applied both to mean that an object exists and also that a proposition is true, or in the wording of the above Stobaeus quote, it means the predicate holds for the subject.

In Aristotle’s theory ὑπάρχειν was a crucial feature of both the predicate and the proposition – a notion which is ambiguous between ‘exist’ of objects and ‘be true’ of propositions (Kneale/Kneale 1962: 151).196


196. “In Stoic terms the whole theory may be summed up thus: a statement or lekton hyparchei (is the case) if what it describes hyparchei (exists) and what is described is true if the statement describing it is true” (Long 1971: 93) ; cf. Long/Sedley (1987: 206): “A true proposition corresponds to the actual state of the item(s) in the world, to which it refers. Unmistakably correct evidence about existing things is conveyed to us through ‘cognitive impressions’, and a proposition which describes that evidence will be true. The Stoics expressed this correspondence theory of truth by using the same verb, (huparchei/ouch huparchei) ... to differentiate true and false propositions and existing and non-existing things.”


[It is probably significant that the Stoics only spoke of accidents (and of this correspondence theory of truth and reality) using intransitive sentences. (For, the issue of truth and reality is a matter of the concord between a real subject and its accidents, and the intransitive structure is a matter of a nominative subject and its predicated attributes.)]


Given the textual evidence provided above,

There would thus seem to be no reason to doubt the persistence of the Peripatetic notions of ὑπάρχειν (‘subsist’) and συμβεβηκότα (‘accidents’) in Stoicism. They are associated with the ability of the proposition to assert truth or falsity in terms of some state of affairs being the case, and the predicate belonging to the subject at the time the statement is made. 


Luhtala then notes that the Stoic sentences in these analyses are intransitive. As far as we can tell, the Stoics only discussed the notion of συμβεβηκότα (‘accidents’) when dealing with intransitive sentences (other types of sentences include transitive and impersonal). In intransitive sentences, “the two constituents pertain to the same referent and [...] show grammatical concord” (114). [This is an important point, but I do not grasp it. It will guess the following. Intransitive sentences seem to be ones of a simple subject predication structure where we are stating some attribute of some thing. (Were it transitive, we might instead be stating how one object is acting upon another, without mentioning the attributes of each.) Thus both the nominative/subject and the predicate pertain to the same referent, namely, the object in the world with those properties.) The grammatical concord might then be the grammatical agreement between subject and predicate, but I am just guessing. It must be something else.] Thus the fact that the Stoics only discussed accidents with intransitive sentences probably means that “these constructions [...] show concord of grammatical accidents” (114).






Luhtala, Anneli. 2000. On the Origin of Syntactical Description in Stoic Logic. Münster: Nodus.



Other texts, cited by Luhtala:


Diogenes Laertius: Lives of eminent philosophers. Translated by Robert D. Hicks. 2 vols. London: William Heinemann / Cambridge, Mass.: Harvard University Press 1950.

The Perseus Greek page for the Diogenes’ passages:



The Perseus English page for the Diogenes’ passages:




Duhot, Jean-Joel. 1989. La conception stoicienne de la causalité. Librairie philosophique. Paris: Vrin.


Goulet, Richard. 1978. “La classification stoïcienne des propositions simples selon Diogene Laërce VII 69-70”. Brunschwig (1978: 171-198).


Kneale, William C. / Kneale, Martha. 1962. The Development of Logic. Oxford: Clarendon Press.


Long, Anthony A. 1971. “Language and Thought in Stoicism”. Long (1971a: 75-113).


Long, Anthony A. 1971a. (ed.) Problems in Stoicism. London: The Athlone Press.


Long, Anthony A. / Sedley, David N. 1987. The Hellenistic philosophers. 2 vols. Cambridge: Cambridge University Press.


Pinborg, Jan. 1975. “Classical Antiquity: Greece”. Sebeok (1975: 69-126).


Sextus Empiricus: Adversus Mathematicos I-XI. Ed. with an English translation by Robert G. Bury. 4 vols. The Loeb Classical Library. London: Heinemann; Cambridge, Mass.: Harvard Univ. Press 1949.

Another version available online:


Online text transcription at:


[specifically here]

Sextus Empiricus. 1914. Sexti Empirici Opera. Vol. 2, Adversus Dogmaticos, libros quinque (Adv. Mathem. VII-XI) continens, edited by Hermannus Mutschmann. Lipsiae [Leipzig]: Teubneri [Teubner].


This entry redoes the one here, made a while ago:





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