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De Mortuis Nil Dicendum Est? On Sextus Empiricus Against the Mathematicians VIII.98 and Stoic Indefinite Propositions

Marion Durand

University of Toronto

What little evidence remains about so-called indefinite propositions in Stoic semantics appears to be contradictory. The Stoics distinguished between three main kinds of affirmative propositions (axiōmata): definite, indefinite and middle (SE M VIII.96-7; DL VII.70). These are distinguished on the basis of their subjects: the subject of a definite proposition is a demonstrative pronoun (paradigmatically οὗτος, “this one”), that of an indefinite proposition is an indefinite pronoun (τις, “someone”) and that of a middle proposition is a proper or common noun (“Socrates”, “man”). In one of the main pieces of evidence on indefinite propositions, Sextus Empiricus reports that an indefinite proposition such as “someone is walking” is true whenever the definite proposition “this one is walking” is found to be true (M VIII.98). This passage has traditionally been understood (e.g. by Crivelli 1994, Bobzien 1999) as giving truth-conditions: “someone is walking” is true whenever there is a true instance of a corresponding true proposition “this one is walking” (that is, when it is true for a given indicated person).

This interpretation of SE M VIII.98 is problematic. As some have noted (e.g. Bobzien 1999, Crivelli 1994), Chrysippus is said to have believed that, while “Dion has died” is true after Dion’s death, the proposition “this one has died” can never be true (Alex. Aphr. An. Pr. 177.25-178.1). Together with the prevailing interpretation of SE M VII.98, this commits the Stoic to the somewhat odd view that “someone has died” can never be true. A yet more serious problem has gone unnoticed in scholarship. As Lloyd 1978 and Brunschwig 1984 show in their account of proper nouns, the Stoics seem to hold that middle propositions imply indefinite propositions: according to the Stoics, “Socrates has died” in fact means “there is something which is Socrates and has died” (Alex. Aphr. An. Pr. 402.12-19). If this is right, then it cannot be the case that “someone has died” is never true, since, for example, “Dion has died” can be true and that implies “someone has died”.

I offer a new reading of SE M VIII.98 which, I suggest, makes sense of this apparently inconsistent set of claims. It differs from the traditional interpretation on two counts. Firstly, I argue that we should remove the requirement for the definite proposition to be a corresponding one. This restriction has been applied by scholars on the basis of the examples provided by Sextus. I suggest that these were added as glosses, and not part of the original theory. Secondly and more significantly, I argue that Sextus is reporting a claim not about the truth-conditions of indefinite propositions but rather about our epistemic access to their truth-value. When he says that an indefinite proposition is true whenever the definite is found to be true, he does not mean that if the definite is never found to be true, the indefinite is false. Rather, he is saying that, without the definite proposition, we cannot know whether the indefinite is true or false. On this interpretation, which permits the alethic independence of the indefinite and the definite, the relationship between the two types of proposition is primarily epistemological.

This account of indefinite propositions is in line with other uses of aoriston and its cognates in philosophical and grammatical contexts (Ap. Dysc. S II.17, 32;  SE MXI.8-14,  PH 198.1-3; cf. Baldarassi 1984:104-5). In addition, this interpretation makes sense of the semantic features of indefinite subjects, which are characterised by a semantic indeterminacy prone to lead to epistemic deficiency. It is also in line with Stoic epistemological commitments (identified, e.g., by Frede 1999:297-8 and Kahn 1969:160) which place a premium on empirical observations. That an empirical observation in the form of a definite proposition would be necessary to guarantee knowledge of the truth of a proposition makes sense given Stoic doctrines. My interpretation thus allows the evidence to be consistent and avoids committing the Stoics to odd views about the dead.

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