BMCR 2023.04.43

The Stoic theory of sign and proof

, The Stoic theory of sign and proof. Philosophical studies in ancient thoughts, 2. Basel; Berlin: Schwabe Verlag, 2022. Pp. 166. ISBN 9783796545559.

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This dense and concise book, a reworking of the author’s doctoral dissertation, focuses on Sextus Empiricus’ report of the Stoic definitions of sign (σημεῖον, PH 2.104, M 8.245) and of proof (ἀπόδειξις, PH 2.135, M 8.314, 422-3) in order to understand these twin notions and to answer to two questions in Stoic dialectics: What is the “logical relation” and the “epistemic relation” between the kind of proposition that is a sign and the proposition, referred to as what is “signified”, which stands as its consequent in a sound conditional? And what are the logical and epistemic relations existing between the premises and the conclusion of a proof, which is a kind of valid argument? In other words: (1) What are the truth conditions of a “sign-conditional”, i.e., a sound conditional containing a sign, and of the type of valid argument constituting a proof? Moreover, (2a) how are the signs and the premises of a proof known, and (2b) how does one pass from knowing a sign to knowing its signified, and from knowing the premises of a proof to knowing its conclusion? The questions are indeed two and not four from Ruge’s perspective, because of “the relevance of the Stoic criterion for the truth of a conditional […] to the validity of arguments” (p. 14) and because of the author’s success in providing a single “discussion of the epistemic requirements for both signs and proofs” (ibid.).

Ruge’s answers to these questions, are: (1) The logical relation of a sign to its signified is the necessary connection between them, and so is the relation between the premises of a proof and its conclusion. (2) The epistemic relation between these elements is a revelatory one, meaning that signs and the premises of a proof must themselves be somehow evident and make evident, respectively, their signified and their conclusion.

The structure of the book reflects its dual goal: the four chapters making it up form two couples, as the first two deal with the logical question and the remaining two with the epistemic ones. The chapters are preceded by an introduction, in which the content, the claims, and the structure of the work is presented, followed by a well-organised review of the current state of research. The book closes on a brief recapitulation of the results of the author’s inquiry and an appendix containing a digression on a particular kind of sign, namely the divinatory.

Chapter 1 is devoted to the truth-conditions of sign-conditionals. By analysing the different accounts of conditionals found in the broader contexts of SE, PH 2.104 and M 8.245 in the light of the doxography of Diogenes Laertius, Ruge recognizes one of these accounts as Stoic (§ 1.1). He then interprets its truth-conditions in terms of relative modality: a conditional is sound if and only if it is necessary that, its antecedent being true, so is its consequent; or, to put it otherwise, the negation of the consequent is impossible “with respect to” the antecedent (§ 1.2). The author goes on to defend the challenging claim that this “conflict” can be not only logical or conceptual, but can also derive from the empirical relation between the realities described by the two propositions. He finally proceeds to look for sign-conditionals among the examples of sound conditionals reported by Sextus, and he detects them in cases in which the two propositions express a “causal connection”, such as that concerning the “interaction between the physical objects described by them” (§ 1.3).

In the following chapter Ruge turns to the truth-conditions of proofs. Now, proofs are valid arguments and, according to SE, PH 2.137, valid arguments depend on the soundness of the conditional whose antecedent is the conjunction of the premises of the argument and whose consequent is the conclusion of the argument. The author thus advocates the hypothesis that the connexion criterion may work for proofs, too (§ 2.1). SE, M 8.413 suggests that arguments can be valid in virtue of their logical form or schema (σχήμα): in this case, the structure of the argument is such that, whatever propositions stand in as its components, the connexion criterion is always satisfied. Ruge argues that, however, not all valid arguments are formally so, meaning that some arguments, though valid, do not correspond to a sound schema: he explains this with reference to the Stoic distinction between syllogisms and non-syllogistically valid arguments and concludes that, ideally, the latter ought to be transformed in the former, in order to grant them a sound schema, viz. a formal validity (§ 2.2).

The third chapter starts tackling the epistemic issues by addressing the concept of evidence attached to signs and proofs: the author explains it as a polysemic term, referring to both things grasped by themselves and inferred knowledge, the latter meaning being applicable to signs and proof-premises. On the other hand, signified and proof-conclusions must be non-evident in the sense that they require their sign and the relevant proof-premises (respectively) to become the object of evident knowledge (κατάληψις) (§ 3.1). Ruge, by challenging the Stoic definition of κατάληψις reported by Sextus, which rules out an inferential meaning of evidence, reaches a broader concept of evidence as the infallible knowledge, however acquired, that a proposition is true (§ 3.2). The author can now show how this concept applies to signs and proofs: signs and proof-premises can be self-evident or (if grasped through a proof) inferentially evident, while signified and proof-conclusions must become evident by means of inference starting, respectively, from their sign and the relevant premises (§ 3.3).

The topic of the last chapter is the “revelation requirement” as to the peculiarity of proofs: Ruge understands it as the premises of a proof being a sign of their conclusion, i.e. making it evident (§ 4.1). The author explains along these lines Sextus’ description of revelation in terms of power (δύναμις) of proof premises: this concept, Ruge argues, seems to denote the truthmakers of these propositions, i.e., the bodies whose causal relations make them true (§ 4.2). In this conceptual frame, what singles out proofs among arguments is their specific “approach” (ἐφοδος): namely, proofs only enjoy one or more justifications of their components, that is, one or more propositions specifying the causal relations between the types of truthmakers relevant for the premises and their conclusion. These justifications, Ruge continues, can plausibly either rely directly on perception or be inferential, but the preservation of κατάληψις throughout proofs demands (he claims, with reference to his causal exegesis) the possibility of reducing inferential justifications to non-inferential ones (§ 4.3). This characteristic of proofs explains their persuasive power (SE, M 8.302), but most importantly their role – of rather impractical application – as “epistemic standard” (DL 7.45) (§ 4.4).

After a short conclusion summarizing the outcome of the author’s research, the book ends with an appendix concerning the status of “divinatory signs” (whose main source is Cicero’s De Divinatione). By these he means forecasts about future events in the form of negations of conjunctions (e.g. “Not: ‘Event A* has happened’ and ‘Event B* will not happen’”). Though they differ from signs in logical form, Ruge maintains that they are signs nonetheless: due to their determinism, the Stoics recognize causal links, sometimes hidden, between types of events, primarily because they co-occur regularly. This allows them to interpret certain events and the propositions stating them as signs – though of a peculiar nature, whence the label “common sign” – respectively of other events and of the propositions describing them.

The book ends with a well-selected bibliography, an index of subjects, and an index of the passages quoted from ancient sources.

As I hope to have shown, this is an extremely interesting reading, from which one has much to learn in content and in scientific methodology. On the one side, Ruge manages to explain in quite a convincing manner two essential and complex notions of Stoic dialectics, in both their more strictly logical and their epistemological aspects, and to solve the most fundamental issues that arise in these domains. Ultimately, his way of advancing throughout the inquiry is clear and to the point, thanks to a rigorous use of a vocabulary which is either taken from the sources or (when needed for exegetical reasons) introduced from contemporary logic and is always precisely defined. This merit of the author goes together with his careful conceptual and linguistic analysis of the relevant ancient sources, as well as with his frequent in-depth dialogue with an extensive selection of up-to-date secondary literature. The latter move proves Ruge’s conscious location of his work within the existing scholarship.

My few critical comments concern, first, a systematic stylistic tendency of the author. As I wrote at the beginning of this review, this is a dense and concise book. If these are strengths analysis-wise, making the research never lose its focus on its object and compressing the writing to what is essential, they may obviously pose a challenge to the reader. Ultimately, all the steps of the investigation become clear but, to borrow the author’s vocabulary, sometimes rather as inferentially evident statements, the inference in question being the reader’s pondering on what a certain sentence means and why things could not be put more simply. With this latter remark I have in mind especially the second and third paragraphs of Chapter 4, in which the density of the (very fruitful) discussion would have benefitted, in my opinion, from a conceptually more diffuse exposition.

It may be, then that my few criticisms of the content result from a failure to grasp the author’s points on a couple of topics. The Stoic notion of cause plays a major role in the first and in the last chapters of the book, since Ruge understands the connexion criterion and the peculiar approach of proofs with reference to physical bodies to have mutual causal relations. In the last case (pp. 121-2), the author appears to struggle to defend the extension of his interpretation to all the relevant cases, in particular to proofs concerning incorporeals, for which he lists a series of demonstrations too hastily sketched and too loosely based on ancient sources. This issue has, in turn, an obvious backlash on the alleged exhaustivity of the explanation of connexion in terms of cause, since, just like proofs, sign-conditionals can concern incorporeals, too. I think a side problem emerges in the appendix, in which the author’s case for categorizing divinatory signs among proper signs is not entirely convincing. But this is forgivable, as this section is only a digression on an intriguing topic to which Ruge will surely want to devote a lengthier treatment elsewhere. For this future occasion he may want to consider a remarkable essay on this subject: J.-B. Gourinat, ‘Les signes du futur dans le stoïcisme : problèmes logiques et philosophiques’, in S. Georgoudi, R. Koch Piettre, F. Schmidt (eds), La Raison des signes. Présages, rites, destin dans les sociétés de la Méditerranée ancienne. Leiden-Boston, Brill, 2012, pp. 557-75.

All in all, this book, ideal for specialists in ancient logic and in Stoicism because of its conceptual depth, marks a significant step forward in our understanding of the logical and epistemological bases of the Stoic theory of knowledge and has the right features to become a landmark in the scholarship.