The Stoic Theory of Sign and Proof

PSA

FABIAN RUGE

The Stoic Theory of Sign and Proof

PHILOSOPHICAL STUDIES IN ANCIENT THOUGHT

02

Philosophical Studies in Ancient Thought

Béatrice Lienemann, Christian Pfeiffer, Christof Rapp (eds.)

Volume 2

Fabian Ruge

The Stoic Theory of Sign and Proof

Schwabe Verlag

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Contents

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

List of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

0.1

Signs and Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

0.2

The State of Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

1 Sound Conditionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21

1.0

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21

1.1

Which Account of Truth Conditions is Relevant for Signs? . . . . . . . .

22

1.2

Connexion and Impossibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

28

1.3

Conceptual and Physical Conflict . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

1.4

Sign-Conditionals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45

2 Valid Arguments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

2.0

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

2.1

Validity and Connexion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

2.2

Schemata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

54

2.3

Valid Arguments and Proof

..................................

64

3 Evidence and Katalêpsis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

67

3.0

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

67

3.1

The Epistemic Status of the Sign and Signified . . . . . . . . . . . . . . . . . . . .

68

3.2

Evidence as Katalêpsis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

74

3.3

Evidence and Proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

83

6

Contents

3.4

Evidence for the Stoics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

90

........................

93

4.0

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

93

4.1

The Final Distinction among Arguments . . . . . . . . . . . . . . . . . . . . . . . .

95

4.2

The Dunamis of the Premises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

4.3

Establishing the Conclusion through the Dunamis of the Premises . . 125

4.4

Proof and Dialectic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

4 The Revelation Requirement for Proof

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 Appendix: Signs in Divination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 1

Editions of Ancient Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

2

Fragment Collections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

3

Secondary Literature

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

Index of Subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 Index of Passages

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

Acknowledgements

This study is a revised version of my doctoral dissertation which was accepted by Ludwig Maximilian University of Munich in the winter semester 2020/21 and which I defended in 2021. I wrote this dissertation with the support of Munich School of Ancient Philosophy for which I would like to thank the directors of that institution. I am particularly indebted to my supervisor and first reviewer Prof. Dr. Christof Rapp for his guidance and helpful comments. Furthermore, my second reviewer Prof. Dr. Marko Malink provided invaluable discussions of every chapter in this study. I am grateful for his help as well as for the opportunity to visit New York early in 2020. Thanks are due as well to Prof. Dr. Peter Adamson for probing questions at several of my presentations and for accepting the responsibility of being third reviewer, and to Prof. Dr. Oliver Primavesi for agreeing to participate in my examination and raising helpful points. Dr. Andreas Anagnostopoulos, Dr. Philipp Brüllmann and Dr. Laura Castelli provided helpful criticism and advice at various stages of my time in Munich. In addition, my fellow students and friends at the Munich School of Ancient Philosophy offered stimulating discussions and companionship. Audiences in Munich, Cambridge and Prague helped me formulate my ideas more clearly. Finally, the editors of the series ‘Philosophical Studies in Ancient Thought’ were kind enough to accept this study and offer additional comments that helped me to improve it further. This book is dedicated to my parents whose support has helped me through many challenges.

List of Abbreviations

Alex. in An. Pr. Alex. in Top. Arist. An. Po. Cic. Div. Cic. Fat. Cic. Fin. Cic. Luc. Cic. ND Cic. Tusc.

DL FDS Gal. Inst. log.

LS Phil. Sign.

SE PH SE M SVF

Alexander, Commentary on Aristotle’s Prior Analytics Alexander, Commentary on Aristotle’s Topics Aristotle, Posterior Analytics Cicero, De Divinatione Cicero, De Fato Cicero, De Finibus Bonorum et Malorum Cicero, Lucullus Cicero, De Natura Deorum Cicero, Tusculanae Disputationes Diogenes Laertius, Vitae philosophorum Hülser, Fragmente zur Dialektik der Stoiker Galen, Institutio logica Long/Sedley, The Hellenistic Philosophers Philodemus, De Signis Sextus Empiricus, Pyrrhoneiai Hypotyposeis Sextus Empiricus, Adversus Mathematicos von Arnim, Stoicorum Veterum Fragmenta

Introduction

0.1 Signs and Proofs The ancient Stoics developed a sophisticated epistemology that includes discussions of the way in which one may gain knowledge of propositions that cannot be justified through perception. To this end they developed a method for achieving such knowledge which is expressed in the Stoic notions of sign and proof. However, since no Stoic treatise on this subject has come down to us, any investigation into this topic must rely on reports of non-Stoic authors. In particular, the definitions of sign and proof as well as explanations of them are reported by the sceptical philosopher Sextus Empiricus: Sign: A sign is a proposition that is the leading antecedent in a sound conditional, revelatory of the consequent. (SE PH 2.104)1 Proof: Proof is then, as they say, an argument that through agreed upon premises reveals a non-evident conclusion according to a deduction.

(SE PH 2.135)2 The definition of sign is attributed to the Stoics in the same paragraph whereas that of proof can be attributed to the Stoics because the parallel report at SE M 8.411–423 is explicitly Stoic (cf. SE M 8.396, 425).

These two definitions are clearly united with respect to some features as both contain a notion of ‘revelation’ as well as some logical relation: that of a sound conditional for the sign and that of a deduction for proof. In fact, proofs are signs (e. g. SE M 8.277, PH 2.134), which presumably means that the conjunction of the premises of a proof fulfils the definition of the sign. But clearly these notions are not interchangeable as there would be no need for giving two definitions otherwise. The main difference is that signs are propositions whereas proofs are arguments. A sign is any proposition that stands in the specified relation to another proposition. But only a proof is also an item that is directly usable 1 σημεῖον εἶναι ἀξίωμα ἐν ὑγιεῖ συνημμένῳ προκαθηγούμενον, ἐκκαλυπτικὸν τοῦ λήγοντος.

All translations in this study are mine.

2 Ἔστιν οὖν, ὡς φασίν, ἡ ἀπόδειξις λόγος δι’ ὁμολογουμένων λημμάτων κατὰ συναγωγὴν ἐπιφορὰν ἐκκαλύπτων ἄδηλον.

12

Introduction

for inferences, and for generating knowledge. I am investigating both the relation between certain kinds of proposition as well as the use of that kind of relation in arguments.

With ‘proposition’ I translate ἀξίωμα, which is a type of sayable (λεκτόν).

The evidence concerning the theory of lekta is difficult and its interpretation contested,3 but it suffices for my purposes to point to SE M 8.10‒12, which makes it clear that lekta are incorporeal things that are signified by linguistic utterances.

These objects come with certain divisions: there are incomplete lekta, such as predicates, but also complete lekta which are signified by complete linguistic expressions (cf. DL 7.63). The ἀξίωμα is among these items the one that has a truth value (cf. DL 7.65, SE M 8.12). Thus, it bears some resemblance to the modern notion of a proposition since it is an incorporeal entity that is signified by an assertion and is a truth bearer. Because of the familiarity of the notion, I will speak of propositions.4 The reason why signs are propositions seems to be two-fold: on the one hand, a sign is supposed to be something that stands in inferential relations and the elements of such relations, for the Stoics, are propositions. On the other hand, signs and proofs are meant to produce knowledge and if, as seems likely, knowledge for the Stoics is always ‘knowledge that’, then signs must be propositional and stand in relations to other propositional items.

That signs are propositions indicates an important demarcation. Language of signification is also used by the Stoics for the relation between linguistic expressions and lekta. But linguistic expressions are corporeal and lekta are incorporeal (cf. SE M 8.11‒12). Yet both our signs and that which they signify are lekta and incorporeal. Therefore, this linguistic signification relation is a different kind of relation than the relation between signs and that which they signify. I am here concerned exclusively with the latter relation.

The aim of this investigation is to explicate the definitions of sign and proof quoted above. As already noted, signs and proofs have two features in common: a certain logical relation and some sort of epistemic relation that goes by the name ‘revelation’. As these are the main features of signs and proofs, two main questions arise: (i) what is the logical relation (a) between a sign and that which it signifies as well as (b) between the premises and the conclusion of a proof?

3 One question is whether lekta are mind-dependent or have an independent ontological status. The tendency in scholarship is towards a mind-independent status, an assessment with which I agree. Some recent literature on this subject: Frede (1994), Schubert (1994), Gourinat (2019), Bronowski (2019).

4 Stoic ἀξιώματα can change their truth value (e. g. DL 7.76) and not all of them subsist eternally (cf. Alex. in An. Pr. 177, 28‒178, 1). They differ in these respects from modern propositions. See further Bobzien (1999, pp. 95–96). The more literal translation ‘assertible’ is favoured by Bobzien (1999) and Barnes (2007).

0.1 Signs and Proofs

And (ii) what does it mean for one proposition – be it a simple proposition or the conjunction of the premises of a proof – to reveal another? A special difficulty in answering these questions is whether for the Stoics a sign reveals that which it signifies merely in virtue of the fact that the sign implies the signified where the sign is already known and the signified as yet unknown. Or is revelation itself a peculiar relation that cannot be reduced to implication? If so, what sort of relation could this be and what is its purpose?

This study focuses on the reconstruction of the definitions of sign and proof.

The definition of sign is introduced and explained at SE PH 2.104‒106 (= FDS 1030 = LS 35C) and SE M 8.245‒256 (= SVF 2.221 = FDS 1029 = LS 51H, part).

The definition of proof is introduced and explained at SE PH 2.134‒143 (= FDS 1038, 1058, 1064 = LS 36B), SE M 8.300‒314 (= FDS 1039, 1059, 1066) and SE M 8.411‒423 (= SVF 2.239 = FDS 1060, 1065). These are my main texts in this study. Aside from these texts, there are also arguments for the existence of signs and proofs in Sextus’ reports. Even though these are interesting, they do not contribute to my goal of finding out what signs and proofs are.

The two main questions for this investigation concern the logical relation and the epistemic relation at issue in the definitions of sign and proof. Chapters 1 and 2 deal with the logical relation and chapters 3 and 4 with the epistemic relation.

Chapter 1 discusses the notion of a sound conditional that is present in the definition of the sign. Chapter 2 treats the notion of a valid argument in the definition of proof. In chapter 1, I argue that, contrary to appearances, the relevant type of truth condition for sign-conditionals is the Stoic account of connexion.

The reports in Sextus appear to ascribe a different account, material implication, to the Stoic theory of signs. However, these texts should not be read as a commitment to material implication but only to the minimal condition that a true conditional must at least not have a true antecedent with a false consequent.

The Stoic account of connexion5 (συνάρτησις) states that a conditional ‘If P, then Q’ is true if and only if there is a conflict between P and not-Q. This account is supposed to exclude conditionals of the form ‘If not-P, then P’ which might be true when not-P is impossible. But the notion of impossibility that is expressed by ‘conflict’ is not the impossibility of a conjunction ‘P and not-Q’, but rather a relative impossibility. If ‘If P, then Q’ is true, then not-Q is impossible with respect to P. And that is why no conditional of the form ‘If not-P, then P’ can be true because not-P, the contradictory of the consequent, is not impossible with respect to itself.

This relative impossibility can be due to the subpropositional components of a conditional on their own or because those components are associated with I choose the translation ‘connexion’ to distinguish this notion from any other connections that I will mention.

5

13

14

Introduction

objects that stand in causal relations of the appropriate kind. The test for the truth of a conditional ‘If P, then Q’ consists in asserting not-Q and checking if one can still truly assert P. This test can and does apply to conditionals that express empirically accessible relations as long as these are causal relations. The test itself is a purely mental operation, but the justification of a conditional, which is this test, must be distinguished from the means by which one can formulate it.

Chapter 2 deals with the notion of a valid argument in the definition of proof. An argument is valid if and only if the conditional ‘If [conjunction of premises], then [conclusion]’ is true. I show the relevance of the Stoic criterion for the truth of a conditional from the previous chapter to the validity of arguments.

In addition, there is a special type of valid argument for which schemata are also relevant. This aspect has an impact on the structure of proofs, all of which have to be valid and some of which are valid in virtue of their logical form. Even though not every valid argument is so in virtue of its form, formal validity is covered by the Stoics’ syllogistic theory with which one can determine the validity of an argument irrespective of its content. That is desirable for a theory and facilitates the use of arguments in discussions so that it is better when a proof is also a formally valid argument. The Stoics also think that their syllogistic theory is applicable to every argument because there is a formally valid argument that corresponds to every non-formally valid argument and establishes the same conclusion from the same simple premises. The difference lies in the complex major premises which connect the simple premises to the conclusion in a syllogism and can be supplied in a non-syllogistically valid argument. That such a complex premise can be supplied for every valid argument is relevant to the revelation requirement for proofs since that involves the justifications for such premises.

The answer to the first main question is that the logical relation between a sign and that which it signifies is characterised by relative necessity in virtue of a causal connection. This applies to all signs, but proofs are both signs and valid arguments. As such, it is preferable if they are formally valid. The modal requirement for signs in general is necessary to ensure one of the requirements for transmitting evidence or katalêpsis to the signified, as becomes clear in chapter 3.

Chapter 3 is about evidence, the epistemic state that is at issue, and chapter 4 is about the revelation requirement in the definition of proof. Together, these chapters provide a discussion of the epistemic requirements for both signs and proofs.

In chapter 3, I show that the Stoic definition of proof as given by Sextus does not preclude chains of proofs. Sextus’ reports on evident and non-evident propositions specify that a proposition is evident if it can be grasped without an inference. If all proofs needed to have premises that are evident in that sense, the conclusion of one proof could not be a premise in another. But the Stoics do use chains of proof. Hence, the premises of proofs need to be evident in a different

0.1 Signs and Proofs

sense. Neither the reports on evident propositions nor on the revelation requirement in signs specify that signs or the premises of a proof must be evident in the sense of ‘non-inferentially graspable’. They only demand that that which is signified or the conclusion of a proof must be non-evident in the sense of ‘only graspable through an inference’.

There is another sense of ‘evident’ which amounts to ‘grasped’: a proposition is evident if it is the content of katalêpsis. Since revelation results in katalêpsis, signs and proofs do make their consequents or conclusions evident in this sense. Unfortunately, katalêpsis is undefinable, but I identify a necessary condition for it, which I call infallibility. It must not be possible to assent to a proposition with some means of justification while it is false. Such a means would be a proof.

This sense of ‘evident’ is the sense in which the premises of a proof must be evident. And this would then apply to atomic signs as well. For the premises of a proof are agreed upon, but further passages in Sextus show that agreement is connected to evidence. But it is connected to the sense of ‘evident’ that amounts to ‘grasped’. This must mean that, when a proposition is grasped by someone through some means of justification, then that proposition should be agreed upon by everyone who has access to that justification.

Finally, if the premises of a proof must be grasped by someone, then proofs are always only proofs to the person who grasps the premises. This follows from my explanation of how the definition of proof allows for chains of proofs. I introduce a distinction between a relative and an absolute sense of ‘proof’ where elements of both senses are present in the definition of proof. Both senses must be assumed to maintain different plausible intuitions that are present in the Stoic fragments.

Chapter 4, then, deals with the preservation of evidence through revelation.

The discussion of revelation in the context of the definition of sign does not explain how the transmission of evidence works. Hence, the focus in chapter 4 shall be on the discussion of the definition of proof.

I focus on the final distinction in the dichotomies that explain the definition of proof. This distinction is among valid arguments with evident premises and a non-evident conclusion. On the one side are revelatory arguments and on the other merely progressive arguments. But the PH 2 report on proof does not seem to treat revelation as an additional requirement for proofs but rather as a feature of some proofs. I argue that it must be assumed throughout that the revelation requirement is a requirement for proof.

In this distinction, Sextus provides one example for each type of argument.

The difference between the examples is supposed to be that the revelatory argument establishes its conclusion through the dunamis of the premises whereas the merely progressive argument establishes its conclusion through trust. Merely progressive arguments in general depend on trust or memory. The point of the

15

16

Introduction

distinction is the relation between the conjunction of the premises of an argument and its conclusion. In revelatory arguments, this is the relation between a sign and its signified, in merely progressive arguments it is not. But that means merely progressive arguments do not preserve katalêpsis even though they could fulfil the infallibility requirement from chapter 3.

The phrase that is used to explain revelation is ‘establish the conclusion through the dunamis of the premises’. The dunamis of a proposition is associated with its truth condition. This notion is spelt out into an outline of an account of truthmaking. The key is the connection between the Stoic account of causation, which is a three-place relation between two bodies that interact and a predicate that obtains because of the interaction, and the theory of lekta. A connection between the theory of causation and reports on the truth conditions for a type of proposition suggests that a body in so far it is acted upon by other bodies to exhibit a certain predicate can be considered the truthmaker of a proposition.

And this would be meant by the dunamis of the proposition in the case of true propositions.

Next, I explain what it means to establish the conclusion through the dunamis of the premises. In general, the antecedent in a conditional is revelatory if (the antecedent being evident and the consequent non-evident) the justification for the conditional is specific to the relation between the relevant truthmakers.

Sextus gives an example of a proof that consists of a conditional and its antecedent as premises and the consequent as the conclusion. That conditional premise is ‘If sweat flows through the skin, there are intelligible pores’. This is true because of the causal interaction of the types of truthmakers for the antecedent and consequent. And the justification of that conditional specifies that causal interaction, namely that the occurrence of pores is among the causes for the occurrence of sweat. In contrast, the major premise of Sextus’ example of a merely progressive argument is ‘If some god told you that this man will be rich, this man will be rich’. Even though this is also true because of a causal relation between the relevant truthmakers, this proposition is sufficiently justified with a principle that invokes the general reliability of the gods. That is, the relation between the truthmakers is not essential to the justification of this proposition.

The explanation for the revelation requirement that Sextus gives seems to pose demands on the justification of the conditional premise. And that is sufficient in these examples to ensure that the relation between all the premises and the conclusion is revelatory. In a proof, the revelation requirement effectively demands that the justification for all the complex premises – they may be present in the argument or can be supplied if they are not present – must be specific to the relevant truthmakers because this will specify the relation between the truthmakers of the premises and the conclusion. The relation is causal. Merely progressive arguments do not preserve katalêpsis because they violate the underlying requirement that the means of justification for a proposition must be accessible

0.2 The State of Research

to the person who assents to it for the assent to be warranted: an argument that depends on trust in the gods has to presuppose that the gods could adequately justify the respective conclusion. Truthmaker-specific principles fulfil this requirement because they contain a specification that is relevant to the conclusion and enable the user of the argument to trace back the causal link between the truthmakers in the argument to the ultimate justification of immediate perception.

I conclude chapter 4 by pointing out that proof is the only correct standard for persuasion for the Stoics, which leads to some implausible consequences in everyday argumentative practice due to the revelation requirement.

The answers to my main questions are as follows: a sign must stand in a necessary relation to that which it signifies. The modal relation ensures that the signified can be assented to infallibly, which is necessary for katalêpsis. But the preservation of katalêpsis has the further requirement that the justification for the connection between the sign and the signified be specific to that which makes those propositions true.

After the main investigation is finished, I address open questions about divination and divinatory signs in an appendix.

0.2 The State of Research My five central reports (SE PH 2.104‒106, SE M 8.245‒256, SE PH 2.134‒143, SE M 8.300‒314, SE M 8.411‒423) have given rise to two different types of question in previous scholarship. One can compare these texts and wonder if they represent a historical development, or one can attempt to explicate the contents of the definitions. This study only addresses the second kind of question at length because I am primarily interested in the philosophical content of the theory of sign and proof.

There is, however, a certain tendency in scholarship, especially after Jacques Brunschwig’s influential paper ‘Proof Defined’, to compare these reports for their differences, explain the differences through different stages in the development of Stoic logic, and then to try to ascribe those stages to different groups or authors.

The main representatives of this type of project are Brunschwig (1980), Ebert (1991) and Allen (2001).6 But it seems rather implausible to approach these texts in this way. For, first, this would mean that Sextus, writing in the second century AD, compared different Stoic (or pre-Stoic) texts that were then between 300 6 Ebert gives the most thorough treatment in this area. His aim is to show that many of the logical reports in Sextus Empiricus are actually pre-Stoic and originated with the so-called Dialectical school, e. g. Philo and Diodorus. He further tries to show that the Stoic logical reports in Sextus are early Stoic and heavily influenced by the earlier Dialectical doctrines. In most cases, this project will not be relevant.

17

18

Introduction

and 500 years old and chose to insert bits of those different theories into his treatment. This insertion of random bits of different doctrines would be entirely unmotivated and without any payoff as his critique stays the same in all the texts.

Second, it would also mean that Sextus Empiricus is an absolutely faithful reporter. For only then could one infer from differences in his text to differences in the original sources. This would in turn presuppose that Sextus cares enough about the reports to reproduce them exactly. However, his project is to construct arguments for and against philosophical theses, not to write a history of philosophy. The reports need not be faithful to every detail to achieve that goal.

Finally, there is good reason to assume that differences in Sextus’ reports, especially between texts from PH 2 and M 8, are due to his treatment of his sources: Janáček (1950, pp. 159–161) found, when he compared the books PH 2‒3 with M 7‒11 which cover the same topics (logic, then physics, then ethics), that the quotations of the dogmatists are changed, according to a uniform style, between those two bodies of texts. The fact that essentially the same quotation can occur in several places with different formulations means that Sextus does not hesitate to change a quotation. Hence, everything he reports is suspect of having been tampered with by him. For if his quotations change according to their location in his works, he does not respect his opponents’ intellectual property enough to quote them properly at all.7 In principle, of course, any reconstruction from Sextus’ reports is thus in danger of being distorted. But, on the other hand, all those different reports do exhibit substantial similarities on which I can rely to reconstruct something that resembles the Stoic theory of sign and proof as closely as possible.

The interest of previous scholarship with regard to the philosophical content of the theory has focused on the question whether the Stoics favour rationalist modes of reasoning or also include empiricist modes of reasoning in their theory. This amounts to the question whether the Stoics only recognise signs that stand in conceptual relations to that which they signify or also observable relations.

First of all, there have been several contributions in recent scholarship dedicated specifically to the question whether there are true Stoic conditionals that express empirical relations. The starting point for the recent debate is found in Frede (1974a) who argues that no empirical relation can be expressed in a true conditional. His argument concerns the Stoic demand that divinatory predictions not be phrased as conditionals but as the negations of conjunctions. Frede maintains that negations of conjunctions, being truth-functional, are only adequate for the expression of relations that are observed to hold between two events and which lack any stronger conceptual link. Thus, the stronger Stoic conditional is supposed to be reserved for these conceptual relations. He is followed in this by 7

This paragraph is inspired by Barnes (1993), a review of Ebert (1991).

0.2 The State of Research

Sedley (1982) who, though he deals with sign-conditionals, makes an argument about Stoic conditionals in general. Sedley approaches this topic from the contrast between Epicurean and Stoic views on signs and conditionals and adduces evidence from a work by Philodemus to show that the Stoics countenanced only true conditionals that express analytic truths.8 I critically engage with these arguments in section 1.3.1. Frede’s view is opposed by Sorabji (1980) and Castagnoli (2004); (2009). Sorabji tends towards the possibility of true Stoic conditionals that express empirical regularities, while Castagnoli is firmly committed to the claim that the Stoics countenance such conditionals. Bobzien (1999) ascribes the view that true Stoic conditionals can express empirical relations at least to some Stoics. I agree with these latter authors and argue for such a view in section 1.3.2.9 The discussion of conditionals and sign-conditionals has been somewhat complicated by the apparent endorsement of the material conditional in the Stoic definition of the sign, which I question in section 1.1.2. But there is a line of contributions which presupposes Frede’s view of Stoic conditionals and explains the endorsement of the material conditional for signs in such a way that there are two types of sign-conditional. This kind of interpretation is found in Brunschwig (1980), Ebert (1991) and Allen (2001) as well as in Burnyeat (1982).10 One type expresses conceptual relations and the other one empirical relations. The definition given at PH 2.104 is then supposed to employ the material conditional because that is the more general and weaker account that can be refined into the stronger Stoic account for some sign-conditionals, which is explicit in Burnyeat’s and Allen’s treatments. Regarding the question of empiricism and rationalism, their view is thus that the Stoics accepted both empiricist and rationalist modes of reasoning as expressible through sign-relations, but that these correspond to two different types of sign-relation. Chapter 1 presents my alternative reading of the definition of the sign according to which that definition presupposes the stronger Stoic account throughout, and that account accommodates empirical relations.

This line of interpretation, which stems from Brunschwig, also has an impact on the definition of proof. Specifically, it appears in Brunschwig’s diagnosis of the dichotomy, within the reports on proof in Sextus Empiricus, between arguments that are revelatory, and hence proofs, and those that are merely progressive. On this interpretation, this difference is due to the kind of sign and sign8 Gourinat (2000) and Allen (2001) also restrict Stoic conditionals to conceptual relations.

LaBarge (2002) and Schallenberg (2008) suggest that the Stoics do accept conditionals that express empirical relations under the label ‘conceptual necessity’.

9 Discussions of whether conditionals should be understood in rationalist or empiricist terms can also be found in: Brochard (1892), Hamelin (1908), Bréhier (1908), Gould (1967), Verbeke (1978).

10 See also Gourinat (2000) and Tuominen (2007).

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