Adversus Mathematicos x is the second book dedicated by Sextus to the discussion of the physical doctrines put forward by dogmatic philosophers. An extensive section deals with Diodorus Cronus' arguments concerning movement.
Adversus Mathematicos x is the second book dedicated by Sextus to the discussion of the physical doctrines put forward by dogmatic philosophers. An extensive section deals with Diodorus Cronus' arguments concerning movement.
ABSTRACT: Part 1 discusses the Stoic notion of propositions (assertibles, axiomata): their definition; their truth-criteria; the relation between sentence and proposition; propositions that perish; propositions that change their truth-value; the temporal dependency of propositions; the temporal dependency of the Stoic notion of truth; pseudo-dates in propositions. Part 2 discusses Stoic modal logic: the Stoic definitions of their modal notions (possibility, impossibility, necessity, non-necessity); the logical relations between the modalities; modalities as properties (...) of propositions; contingent propositions; the relation between the Stoic modal notions and those of Diodorus Cronus and Philo of Megara; the role of ‘external hindrances’ for the modalities; the temporal dependency of the modalities; propositions that change their modalities; the principle that something possible can follow from something impossible; the interpretations of the Stoic modal system by B. Mates, M. Kneale, M. Frede, J. Vuillemin and M. Mignucci are evaluated. -/- For a much shorter English version of Part 1 of the book see my ‘Stoic Logic’, in K. Algra et al. (eds), The Cambridge History of Hellenistic Philosophy, Cambridge 1999, 92-157. For a shorter, updated, English version of Part 2 of the book see my 'Chrysippus' Modal Logic and its Relation to Philo and Diodorus', in K. Doering / Th. Ebert (eds) Dialektiker und Stoiker (Stuttgart 1993) 63-84. (shrink)
ABSTRACT: An introduction to Stoic logic. Stoic logic can in many respects be regarded as a fore-runner of modern propositional logic. I discuss: 1. the Stoic notion of sayables or meanings (lekta); the Stoic assertibles (axiomata) and their similarities and differences to modern propositions; the time-dependency of their truth; 2.-3. assertibles with demonstratives and quantified assertibles and their truth-conditions; truth-functionality of negations and conjunctions; non-truth-functionality of disjunctions and conditionals; language regimentation and ‘bracketing’ devices; Stoic (...) basic principles of propositional logic; 4. Stoic modal logic; 5. Stoic theory of arguments: two premisses requirement; validity and soundness; 6. Stoic syllogistic or theory of formally valid arguments: a reconstruction of the Stoic deductive system, which consisted of accounts of five types of indemonstrable syllogisms, which function as nullary argumental rules that identify indemonstrables or axioms of the system, and four deductive rules (themata) by which certain complex arguments can be reduced to indemonstrables and thus shown to be formally valid themselves; 7. arguments that were considered as non-syllogistically valid (subsyllogistic and unmethodically concluding arguments). Their validity was explained by recourse to formally valid arguments. (shrink)
ABSTRACT: A detailed presentation of Stoic logic, part one, including their theories of propositions (or assertibles, Greek: axiomata), demonstratives, temporal truth, simple propositions, non-simple propositions(conjunction, disjunction, conditional), quantified propositions, logical truths, modal logic, and general theory of arguments (including definition, validity, soundness, classification of invalid arguments).
ABSTRACT: The 3rd BCE Stoic logician "Chrysippus says that the number of conjunctions constructible from ten propositions exceeds one million. Hipparchus refuted this, demonstrating that the affirmative encompasses 103,049 conjunctions and the negative 310,952." After laying dormant for over 2000 years, the numbers in this Plutarch passage were recently identified as the 10th (and a derivative of the 11th) Schröder number, and F. Acerbi showed how the 2nd BCE astronomer Hipparchus could have calculated them. What remained unexplained is (...) why Hipparchus’ logic differed from Stoic logic, and consequently, whether Hipparchus actually refuted Chrysippus. This paper closes these explanatory gaps. (1) I reconstruct Hipparchus’ notions of conjunction and negation, and show how they differ from Stoic logic. (2) Based on evidence from Stoic logic, I reconstruct Chrysippus’ calculations, thereby (a) showing that Chrysippus’ claim of over a million conjunctions was correct; and (b) shedding new light on Stoic logic and – possibly – on 3rd century BCE combinatorics. (3) Using evidence about the developments in logic from the 3rd to the 2nd centuries, including the amalgamation of Peripatetic and Stoic theories, I explain why Hipparchus, in his calculations, used the logical notions he did, and why he may have thought they were Stoic. OPEN ACCESS LINK. (shrink)
Propositions are generally thought to have a truth-value only relative to some parameter or sequence of parameters. Many apparently straightforward notions, like what it is to disagree or retain a belief, become harder to explain once propositional truth is thus relativized. An account of disagreement within a framework involving such ‘stoic’ propositions is here presented. Some resources developed in that account are then used to respond to the eternalist charge that temporalist propositions can't function as belief (...) contents because they don't allow us to make adequate sense of what belief retention amounts to. (shrink)
ABSTRACT: The modal systems of the Stoic logician Chrysippus and the two Hellenistic logicians Philo and Diodorus Cronus have survived in a fragmentary state in several sources. From these it is clear that Chrysippus was acquainted with Philo’s and Diodorus’ modal notions, and also that he developed his own in contrast of Diodorus’ and in some way incorporated Philo’s. The goal of this paper is to reconstruct the three modal systems, including their modal definitions and modal theorems, and to (...) make clear the exact relations between them; moreover, to elucidate the philosophical reasons that may have led Chrysippus to modify his predessors’ modal concept in the way he did. It becomes apparent that Chrysippus skillfully combined Philo’s and Diodorus’ modal notions, with making only a minimal change to Diodorus’ concept of possibility; and that he thus obtained a modal system of modalities (logical and physical) which fit perfectly fit into Stoic philosophy. (shrink)
One of the most intriguing claims of Stoic logic is Chrysippus's denial of the modal principle that the impossible does not follow from the possible. Chrysippus's argument against this principle involves the idea that some propositions are ?destroyed? or ?perish?. According to the standard interpretation of Chrysippus's argument, propositions cease to exist when they are destroyed. Ide has presented an alternative interpretation according to which destroyed propositions persist after destruction and are false. I argue that Ide's (...) alternative interpretation as well as some versions of the standard interpretation conflict with Stoic doctrines about the nature of propositions. I propose another version of the standard interpretation based on Frede's account of the Stoic theory of the proposition. I hold that this version of the standard interpretation both escapes Ide's objections and is consistent with Stoic logic and philosophy of language. (shrink)
The Stoic philosopher Chrysippus wrote extensively on the liar paradox, but unfortunately the extant testimony on his response to the paradox is meager and mainly hostile. Modern scholars, beginning with Alexander Rüstow in the first decade of the twentieth century, have attempted to reconstruct Chrysippus? solution. Rüstow argued that Chrysippus advanced a cassationist solution, that is, one in which sentences such as ?I am speaking falsely? do not express propositions. Two more recent scholars, Walter Cavini and Mario Mignucci, (...) have rejected Rüstow's thesis that Chrysippus used a cassationist approach. Each has proposed his own thesis about Chrysippus? solution. I argue that Rüstow's view is fundamentally correct, and that the cassationist thesis gains greater plausibility when viewed in light of a passage in Sextus Empiricus? Adversus mathematicos that the previous commentators have ignored, and when understood within the broader context of Stoic logical theory and philosophy of language. I close with a brief remark on the significance of Chrysippus? work for the modern debate on the semantic paradoxes. (shrink)
An examination of a particular passage in Cicero's De fato?Fat. 13?17?is crucial to our understanding of the Stoic theory of the truth-conditions of conditional propositions, for it has been uniquely important in the debate concerning the kind of connection the antecedent and consequent of a Stoic conditional should have to one another. Frede has argued that the passage proves that the connection is one of logical necessity, while Sorabji has argued that positive Stoic attitudes toward empirical (...) inferences elsewhere suggest that that cannot be the right interpretation of the passage. I argue that both parties to the debate have missed a position somewhere between them which both renders a connection between antecedent and consequent that is not merely empirical and makes sense of the actual uses to which the Stoics put the conditional. This will be an account which grounds the connection between antecedent and consequent in a prolêpsis, a special kind of concept which plays a special epistemological role for the Stoics, especially in grounding scientific explanations. My contention will be that Stoic conditionals are true when there is a conceptually necessary connection between antecedent and consequent such that the former explains the latter via a prolêpsis. (shrink)
ABSTRACT: This paper discusses the Stoic treatment of fallacies that are based on lexical ambiguities. It provides a detailed analysis of the relevant passages, lays bare textual and interpretative difficulties, explores what the Stoic view on the matter implies for their theory of language, and compares their view with Aristotle’s. In the paper I aim to show that, for the Stoics, fallacies of ambiguity are complexes of propositions and sentences and thus straddle the realms of meaning (which (...) is the domain of logic) and of linguistic expressions (which is the domain of linguistics), but also involve a pragmatic element; that the Stoics believe that the premises of the fallacies, when uttered, have only one meaning and are true, and thus should be conceded; that hence there is no need for a mental process of disambiguation in the listeners; that Aristotle, by contrast, appears to assume that the premises always have all their meanings, and accordingly recommends that the listeners explicitly disambiguate them, which presupposes a process of mental disambiguation. I proffer two readings of the Stoic advice that we ‘be silent’ when confronted with a fallacy of ambiguity in dialectical discourse, and explicate how each leads to an overall consistent interpretation of the textual evidence. Finally, I demonstrate that the method advocated by the Stoics works in all cases of fallacies of lexical ambiguity. (shrink)
Commentators have not said much regarding Berkeley and Stoicism. Even when they do, they generally limit their remarks to Berkeley’s Siris (1744) where he invokes characteristically Stoic themes about the World Soul, “seminal reasons,” and the animating fire of the universe. The Stoic heritage of other Berkeleian doctrines (e.g., about mind or the semiotic character of nature) is seldom recognized, and when it is, little is made of it in explaining his other doctrines (e.g., immaterialism). None of this (...) is surprising, considering how Stoics are considered arch-materialists and determinists. My aim is to suggest that our understanding of Berkeley’s philosophy is improved significantly by acknowledging its underlying Stoic character. I argue that Berkeley proposes not only a semantic ontology based on assumptions of Stoic logic but also a doctrine in which perceptions or ideas are intelligible precisely because they are always embedded in the propositions of a discourse or language. (shrink)
ABSTRACT: In this paper I argue (i) that the hypothetical arguments about which the Stoic Chrysippus wrote numerous books (DL 7.196) are not to be confused with the so-called hypothetical syllogisms" but are the same hypothetical arguments as those mentioned five times in Epictetus (e.g. Diss. 1.25.11-12); and (ii) that these hypothetical arguments are formed by replacing in a non-hypothetical argument one (or more) of the premisses by a Stoic "hypothesis" or supposition. Such "hypotheses" or suppositions differ from (...)propositions in that they have a specific logical form and no truth-value. The reason for the introduction of a distinct class of hypothetical arguments can be found in the context of dialectical argumentation. The paper concludes with the discussion of some evidence for the use of Stoic hypothetical arguments in ancient texts. (shrink)
ABSTRACT: A comprehensive introduction to ancient (western) logic from earliest times to the 6th century CE, with an emphasis on topics which may be of interest to contemporary logicians. Content: 1. Pre-Aristotelian Logic 1.1 Syntax and Semantics 1.2 Argument Patterns and Valid Inference 2. Aristotle 2.1 Dialectics 2.2 Sub-sentential Classifications 2.3 Syntax and Semantics of Sentences 2.4 Non-modal Syllogistic 2.5 Modal Logic 3. The early Peripatetics: Theophrastus and Eudemus 3.1 Improvements and Modifications of Aristotle's Logic 3.2 Prosleptic Syllogisms 3.3 Forerunners (...) of Modus Ponens and Modus Tollens 3.4 Wholly Hypothetical Syllogisms 4. Diodorus Cronus and Philo the Logician 5. The Stoics 5.1 Logical Achievements Besides Propositional Logic 5.2 Syntax and Semantics of Complex Propositions 5.3 Arguments 5.4 Stoic Syllogistic 5.5 Logical Paradoxes 6. Epicurus and the Epicureans 7. Later Antiquity. (shrink)
Aristotle and Aquinas may have held that the things we believe and assert can have different truth-values at different times. Stoic logicians did; they held that there were “vacillating assertibles”—assertibles that are sometimes true and sometimes false. Frege and Russell endorsed the now widely accepted alternative, where the propositions believed and asserted are always specific with respect to time. This paper brings a new perspective to this question. We want to figure out what sorts of propositions speakers (...) believe. Some philosophers have argued that we must take agents to believe temporalist propositions—propositions that are inspecific with respect to time—if we’re to explain the agent’s own thoughts and inferences. I’ll explore another strategy. I’ll focus on our ability to think and reason about the beliefs that other people have. I’ll suggest that an adequate account of that ability requires that we take others to believe some temporalist propositions. I also ask whether all propositions can be specific with respect to worlds, and close by exploring some general issues. (shrink)
This monograph discusses the sources for ancient propositional logic, mainly in Sextus Empiricus and Diogenes Laertius bk. VII. It is argued that most of the sources in Sextus which have hitherto been taken to be sources for Stoic logic either do not report Stoic logic at all or report pre-Chrysippean Stoic logic. These texts report (in the first case) a group labelled the Dialecticians whose most prominent members were Diodorus Cronus and Philo or else (in the second (...) case) early Stoic logicians heavily influenced by the Dialecticians. The texts discusssed concern the theory of signs, the theory of proof and the classifications of propositions and of arguments. (shrink)
In this paper I defend the existence of a Dialectical school proper against criticisms brought forward by Klaus Döring and by Jonathan Barnes. Whereas Döring claims that there was no Dialectical school separate from the Megarians, Barnes takes issue with my claim (argued for in “Dialektiker und frühe Stoiker bei Sextus Empiricus”) that most of the reports in Sextus on the dialecticians refer to members of the Dialectical school. Barnes contends that these dialecticians are in fact Stoic logicians. As (...) against Döring, I argue that the passage in Diogenes Laertius II 113 (first drawn attention to by David Sedley) which talks of a the Megarian Stilpo winning over disciples from the Dialecticians is not refuted by Döring’s arguments. It clearly shows that the Dialecticians and the Megarians at the time were taken to be different philosophical sects. As against Barnes I insist on the differences between the report in Ps.-Galen’s Historia 9 and the Sextan report on the theory of sign in AM VIII. These reports offer incompatible definitions of the indicative sign. Moreover, the classification of simple propositions reported by Sextus at AM VIII 96f. cannot be a truncated version of the (Stoic) list to be found in Diogenes Laertius VII 69f. since in Sextus’ report one of the three classes of simple propositions is labelled middle (meson). This is a certain sign that we are dealing with a triad, and hence that this list is meant to be complete. Therefore the classification found in Sextus and attributed to the dialecticians and the one in Diogenes Laertius reporting Stoic material do come from different sources. (shrink)
This paper argues that attitudinal objects, entities of the sort of John's judgment, John's thought, and John's claim, should play the role of propositions, as the cognitive products of cognitive acts, not the acts themselves.
Propositions are often aligned with truth-conditions. The view is mistaken, since propositions discriminate where truth conditions do not. Propositions are hyperintensional: they are sensitive to necessarily equivalent differences. I investigate an alternative view on which propositions are truthmaker conditions, understood as sets of possible truthmakers. This requires making metaphysical sense of merely possible states of affairs. The theory that emerges illuminates the semantic phenomena of samesaying, subject matter, and aboutness.
Kaplan (drawing on Montague and Prior, inter alia) made explicit the idea of world and time neutral propositions, which bear truth values only relative to world and time parameters. There was then a debate over the role of time. Temporalists sided with Kaplan in maintaining time neutral propositions with time relative truth values, while eternalists claimed that all propositions specify the needed time information and so bear the same truth value at all times. But there never was (...) much of a parallel debate over the role of worlds. Let contingentism be the view (parallel to temporalism) that sides with Kaplan in maintaining world neutral propositions with world relative truth values, and let necessitarianism be the view (parallel to eternalism) that propositions specify the needed world information and so bear the same truth value at all worlds. This is the story of how the debate between the contingentists and the necessitarians might begin. (shrink)
Propositions play a central role in contemporary semantics. On the Russellian account, propositions are structured entities containing particulars, properties and relations. This contrasts sharply with the sets-of-possible-worlds view of propositions. I’ll discuss how to extend the sets-of-worlds view to accommodate fine-grained hyperintensional contents. When this is done in a satisfactory way, I’ll argue, it makes heavy use of entities very much like Russellian tuples. The two notions of proposition become inter-definable and inter-substitutable: they are not genuinely distinct (...) accounts of how propositions represent what they represent. Semantic theorists may move freely between the two conceptions of what propositions are. Nevertheless, the two approaches give different accounts of the metaphysical nature of propositions. I argue that the sets-of-worlds view provides an adequate account of the nature of propositions, whereas the Russellian view cannot. (shrink)
The topic of this article is the ontology of practical reasons. We draw a critical comparison between two views. According to the first, practical reasons are states of affairs; according to the second, they are propositions. We first isolate and spell out in detail certain objections to the second view that can be found only in embryonic form in the literature – in particular, in the work of Jonathan Dancy. Next, we sketch possible ways in which one might respond (...) to each one of these objections. A careful evaluation of these complaints and responses, we argue, shows that the first view is not as obviously compelling as it is thought by Dancy. Indeed, it turns out that the view that practical reasons are propositions is by no means unworkable and in fact, at least under certain assumptions, explicit considerations can be made in favour of a propositional construal of reasons. (shrink)
Speaks defends the view that propositions are properties: for example, the proposition that grass is green is the property being such that grass is green. We argue that there is no reason to prefer Speaks's theory to analogous but competing theories that identify propositions with, say, 2-adic relations. This style of argument has recently been deployed by many, including Moore and King, against the view that propositions are n-tuples, and by Caplan and Tillman against King's view that (...)propositions are facts of a special sort. We offer our argument as an objection to the view that propositions are unsaturated relations. (shrink)
ABSTRACT: For the Stoics, a syllogism is a formally valid argument; the primary function of their syllogistic is to establish such formal validity. Stoic syllogistic is a system of formal logic that relies on two types of argumental rules: (i) 5 rules (the accounts of the indemonstrables) which determine whether any given argument is an indemonstrable argument, i.e. an elementary syllogism the validity of which is not in need of further demonstration; (ii) one unary and three binary argumental rules (...) which establish the formal validity of non-indemonstrable arguments by analysing them in one or more steps into one or more indemonstrable arguments (cut type rules and antilogism). The function of these rules is to reduce given non-indemonstrable arguments to indemonstrable syllogisms. Moreover, the Stoic method of deduction differs from standard modern ones in that the direction is reversed (similar to tableau methods). The Stoic system may hence be called an argumental reductive system of deduction. In this paper, a reconstruction of this system of logic is presented, and similarities to relevance logic are pointed out. (shrink)
Accounts of propositions as sets of possible worlds have been criticized for conflating distinct impossible propositions. In response to this problem, some have proposed to introduce impossible worlds to represent distinct impossibilities, endorsing the thesis that impossible worlds must be of the same kind; this has been called the parity thesis. I show that this thesis faces problems, and propose a hybrid account which rejects it: possible worlds are taken as concrete Lewisian worlds, and impossibilities are represented as (...) set-theoretic constructions out of them. This hybrid account (1) distinguishes many intuitively distinct impossible propositions; (2) identifies impossible propositions with extensional constructions; (3) avoids resorting to primitive modality, at least so far as Lewisian modal realism does. (shrink)
A singular thought about an object o is one that is directly about o in a characteristic way—grasp of that thought requires having some special epistemic relation to the object o, and the thought is ontologically dependent on o. One account of the nature of singular thought exploits a Russellian Structured Account of Propositions, according to which contents are represented by means of structured n-tuples of objects, properties, and functions. A proposition is singular, according to this framework, if and (...) only if it contains an object as a constituent. One advantage of the framework of Russellian Structured propositions is that it promises to provide a metaphysical basis for the notion of a singular thought about an object, grounding it in terms of constituency. In this paper, we argue that the attempt to ground the peculiar features of singular thoughts in terms of metaphysical constituency fails, and draw some consequences of our discussion for other debates. (shrink)
Do Russellian propositions have their constituents as parts? One reason for thinking not is that if they did, they would generate apparent counterexamples to plausible mereological principles. As Frege noted, they would be in tension with the transitivity of parthood. A certain small rock is a part of Etna but not of the proposition that Etna is higher than Vesuvius. So, if Etna were a part of the given proposition, parthood would fail to be transitive. As William Bynoe has (...) noted (speaking of facts rather than propositions), they would seem to violate certain supplementation principles. Consider the singular proposition, concerning identity, that it is identical with itself. Given the relevant form of Russellianism, this proposition would have identity as a proper part, but it would not have any parts disjoint from identity, and indeed it would not have even a single pair of disjoint parts, in violation of various supplementation principles. This chapter offers a unified solution to the problems about transitivity and supplementation. One key ingredient in the solution is the view that parthood is a four-place relation expressed by ‘x at y is a part of z at w’. Another key ingredient is the view that the semantic contents of predicates and sentential connectives have ‘slots’ or ‘argument positions’ in them. (Both ingredients are independently motivated elsewhere.) Four-place analogues of the transitivity and supplementation principles are set out, and it is argued that these are not threatened by the examples from Frege and Bynoe. (shrink)
It is our contention that an ontological commitment to propositions faces a number of problems; so many, in fact, that an attitude of realism towards propositions—understood the usual “platonistic” way, as a kind of mind- and language-independent abstract entity—is ultimately untenable. The particular worries about propositions that marshal parallel problems that Paul Benacerraf has raised for mathematical platonists. At the same time, the utility of “proposition-talk”—indeed, the apparent linguistic commitment evident in our use of 'that'-clauses (in offering (...) explanations and making predictions)—is also in need of explanation. We account for this with a fictionalist analysis of our use of 'that'-clauses. Our account avoids certain problems that arise for the usual error-theoretic versions of fictionalism because we apply the notion of semantic pretense to develop an alternative, pretense-involving, non-error-theoretic, fictionalist account of proposition-talk. (shrink)
Trenton Merricks presents an original argument for the existence of propositions, and defends an account of their nature. He draws a variety of controversial conclusions, for instance about supervaluationism, the nature of possible worlds, truths about non-existent entities, and whether and how logical consequence depends on modal facts.
This paper discusses two distinct strategies that have been adopted to provide fine-grained propositions; that is, propositions individuated more finely than sets of possible worlds. One strategy takes propositions to have internal structure, while the other looks beyond possible worlds, and takes propositions to be sets of circumstances, where possible worlds do not exhaust the circumstances. The usual arguments for these positions turn on fineness-of-grain issues: just how finely should propositions be individuated? Here, I compare (...) the two strategies with an eye to the fineness-of-grain question, arguing that when a wide enough range of data is considered, we can see that a circumstance-based approach, properly spelled out, outperforms a structure-based approach in answering the question. (Part of this argument involves spelling out what I take to be a reasonable circumstance-based approach.) An argument to the contrary, due to Soames, is also considered. (shrink)
Theories of propositions as sets of truth-supporting circumstances are committed to the thesis that sentences or other representations true in all and only the same circumstances express the same proposition. Theories of propositions as complex, structured entities are not committed to this thesis. As a result, structured propositions can play a role in our theories of language and thought that sets of truth-supporting circumstances cannot play. To illustrate this difference, I sketch a theory of transparent, non-deflationary truth (...) consistent with some theories of structured propositions, but inconsistent with any theory of propositions as sets of truth-supporting circumstances. (shrink)
Bertrand Russell offered an influential paradox of propositions in Appendix B of The Principles of Mathematics, but there is little agreement as to what to conclude from it. We suggest that Russell's paradox is best regarded as a limitative result on propositional granularity. Some propositions are, on pain of contradiction, unable to discriminate between classes with different members: whatever they predicate of one, they predicate of the other. When accepted, this remarkable fact should cast some doubt upon some (...) of the uses to which modern descendente of Russell's paradox of propositions have been put in recent literature. (shrink)
Philosophers often talk about the things we say, or believe, or think, or mean. The things are often called ‘propositions’. A proposition is what one believes, or thinks, or means when one believes, thinks, or means something. Talk about propositions is ubiquitous when philosophers turn their gaze to language, meaning and thought. But what are propositions? Is there a single class of things that serve as the objects of belief, the bearers of truth, and the meanings of (...) utterances? How do our utterances express propositions? Under what conditions do two speakers say the same thing, and what (if anything) does this tell us about the nature of propositions? There is no consensus on these questions—or even on whether propositions should be treated as things at all. During the second Propositions and Same-Saying workshop, which took place on July 19–21 2010 at the University of Sydney, philosophers debated these (and related) questions. The workshop covered topics in the philosophy of language, perception, and metaphysics. The present volume contains revised and expanded versions of the papers presented at the workshop. (shrink)
No semantic theory satisfying certain natural constraints can identify the semantic contents of sentences (the propositions they express), with sets of circumstances in which the sentences are true–no matter how fine-grained the circumstances are taken to be. An objection to the proof is shown to fail by virtue of conflating model-theoretic consequence between sentences with truth-conditional consequence between the semantic contents of sentences. The error underlines the impotence of distinguishing semantics, in the sense of a truth-based theory of logical (...) consequence, and semantics, in the sense of a theory of meaning. (shrink)
ABSTRACT: In contemporary discussions of freedom in Stoic philosophy we often encounter the following assumptions: (i) the Stoics discussed the problem of free will and determinis; (ii) since in Stoic philosophy freedom of the will is in the end just an illusion, the Stoics took the freedom of the sage as a substitute for it and as the only true freedom; (iii) in the c. 500 years of live Stoic philosophical debate, the Stoics were largely concerned with (...) the same philosophical problems of freedom. In this paper I argue that (i) can be upheld only in a very restricted way; (ii) is altogether untenable; and regarding (iii), that, although there may have occurred little change in the Stoic philosophical position on freedom over the centuries, we can detect more than one transformation of the philosophical problems that were at the forefront of the discussion. Moreover, that all the conceptions and problems of freedom were linked to Stoic ethics, and that the differences between them become transparent when one considers their various roles in this context. (shrink)
For Berkeley, minds are not Cartesian spiritual substances because they cannot be said to exist (even if only conceptually) abstracted from their activities. Similarly, Berkeley's notion of mind differs from Locke's in that, for Berkeley, minds are not abstract substrata in which ideas inhere. Instead, Berkeley redefines what it means for the mind to be a substance in a way consistent with the Stoic logic of 17th century Ramists on which Leibniz and Jonathan Edwards draw. This view of mind, (...) I conclude, is definitely not the bundle theory that some critics have portrayed it as being. (shrink)
Soames (Philos Top 15:44–87, 1987 , J Philos Logic 37:267–276, 2008 ) has argued that propositions cannot be sets of truth-supporting circumstances. This argument is criticized for assuming that various singular terms are directly referential when in fact there are good grounds to doubt this.
In Jeffrey King’s theory of structured propositions, propositional structure mirrors the syntactic structure of natural language sentences that express it. I provide cases where this claim individuates propositions too finely across languages. Crucially, King’s paradigmatic proposition-fact ^that Dara swims^ cannot be believed by a monolingual Greek speaker, due to Greek syntax requiring an obligatory article in front of proper names. King’s two possible replies are: (i) to try to streamline the syntax of Greek and English; or (ii) to (...) insist that English speakers can believe propositions inexpressible in Greek. I argue that the former option entails giving up a neo-Russelian framework, and the latter makes King’s account arbitrary or trivial. I conclude that the mirroring claim is untenable. (shrink)
It is argued that propositions cannot be the compositional semantic values of sentences (in context) simply due to issues stemming from the compositional semantics of modal operators (or modal quantifiers). In particular, the fact that the arguments for double indexing generalize to multiple indexing exposes a fundamental tension in the default philosophical conception of semantic theory. This provides further motivation for making a distinction between two sentential semantic contents—what (Dummett 1973) called “ingredient sense” and “assertoric content”.
ABSTRACT: This paper traces the evidence in Galen's Introduction to Logic (Institutio Logica) for a hypothetical syllogistic which predates Stoic propositional logic. It emerges that Galen is one of our main witnesses for such a theory, whose authors are most likely Theophrastus and Eudemus. A reconstruction of this theory is offered which - among other things - allows to solve some apparent textual difficulties in the Institutio Logica.
It is argued that taken together, two widely held claims ((i) sentences express structured propositions whose structures are functions of the structures of sentences expressing them; and (ii) sentences have underlying structures that are the input to semantic interpretation) suggest a simple, plausible theory of propositional structure. According to this theory, the structures of propositions are the same as the structures of the syntactic inputs to semantics they are expressed by. The theory is defended against a variety of (...) objections. (shrink)
ABSTRACT: Alexander of Aphrodisias’ commentaries on Aristotle’s Organon are valuable sources for both Stoic and early Peripatetic logic, and have often been used as such – in particular for early Peripatetic hypothetical syllogistic and Stoic propositional logic. By contrast, this paper explores the role Alexander himself played in the development and transmission of those theories. There are three areas in particular where he seems to have made a difference: First, he drew a connection between certain passages from Aristotle’s (...) Topics and Prior Analytics and the Stoic indemonstrable arguments, and, based on this connection, appropriated at least four kinds of Stoic indemonstrables as Aristotelian. Second, he developed and made use of a specifically Peripatetic terminology in which to describe and discuss those arguments – which facilitated the integration of the indemonstrables into Peripatetic logic. Third, he made some progress towards a solution to the problem of what place and interpretation the Stoic third indemonstrables should be given in a Peripatetic and Platonist setting. Overall, the picture emerges that Alexander persistently (if not always consistently) presented passages from Aristotle’s logical œuvre in a light that makes it appear as if Aristotle was in the possession of a Peripatetic correlate to the Stoic theory of indemonstrables. (shrink)
In this paper, I discuss two concerns for pluralist truth theories: a concern about a key detail of these theories and a concern about their viability. The detailed-related concern is that pluralists have relied heavily upon the notion of a domain, but it is not transparent what they take domains to be. Since the notion of a domain has been present in philosophy for some time, it is important for many theorists, not only truth pluralists, to be clear on what (...) domains are and what work they can do. The viability-related concern is that it’s not clear how a pluralist truth theory could explain the truth-conditions of mixed atomic propositions. To address this concern, truth pluralists should recognize something to which they have not been sufficiently attentive: that some atomic propositions belong to more than one domain. But, recognizing this requires rethinking the relationships between the nature of propositions, their membership in domains, and their truth. I address these issues and propose an understanding of them that is preferable to the best existing account of them, that offered by Michael Lynch. (shrink)
Toward the end of his classic treatise An Essay on Free Will, Peter van Inwagen offers a modal argument against the Principle of Sufficient Reason which he argues shows that the principle “collapses all modal distinctions.” In this paper, a critical flaw in this argument is shown to lie in van Inwagen’s beginning assumption that there is such a thing as the conjunction of all contingently true propositions. This is shown to follow from Cantor’s theorem and a property of (...) conjunction with respect to contingent propositions. Given the failure of this assumption, van Inwagen’s argument against the Principle of Sufficient Reason cannot succeed, at least not without the addition of some remarkable and previously unacknowledged qualifications. (shrink)
Scholars have long recognised the interest of the Stoics' thought on geometrical limits, both as a specific topic in their physics and within the context of the school's ontological taxonomy. Unfortunately, insufficient textual evidence remains for us to reconstruct their discussion fully. The sources we do have on Stoic geometrical themes are highly polemical, tending to reveal a disagreement as to whether limit is to be understood as a mere concept, as a body or as an incorporeal. In my (...) view, this disagreement held among the historical Stoics, rather than simply reflecting a doxographical divergence in transmission. This apparently Stoic disagreement has generated extensive debate, in which there is still no consensus as to a standard Stoic doctrine of limit. The evidence is thin, and little of it refers in detail to specific texts, especially from the school's founders. But in its overall features the evidence suggests that Posidonius and Cleomedes differed from their Stoic precursors on this topic. There are also grounds for believing that some degree of disagreement obtained between the early Stoics over the metaphysical status of shape. Assuming the Stoics did so disagree, the principal question in the scholarship on Stoic ontology is whether there were actually positions that might be called "standard" within Stoicism on the topic of limit. In attempting to answer this question, my discussion initially sets out to illuminate certain features of early Stoic thinking about limit, and then takes stock of the views offered by late Stoics, notably Posidonius and Cleomedes. Attention to Stoic arguments suggests that the school's founders developed two accounts of shape: on the one hand, as a thought-construct, and, on the other, as a body. In an attempt to resolve the crux bequeathed to them, the school's successors suggested that limits are incorporeal. While the authorship of this last notion cannot be securely identified on account of the absence of direct evidence, it may be traced back to Posidonius, and it went on to have subsequent influence on Stoic thinking, namely in Cleomedes' astronomy. (shrink)
This paper defends a key aspect of the Peircean conception of truth—the idea that truth is in some sense epistemically-constrained. It does so by exploring parallels between Peirce’s epistemology of inquiry and that of Wittgenstein in On Certainty. The central argument defends a Peircean claim about truth by appeal to a view shared by Peirce and Wittgenstein about the structure of reasons. This view relies on the idea that certain claims have a special epistemic status, or function as what are (...) popularly called ‘hinge propositions’. (shrink)
The pressure to individuate propositions more finely than intensionally—that is, hyper-intensionally—has two distinct sources. One source is the philosophy of mind: one can believe a proposition without believing an intensionally equivalent proposition. The second source is metaphysics: there are intensionally equivalent propositions, such that one proposition is true in virtue of the other but not vice versa. I focus on what our theory of propositions should look like when it's guided by metaphysical concerns about what is true (...) in virtue of what. In this paper I articulate and defend a metaphysical theory of the individuation of propositions, according to which two propositions are identical just in case they occupy the same nodes in a network of invirtuation relations. Invirtuation is here taken to be a primitive relation of metaphysical explanation exemplified by propositions that, in conjunction with truth, defines the notion of true in virtue of. After formulating the theory, I compare it with a view.. (shrink)