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: 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: 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. (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: 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)
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.
Truth, falsity, and unity -- Sentences, lists, and collections -- Declarative and other kinds of sentence -- Declarative sentences and propositions -- Sentences, propositions, and truth-values -- Sentences, propositions, and unity -- Unity and complexity -- Reference and supposition -- Reference and signification -- Linguistic idealism and empirical realism -- Russell on truth, falsity, and unity (I) : 1903 -- Russell on truth, falsity, and unity (II) : 1910-13 -- Russell on truth, falsity, and unity (III) : 1918 -- Sense, (...) reference, and propositions -- Russellian propositions, Fregean thoughts, and facts -- The location of propositions -- Proper names, concept-expressions, and definite descriptions -- Concept-expressions and Carnapian intensions -- Carnapian intensions and understanding -- Carnapian intensions and Russellian propositions -- Russellian propositions and functionality -- A revised semantic map -- Sentences as referring expressions -- False propositions at the level of reference -- The world's own language -- Signification and supposition revisited -- Frege and Russell on unity -- Saturatedness and unsaturatedness -- The copula as secundum adiacens and as tertium adiacens -- Frege and the Copula -- The paradox of the concept horse -- Russell on unity and the paradox -- An unsuccessful attempt to avoid the paradox -- The paradox and the level of language -- Reforming Frege's treatment of concept-expressions -- Concepts and functions -- The reformed Frege : refinements and objections -- Frege, Russell, and the anti-fregean strategy -- The anti-fregean strategy : the case of names -- Disquotation and propositional form -- The context principle -- Prabhakara semantics and the related designation theory -- For that is not a word which is not the name of a thing -- The impartial strategy -- Secundum and tertium adiacens, matter and form -- The hierarchy of levels and the syntactic priority thesis -- Fregean and anti-fregean strategies -- The anti-fregean strategy and relations (I) -- Interlude: The subject--predicate distinction -- The anti-fregean strategy and relations (II) -- The reality of relations -- Polyadicity, monadicity, and identity -- The anti-fregean strategy and Montague grammar -- Fregean and anti-fregean strategies : further comparison -- Ramsey on the subject : predicate distinction -- Dummett's attack on the anti-fregean strategy -- Linguistic idealism revisited -- Alternative hierarchies and the context principle -- The linguistic hierarchy and categorial nonsense -- Logical syntax and the context principle -- Proper names, singular terms, and the identity test -- Proper names, Leibniz's law, and the identity of indiscernibles -- The negation asymmetry test -- Dummett's tests for singular termhood -- Discarding the syntactic priority thesis -- Logical predication, logical form, and Bradley's regress -- Names, verbs, and the replacement test -- Analysis and paradox -- Simple, complex, and logical predicates -- The grammatical copula and the logical copula -- Predication in Frege -- Two exegetical problems in Frege -- Inference and the logical predicate -- Unity and the logical predicate -- Bradley's regress and the tradition -- Russell and the general form of the proposition -- Wittgenstein's criticism of Russell -- Logical form in theTractatus -- Bradley's regress and the unity of the proposition -- The logical copula and theories of meaning -- Reference and the logical copula -- Bradley's regress and the analysis of meaning -- Vicious practical regresses -- Bradley's regress and the solution to the unity problem -- Propositions, sets, sums, and the objects themselves -- Bradley's regress and the infinite -- Vallicella's onto-theology -- A comparison with other innocent regresses -- Truth, falsity, and unity revisited -- Bradley's regress, realism, and states of affairs -- Unity and use -- The unity of sentences and the unity of complex names (I) -- The unity of sentences and the unity of complex names (II) -- Congruence, functionality, and propositional unity -- Davidson on predication -- Epilogue: The limits of language. (shrink)
It is very difficult to get a clear picture of how the Stoic is supposed to deliberate. This paper considers a number of possible pictures, which cover such a wide range of options that some look Kantian and others utilitarian. Each has some textual support but is also unworkable in certain ways: there seem to be genuine and unresolved conflicts at the heart of Stoic ethics. And these are apparently due not to developmental changes within the school, but (...) to the Stoics’ having adopted implicitly incompatible solutions in response to different philosophical challenges. (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)
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)
The tremendous influence Stoicism has exerted on ethical thought from early Christianity through Immanuel Kant and into the twentieth century is rarely understood and even more rarely appreciated. Throughout history, Stoic ethical doctrines have both provoked harsh criticisms and inspired enthusiastic defenders. The Stoics defined the goal in life as living in agreement with nature. Humans, unlike all other animals, are constituted by nature to develop reason as adults, which transforms their understanding of themselves and their own true good. (...) The Stoics held that virtue is the only real good and so is both necessary and, contrary to Aristotle, sufficient for happiness; it in no way depends on luck. The virtuous life is free of all passions, which are intrinsically disturbing and harmful to the soul, but includes appropriate emotive responses conditioned by rational understanding and the fulfillment of all one's personal, social, professional, and civic responsibilities. The Stoics believed that the person who has achieved perfect consistency in the operation of his rational faculties, the "wise man," is extremely rare, yet serves as a prescriptive ideal for all. The Stoics believed that progress toward this noble goal is both possible and vitally urgent. (shrink)
In The Theory of Moral Sentiments (TMS) Adam Smith draws on the Stoic idea of a Providence that uses everything for the good of the whole. The process is often painful, so the Stoic ethic insisted on conscious cooperation. Stoic ideas contributed to the rise of science and enjoyed wide popularity in Smith's England. Smith was more influenced by the Stoicism of his professors than by the Epicureanism of Hume. In TMS, Marcus Aurelius's "helmsman" becomes the "impartial (...) spectator," who judges actions in terms of the way they are seen by others. This is the key to justice, without which society collapses. Business school students should be taught that Smith's "invisible hand" is best understood as a universal rationality that uses just actions for the benefit of the whole. (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)
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)
This article attempts to explore ancient Chinese philosophical thought by analyzing how pioneering Chinese thinkers made judgments and inferences, and compares it to ancient Greek philosophy. It first addresses the starting-point and the object of cognition in Chinese ancient philosophy, then analyses how early thinkers construed definition and proposition, and finally discusses how they made inferences on the basis of definition and proposition. It points out that categorization is an important methodology in ancient Chinese philosophy, and that rectification (...) of names and the doctrine of the mean are key criteria in making judgments. (shrink)
ABSTRACT: Although from the 2nd century BC to the 3rd AD the problems of determinism were discussed almost exclusively under the heading of fate, early Stoic determinism, as introduced by Zeno and elaborated by Chrysippus, was developed largely in Stoic writings on physics, independently of any specific "theory of fate ". Stoic determinism was firmly grounded in Stoic cosmology, and the Stoic notions of causes, as corporeal and responsible for both sustenance and change, and of (...) effects as incorporeal and as predicates, are indispensable for a full understanding of the theory. Stoic determinism was originally not presented as causal determinism, but with a strong teleological element, in the context of a theory of natural motions, which makes use of a distinction between a global and an inner-worldly perspective on events. However, Chrysippus also employed his conception of causality in order to explicate his determinism, and can be shown to have maintained a universal causal determinism in the modern sense of the erm. The teleological and mechanical elements of early Stoic determinism were brought together in Chrysippus' conception of fate, which places elements of rationality in every cause. (shrink)
Richard Gaskin’s work on the problem of the unity of the proposition (“the problem”, henceforth) has sometimes been called magisterial due to its vast historical and conceptual scope. Indeed, the author engages in lengthy discussions of the conceptions of propositions that have been overlooked by most previous investigations on the problem. Not only aspects of Frege’s and Russell’s theories of propositions that appear most problematic are subject to Gaskin’s investigation, it also includes Prabhākara semantics, the approach of Gregory of (...) Rimini and various parts of Abelard’s thought just to name a few. Furthermore, the purpose of this work is manifold. It is not solely a historical account of the importance of the problem, nor is it only a critique of the views explored. Gaskin ventures to provide his own original solution to the problem of the unity of the proposition. The solution and the arguments in its favour, however, are deeply embedded in the structure of the extensive historical treatment of the problem and, hence, cannot be precisely depicted due to limited space. In what follows I shall hope to provide a general idea of how Gaskin approaches the topic historically and what is his endorsement towards it. Lastly, I discuss the proposed solution to the problem. (shrink)
Part of rethinking philosophy today, the author believes, is to rethink our logical concepts. The author questions the ontological existence of the proposition as the content of sentential utterances—written or spoken—as it was originally proposed by John Searle. While a performative is an utterance where the speaker not only utters a sentential or illocutionary content such as a statement, but also performs the illocutionary force such as the act of stating, the author reasserts John Austin’s constative as the general (...) label (genus) of specific utterances (species) that can be rendered true or false such as a statement, assertion, description, and prediction. In the remainder of the paper, the author tries to show that it is a category mistake for someone to assert a statement or to state an assertion. (shrink)
Discussing the concept of duty in Groundwork 1, Kant refers to a and a , the latter being a . However, Kant does not identify what the is. In this paper, I will argue that the first proposition is this: An action from duty is an action from respect for the moral law. I defend this claim against a critique put forward by Allison according to which is a concept that is not, and could not be, introduced in paragraphs (...) 9FolgerungFolgerung’ could be understood as a corollary rather than a conclusion. Finally, Allison's own interpretation will be criticized. (shrink)
I argue that the best way to solve Russell's problem of the relationship between propositions and their constituents is to think of propositions as properties of worlds. I argue that this view preserves the strengths and avoids some of the weaknesses of the view of the metaphysics of propositions defended by Jeff King in his _The Nature and Structure of Content_, and that it provides an explanation of the representational properties of propositions and the nature of indexical belief. I conclude (...) by discussing some problems about how to think about the semantics of propositional attitude ascriptions, if a view of this sort is correct. (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)
A study of the reception of Aristotle's Prior Analytics in the first half of the twelfth century. It is shown that Peter Abaelard was perhaps acquainted with as much as the first seven chapters of Book I of the Prior Analytics but with no more. The appearance at the beginning of the twelfth century of a short list of dialectical loci which has puzzled earlier commentators is explained by noting that this list formalises the classification of extensional relations between general (...) terms and that this classification had already be put forward by Boethius in his de Syllogismo Categorico and Introductio ad Syllogismos Categoricas . It is pointed out the kind of text referred to as an ` Introductio ' at the beginning of the twelfth-century follows very closely the structure of Boethius own Introductio and adds to it material drawn from his accounts of loci and the conditional propositions. It is argued that the reception of the Prior Analytics has to be understood against the background of this well developed tradition of treating together syllogisms, loci , and conditional propostions. Referring to a challenge to the formal validity of Darapti in the Ars Meliduna the paper concludes by illustrating that the theory of the syllogism presented in Prior Analytics was still controversial in the middle of the twelfth-century. (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)
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)
This monograph offers a reappraisal of the role of Bertrand Russell's philosophical works in establishing the analytical tradition in philosophy. It's main aims are to improve our understanding of the history of analytical philosophy, to engage in the important disputes surrounding the interpretation of Russell's philosophy, and to make a contribution to central issues in current analytical philosophy. Hence, this book will find a place on the bookshelf of many philosophers across the world.
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)
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)
This paper is chiefly aimed at individuating some deep, but as yet almost unnoticed, similarities between Aristotle's syllogistic and the Stoic doctrine of conditionals, notably between Aristotle's metasyllogistic equimodality condition (as stated at APr. I 24, 41b27–31) and truth-conditions for third type (Chrysippean) conditionals (as they can be inferred from, say, S.E. P. II 111 and 189). In fact, as is shown in §1, Aristotle's condition amounts to introducing in his (propositional) metasyllogistic a non-truthfunctional implicational arrow '', the truth-conditions (...) of which turn out to be logically equivalent to truth-conditions of third type conditionals, according to which only the impossible (and not the possible) follows from the impossible. Moreover, Aristotle is given precisely this non-Scotian conditional logic in two so far overlooked passages of (Latin and Hebraic translations of) Themistius' Paraphrasis of De Caelo (CAG V 4, 71.8–13 and 47.8–10 Landauer). Some further consequences of Aristotle's equimodality condition on his logic, and notably on his syllogistic (no <span class='Hi'>matter</span> whether modal or not), are pointed out and discussed at length. A (possibly Chrysippean) extension of Aristotle's condition is also discussed, along with a full characterization of truth-conditions of fourth type conditionals. (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)
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)
Tad Brennan explains how to live the Stoic life--and why we might want to. Stoicism has been one of the main currents of thought in Western civilization for two thousand years: Brennan offers a fascinating guide through the ethical ideas of the original Stoic philosophers, and shows how valuable these ideas remain today, both intellectually and in practice. He writes in a lively informal style which will bring Stoicism to life for readers who are new to ancient philosophy. (...) The Stoic Life will also be of great interest to philosophers and classicists seeking a full understanding of the intellectual legacy of the Stoics. (shrink)
Bobzien presents the definitive study of one of the most interesting intellectual legacies of the ancient Greeks: the Stoic theory of causal determinism. She explains what it was, how the Stoics justified it, and how it relates to their views on possibility, action, freedom, moral responsibility, moral character, fatalism, logical determinism and many other topics. She demonstrates the considerable philosophical richness and power that these ideas retain today.
In view of recent articles citing the Stoics as a defence or refutation of cosmopolitanism it is legitimate to ask whether the Stoics did in fact have an argument for cosmopolitanism which may be useful to contemporary political philosophers. I begin by discussing an interpretation of Stoic views on cosmopolitanism by Martha Nussbaum and A.A. Long and show that the arguments they attribute to the Stoics are not tenable in the light of present day philosophy. I then argue that (...) the Stoics did offer a very different argument for cosmopolitanism which is both more interesting and more plausible in that it draws on a conception of human nature similar to Aristotles and contemporary virtue ethics. Lastly I consider an objection made to their particular brand of cosmopolitanism by Martha Nussbaum, namely that a Stoic cosmopolitan life is devoid of personal affiliation and therefore unbearably lonely. I argue that this objection is in fact unfounded. (shrink)
This book collects a series of important new studies on one of the richest and most influential intellectual traditions of antiquity. Leading scholars combine careful analytical attention to the original texts with historical sensitivity and philosophical acuity to point the way to a better understanding of Stoic ethics, political theory, logic, and science.