Essays on Aristotle's Sea-Battle, Lazy Argument, Argument Reaper, Diodorus' Master Argument -/- The book is devoted to the ancient logical theories, reconstruction of their semantic proprieties and possibilities of their interpretation by modern logical tools. The Ancient arguments are frequently misunderstood in modern interpretations since authors usually have tendency to ignore their historical proprieties and theoretical background what usually leads to a quite inappropriate picture of the argument’s original form and mission. Author’s primary intention was to draw attention to the (...) complexity of some historical arguments and to the theoretical context in which arguments were created, circulated, developed, and finally tuned. Four well-known ancient arguments – with a common central subject related to the future contingencies problem – are reconstructed from available historical sources: “The Sea Battle”, which is drawn from Aristotle’s treatise De Interpretatione; two arguments, usually ascribed to the Stoics, “The Lazy Argument” and “The Reaper”; “The Master Argument” of the Megarian philosopher Diodorus. Arguments are linguistically and semantically detaily analyzed, formally presented by reflecting some relevant corresponding hypotheses based on physical or logical theories of their ancient authors, and finally covered by appropriate logical tools familiar to a modern reader. Two appendices are added at the closing part of the book. One covering some assumptions relevant for understanding of rival streams in ancient theories of meaning related to the nature of names and naming; the other is devoted to the ancient understanding of logical proposition and attempts to find an adequate Latin translation of the Greek delicate philosophical term “ἀξίωμα”. (shrink)

I argue that Quinean naturalists’ holism-based arguments against analyticity and apriority are more difficult to resist than is generally supposed, for two reasons. First, although opponents of naturalism sometimes dismiss these arguments on the grounds that the holistic premises on which they depend are unacceptably radical, it turns out that the sort of holism required by these arguments is actually quite minimal. And second, although it’s true, as Grice and Strawson pointed out long ago, that these arguments can succeed only (...) if there isn’t any principled criterion for meaning change, such a criterion turns out to be hard to come by. David Chalmers has recently argued that such a criterion must exist, since the norms governing belief revision are subject to obvious exceptions that can be explained only by appeal to meaning change. But this, I argue, is incorrect: if choices about how to use language are themselves rationally assessable, then there are no such exceptions to be explained. To show that this is so, I formulate a new kind of coherence norm that may be useful for reasoning formally about the relationship between meaning and evidence. (shrink)

The general question to be considered in this paper points to the nature of the world described by chemistry: what is macro-chemical ontology like? In particular, we want to identify the ontological categories that underlie chemical discourse and chemical practice. This is not an easy task, because modern Western metaphysics was strongly modeled by theoretical physics. For this reason, we attempt to answer our question by contrasting macro-chemical ontology with the mainstream ontology of physics and of traditional metaphysics. In particular, (...) we introduce the distinction between stuff-ontology, proper of chemistry, and individual-ontology, proper of physics. These two ontologies differ from each other in the basic categories of their own structures. On this basis, we characterize individual-ontology in such a way that the features of stuff-ontology will arise by contrast with it. (shrink)

We present a procedure which allows us to recover classical and nonclassical logical structures as concrete logics associated with physical theories expressed by means of classical languages. This procedure consists in choosing, for a given theory ${{\mathcal{T}}}$ and classical language ${{\fancyscript{L}}}$ expressing ${{\mathcal{T}}, }$ an observative sublanguage L of ${{\fancyscript{L}}}$ with a notion of truth as correspondence, introducing in L a derived and theory-dependent notion of C-truth (true with certainty), defining a physical preorder $\prec$ induced by C-truth, and finally selecting (...) a set of sentences ϕ V that are verifiable (or testable) according to ${{\mathcal{T}}, }$ on which a weak complementation ⊥ is induced by ${{\mathcal{T}}. }$ The triple $(\phi_{V},\prec,^{\perp})$ is then the desired concrete logic. By applying this procedure we recover a classical logic and a standard quantum logic as concrete logics associated with classical and quantum mechanics, respectively. The latter result is obtained in a purely formal way, but it can be provided with a physical meaning by adopting a recent interpretation of quantum mechanics that reinterprets quantum probabilities as conditional on detection rather than absolute. Hence quantum logic can be considered as a mathematical structure formalizing the properties of the notion of verification in quantum physics. This conclusion supports the general idea that some nonclassical logics can coexist without conflicting with classical logic (global pluralism) because they formalize metalinguistic notions that do not coincide with the notion of truth as correspondence but are not alternative to it either. (shrink)

The Lazy Argument, as it is preserved in historical testimonies, is not logically conclusive. In this form, it appears to have been proposed in favor of part-time fatalism (including past time fatalism). The argument assumes that free will assumption is unacceptable from the standpoint of the logical fatalist but plausible for some of the nonuniversal or part-time fatalists. There are indications that the layout of argument is not genuine, but taken over from a Megarian source and later transformed. The genuine (...) form of the argument seems to be given in different form and far closer to Megarian logical fatalism and its purpose is not to defend laziness. If the historical argument has to lead to a logically satisfactory solution, some additional assumptions and additional tuning is needed. (shrink)

What is the rational response when confronted with a set of propositions each of which we have some reason to accept, and yet which taken together form an inconsistent class? This was, in a nutshell, the problem addressed by the Jaina logicians of classical India, and the solution they gave is, I think, of great interest, both for what it tells us about the relationship between rationality and consistency, and for what we can learn about the logical basis of philosophical (...) pluralism. The Jainas claim that we can continue to reason in spite of the presence of inconsistencies, and indeed construct a many-valued logical system tailored to the purpose. My aim in this paper is to offer a new interpretation of that system and to try to draw out some of its philosophical implications. (shrink)

This chapter focuses on alternative logics. It discusses a hierarchy of logical reform. It presents case studies that illustrate particular aspects of the logical revisionism discussed in the chapter. The first case study is of intuitionistic logic. The second case study turns to quantum logic, a system proposed on empirical grounds as a resolution of the antinomies of quantum mechanics. The third case study is concerned with systems of relevance logic, which have been the subject of an especially detailed reform (...) program. Finally, the fourth case study is paraconsistent logic, perhaps the most controversial of serious proposals. (shrink)

In 1880, when Oliver Wendell Holmes (later to be a Justice of the U.S. Supreme Court) criticized the logical theology of law articulated by Christopher Columbus Langdell (the first Dean of Harvard Law School), neither Holmes nor Langdell was aware of the revolution in logic that had begun, the year before, with Frege's Begriffsschrift. But there is an important element of truth in Holmes's insistence that a legal system cannot be adequately understood as a system of axioms and corollaries; and (...) this element of truth is not obviated by the more powerful logical techniques that are now available. (shrink)

Realism is multiply ambiguous. The central concern of Part 1 of this paper is to distinguish several of its many senses — four (Theoretical Realism, Cumulative Realism, Progressive Realism and Optimistic Realism) in which it refers to theses about the status of scientific theories, and five (Minimal Realism, Ambitious Absolutism, Transcendentalism, Nidealism, Scholastic Realism) in which it refers to theses about the nature of truth or truth-bearers. Because Realism has these several, largely independent, senses, the conventional wisdom that Tarski's theory (...) of truth supports realism, and that the Meaning-Variance thesis undermines it, needs re-evaluation. The concern of the rest of the paper is to sort out in which senses the conventional wisdom, with respect to Tarski's theory (Part 2) and the Meaning-Variance thesis (Part 3), is correct. (shrink)

The object of this paper is to show why recent research in the psychology of deductive and probabilistic reasoning does not have.

In this paper I argue that there can be genuine (as opposed to merely verbal) disputes about whether a sentence form is logically true or an argument form is valid. I call such disputes ?cases of deviance?, of which I distinguish a weak and a strong form. Weak deviance holds if one disputant is right and the other wrong, but the available evidence is insufficient to determine which is which. Strong deviance holds if there is no fact of the matter. (...) In section 2 I argue that weak deviance need not be trivial and may even be interesting. Section 3 considers what it could mean to say that logic is determined by a theory, especially a theory of meaning, an idea that arises in section 2. In section 4 I discuss the dispute between classical and relevance logicians over entailment and argue that it is a case of strong deviance. Finally, in section 5 I show that the result of the previous section is not absolute but relative to the background logic used in reaching it. (shrink)

Modern logic is undergoing a cognitive turn, side-stepping Frege’s ‘antipsychologism’. Collaborations between logicians and colleagues in more empirical fields are growing, especially in research on reasoning and information update by intelligent agents. We place this border-crossing research in the context of long-standing contacts between logic and empirical facts, since pure normativity has never been a plausible stance. We also discuss what the fall of Frege’s Wall means for a new agenda of logic as a theory of rational agency, and what (...) might then be a viable understanding of ‘psychologism’ as a friend rather than an enemy of logical theory. (shrink)

What I will call “the deviant logician objection” [DLO] is one line of attack against the common and compelling tenet that our justification for logical truths is grounded in our understanding of their constituent concepts. This objection seeks to undermine the possibility of any deep constitutive connection, in the epistemology of logic, between understanding and justification. I will consider varieties of the deviant logician objection developed by Horwich and by Williamson. My thesis is that while the deviant logician objection falls (...) short of proving that this traditional tenet must be rejected, nonetheless it serves to bolster some important refinements. (shrink)

A vagueza é comumente representada pela adoção de significados imprecisos na linguagem natural. Ela é analisada como um caso limítrofe e formalizada de diversas maneiras pelas suas teorias “clássicas”. Este trabalho propõe uma abordagem diferente do tema através da adoção do conceito de Racionalidade Soft ( Soft Rationality ), elaborado por Marcelo Dascal, e da sua interpretação como o uso da “semelhança” ao invés da “análise” para a compreensão dos termos da linguagem natural. Aqui será feita a sugestão de que (...) a Racionalidade Soft (branda), enquanto teoria sobre a vagueza, permanece no domínio da ‘intensionalidade’ ao invés de buscar uma explicação formalizada e ‘extensional’ para o tema. DOI:10.5007/1808-1711.2011v15n2p349. (shrink)

This paper compares two ways of holding that logic is special among the sciences in that it has no restricted class of entities as its subject matter, but instead concerns all entities alike. One way is Williamson’s explanation of how inquiry into logical consequence and logical truth only superficially concerns the linguistic or conceptual entities that bear these properties. Williamson draws on ideas familiar from deflationism about truth, and his account has been called “deflationary.” I argue that the analogy is (...) misleading. While there’s a broad sense in which Williamson offers a deflationary account of logical inquiry, his view differs from deflationism about truth in being best understood as a form of instrumentalism. By contrast, I elaborate a deflationism about logical properties modeled on deflationism about truth. I defend this expressive device deflationism as an explanation of our use of logical predicates. (shrink)

The aim of this paper is threefold. Firstly, §1 and §2 introduce the novel concept logical akrasia by analogy to epistemic akrasia. If successful, the initial sections will draw attention to an interesting akratic phenomenon which has not received much attention in the literature on akrasia (although it has been discussed by logicians in different terms). Secondly, §3 and §4 present a dilemma related to logical akrasia. From a case involving the consistency of Peano Arithmetic and Gödel’s Second Incompleteness Theorem (...) it’s shown that either we must be agnostic about the consistency of Peano Arithmetic or akratic in our arithmetical theorizing. If successful, these sections will underscore the pertinence and persistence of akrasia in arithmetic (by appeal to Gödel’s seminal work). Thirdly, §5 concludes by suggesting a way of translating the dilemma of arithmetical akrasia into a case of regular epistemic akrasia; and further how one might try to escape the dilemma when it’s framed this way. (shrink)

Logic ought to guide our thinking. It is better, more rational, more intelligent to think logically than to think illogically. Illogical thought leads to bad judgment and error. In any case, if logic had no role to play as a guide to thought, why should we bother with it?The somewhat naïve opinions of the previous paragraph are subject to attack from many sides. It may be objected that an activity does not count as thinking at all unless it is at (...) least minimally logical, so logic is constitutive of thought rather than a guide to it. Or it may be objected that whereas logic describes a system of timeless relations between propositions, thinking is a dynamic process involving revisions, and so could not use a merely static guide. Or again the objection may be that there is no such thing as logic, only a whole variety of different logics, not all of which could possibly be good guides. (shrink)

The paradoxes of self reference have to be dealt with by anyone seeking to give a satisfactory account of the logic of truth, of properties, and even of sets of numbers. Unfortunately, there is no widespread agreement as to how to deal with these paradoxes. Some approaches block the paradoxical inferences by rejecting as invalid a move that classical logic counts as valid. In the recent literature, this deviant logic analysis of the paradoxes has been called into question.This disagreement motivates (...) a re-examination of the philosophy of formal logic and the status of logical truths and rules. In this paper I do some of this work, and I show that this gives us the means to defend the deviant approaches against such criticisms. As a result I hope to show that these analyses of the paradoxes are worthy of more serious consideration than they have so far received. (shrink)

Informal accounts of the sorites paradox usually emphasize that the problem is one of vagueness. The paper uses the idea of fuzzy truth values to provide a formal semantics which shows precisely how sorites-Type arguments are formally invalid.

The fundamental problem of Christology is the apparent contradiction of Christ as recorded at Chalcedon. Christ is human and Christ is divine. Being divine entails being immutable. Being human entails being mutable. Were Christ two different persons there’d be no apparent contradiction. But Chalcedon rules as much out. Were Christ only partly human or only partly divine there’d be no apparent contradiction. But Chalcedon rules as much out. Were the very meaning of ‘mutable’ and/or ‘immutable’ other than what they are, (...) there’d be no apparent contradiction. But the meaning is what it is, and changing the meaning of our terms to avoid the apparent contradiction of Christ is an apparent flight from reality. What, in the end, is the explanation of the apparent contradiction of Christ? Theologians and philosophers have long advanced many consistency-seeking answers, all of which increase the metaphysical or semantical complexity of the otherwise strikingly simple but radical core of Christianity’s GodMan. In this paper, I put the simplest explanation on the theological table: namely, Christ appears to be contradictory because Christ is contradictory. This explanation may sound complicated to the many who are steeped in the mainstream account of logic according to which logic precludes the possibility of true contradictions. But the mainstream account of logic can and should be rejected. Ridding theology of the dogma of mainstream logic illuminates the simple though striking explanation of the apparent contradiction of Christ — namely, that Christ is a contradictory being. Just as the simplest explanation to the apparent roundness of the earth has earned due acceptance, so too should the simplest explanation of the apparent contradiction of Christ. (shrink)

In a famous and controversial paper, B. H. Slater has argued against the possibility of paraconsistent logics. Our reply is centred on the distinction between two aspects of the meaning of a logical constant *c* in a given logic: its operational meaning, given by the operational rules for *c* in a cut-free sequent calculus for the logic at issue, and its global meaning, specified by the sequents containing *c* which can be proved in the same calculus. Subsequently, we use the (...) same strategy to counter Quine's meaning variance argument against deviant logics. In a nutshell, we claim that genuine rivalry between (similar) logics *L* and *L'* is possible whenever each constant in *L* has the same operational meaning as its counterpart in *L'* although differences in global meaning arise in at least one case. (shrink)

I discuss paradoxes of implication in the setting of a proof-conditional theory of meaning for logical constants. I argue that a proper logic of implication should be not only relevant, but also constructive and nonmonotonic. This leads me to select as a plausible candidate LL, a fragment of linear logic that differs from R in that it rejects both contraction and distribution.

This essay takes competitive aeromodelling as a test case for certain contentious issues in philosophy of sport. More specifically, I look at the challenge it presents to prevailing ideas of what properly counts as ?sport?, which in turn have their source in other, more basic or deep-rooted preconceptions. Among them are a range of ?common-sense? beliefs about the properly (naturally) human, the mind/body relationship, the role (if any) of scientific-technological innovation as a means of performance enhancement, and ? most fundamentally (...) ? the distinction between nature and culture in so far as it bears on these questions. My approach is broadly deconstructionist in taking them as genuine questions and in pressing hard on those unresolved problems thrown up by any attempt to secure a definition of ?sport? that would pre-emptively exclude any kind of advanced technological adjunct (or Derridean ?supplement?) that seemed to lead outside and beyond the realm of ?natural? human powers, capacities and skills. On the other hand I acknowledge ? as against ?strong?-conventionalist (e.g. Wittgensteinian) approaches ? that the category ?sport? cannot be relativised or culturally contextualised to the point where it loses all determinate sense or normative significance. My main purpose here is to assess various claims and counter-claims by running them past a fairly detailed account of competitive aeromodelling ? or one particular branch thereof ? and the kinds of difficulty it creates not only for conservative, essentialist or naturalising definitions but also for that other reactive trend towards all-out cultural-relativist or social-constructivist doctrines. In addition, though far from incidentally, I want to make the case that this is indeed a sport on any reasonable, fair, or adequately informed reckoning and that its recognition as such might help to clarify certain obscure corners of current philosophical thinking about these issues. (shrink)

In this essay, I offer a critical evaluation of Hilary Putnam's writings on epistemology and philosophy of science, in particular his engagement with interpretative problems in quantum mechanics. I trace the development of his thinking from the late 1960s when he adopted a strong causal-realist position on issues of meaning, reference, and truth, via the "internal realist" approach of his middle-period writings, to the various forms of pragmatist, naturalized, or "commonsense" epistemology proposed in his latest books. My contention is that (...) Putnam's retreat from a full-fledged realist outlook has been prompted in large part by his belief that it cannot possibly be reconciled with the implications of quantum mechanics for our understanding of processes and events in the subatomic domain. However, I suggest, this response should be seen as premature given the range of as-yet unresolved problems with quantum mechanics on the orthodox (Copenhagen) interpretation and also the existence of an alternative account - David Bohm's hidden-variables theory - which perfectly matches the established predictive-observational results while providing a credible realist ontology. I also examine Putnam's case for adopting a nonstandard (three-valued) "quantum logic" in relation to the thinking of other philosophers - Michael Dummett among them - who have espoused a more global or doctrinaire version of anti-realism. I conclude that Putnam's early (causal-realist) position is by no means untenable in light of the various arguments that he now takes as counting decisively against it. (shrink)

This article offers a critical review of various ontological-relativist arguments, mostly deriving from the work of W. V. Quine and Thomas K hn. I maintain that these arguments are (1) internally contradictory, (2) incapable of accounting for our knowledge of the growth of scientific knowledge, and (3) shown up as fallacious from the standpoint of a causal-realist approach to issues of truth, meaning, and interpretation. Moreover, they have often been viewed as lending support to such programmes as the 'strong' sociology (...) of knowledge and the turn towards wholesale cultural-relativist doctrines, whether of the Wittgensteinian ('language-games') or Heideggerian (depth-hermeneutic) varieties. Thus Richard Rorty recommends that we should henceforth drop all that old-fashioned talk of 'truth', 'knowledge', or 'reality', since whatever warrants those descriptions from time to time is just the product of some currently favoured language-game or range of elective metaphors. Such ideas have little in common with Quine's general outlook of robust physicalism, nor again - though the case is less clear - with Kuhn's reconsidered approach to these issues as set forth in his 1969 Postscript to The Structure of Scientific Revolutions . However, both thinkers have left themselves open to misconstrual by adopting a sceptical-relativist fallback position in response to the well-known problems with logical empiricism. This essay therefore reviews those problems with reference to alternative, more adequate accounts of what is involved in the process of scientific discovery and theory-change. (shrink)

In this essay I consider what is meant by the description ‘great’ philosophy and then offer some broadly applicable criteria by which to assess candidate thinkers or works. On the one hand are philosophers in whose case the epithet, even if contested, is not grossly misconceived or merely the product of doctrinal adherence on the part of those who apply it. On the other are those – however gifted, acute, or technically adroit – to whom its application is inappropriate because (...) their work cannot justifiably be held to rise to a level of creative-exploratory thought where the description would have any meaningful purchase. I develop this contrast with reference to Thomas Kuhn’s distinction between ‘revolutionary’ and ‘normal’ science, and also in light of J.L. Austin’s anecdotal remark – à propos Leibniz – that it was the mark of truly great thinkers to make great mistakes, or to risk falling into certain kinds of significant or consequential error. My essay goes on to put the case that great philosophy should be thought of as involving a constant readiness to venture and pursue speculative hypotheses beyond any limits typically imposed by a culture of ‘safe’, well-established, or academically sanctioned debate. At the same time – and just as crucially – it must be conceived as subject to the strictest, most demanding standards of formal assessment, i.e., with respect to basic requirements of logical rigour and conceptual precision. Focusing mainly on the work of Jacques Derrida and Alain Badiou I suggest that these criteria are more often met by philosophers in the broadly ‘continental’ rather than the mainstream ‘analytic’ line of descent. However – as should be clear – the very possibility of meeting them, and of their being jointly met by any one thinker, is itself sufficient indication that this is a false and pernicious dichotomy. (shrink)

Papineau has suggested that the Principle of Non-Contradiction is a logical law that ?verificationists? are not entitled to claim as a prioritrue. The Principle, like that of Excluded Middle, is not sufficiently grounded in the ?miserly? epistemology of verificationism to be proven in ?verificationist logic?. We examine who might be challenged by this claim: who are the ?verificationists?? We defend our candidates against Papineau's criticisms and other attacks, but this leaves the verificationist open to a different criticism.