This paper deals with the problem of future contingents, and focuses on two classical logical principles, excluded middle and bivalence. One may think that different attitudes are to be adopted towards these two principles in order to solve the problem. According to what seems to be a widely held hypothesis, excluded middle must be accepted while bivalence must be rejected. The paper goes against that line of thought. In the first place, it shows how the rejection of bivalence leads to (...) implausible consequences if excluded middle is accepted. In the second place, it addresses the question of why one should reject bivalence, and finds no satisfactory answer. /// Este artículo trata el problema de los futuros contingentes, y se enfoca en dos principios lógicos clásicos: el tercero excluido y la bivalencia. Se podría pensar que una solución del problema requiere actitudes diferentes hacia estos dos principios. Según una hipótesis que parece ampliamente compartida, el tercero excluido debe ser aceptado, mientras que la bivalencia debe ser rechazada. Este artículo argumenta en contra de esta línea de pensamiento. En primer lugar, se aborda cómo el rechazo de la bivalencia lleva a consecuencias poco plausibles si el tercero excluido es aceptado. En segundo lugar, se enfrenta la cuestión de por qué se debería rechazar la bivalencia, sin encontrar una respuesta satisfactoria. (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)

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)

Classical (Bayesian) probability (CP) theory has led to an influential research tradition for modeling cognitive processes. Cognitive scientists have been trained to work with CP principles for so long that it is hard even to imagine alternative ways to formalize probabilities. However, in physics, quantum probability (QP) theory has been the dominant probabilistic approach for nearly 100 years. Could QP theory provide us with any advantages in cognitive modeling as well? Note first that both CP and QP theory share the (...) fundamental assumption that it is possible to model cognition on the basis of formal, probabilistic principles. But why consider a QP approach? The answers are that (1) there are many well-established empirical findings (e.g., from the influential Tversky, Kahneman research tradition) that are hard to reconcile with CP principles; and (2) these same findings have natural and straightforward explanations with quantum principles. In QP theory, probabilistic assessment is often strongly context- and order-dependent, individual states can be superposition states (that are impossible to associate with specific values), and composite systems can be entangled (they cannot be decomposed into their subsystems). All these characteristics appear perplexing from a classical perspective. However, our thesis is that they provide a more accurate and powerful account of certain cognitive processes. We first introduce QP theory and illustrate its application with psychological examples. We then review empirical findings that motivate the use of quantum theory in cognitive theory, but also discuss ways in which QP and CP theories converge. Finally, we consider the implications of a QP theory approach to cognition for human rationality. (shrink)

Three misrepresentations of informal and formal logic by two feminist writers are discussed. Andrea Nye's criticism that the semantics for formal logic abstracts from context is a misrepresentation of formal logic because Nye ignores the development of intensional logics. Second, Nye's criticism that informaIlogicians ignore the origins of arguments is a misrepresentation of fallacy theory. Prominent writers in the field specifiy numerous cases where the origins of an argument are relevant to its evaluation. Third, Valerie Plumwood's criticism that negation in (...) classical logic rests on an exclusivistic dualism that encourages the exclusion of women is shown to be false. (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)

Kniha, jako je tato, nemůže být tak docela dílem jediného člověka. Dovést ji do podoby koherentního celku bych nedokázal bez pomoci svých kolegů, kteří po mně text četli a upozornili mě na spoustu chyb a nedůsledností, které se v něm vyskytovaly. Můj dík v tomto směru patří zejména Vojtěchu Kolmanovi, Liboru Běhounkovi a Martě Bílkové. Za připomínky k různým částem rukopisu jsem vděčen i Pavlu Maternovi, Milanu Matouškovi, Prokopu Sousedíkovi, Vladimíru Svobodovi, Petru Hájkovi a Grahamu Priestovi. Kniha vznikla v rámci (...) projektu podpořeného grantem AV ČR číslo A0009001/00. (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)

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)

The recent development and exploration of mixed metainferential logics is a breakthrough in our understanding of nontransitive and nonreflexive logics. Moreover, this exploration poses a new challenge to theorists like me, who have appealed to similarities to classical logic in defending the logic ST, since some mixed metainferential logics seem to bear even more similarities to classical logic than ST does. There is a whole ST-based hierarchy, of which ST itself is only the first step, that seems to become more (...) and more classical at each level. I think this seeming is misleading: for certain purposes, anyhow, metainferential hierarchies give us no reason to move on from ST. ST is indeed only the first step on a grand metainferential adventure; but one step is enough. This paper aims to explain and defend that claim. Along the way, I take the opportunity also to develop some formal tools and results for thinking about metainferential logics more generally. (shrink)

The three definitions of the law of non-contradiction highlighted by Jan Łukasiewicz in Aristotle’s Metaphysics included, aside from its ontological and logical versions, also the psychological one. Commentators have not reached a consensus as to its precise character. Below I shall present the existing discrepancies and propose a solution.

Logical pluralism is the view that there is more than one correct logic. This very general characterization gives rise to a whole family of positions. I argue that not all of them are stable. The main argument in the paper is inspired by considerations known as the “collapse problem”, and it aims at the most popular form of logical pluralism advocated by JC Beall and Greg Restall. I argue that there is a more general argument available that challenges all variants (...) of logical pluralism that meet the following three conditions: that there are at least two correct logical systems characterized in terms of different consequence relations, that there is some sort of rivalry among the correct logics, and that logical consequence is normative. The hypothesis I argue for amounts to conditional claim: If a position satisfies all these conditions, then that position is unstable in the sense that it collapses into competing positions. (shrink)

Logical pluralism is commonly described as the view that there is more than one correct logic. It has been claimed that, in order for that view to be interesting, there has to be at least a potential for rivalry between the correct logics. This paper offers a detailed assessment of this suggestion. I argue that an interesting version of logical pluralism is hard, if not impossible, to achieve. I first outline an intuitive understanding of the notions of rivalry and correctness. (...) I then discuss a natural account of rivalry in terms of disagreement about validity claims and the argument from meaning variance that has been raised against it. I explore a more refined picture of the meaning of validity claims that makes use of the character-content distinction of classical two dimensional semantics. There are three ways in which pluralists can use that framework to argue for the view that different logics may be rivals but could nevertheless be equally correct. I argue that none of them is convincing. (shrink)

Starting from a proof-theoretic perspective, where meaning is determined by the inference rules governing logical operators, in this paper we primarily aim at developing a proof-theoretic alternative to the model-theoretic meaning-invariant logical pluralism discussed in Beall and Restall. We will also outline how this framework can be easily extended to include a form of meaning-variant logical pluralism. In this respect, the framework developed in this paper—which we label two-level proof-theoretic pluralism—is much broader in scope than the one discussed in Beall (...) and Restall’s book. (shrink)

Substructural pluralism about the meaning of logical connectives is best understood as the view that natural language connectives have all (and only) the properties conferred by classical logic, but that particular occurrences of these connectives cannot simultaneously exhibit all these properties. This is just a more sophisticated way of saying that while natural language connectives are ambiguous, they are not so in the way classical logic intends them to be. Since this view is usually framed as a means to resolve (...) paradoxes, little attention is paid to the logical properties of the ambiguous connectives themselves. The present paper sets out to fill this gap. First, I argue that substructural logicians should care about these connectives; next, I describe a consequence relation between a set of ambiguous premises and an ambiguous conclusion, and review the logical properties of ambiguous connectives; and finally, I highlight how ambiguous connectives can explain our intuitions about logical rivalry. (shrink)

n the analytic tradition, the appeal to intuition has been a common philosophical practice that supposedly provides us with epistemic standards. The authoress argues that the high epistemological standards of traditional analytic philosophy cannot be pursued by this method. Perhaps within a naturalistic, reliable frame intuitions can be evoked more coherently. Philosophers can use intuition as scientists do, in hypothesis- construction or data- collection. This is an ironic conclusion: Traditional analytic epistemologists rely on the appeal to intuition, but cannot justify (...) it. Naturalists, on the other hand, are not those who need such a method; yet they can better accommodate it within their view. (shrink)

Two-by-two grids are a popular means of exposition of management thought. In this note such grids are identified with Carroll diagrams, developed by the Oxford mathematician and logician Charles Dodgson. Using this insight, the nature of the conceptual tool frequently used by management authors is reflected upon. Two-by-two grids are a clear means of exposition and can be a valuable vehicle for identifying hitherto neglected aspects of a management issue, but there is also a risk that, in their relatively parsimonious (...) treatment of management topics, they fail to capture important features of practice. Two particular areas of risk are identified and discussed. (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)

Two-by-two grids are a popular means of exposition of management thought. In this note such grids are identified with Carroll diagrams, developed by the Oxford mathematician and logician Charles Dodgson. Using this insight, the nature ofthe conceptual tool frequently used by management authors is reflectedupon. Two-by-two grids are a clear means of exposition and can be a valuable vehicle for identifying hitherto neglected aspects of a management issue, but there is also a risk that, in their relatively parsimonious treatment of (...) management topics, they fail to capture important features of practice. Two particular areas of risk are identified and discussed. (shrink)

Popper welcomes Tarski's theory of truth as a vindication of the ‘objective or absolute or correspondence theory of truth’: -/- Tarski's greatest achievement, and the real significance of his theory for the philosophy of the empirical sciences, is that he rehabilitated the correspondence theory of absolute or objective truth … He vindicated the free use of the intuitive idea of truth as correspondence to the facts ….

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 considering the very possibility of deviant logic, we face the following question: what makes us see an operator of one logical system as a deviant version of an operator of another system? Why not see it simply as a different operator? Why do we see, say, intuitionist implication as an operator 'competing' with classical implication? Is it only because both happen to be called implications?1 It is clear that if we want to make cross-systemic comparisons, we need an 'Archimedean (...) point' external to the systems compared. Some logicians and philosophers, including Quine (1986), come close to saying that no such Archimedean point is available, and hence that there can be no deviant logics, for if two operators are governed by different axioms, then they are simply two different operators (or, if you prefer, operators with different meanings). From this viewpoint, intuitionist implication is no less different from classical implication than, say, intuitionist or classical conjunction. This conclusion is indeed plausible if we consider logical calculi simply as algebraic structures2; however, things are different if we see them as a means of accounting for something that is already 'there' before we establish the structures and is to be explicated by them. From such a perspective, two operators of different systems may be variants of the same operator in virtue of the fact that they are both means of capturing the same pretheoretical item. What might these items be? Sometimes it seems that logicians tacitly assume that there are some mythical archetypes of implication, conjunction etc., located somewhere in some Platonic heaven or somehow underlying the a priori structures of our mind, which logic tries to capture (for better or worse). However, when it comes to the comparison of the concrete outcomes of our logical efforts, say the classical and the intuitionist implications with the archetypal Implication, the latter can never be materialized so distinctly as to be of any help. A more constructive proposal is that the operators are related to elements or constructions of our language.. (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)

The paper consists of two parts. The first part begins with the problem of whether the original three-valued calculus, invented by J. Łukasiewicz, really conforms to his philosophical and semantic intuitions. I claim that one of the basic semantic assumptions underlying Łukasiewicz's three-valued logic should be that if under any possible circumstances a sentence of the form "X will be the case at time t" is true (resp. false) at time t, then this sentence must be already true (resp. false) (...) at present. However, it is easy to see that this principle is violated in Lukasiewicz's original calculus (as the cases of the law of excluded middle and the law of contradiction show). Nevertheless it is possible to construct (either with the help of the notion of "supervaluation", or purely algebraically) a different three-valued, semi-classical sentential calculus, which would properly incorporate Łukasiewicz's initial intuitions. Algebraically, this calculus has the ordinary Boolean structure, and therefore it retains all classically valid formulas. Yet because possible valuations are no longer represented by ultrafilters, but by filters (not necessarily maximal), the new calculus displays certain non-classical metalogical features (like, for example, nonextensionality and the lack of the metalogical rule enabling one to derive "p is true or q is true" from" 'p ∨ q' is true"). The second part analyses whether the proposed calculus could be useful in formalizing inferences in situations, when for some reason (epistemological or ontological) our knowledge of certain facts is subject to limitation. Special attention should be paid to the possibility of employing this calculus to the case of quantum mechanics. I am going to compare it with standard non-Boolean quantum logic (in the Jauch-Piron approach), and to show that certain shortcomings of the latter can be avoided in the former. For example, I will argue that in order to properly account for quantum features of microphysics, we do not need to drop the law of distributivity. Also the idea of "reading off" the logical structure of propositions from the structure of Hilbert space leads to some conceptual troubles, which I am going to point out. The thesis of the paper is that all we need to speak about quantum reality can be acquired by dropping the principle of bivalence and extensionality, while accepting all classically valid formulas. (shrink)