The paper has two parts: 1. A brief exposition of proof-theoretic semantics, not necessarily in connection to natural language. 2. A review, with a contrastive flavour, of some of the applications of PTS to NL with an indication of advantages of PTS as a theory of meaning for NL.

The paper suggests a revision of the notion of harmony, a major necessary condition in proof-theoretic semantics for a natural-deduction proof-system to qualify as meaning conferring, when moving to a bilateral proof-system. The latter considers both forces of assertion and denial as primitive, and is applied here to positive logics, lacking negation altogether. It is suggested that in addition to the balance between introduction and elimination rules traditionally imposed by harmony, a balance should be imposed also on: negative introduction and (...) elimination rules, and positive and negative introduction rules. The paper suggests a proof-theoretical definition of duality, using which double harmony is defined. The paper proves that in a doubly-harmonious system, the coordination rule, typical to bilateral systems, is admissible. (shrink)

The paper provides a proof-theory for a negative presentation of classical logic based on a single primitive of exclusion, generalizing the known presentation via the binary ‘nand. The completeness is established via deductive equivalence to Gentzens NK/LK systems.

In the proof-theoretic semantics approach to meaning, harmony , requiring a balance between introduction-rules (I-rules) and elimination rules (E-rules) within a meaning conferring natural-deduction proof-system, is a central notion. In this paper, we consider two notions of harmony that were proposed in the literature: 1. GE-harmony , requiring a certain form of the E-rules, given the form of the I-rules. 2. Local intrinsic harmony : imposes the existence of certain transformations of derivations, known as reduction and expansion . We propose (...) a construction of the E-rules (in GE-form) from given I-rules, and prove that the constructed rules satisfy also local intrinsic harmony. The construction is based on a classification of I-rules, and constitute an implementation to Gentzen’s (and Pawitz’) remark, that E-rules can be “read off” I-rules. (shrink)

The combination of quantifiers with a semantics for epistemic operators in a modal framework is one of the major contributions of Hintikka in intensional logic. Hintikka’s starting point is his diagnosis of the failure of existential generalization and the substitution of identicals in terms of referential multiplicity. In this paper, I introduce Hintikka as a free logician. Indeed, Hintikka’s first-order epistemic logic is grounded on a logic free of ontological presuppositions with respect to singular terms. It is also a logic (...) free of presuppositions of uniqueness of reference. After having focused on the use of quantifiers and singular terms in Hintikka’s epistemic logic, I discuss some consequences from a semantico-logical perspective, but also from a philosophical one. By arguing against the so-called contingent a priori truths defended by Kripke, I conclude with a proposal in favour of Hintikka’s non-rigid interpretation of proper names. (shrink)

In "'Yes" and "No'" (2000), Ian Rumfitt proposed bilateralism--a use-based account of the logical words, according to which the sense of a sentence is determined by the conditions under which it is asserted and denied. One of Rumfitt's key claims is that bilateralism can provide a justification of classical logic. This paper raises a techical problem for Rumfitt's proposal, one that seems to undermine the bilateralist programme.

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)

Social choice and welfare economics are subjects at the frontier of many disciplines. Even if economics played the major role in their development, sociology, psychology and, principally, political science, mathematics and philosophy have been central for the manifold inventiveness of the employed methods and for the diversity of the studied topics. This phenomenon can be compared with game theory, a subject which has, of course, many connections with social choice and welfare. This fact is reflected by the disciplinary origins of (...) the contributors to the subject and, as an anecdote, by the disciplinary origins of the board of editors of this journal. Philosophers are expected to contribute mainly to the study of social justice and related ethical questions. But there is a tradition among logicians for studying voting theory. A famous example is C. L. Dodgson (Lewis Carroll), even though the complete works of Dodgson on voting occupy only a few pages. A major recent example is Michael Dummett. Michael Dummett is famous among social choice theorists for his joint paper with Robin Farquharson published in Econometrica in 1961. Later he wrote two important books on voting (Dummett (1984, 1997); for an overview see Salles (2006)). But it must be outlined that Michael Dummett is also, and above all, one of the greatest contemporary philosophers whose work on the German logician Frege, on intuitionism, realism, anti-realism, justificationism has been central for the development of analytical philosophy in the second part of the last century and in this century (an example is the Symposium in a recent issue of Mind (see Peacocke (2005) and Dummett (2005)). Sir Michael Dummett is Wykeham Professor of Logic emeritus at Oxford University. His interview was conducted at New College, Oxford in September 2004. (shrink)

Je suis trés reconnaissant à Michel Seymour d'avoir soumis mon livre à un examen détaillé, pénétrant, et charitable et d'avoir, par ses objections, mis le doigt sur un certain nombre de présupposés des thèses défendues dans ce livre, qu'il a souvent articulés bien mieux que je n'ai été capable de le faire. Le principal de ces présupposés est mon rejet implicite de la thése quinienne de l'indétermination de la traduction, qui m'engage, selon Seymour, à défendre une conception conservatrice de la (...) logique et à insister sur une détermination de son domaine qui lui paraît injustifiée. Seymour soutient au contraire qu'il faut admettre cette thése, qui «commande une tout autre perspective» que la mienne. Je voudrais à la fois résister à la prémisse et à la conclusion de cette inférence. (shrink)

The main thesis of this paper is that we sometimes are disposed to accept false and even jointly inconsistent claims by virtue of our semantic competence, and that this comes to light in the sorites and liar paradoxes. Among the subsidiary theses are that this is an important source of indeterminacy in truth conditions, that we must revise basic assumptions about semantic competence, and that classical logic and bivalence can be upheld in the face of the sorites paradox.

In this paper I investigate the claim that truth is a relational property. What does this claim really mean? What is its import?—Is it a basic feature of the concept of truth; or a distinctive feature of the correspondence theory of truth; or even both? After introducing some general ideas about truth, I begin by highlighting an ambiguity in current uses of the term ‘relational property’ in the truth debate, and show that we need to distinguish two separate ideas: that (...) truth is a relational property, and that truth is an extrinsic property. I go on to examine what both of these ideas are in more detail, and consider what would need to hold for truth to be in either of these categories. I then discern where all the main competitors in the truth debate stand on these issues. In doing so we learn more about these views and what they entail, and build a general picture of what stances different theories of truth take on whether truth is extrinsic or relational. Moreover, in doing this we will be able to answer one of the questions with which we began: whether truth’s being extrinsic or relational is something that, if accepted, lends support to the correspondence theory of truth. We will see that this is not so, and discern some interesting variations between various theories of truth on the issues of whether truth is extrinsic or relational. Following this we will be in a better position to judge whether the notions of extrinsicality or relationality are basic features of the concept of truth. In the final part of the paper I argue that, even if we are not in a position to conclude that they are basic features, they are features that any prospective theory of truth needs to take seriously. (shrink)

This paper identifies the difficulties in confronting novel history from both a rigorous scientific and artistic literary perspectives and suggests a practical reconciliation—in the form of a discussion and metaphorical opening space—between the two apparent poles of historical understanding and their accompanying genres, types, and tropes.

Our utterances are typically if not always "situated," in the sense that they are true or false relative to unarticulated parameters of the extra-linguistic context. The problem is to explain how these parameters are determined, given that nothing in the uttered sentences indicates them. It is tempting to claim that they must be determined at the level of thought or intention. However, as many philosophers have observed, thoughts themselves are no less situated than utterances. Unarticulated parameters need not be mentally (...) represented. In this paper, I try to make precise the notion of representation at stake here. In one sense of 'representation', something is represented if it is inferentially relevant. In another, less demanding sense, something is represented if it is relevant to the construction of a context-sensitive, ad hoc concept. Ad hoc concepts act as "proxies" for cognitively more demanding representations. They "imitate" the latter's epistemic and pragmatic roles while being inferentially less sophisticated. Thus, there are two senses in which a thought can be said to be situated: (1) its truth-value is relative to a non-represented contextual parameter, (2) its truth-value is not itself relative, but it involves a context-sensitive, ad hoc concept. (shrink)

What accounts for how we know that certain rules of reasoning, such as reasoning by Modus Ponens, are valid? If our knowledge of validity must be based on some reasoning, then we seem to be committed to the legitimacy of rule-circular arguments for validity. This paper raises a new difficulty for the rule-circular account of our knowledge of validity. The source of the problem is that, contrary to traditional wisdom, a universal generalization cannot be inferred just on the basis of (...) reasoning about an arbitrary object. I argue in favor of a more sophisticated constraint on reasoning by universal generalization, one which undermines a rule-circular account of our knowledge of validity. (shrink)

Intra-theoretical logical pluralism is a form of meaning-invariant pluralism about logic, articulated recently by Hjortland :355–373, 2013). This version of pluralism relies on it being possible to define several distinct notions of provability relative to the same logical calculus. The present paper picks up and explores this theme: How can a single logical calculus express several different consequence relations? The main hypothesis articulated here is that the divide between the internal and external consequence relations in Gentzen systems generates a form (...) of intra-theoretical logical pluralism. (shrink)

A logical constant is weakly disharmonious if its elimination rules are weaker than its introduction rules. Substructural weak disharmony is the weak disharmony generated by structural restrictions on the eliminations. I argue that substructural weak disharmony is not a defect of the constants which exhibit it. To the extent that it is problematic, it calls into question the structural properties of the derivability relation. This prompts us to rethink the issue of controlling the structural properties of a logic by means (...) of harmony. I argue that such a control is possible and desirable. Moreover, it is best achieved by global tests of harmony. (shrink)

Proof-theoretic semantics is an alternative to model-theoretic semantics. It aims at explaining the meaning of the logical constants in terms of the inference rules that govern their behaviour in proofs. We argue that this must be construed as the task of explaining these meanings relative to a logic, i.e., to a consequence relation. Alas, there is no agreed set of properties that a relation must have in order to qualify as a consequence relation. Moreover, the association of a consequence relation (...) to a logical calculus is not as straightforward as it may seem. We show that these facts are problematic for the proof-theoretic project but the problems can be solved. Our thesis is that the consequence relation relevant for proof-theoretic semantics is the one given by the sequent-to-sequent derivability relation in Gentzen systems. (shrink)

In the recent literature on proof-theoretic semantics, there is mention of a generality condition on defining rules. According to this condition, the schematic formulation of the defining rules must be maximally general, in the sense that no restrictions should be placed on the contexts of these rules. In particular, context variables must always be present in the schematic rules and they should range over arbitrary collections of formulae. I argue against imposing such a condition, by showing that it has undesirable (...) results and that it is ill-supported by the arguments brought in its favour. (shrink)

This paper develops a new account of reference-fixing for proper names. The account is built around an intuitive claim about reference fixing: the claim that I am a participant in a practice of using α to refer to o only if my uses of α are constrained by the representationally relevant ways it is possible for o to behave. §I raises examples that suggest that a right account of how proper names refer should incorporate this claim. §II provides such an (...) account. (shrink)

On a bilateralist reading, sequents are interpreted as statements to the effect that, given the assertion of the antecedent it is incoherent to deny the succedent. This interpretation goes against its own ecumenical ambitions, endowing Cut with a meaning very close to that of tertium non datur and thus rendering it intuitionistically unpalatable. This paper explores a top-down route for arguing that, even intuitionistically, a prohibition to deny is as strong as a licence to assert.

A central problem in the interpretation of non-relativistic quantum mechanics is to relate the conceptual structure of the theory to the classical idea of the state of a physical system. This paper approaches the problem by presenting an analysis of the notion of an elementary physical proposition. The notion is shown to be realized in standard formulations of the theory and to illuminate the significance of proofs of the impossibility of hidden variable extensions. In the interpretation of quantum mechanics that (...) emerges from this analysis, the philosophically distinctive features of the theory derive from the fact that it seeks to represent a reality of which complete knowledge is essentially unattainable. (shrink)

In this paper we provide a detailed proof-theoretical analysis of a natural deduction system for classical propositional logic that (i) represents classical proofs in a more natural way than standard Gentzen-style natural deduction, (ii) admits of a simple normalization procedure such that normal proofs enjoy the Weak Subformula Property, (iii) provides the means to prove a Non-contamination Property of normal proofs that is not satisfied by normal proofs in the Gentzen tradition and is useful for applications, especially in formal argumentation, (...) (iv) naturally leads to defining a notion of depth of a proof, to the effect that, for every fixed natural k, normal k-depth deducibility is a tractable problem and converges to classical deducibility as k tends to infinity. (shrink)

What is the role of a notion of truth in our form of life? What is it to possess a notion of truth? How different would we be, if we did not possess a notion of truth? Gulliver’s description of three peoples encountered during his fifth travel will help me to answer. One might say that the basic anti-realist tenet is that we should explain the notion of truth by connecting it with our practice of assertion. In this sense the (...) outcome of my commentary of the fifth part of Gulliver’s Travels will amount to a non-reductive anti-realist conception of truth. It can be called a dialectical conception of truth because it focuses on a particular way of resolving disagreements: an epistemically virtuous practice of verbal exchange that cares for truth. The main thesis is that an implicit awareness of the epistemically virtuous practice is a necessary condition for being in full possession of the notion of truth. The commentary will also involve an argument against deflationism and a critique of some claims made by Huw Price. (shrink)

The semantic inferentialist account of the social institution of semantic meaning can be naturally extended to account for social ontology. I argue here that semantic inferentialism provides a framework within which mathematical ontology can be understood as social ontology, and mathematical facts as socially instituted facts. I argue further that the semantic inferentialist framework provides resources to underpin at least some aspects of the objectivity of mathematics, even when the truth of mathematical claims is understood as socially instituted.

If correct, Christopher Peacocke’s [20] “manifestationism without verificationism,” would explode the dichotomy between realism and inferentialism in the contemporary philosophy of language. I first explicate Peacocke’s theory, defending it from a criticism of Neil Tennant’s. This involves devising a recursive definition for grasp of logical contents along the lines Peacocke suggests. Unfortunately though, the generalized account reveals the Achilles’ heel of the whole theory. By inventing a new logical operator with the introduction rule for the existential quantifier and the elimination (...) rule for the universal quantifier, I am able to show that Peacocke’s theory only avoids verificationism to the extent that it does not satisfy manifestationism. (shrink)

The paper explores what it could mean to speak of love as involving a delight in ‘the simple actuality’ of another, or, as Buber does, of the ‘touchable’ human being as ‘unique and devoid of qualities’. Developing strands in Merleau-Ponty’s treatment of perception, it is argued that the relation between recognising this as a particular individual and recognising particular qualities in her may be close to the reverse of what might be supposed: a recognition of this distinctive smile being dependent (...) on a recognition of who this is. The fundamental place of particulars, as opposed to kinds, in our thought about those we know and care for is developed in part through a phenomenological treatment of our perception of faces. That treatment is set in a context of the justification of our judgements about who someone is, and is linked with a critique of treatments of proper names of individuals in the spirit of Frege. It is in our speaking to those we know that we find a relation to a particular that is direct—not mediated by a description of its properties—that Russell sought in ‘knowledge by acquaintance’. (shrink)

It is often supposed that, unlike typical axioms of mathematics, the Continuum Hypothesis (CH) is indeterminate. This position is normally defended on the ground that the CH is undecidable in a way that typical axioms are not. Call this kind of undecidability “absolute undecidability”. In this paper, I seek to understand what absolute undecidability could be such that one might hope to establish that (a) CH is absolutely undecidable, (b) typical axioms are not absolutely undecidable, and (c) if a mathematical (...) hypothesis is absolutely undecidable, then it is indeterminate. I shall argue that on no understanding of absolute undecidability could one hope to establish all of (a)–(c). However, I will identify one understanding of absolute undecidability on which one might hope to establish both (a) and (c) to the exclusion of (b). This suggests that a new style of mathematical antirealism deserves attention—one that does not depend on familiar epistemological or ontological concerns. The key idea behind this view is that typical mathematical hypotheses are indeterminate because they are relevantly similar to CH. (shrink)

This paper considers whether there can be any such thing as a naturalized metaphysics of color—any distillation of the commitments of perceptual science with regard to color ontology. I first make some observations about the kinds of philosophical commitments that sometimes bubble to the surface in the psychology and neuroscience of color. Unsurprisingly, because of the range of opinions expressed, an ontology of color cannot simply be read off from scientists’ definitions and theoretical statements. I next consider two alternative routes. (...) First, conceptual pluralism inspired by Mark Wilson's analysis of scientific representation. I argue that these findings leave the prospects for a naturalized color ontology rather dim. Second, I outline a naturalized epistemology of perception. I ask how the correctness and informativeness of perceptual states is understood by contemporary perceptual science. I argue that the detectionist ideal of correspondence should be replaced by the pragmatic ideal of usefulness. I argue that this result has significant implications for the metaphysics of color. (shrink)

One diagnosis of Fitch’s paradox of knowability is that it hinges on the factivity of knowledge: that which is known is true. Yet the apparent role of factivity and non-factive analogues in related paradoxes of justified belief can be shown to depend on familiar consistency and positive introspection principles. Rejecting arguments that the paradox hangs on an implausible consistency principle, this paper argues instead that the Fitch phenomenon is generated both in epistemic logic and logics of justification by the interaction (...) of analogues of the knowability principle and positive introspection theses that are characteristic of, even if not entailed by, epistemic internalism. (shrink)

Some philosophers find the following thesis attractive: for every logical constant C there is a set of logical rules of inference R such that a subject knows the meaning of C if and only if she accepts the rules in R. I point out some obvious but, apparently, easily forgotten difficulties concerning this thesis.

Modus ponens is the argument from premises of the form If A, then B and A to the conclusion B. Nearly all participants agree that the modus ponens conclusion logically follows when the argument appears in this Basic form. However, adding a further premise can lower participants’ rate of agreement—an effect called suppression. We propose a theory of suppression that draws on contemporary ideas about conditional sentences in linguistics and philosophy. Semantically, the theory assumes that people interpret an indicative conditional (...) as a context-sensitive strict conditional: true if and only if its consequent is true in each of a contextually determined set of situations in which its antecedent is true. Pragmatically, the theory claims that context changes in response to new assertions, including new conditional premises. Thus, the conclusion of a modus ponens argument may no longer be accepted in the changed context. Psychologically, the theory describes people as capable of reasoning about broad classes of possible situations, ordered by typicality, without having to reason about individual possible worlds. The theory accounts for the main suppression phenomena, and it generates some novel predictions that new experiments confirm. (shrink)

Reasons motivate our intentions and thus our actions, justify our beliefs, ground our hopes and connect our feelings of shame and pride to our thoughts. Given that intentions, beliefs and emotions are intentional states, intentionality is strongly connected with normativity. Yet what is more precisely their relationship? Some philosophers, notably Brandom and McDowell, contend at places that intentionality is intrinsically normative. In this paper, we discuss Brandom and McDowell’s thesis and the arguments they provide for its defence. In contrast to (...) what they hold, we argue that neither reference intentionality nor content intentionality are intrinsically normative, although at least content intentionality has normative implications. More precisely, we argue that neither species of intentionality are normative from a semantical viewpoint, because being in an intentional state is not being in a state that is semantically correct or incorrect. Nevertheless, being in a state endowed with content may be a reason for believing or acting. Thus, we argue that content intentionality has normative implications. More precisely, we argue that any content is such that, if it is the content of a state that is sensitive to reasons - as judging paradigmatically is – then it entitles the subject of that state to have further states or to act in certain ways. (shrink)

Scott Soames has recently argued that traditional accounts of propositions as n-tuples or sets of objects and properties or functions from worlds to extensions cannot adequately explain how these abstract entities come to represent the world. Soames’ new cognitive theory solves this problem by taking propositions to be derived from agents representing the world to be a certain way. Agents represent the world to be a certain way, for example, when they engage in the cognitive act of predicating, or cognizing, (...) an act that takes place during cognitive events, such as perceiving, believing, judging and asserting. On the cognitive theory, propositions just are act types involving the act of predicating and certain other mental operations. This theory, Soames argues, solves not only the problem of how propositions come to represent but also a number of other difficulties for traditional theories, including the problem of de se propositions and the problems of accounting for how agents are capable of grasping propositions and how they come to stand in the relation of expression to sentences. I argue here that Soames’ particular version of the cognitive theory makes two problematic assumptions about cognitive operations and the contents of proper names. I then briefly examine what can count as evidence for the nature of the constituents of the cognitive operation types that produce propositions and argue that the common nature of cognitive operations and what they operate on ought to be determined empirically in cross-disciplinary work. I conclude by offering a semantics for cognitive act types that accommodates one type of empirical evidence. (shrink)

A common view relating compositional semantics and the objects of assertion holds the following: Sentences φ and ψ expresses the same proposition iff φ and ψ have the same modal profile. Following Dummett, Evans, and Lewis, Stanley argues that this view is fundamentally mistaken. According to Dummett, we must distinguish the semantic contribution a sentence makes to more complex expressions in which it occurs from its assertoric content. Stojnić insists that views which distinguish the roles of content and semantic value (...) must nevertheless ensure a tight connection between the two. But, she contends, there is a crucial disanalogy between the views that follow Lewis and the views that follow Dummett. Stanley’s Dummettian view is argued to contain a fatal flaw: On such views, there is no way to secure an appropriate connection between semantic value and a theoretically motivated notion of assertoric content. I will review the background issues from Dummett, Evans, Lewis, and Stanley, and provide a principled way of bridging the gap between semantic value and a theoretically motivated notion of assertoric content. (shrink)

The standard paradigm for mental causation is a person’s acting for a reason. Something happens - she intentionally φ’s - the occurrence of which we explain by citing a relevant belief or desire. In the present context, I simply take for granted the following two conditions on the appropriateness of this explanation. First, the agent φ’s _because_ she believes/desires what we say she does, where this is expressive of a _causal_ dependence.1 Second, her believing/desiring this gives her a _reason_ for (...) φ-ing: recognizing that she has this belief/desire makes her φ-ing intelligible as rational in the light of her other attitudes and circumstances. A further condition must be met, though, if this is to be a genuine psychological explanation, a case of her acting _for_ the reason in question. Consider the following example of Davidson’s (1973, p. 79). An exhausted climber is desperate to rid herself of the weight and danger of holding her partner on a rope; and her sudden realization that simply letting go would achieve this so unnerves her that her grip loosens slightly and he falls. Her releasing him causally depends upon her having this belief and desire, which provide _a_ reason for doing what she does. But this is not _why_ she does it: it would be at best misleading to say that she dropped him, intentionally, because she was fed up with holding his weight, or because she thought that she might otherwise fall. Her letting go does not depend upon her having these reasons in the right way. The reason-giving relation is causally irrelevant. If we are to explain a person’s acting _for_ a reason, then her doing. (shrink)

Ignacio Jane has argued that second-order logic presupposes some amount of set theory and hence cannot legitimately be used in axiomatizing set theory. I focus here on his claim that the second-order formulation of the Axiom of Separation presupposes the character of the power set operation, thereby preventing a thorough study of the power set of infinite sets, a central part of set theory. In reply I argue that substantive issues often cannot be separated from a logic, but rather must (...) be presupposed. I call this the logic-metalogic link. There are two facets to the logic-metalogic link. First, when a logic is entangled with a substantive issue, the same position on that issue should be taken at the meta- level as at the object level; and second, if an expression has a clear meaning in natural language, then the corresponding concept can equally well be deployed in a formal language. The determinate nature of the power set operation is one such substantive issue in set theory. Whether there is a determinate power set of an infinite set can only be presupposed in set theory, not proved, so the use of second-order logic cannot be ruled out by virtue of presupposing one answer to this question. Moreover, the legitimacy of presupposing in the background logic that the power set of an infinite set is determinate is guaranteed by the clarity and definiteness of the notions of all and of subset. This is also exactly what is required for the same presupposition to be legitimately made in an axiomatic set theory, so the use of second-order logic in set theory rather than first-order logic does not require any new metatheoretic commitments. (shrink)

What is a logical constant? The question is addressed in the tradition of Tarski's definition of logical operations as operations which are invariant under permutation. The paper introduces a general setting in which invariance criteria for logical operations can be compared and argues for invariance under potential isomorphism as the most natural characterization of logical operations.

Conceptual analysis is an integral part of legal theory, but the nature and purpose of such inquiries are often not clearly stated. In this article, I attempt to elaborate upon some of the differing reasons for conceptual analysis and what consequences may follow from choosing one objective rather than another. By showing that divergent purposes are often present in competing analyses of the same concept, I also hope to indicate why some “debates” in the jurisprudential literature are best understood as (...) theorists talking past one another. (shrink)

This critical notice explores the distinction central to analytic philosophy between the logical study of the normative principles governing rational thought and the psychological study of the processes of thinking. Thomas Nagel maintains (1) that the fundamental principles of reasoning have normative force and make claims to universal validity; (2) that the fundamental principles of reasoning cannot be construed as the expression of contingent forms of life; and (3) that the identification of fundamental principles of reasoning should be completely independent (...) of psychological facts about how people reason. The notice draws upon intuitionist critiques of classical logic and the Allais paradox in expected utility theory to argue that (1) can be consistently combined with the denial of (2) and (3). (shrink)

In different papers, Carnielli, W. & Rodrigues, A., Carnielli, W. Coniglio, M. & Rodrigues, A. and Rodrigues & Carnielli, present two logics motivated by the idea of capturing contradictions as conflicting evidence. The first logic is called BLE and the second—that is a conservative extension of BLE—is named LETJ. Roughly, BLE and LETJ are two non-classical logics in which the Laws of Explosion and Excluded Middle are not admissible. LETJ is built on top of BLE. Moreover, LETJ is a Logic (...) of Formal Inconsistency. This means that there is an operator that, roughly speaking, identifies a formula as having classical behavior. Both systems are motivated by the idea that there are different conditions for accepting or rejecting a sentence of our natural language. So, there are some special introduction and elimination rules in the theory that are capturing different conditions of use. Rodrigues & Carnielli’s paper has an interesting and challenging idea. According to them, BLE and LETJ are incompatible with dialetheia. It seems to show that these paraconsistent logics cannot be interpreted using truth-conditions that allow true contradictions. In short, BLE and LETJ talk about conflicting evidence avoiding to talk about gluts. I am going to argue against this point of view. Basically, I will firstly offer a new interpretation of BLE and LETJ that is compatible with dialetheia. The background of my position is to reject the one canonical interpretation thesis: the idea according to which a logical system has one standard interpretation. Then, I will secondly show that there is no logical basis to fix that Rodrigues & Carnielli’s interpretation is the canonical way to establish the content of logical notions of BLE and LETJ. Furthermore, the system LETJ captures inside classical logic. Then, I am also going to use this technical result to offer some further doubts about the one canonical interpretation thesis. (shrink)

Later Wittgenstein is famous for having related meaning and use. Nonetheless, thanks to Dummett and Kripke, and the debates they provoked, a conventional wisdom is nowadays available: Wittgenstein, so the story goes, adopted a theory of meaning in terms of assertability conditions. This paper claims that it is wrong to attribute such a theory to the Investigations. For such a thesis to go through, one of the following two scenarios should be confirmed. It should either be true that Wittgenstein reduces (...) all meaning-engendering uses and conditions of use to assertion and assertability conditions, or that he invokes assertability conditions to show that meaning is always use. But, I will be claiming, the first scenario is excluded by Wittgenstein’s thoughts about the role of assertion and his thoughts about the sense-force distinction, while the second scenario is excluded by Wittgenstein’s thoughts about truth. (shrink)

Various attempts at demarcating logic were undertaken, many of them based on specific understanding of how logical knowledge is formal and not material. MacFarlane has persuasively shown that general idea of formality of logic can be understood in various ways. I take two of the accounts of formality, namely the requirement of conservativity and the requirement of schematicity of logical vocabulary, into consideration as promising candidates to make the all too unclear notion of formality more precise and study to what (...) degree they could be considered as either necessary or sufficient conditions for logicality of some piece of vocabulary. Finding both notion unsatisfactory, as they stand, I propose combining them and envisage a hierarchy of logicality of expressions of a given language. Such a hierarchy is complicated and not linear, yet still offers a valuable explication of both the range and pragmatic significance of logic, if we combine it with logical expressivism. (shrink)

Whether meaning is compositional has been a major issue in linguistics and formal philosophy of language for the last 2 decades. Semantic holism is widely and plausibly considered as an objection to the principle of semantic compositionality therein. It comes as a surprise that the holistic peculiarities of scientific language have been rarely addressed in formal accounts so far, given that semantic holism has its roots in the philosophy of science. For this reason, a model-theoretic approach to semantic holism in (...) the language of science is presented here. This approach preserves compositionality to a large extent. *Received September 2009; revised February 2010. †To contact the author, please write to: Seminar for Philosophy, Logic, and Theory of Science, Hauspostfach 49, Ludwig-Maximilians-Universität, Munich 80539, Germany; e-mail: [email protected]. (shrink)

Modal logic has been applied in many different areas, as reasoning about time, knowledge and belief, necessity and possibility, to mention only some examples. In the present paper, an attempt is made to use modal logic to account for the semantics of theoretical sentences in scientific language. Theoretical sentences have been studied extensively since the work of Ramsey and Carnap. The present attempt at a modal analysis is motivated by there being several intended interpretations of the theoretical terms once these (...) terms are introduced through the axioms of a theory. (shrink)