Elia Zardini

A new semantic paradox developed by Richard Heck and relying on very minimal logical and truth-theoretic resources is rehearsed. A theory of truth restricting the structural metarule of contraction is presented and some of the theory's relevant features are made explicit. It is then shown how the theory provides a principled solution to the paradox while preserving the extremely compelling truth-theoretic principles at stake, thus bringing out a significant advantage that the theory enjoys over virtually all other non-dialetheic theories. It is finally argued that such advantage is amplified by theoretical considerations made available by the adoption of a correspondentist perspective in the philosophy of truth

According to the naive theory of vagueness, the vagueness of an expression consists in the existence of both positive and negative cases of application of the expression and in the non- existence of a sharp cut-off point between them. The sorites paradox shows the naive theory to be inconsistent in most logics proposed for a vague language. The paper explores the prospects of saving the naive theory by revising the logic in a novel way, placing principled restrictions on the transitivity of the consequence relation. A lattice-theoretical framework for a whole family of “tolerant logics” is proposed and developed. Particular care is devoted to the relation between the salient features of the formal apparatus and the informal logical and semantic notions they are supposed to model. A suitable non-transitive counterpart to classical logic is defined. Some of its properties are studied, and it is eventually shown how an appropriate regimentation of the naive theory of vagueness is consistent in such a logic.

The paper offers a critical examination of a prominent, “quasi-deflationist” argument advanced in the contemporary debate on the semantic paradoxes against non-naive and non-transparent theories of truth. The argument claims that truth unrestrictedly fulfils certain expressive functions, and that its so doing requires the unrestricted validity of naivety and transparency principles. The paper criticises the quasi-deflationist argument by considering some kinds of cases in which transparency and naivety arguably fail. In some such cases truth still fulfils the relevant expressive functions without being transparent or naive; in some other such cases, truth does not fulfil the relevant expressive functions and other conceptual resources must be called upon. Thus, in different ways, all such cases belie the quasi-deflationist argument’s insistence that naivety and transparency should be unrestrictedly valid for truth unrestrictedly to fulfil the relevant expressive functions. There might however be other reasons for solving the semantic paradoxes by revising classical logic, and the paper in effect closes by offering versions of the liar paradox that rely on compelling but opacity-friendly truth-theoretic principles

After providing some historical and systematic background, I introduce the structure of a very natural and influential sceptical underdetermination argument. The argument assumes that it is metaphysically possible for a deceived subject to have the same evidence that a non-deceived subject has, and tries to draw consequences about justification from that assumption of metaphysical possibility. I first variously object to the transition from the assumption to its supposed consequences. In the central part of the paper, I then critically consider some influential ways of bridging the gap between the assumption and its supposed consequences, which generally consist in strengthening the assumption from one of metaphysical possibility into one of either counterfactual implication or entailment. The discussion indicates that epistemic facts are much more independent from metaphysically modal facts than the sceptical underdetermination argument requires

The paper discusses some ways in which the phenomenon of borderline cases may be thought to bear on the traditional philosophical idea that certain domains of facts are fully open to our view. The discussion focusses on a very influential argument (due to Tim Williamson) to the effect that, roughly, no such domains of luminous facts exist. Many commentators have felt that the vagueness unavoidably inherent in the description of the facts that are best candidates for being luminous plays an illicit role in the argument. The paper investigates this issue by centring around the idea that vagueness brings with itself borderline cases, and that these in turn generate absence of a fact of the matter and hence epistemically benign lack of knowledge. It is argued that, given the possibility of absence of a fact of the matter, the idea of luminosity should be reformulated using the notion of determinacy, and that the resulting reformulation is not immediately subject to the original anti-luminosity argument. However, it is shown that the specific understanding of determinacy required by this strategy validates a new argument against the reformulated version of luminosity. Moreover, reflection on the connection between mistake and absence of a fact of the matter offers another argument against such version, with the surprising upshot that, granting the soundness of the original anti-luminosity argument, not even the determinacy of a certain fact would guarantee its knowability

The naive theory of vagueness holds that the vagueness of an expression consists in its failure to draw a sharp boundary between positive and negative cases. The naive theory is contrasted with the nowadays dominant approach to vagueness, holding that the vagueness of an expression consists in its presenting borderline cases of application. The two approaches are briefly compared in their respective explanations of a paramount phenomenon of vagueness: our ignorance of any sharp boundary between positive and negative cases. These explanations clearly do not provide any ground for choosing the dominant approach against the naive theory. The decisive advantage of the former over the latter is rather supposed to consist in its immunity to any form of sorites paradox. But another paramount phenomenon of vagueness is higher-order vagueness: the expressions introduced in order to express in the object language the vagueness of the object language are themselves vague. Two highly plausible claims about higher-order vagueness are articulated and defended: the existence of “definitely ω ” positive and negative cases and the “radical” character of higher-order vagueness itself. Using very weak logical principles concerning vague expressions and the ‘definitely’-operator, it is then shown that, in the presence of higher-order vagueness as just described, the dominant approach is subject to higher-order sorites paradoxes analogous to the original ones besetting the naive theory, and therefore that, against the communis opinio, it does not fare substantially better with respect to immunity to any form of sorites paradox

A notion of truth as applicable to events of assertoric use ( utterances ) of a sentence token is arguably presupposed and required by our evaluative practices of the use of language. The truth of an utterance seems clearly to depend on what the utterance says . This fundamental dependence seems in turn to be captured by the schema that, if an utterance u says that P , then u is true iff P . Such a schema may thus be thought to constitute a suitable basis for an adequate theory of utterance truth, so much so that it seems straightforwardly to avoid the problems arising from context dependence and the semantic paradoxes which notoriously beset theories of utterance truth based on a simple disquotational schema. The paper argues that appearances are deceptive in both cases. On the one hand, the schema cannot allow for plausible if not uncontroversial non-indexical forms of context dependence, arising from the possibility that what an utterance says can be the case or not relative to different situations and that the truth of an utterance u of a sentence φ arguably depends on the truth of φ at the situation "associated" with u . On the other hand, a quantified utterance-truth variation on the liar paradox shows that the schema entails some consequence φ and at the same time the untruth of any utterance of φ; moreover, a resilient quantified propositional variation on the contingent liar paradox is offered, which only relies on resources usually employed by theories of utterance truth based on the schema.

The paper is concerned with a logical difficulty which Lionel Shapiro’s deflationist theory of logical consequence (as well as the author’s favoured, non-deflationist theory) gives rise to. It is argued that Shapiro’s non-contractive approach to solving the difficulty, although correct in its broad outlines, is nevertheless extremely problematic in some of its specifics, in particular in its failure to validate certain intuitive rules and laws associated with the principle of modus ponens. An alternative non-contractive theory is offered which does not suffer from the same problem

In a series of very influential works, Tim Williamson has advanced and defended a much discussed theory of evidence containing, among other claims, the thesis that, if one knows P, P is part of one's evidence. I argue that K ⊆ E is false, and indeed that it is so for a reason that Williamson himself essentially provides in arguing against the thesis that, if one has a justified true belief in P, P is part of one's evidence: together with a very plausible principle governing the acquisition of knowledge by non-deductive inference based on evidence, K ⊆ E leads, in a sorites-like fashion, to what would seem a series of unacceptably bootstrapping expansions of one's evidence. I then develop some considerations about the functions of and conditions for evidence which are suggested by the argument against K ⊆ E. I close by discussing the relationship of the argument with anti-closure arguments of the style exemplified by the preface paradox: I contend that, if closure is assumed, it is extremely plausible to expect that the diagnosis of what goes wrong in the preface-paradox-style argument cannot be used to block my own argument.

Some apparently valid arguments crucially rely on context change. To take a kind of example first discussed by Frege, ‘Tomorrow, it’ll be sunny’ taken on a day seems to entail ‘Today, it’s sunny’ taken on the next day, but the first sentence taken on a day sadly does not seem to entail the second sentence taken on the second next day. Mid-argument context change has not been accounted for by the tradition that has extensively studied the distinctive logical properties of context-dependent languages, for that tradition has focussed on arguments whose premises and conclusions are taken at the same context. I first argue for the desiderability of having a logic that accounts for mid-argument context change and I explain how one can informally understand such context change in a standard framework in which the relation of logical consequence holds among sentences. I then propose a family of simple temporal “intercontextual” logics that adequately model the validity of certain arguments in which the context changes. In particular, such logics validate the apparently valid argument in the Fregean example. The logics lack many traditional structural properties (reflexivity, contraction, commutativity etc.) as a consequence of the logical significance acquired by the sequence structure of premises and conclusions. The logics are however strong enough to capture in the form of logical truths all the valid arguments of both classical logic and Kaplan-style “intracontextual” logic. Finally, I extend the framework by introducing new operations into the object language, such as intercontextual conjunction, disjunction and implication, which, contrary to intracontextual conjunction, disjunction and implication, perfectly match the metalinguistic, intercontextual notions of premise combination, conclusion combination and logical consequence by representing their respective two operands as taken at different contexts

The concept of truth arguably plays a central role in many areas of philosophical theorizing. Yet, what seems to be one of the most fundamental principles governing that concept, i.e. the equivalence between P and , is inconsistent in full classical logic, as shown by the semantic paradoxes. I propose a new solution to those paradoxes, based on a principled revision of classical logic. Technically, the key idea consists in the rejection of the unrestricted validity of the structural principle of contraction. I first motivate philosophically this idea with the metaphysical picture of the states-of-affairs expressed by paradoxical sentences as being distinctively . I then proceed to demonstrate that the theory of truth resulting from this metaphysical picture is, in many philosophically interesting respects, surprisingly stronger than most other theories of truth endorsing the equivalence between P and (for example, the theory vindicates the validity of the traditional laws of excluded middle and of non-contradiction, and also vindicates the traditional constraint of truth preservation on logical consequence). I conclude by proving a cutelimination theorem that shows the consistency of the theory

This paper investigates how naive theories of truth fare with respect to a set of extremely plausible principles of restricted quantification. It is first shown that both nonsubstructural theories as well as certain substructural theories cannot validate all those principles. Then, pursuing further an approach to the semantic paradoxes that the author has defended elsewhere, the theory of restricted quantification available in a specific naive theory that rejects the structural property of contraction is explored. It is shown that the theory validates all the principles in question, and it is argued that other prima facie plausible principles that the theory fails to validate are objectionable on independent grounds.

The paper discusses some ways in which vagueness and its phenomena may be thought to impose certain limits on our knowledge and, more specifically, may be thought to bear on the traditional philosophical idea that certain domains of facts are luminous, i.e., roughly, fully open to our view. The discussion focuses on a very influential argument to the effect that almost no such interesting domains exist. Many commentators have felt that the vagueness unavoidably inherent in the description of the facts that are best candidates for being luminous plays an illicit role in such argument. The paper centres around the idea that vagueness brings with itself the prima facie plausibility of soritical principles. Using the diagnostics of sharpenings, it is first pointed out that, despite certain considerations to the contrary, the margin‐for‐error principle required by the anti‐luminosity argument may well derive all of its plausibility from an underlying soritical principle. The notion of confidence that is relevant to the argument is then isolated and sharply distinguished from the notion of subjective probability. Against this background, it is argued that the reasoning about confidence involved in the argument in favour of the problematic margin‐for‐error principle is fallacious in the same way in which sorites reasoning is. This reveals the possibility of having reliable knowledge even at the penumbral limit with falsity, a possibility for which a concrete formal model is constructed. The model in turn permits a deeper appreciation of the role played in the dialectic by the distinction between confidence and subjective probability as well as by confidence requirements on knowledge. It is concluded that careful heeding of vagueness and its phenomena, far from forcing new and surprising limits on our knowledge, actually removes one of the main barriers – unreliability – often thought to stand in its way

In this paper, we present a number of problems for intellectualism about knowledge-how, and in particular for the version of the view developed by Stanley & Williamson 2001. Their argument draws on the alleged uniformity of 'know how'-and 'know wh'-ascriptions. We offer a series of considerations to the effect that this assimilation is problematic. Firstly, in contrast to 'know wh'-ascriptions, 'know how'-ascriptions with known negative answers are false. Secondly, knowledge-how obeys closure principles whose counterparts fail for knowledge-wh and knowledge-that. Thirdly, as opposed to knowledge-wh and knowledge-that, knowledge-how is inferentially isolated from further knowledge-that. We close by providing some evidence against the further reduction of knowledge-wh to knowledge-that, which is presupposed by the intellectualist theory under discussion.

After introducing semantic anti-realism and the paradox of knowability, the paper offers a reconstruction of the anti-realist argument from understanding. The proposed reconstruction validates an unrestricted principle to the effect that truth requires the existence of a certain kind of “demonstration”. The paper shows that that principle fails to imply the problematic instances of the original unrestricted feasible-knowability principle but that the overall view underlying the new principle still has unrestricted epistemic consequences. Appealing precisely to the paradox of knowability, the paper also argues, against the BHK semantics, for the non- constructive character of the demonstrations envisaged by semantic anti-realism, and contends that, in such setting, one of the most natural arguments for a broadly intuitionist revision of classical logic loses all its force.Tras presentar el anti-realismo semántico y la paradoja de la cognoscibilidad, el artículo ofrece una reconstrucción del argumento anti-realista basado en la comprensión. La reconstrucción que se propone valida un principio irrestricto, del que se sigue que la verdad requiere la existencia de un determinado tipo de “demostración”. El artículo muestra que este principio no implica las instancias problemáticas del original principio irrestricto de la cognoscibilidad realizable, y que la concepción general que subyace al nuevo principio todavía tiene consecuencias epistémicas irrestrictas. Apelando precisamente a la paradoja de la cognoscibilidad, el artículo argumenta además, en contra de la semántica BHK, a favor del carácter no constructivo de las demostraciones que contempla el anti-realismo semántico, y defiende que, en ese marco, uno de los argumentos más naturales a favor de una revisión a grandes rasgos intuicionista de la lógica clásica pierde toda su fuerza.