Massimiliano Carrara

The goal of [3] is to sketch the construction of a syntactic categorical model of the bi-intuitionistic logic of assertions and hypotheses AH, axiomatized in a sequent calculus AH-G1, and to show that such a model has a chirality-like structure inspired by the notion of dialogue chirality by P-A. Melliès [8]. A chirality consists of a pair of adjoint functors L ⊣ R, with L: A → B, R: B → A, and of a functor (.)* : A → Bop(0,1) satisfying certain conditions. The definition of the logic AH in [3] needs to be modified so that our categories A and B are actually dual. With this modification, a more complex structure emerges.

Nicholas Rescher, in The Limits of Science (1984), argued that: «perfected science is a mirage; complete knowledge a chimera». He reached the above conclusion from a logical argument known as Fitch’s Paradox of Knowability. The argument, starting from the assumption that every truth is knowable, proves that every truth is also actually known and, given that some true propositions are not actually known, it concludes, by modus tollens, that there are unknowable truths. Prima facie, this argument seems to seriously narrow our epistemic possibilities and to constitute a limit for knowledge (included scientific knowledge). Rescher’s above quoted conclusion follows the same sort of reasoning. Recently, Bernard Linsky exploited a possible way to block the argument employing a type-distinction of knowledge. If the Knowability paradox is blocked, then Rescher’s conclusion cannot be drawn. After an introduction to the paradox, we suggest, in our paper, a possible way of justifying a type-solution for it in the scientific field. A noteworthy point is that the effectiveness of this solution depends on the degree of reductionism adopted in science: the given solution is available only if we do not adopt a complete reductionism in science so that there is just one kind of scientific knowledge and, consequently, of scientific justification. Otherwise Rescher's argument still works.

From a logical point of view, identity criteria should mirror the identity relation in being reflexive, symmetrical, and transitive. However, the relation representing the identity condition fails to be transitive in many cases. We consider the proposals given so far to give logical adequacy to inadequate identity conditions. We focus on the most refined proposal and expand its formal framework by taking into account two further aspects that we consider essential in the formal treatment of identity criteria: contexts and granular levels.

The Knowability Paradox is a logical argument that, starting from the plainly innocent assumption that every true proposition is knowable, reaches the strong conclusion that every true proposition is known; i.e. if there are unknown truths, there are unknowable truths. The paradox has been considered a problem for every theory assuming the Knowability Principle, according to which all truths are knowable and, in particular, for semantic anti-realist theories. A well known criticism to the Knowability Paradox is the so called restriction strategy. It bounds the scope of the universal quantification in (KP) to a set of formulas whose logical form avoids the paradoxical conclusion. Specifically, Tennant suggests to restrict the quantifier in (KP) to propositions whose knowledge is provably inconsistent. He calls them Anti-Cartesian propositions and distinguished them in three kinds. In this paper we will not be concerned with the soundness of the restriction proposal and the criticisms it has received. Rather, we are interested in analyzing the proposed distinction. We argue that Tennant’s distinction is problematic because it is not completely clear, it is not grounded on an adequate logical analysis, and it is incomplete. We suggest an alternative distinction, and we give some reasons for accepting it: it results logically grounded and more complete than Tennant’s one, inclusive of it and independent from non-epistemic notions.

This is an excerpt from the contentIn the introduction to part I of the symposium we stated that a rational agent could be thought of as an agent who has good reasons for its actions. In formal analyses of economic, medical, political, military and forensic decisions rationality, that is the “goodness” of those reasons, is inextricably intertwined with probability. Typically, those analyses concern decisions in a particular class of uncertain situations, namely “risky” situations, where all the relevant available alternative actions are known, each or most actions are non-deterministic , and the probability of each outcome is known to some degree of approximation. As yet, formal analyses have only begun to scratch the surface of the subtleties implicated in uncertain, but not risky, situations, where the available courses of actions, and/or their possible outcomes, and/or the probabilities of those outcomes, are not all

The Knowability Paradox is a logical argument to the effect that, if there are truths not actually known, then there are unknowable truths. Recently, Alexander Paseau and Bernard Linsky have independently suggested a possible way to counter this argument by typing knowledge. In this article, we argue against their proposal that if one abstracts from other possible independent considerations supporting reasons for typing knowledge and considers the motivation for a type-theoretic approach with respect to the Knowability Paradox alone, there is no substantive philosophical motivation to type knowledge, except that of solving the paradox. Every attempt to independently justify the typing of knowledge is doomed to failure.

The book's aim is to give a working representation of what metaphysics is today. The historical contributions reveal the roots of metaphysical themes and how today's methods are linked to their Aristotelian and Leibnizian past. The volume also touches on the relationships between ontological and linguistic analysis, the questions of realism and ontological commitment, the nature of abstract objects, the existential meaning of particular quantification, the primitiveness of identity, the question of epistemic versus ontological vagueness, the necessity of origin, the nature of natural necessity, the possibility of intermittent existence, the notion of a temporal part and its place in an account of persistence, the question of identity and change across time and possible worlds, and many more. Readership: A toolbox for any researcher in metaphysics and an essential source for any PhD student with ontological interests.

This special issue of GPS collects 11 papers (and a long introduction), by leading philosophers and young researchers, which tackle more or less from close the topic of propositions by trying to provide the reader with a cross-section of the ongoing debate in this area. The raised issues range over the semantics, the ontology, the epistemology, and the philosophy of mathematics and stimulate the reader to reflect on crucial problems such as the following: are propositions objects? In the positive case, what kind of objects are they? Can they be grasped by cognitive creatures such as we are? When can we say that two people entertain the same proposition? Have propositions any role to play in speech act theory? Even though the notion of proposition has received considerable attention in the past philosophical debate, it is still of great interest, in particular in connection with the attacks which have recently been launched against it in the theory of language. The volume, which is equipped with a long and detailed introduction that supplies the young reader with useful background information on the different stances in the debate, could prove useful also for didactic purposes.

The entailment connective is introduced by Priest (2006b). It aims to capture, in a dialetheically acceptable way, the informal notion of logical consequence. This connective does not “fall foul” of Curry’s Paradox by invalidating an inference rule called “Absorption” (or “Contraction”) and the classical logical theorem called “Assertion”. In this paper we show that the semantics of entailment, given by Priest in terms of possible worlds, is inadequate. In particular, we will argue that Priest’s counterexamples to Absorption and Assertion use in the metalanguage a dialetheically unacceptable principle. Furthermore, we show that the rejection of Assertion undermines Priest’s claim that the entailment connective expresses the notion of logical consequence.