Gabriel Sandu

This work presents an overview of four different approaches to the problem of future contingency and determinism in temporal logics. All of them are bivalent, viz. they share the assumption that propositions concerning future contingent facts have a determinate truth-value. We introduce Ockhamism, Peirceanism, Actualism and T x W semantics, the four most relevant bivalent alternatives in this area, and compare them from the point of view of their expressiveness and their underlying metaphysics of time.

In this paper, we introduce a new approach to independent quantifiers, as originally introduced in Informational independence as a semantic phenomenon by Hintikka and Sandu [9] under the header of independence-friendly languages. Unlike other approaches, which rely heavily on compositional methods, we shall analyze independent quantifiers via equilibriums in strategic games. In this approach, coined equilibrium semantics, the value of an IF sentence on a particular structure is determined by the expected utility of the existential player in any of the game’s equilibriums. This approach was suggested in Henkin quantifiers and complete problems by Blass and Gurevich [2] but has not been taken up before. We prove that each rational number can be realized by an IF sentence. We also give a lower and upper bound on the expressive power of IF logic under equilibrium semantics

This book presents a collection of studies by Romanian philosophers, addressing foundational issues currently debated in contemporary philosophy of science. It offers a historical survey of the tradition of scientific philosophy in Romania. It examines some problems in the foundations of logic, mathematics, linguistics, the natural and social sciences. Among the more specific topics, it discusses scientific explanation, models, and mechanisms, as well as memory, artifacts, and rules of research. The book is useful to those interested in the philosophy of real science, but also to those interested in Romanian philosophy.

This book focuses on the game-theoretical semantics and epistemic logic of Jaakko Hintikka. Hintikka was a prodigious and esteemed philosopher and logician, and his death in August 2015 was a huge loss to the philosophical community. This book, whose chapters have been in preparation for several years, is dedicated to the work of Jaako Hintikka, and to his memory. This edited volume consists of 23 contributions from leading logicians and philosophers, who discuss themes that span across the entire range of Hintikka’s career. Semantic Representationalism, Logical Dialogues, Knowledge and Epistemic logic are among some of the topics covered in this book's chapters. The book should appeal to students, scholars and teachers who wish to explore the philosophy of Jaako Hintikka.

Tarski has exerted enormous influence not only on the development of mathematical logic, but on twentieth-century philosophy and philosophical analysis. This influence has been twofold, with the two components pulling in a sense in opposite directions. A comparison with the influence of the Vienna Circle provides an instructive vantage point in viewing Tarski’s influence. On the one hand, Tarski has provided powerful tools for logical analysis in philosophy. His first and most important contribution was to show that — and how — the crucial semantical concept of truth can be defined for various formal languages. They include the most central types of language used and studied by twentieth century logicians and philosophers. The subsequent work by Tarski and his school in creating contemporary model theory in its narrow sense as a branch of technical logic has likewise enriched tremendously the conceptual arsenal of philosophers. The extent and depth of Tarski’s influence is in fact easily underestimated. In comparison, Carnap’s well-known books in logical syntax and logical semantics did not in the same way contribute to the logical techniques that philosophers might find useful. A large part of Tarski’s influence lies in facilitating a switch of emphasis from purely syntactical to model-theoretical, semantical methods. It was Gödel’s and Tarski’s early work that forced logicians and philosophers for the first time to take seriously the distinction between semantical and syntactical concepts and methods. The general theoretical implications of the distinction were not realized at once. In the light of hindsight, it is for instance quite striking that Tarski still in his classical monograph repeatedly assimilates to each other the task of defining truth for some part of mathematics or logic and axiomatizing its truths in a sense that involves explicit syntactical rules of inference. It was nevertheless Tarski more than anyone else who began to develop and exploit systematically model-theoretical concepts in logical theory. In comparison, Gödel never developed systematically the model-theoretical aspects of logic. Others, for instance Quine, stubbornly remained within the syntactical tradition. Carnap, who did switch his attention from the syntactical to a semantical approach, was not powerful enough a logician to create a sufficiently rich store of model-theoretical techniques and ideas to be equally helpful in philosophical analysis. In contrast, several major developments in analytic philosophy have had their starting points in Tarski’s ideas. Well-known cases in point are Davidson’s truth-conditional semantics and the possible worlds semantics developed by Tarski’s favorite former student Richard Montague

We study partiality in propositional logics containing formulas with either undefined or over-defined truth-values. Undefined values are created by adding a four-place connective W termed transjunction to complete models which, together with the usual Boolean connectives is shown to be functionally complete for all partial functions. Transjunction is seen to be motivated from a game-theoretic perspective, emerging from a two-stage extensive form semantic game of imperfect information between two players. This game-theoretic approach yields an interpretation where partiality is generated as a property of non-determinacy of games. Over-defined values are produced by adding a weak, contradictory negation or, alternatively, by relaxing the assumption that games are strictly competitive. In general, particular forms of extensive imperfect information games give rise to a generalised propositional logic where various forms of informational dependencies and independencies of connectives can be studied

Linguistique et philosophie logique du langage: deux traditions de pensee que bien des choses opposent. La premiere est plutot mentaliste, et orientee vers l'etude de la syntaxe; la seconde, plus preoccupee de semantique, cherche volontiers le sens dans les conditions de verite des phrases. Ce portrait n'est pas faux, mais il est incomplet: entre logique et linguistique, les relations n'ont pas ete, ne sont pas que d'opposition. Dans cet ouvrage, les auteurs proposent une sorte d'histoire conceptuelle des interactions fecondes entre les deux disciplines au cours du XXe siecle. La premiere partie, consacree a la notion de categorie semantique et/ou syntaxique, raconte comment les theories a priori de la signification (Husserl, Frege, Russell) ont progressivement donne lieu au programme des grammaires categorielles, d'inspiration plus descriptive et empirique. La deuxieme partie traite d'un autre episode, datant des annees cinquante a soixante-dix, et lie a la naissance des grammaires generatives: celui au cours duquel l'opposition entre la these avancee par Chomsky de l'autonomie de la syntaxe, et l'idee de la priorite conceptuelle de la semantique, soutenue par des logiciens comme Montague, vient au premier plan. Enfin la troisieme partie traite des recherches tout a fait contemporaines concernant l'etude des expressions indefinies et des relations anaphoriques qu'elles soutiennent, theme ou se dessinent des convergences nouvelles entre l'analyse logique et l'analyse linguistique: la comprehension des rapports entre generalite et reference dans les langages naturels y gagnera certainement en finesse et en adequation empirique.

In his article The Foundations of Mathematics (1925) Ramsey was concerned with the nature of the statements of 'pure mathematics' and the way these statements differ from those in empirical sciences. He thought that the answer given to these questions by Hilbert and the formalist school according to which mathematical statements are meaningless formulas, is unsatisfactory for several reasons, which will not be discussed here. He also expressed serious doubts about the intuitionist program developed by Brouwer and Weyl. It is the logicist school of Frege, Russell and Whitehead, which attempted to reduce mathematics to few logical concepts, that came closest to Ramsey’s views, although he was not completely satisfied with it, either.

In this paper we relax the assumption that the logical constants of ordinary first-order logic be linearly ordered. As a consequence, we shall have formulas involving not only partially ordered quantifiers, but also partially ordered connectives. The resulting language, called the language of informational independence will be given an interpretation in terms of games of imperfect information. The II-logic will be seen to have some interesting properties: It is very natural to define in this logic two negations, weak negation as failure to verify a sentence, and strong negation as the existence of a falsifying strategy: One can express in this logic complete problems of finite structures, like the non-connectedness and 3-colorability of finite graphs, the satisfiability problem for Boolean circuits built up from NAND-gates, etc

entities in mathematics There is a line of argument which keeps ontological commitments to the minimum by making use of conservativity results. The argument goes back to Hilbert who set its general frame. Hilbert’s concern was with certain abstract (ideal) entities in mathematics but the argument has been applied without discrimination to avoid ontological commitment to mathematical entities in physics (Field) or to avoid an ontological commitment to substantial properties in the case of truth (Horwich, Field, Williams).