Gabriel Sandu

A crucial aspect of the revolution that affected logic at the beginning of the twentieth century concerns the severance of its traditional dependence on the form and structure of natural language. Such a breakdown has had enormous consequences not only for the development of formal logic, but also for the opening of new perspectives in the study of language. This peculiar relationship between mathematical logic and language inquiry is best illustrated by Willard V. O. Quine (1961: 1): Mathematicians expedite their special business by deviating from ordinary language. Each such departure is prompted by specific considerations of utility for the mathematical venture afoot. Such reforms may be expected to reflect light on the ordinary language from which they depart. As a major consequence of its “reforms”, the new mathematical logic has been able to revivify and boost the notion of philosophical and logical grammar, typical of the seventeenth and eighteenth century rationalist tradition. New life has therefore been given to the idea that there exists a common grammatical core shared by every language and determinable a priori, with respect to which diversity and variation are just prima facie features of natural language, hiding its universal logical structure.

In (Barbero and Sandu 2020 Journal of Philosophical Logic, 50, 471-521), we showed that languages encompassing interventionist counterfactuals and causal notions based on them (as e.g. in Pearl’s and Woodward’s manipulationist approaches to causation) as well as information-theoretic notions (such as learning and dependence) can be interpreted in a semantic framework which combines the traditions of structural equation modeling and of team semantics. We now present a further extension of this framework (causal multiteams) which allows us to talk about probabilistic causal statements. We analyze the expressivity resources of two causal-probabilistic languages, one finitary and one infinitary. We show that many causal-probabilistic notions from the literature on causal inference can already be expressed in the finitary language, and we prove a normal form theorem that throws a new light on Pearl’s “ladder of causation”. In addition, we provide an exact semantic characterization of the infinitary language, which shows that this language captures precisely those causal-probabilistic statements that do not commit us to any specific interpretation of probability; and we prove that no usual, countable language is apt for this task.

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 × 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.

Hodges' Extension Theorem is perfectly designed for the kind of extension problem of principle of compositionality, which arises in the so-called IF languages. These languages satisfy the conditions of the application of the Extension Theorem. They are extensions of standard first-order languages closed under atomic and negations of atomic formulas and disjunctions and conjunctions of IF-formulas. Hodges' extension theorem shows that when certain conditions are satisfied, a language has a unique compositional interpretation, which agrees with the initially given partial one. Accordingly, any two such compositional interpretations must be formally equivalent. Kaplan separates the indices, which contribute to the semantic value of a sentence into those that make the context of utterance, and those that constitute the circumstances of evaluation. The former determine what is said and the latter determine whether what is said is true or false.

Team semantics is a highly general framework for logics which describe dependencies and independencies among variables. Typically, the dependencies considered in this context are properties of sets of configurations or data records. We show how team semantics can be further generalized to support languages for the discussion of interventionist counterfactuals and causal dependencies, such as those that arise in manipulationist theories of causation. We show that the “causal teams” we introduce in the present paper can be used for modelling some classical counterfactual scenarios which are not captured by the usual causal models. We then analyse the basic properties of our counterfactual languages and discuss extensively the differences with respect to the Lewisian tradition.

Both Frege's Grundgesetze, and Lagrange's treatises on analytical functions pursue a foundational purpose. Still, the former's program is not only crucially different from the latter's. It also depends on a different idea of what foundation of mathematics should be like . Despite this contrast, the notion of function plays similar roles in their respective programs. The purpose of my paper is emphasising this similarity. In doing it, I hope to contribute to a better understanding of Frege's logicism, especially in relation to its crucial differences with a set-theoretic foundational perspective. This should also spread some light on a question arisen by J. Hintikka and G. Sandu in a widely discussed paper, namely whether Frege should or should not be credited with the notion of arbitrary function underlying our standard interpretation of second-order logic. In section 1, I account for Lagrange's notion of function. In section 2, I advance some remarks on connected historical matters. This will provide an appropriate framework for discussing the role played by the notion of function in Frege's Grundgesetze. Section 3 is devoted to this. Some concluding remarks will close the paper

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.

Our aim in this paper is to provide a referential account of functional anaphora within a Skolem functions framework. We will give an interpretation of indefinite NPs as Skolem terms in order to show that the referential link established between an anaphoric pronoun and its antecedent is a descriptive one. Then we will argue that functional anaphora can be understood as a particular kind of E-type pronouns, in the sense that, for a large corpus, the pronoun can be replaced by a descriptive expression of a first-order language. It will next be shown that the functional framework can be fruitfully applied to other kinds of sentences involving pronominal anaphora,especially in modal contexts.

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.