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.

Tarski and Mautner proposed to characterize the "logical" operations on a given domain as those invariant under arbitrary permutations. These operations are the ones that can be obtained as combinations of the operations on the following list: identity; substitution of variables; negation; finite or infinite disjunction; and existential quantification with respect to a finite or infinite block of variables. Inasmuch as every operation on this list is intuitively "logical", this lends support to the Tarski-Mautner proposal.

The paper starts with an examination and critique of Tarski’s wellknown proposed explication of the notion of logical operation in the type structure over a given domain of individuals as one which is invariant with respect to arbitrary permutations of the domain. The class of such operations has been characterized by McGee as exactly those definable in the language L∞,∞. Also characterized similarly is a natural generalization of Tarski’s thesis, due to Sher, in terms of bijections between domains. My main (...) objections are that on the one hand, the Tarski-Sher thesis thus assimilates logic to mathematics, and on the other hand fails to explain the notion of same logical operation across domains of different sizes. A new notion of homomorphism invariant operation over functional type structures (with domains M0 of individuals and {T, F} at their base) is introduced to accomplish the latter. The main result is that an operation is definable from.. (shrink)

After a short preface, the first of the three sections of this paper is devoted to historical and philosophic aspects of categoricity. The second section is a self-contained exposition, including detailed definitions, of a proof that every mathematical system whose domain is the closure of its set of distinguished individuals under its distinguished functions is categorically characterized by its induction principle together with its true atoms (atomic sentences and negations of atomic sentences). The third section deals with applications especially those (...) involving the distinction between characterizing a system and axiomatizing the truths of a system. (shrink)

This is a collection of new investigations and discoveries on the history of a great tradition, the Lvov-Warsaw School of logic , philosophy and mathematics, by the best specialists from all over the world. The papers range from historical considerations to new philosophical, logical and mathematical developments of this impressive School, including applications to Computer Science, Mathematics, Metalogic, Scientific and Analytic Philosophy, Theory of Models and Linguistics.

We are pleased to present this special issue of the journal History and Philosophy of Logic dedicated to the square of opposition.The square of opposition is a diagram and a theory of opposition re...

Notes on the life of Adolf Lindenbaum, a complete bibliography of his published works, and selected references to his unpublished results.

This special issue is related to the 6th World Congress on the Square of Opposition which took place at the Orthodox Academy of Crete in November 2018. In this introductory paper we explain the context of the event and the topics discussed.

I discuss the origin and development of logic prizes around the world. In a first section I describe how I started this project by creating the Newton da Costa Logic Prize in Brazil in 2014. In a second section I explain how this idea was extended into the world through the manifesto A Logic Prize in Every Country! and how was organized the Logic Prizes Contest at the 6th UNILOG in Vichy in June 2018 with the participation of 9 logic (...) prizes winners from 9 countries. In a third section I discuss how this project will develop in the future with the creation of more logic prizes, an Encyclopædia of Logic, the book series Logic PhDs, as well as the creation of a World Logic Day, January 14, day of birth of Alfred Tarski and of death of Kurt Gödel. (shrink)

This paper presents the life and work of Alfred Tarski, one of the most distinguished and influential logicians in the entire history.

We try to explain Tarski's conception of logical notions, as it emerges from alecture of his, delivered in 1966 and published posthumously in 1986 (Historyand Philosophy of Logic 7, 143–154), a conception based on the idea ofinvariance. The evaluation of Tarski's proposal leads us to consider an interesting(and neglected) reply to Skolem in which Tarski hints at his own point of view onthe foundations of set theory. Then, comparing the lecture of 1966 with Tarski'slast work and with an earlier paper (...) written with Lindenbaum, it is shown thatTarski's conception of logical notions, with its essentially type-theoretic character,did not undergo any significant modifications throughout his life. A remark onTarski's prudential attitude on the topic in the famous paper on the concept oflogical consequence (and elsewhere) concludes our paper. (shrink)

We assess the celebration of the 1st World Logic Day which recently took place all over the world. We then answer the question Why a World Logic Day? in two steps. First we explain why promoting logic, emphasizing its fundamental importance and its relations with many other fields. Secondly we examine the sense of a one-day celebration: how this can help reinforcing logic day-to-day and why logic deserves it. We make a comparison with other existing one-day celebrations. We end by (...) presenting and commenting the logo of the World Logic Day. (shrink)

In this article the author first described the developments which brought to focus the importance of consistency proofs for mathematics, and which led Hilbert to promote the science of metamathemat-ics. Further comments and remarks concern the (partly analogous) beginnings of the work on the decision problem, Gödel?s theorems and related matters, and general metamathematics. An appendix summarizes a text by the author on completeness and categoricity.

. This papers examines formal properties of logical squares and their generalizations in the form of hexagons and octagons. Then, several applications of these constructions in philosophical analysis are elaborated. They concern contingency (accidentality), possibility, permission, axiological concepts (bonum and malum), the generalized Hume thesis (deontic and epistemic modalities), determinism, truth and consistency (in various senses. It is shown that relations between notions used in various branches of philosophy fall into the same formal scheme.

The semantic theory of truth, formulated by Alfred Tarski in the 1939s, is primarily a mathematical theory. On the other hand, it also has a considerable philosophical content. This paper presents the second aspect of this theory. It can be shown that several traditional philosophical issues pertaining to the concept of truth can be illuminated by Tarski’s account of truth. It concerns, for instance, the idea of correspondence, the relation of truth and logic, the problem of the relativity/absoluteness of truth, (...) etc. (shrink)

I discuss various aspects of the Lvov-Warsaw School: its past, present and future; its location, evolution, mathematics; the variety of its members. I develop this analysis on the basis of my 25-year experience with Poland.

This paper revisits the life of Adolf Lindenbaum in light of new research findings, then looks at two areas among many—metric spaces, and decompositions of point sets—where his work has been underappreciated.

This paper presents life and work in logic of Jerzy Słupecki, a distinguished Polish logician.