Since the early days of physics, space has called for means to represent, experiment, and reason about it. Apart from physicists, the concept of space has intrigued also philosophers, mathematicians and, more recently, computer scientists. This longstanding interest has left us with a plethora of mathematical tools developed to represent and work with space. Here we take a special look at this evolution by considering the perspective of Logic. From the initial axiomatic efforts of Euclid, we revisit the major milestones (...) in the logical representation of space and investigate current trends. In doing so, we do not only consider classical logic, but we indulge ourselves with modal logics. These present themselves naturally by providing simple axiomatizations of different geometries, topologies, space-time causality, and vector spaces. (shrink)

Frege famously held that numbers play the role of objects in our language and thought, and that this role is on display when we use sentences like "The number of Jupiter's moons is four". I argue that this role is an example of a general pattern that also encompasses persons, times, locations, reasons, causes, and ways of appearing or acting. These things are 'objects' simply in the sense that they are answers to questions: they are the sort of thing we (...) search for and specify during investigation or inquiry. I support this epistemological conception of objects by studying specificational sentences, a class of sentences which includes Frege's original example. I defend an analysis of such sentences as question-answer pairs, and show how to formally represent this analysis using game-theoretical semantics. (shrink)

This paper is an edited form of a letter written by the two authors (in the name of Tarski) to Wolfram Schwabhäuser around 1978. It contains extended remarks about Tarski's system of foundations for Euclidean geometry, in particular its distinctive features, its historical evolution, the history of specific axioms, the questions of independence of axioms and primitive notions, and versions of the system suitable for the development of 1-dimensional geometry.

This article presents Tarski's Address at the Princeton Bicentennial Conference on Problems of Mathematics, together with a separate summary. Two accounts of the discussion which followed are also included. The central topic of the Address and of the discussion is decision problems. The introductory note gives information about the Conference, about the background of the subjects discussed in the Address, and about subsequent developments to these subjects.

(1995). In the shadow of giants: The work of mario pieri in the foundations of mathematics. History and Philosophy of Logic: Vol. 16, No. 1, pp. 107-119.