This is an open access title available under the terms of a CC BY-NC-ND 4.0 licence. It is
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In this essay,“mathematical structuralism” will be understood mainly as a style of work, a
methodology for mathematics—but methodological choices can hardly be made without …

This chapter focuses on two different facets of axiomatics: 1. the formal-logical side, linked to
careful, rigorous establishing of the inferential structure of a theory, and 2. the conceptual …

After briefly reviewing the standard set-theoretic resolutions of the Burali-Forti paradox, we
examine how the paradox arises in set theory formalized with plural quantifiers. A significant …

In this article we address the historical and epistemological study of infinity as a
mathematical concept, focusing on identifying difficulties, counter-intuitive ideas and …

Besides Frege's and Russell's paradigmatic positions and besides current neo-logicism,
some more unorthodox forms of logicism are noteworthy as well, from both historical and …

This article was motivated by the discovery of a potential new foundation for mainstream
mathematics. The goals are to clarify the relationships between primitives, foundations, and …

For Brentano, an act of consciousness features a presentation of an object joined with an
inner presentation–an 'inner consciousness' or inner awareness–of that object-presentation …

Near the end of the nineteenth century, a part of mathematical research was focused on
unification: the goal was to find 'one sort of thing'that mathematics is (or could be taken to be) …

My dissertation concerns the proper foundation for the intuitionistic mathematics whose
development began with LEJ Brouwer's work in the first half of the 20th Century. It is taken …