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  1. Proofs as Spatio-Temporal Processes.Petros Stefaneas & Ioannis M. Vandoulakis - 2014 - Philosophia Scientiae 18:111-125.
    The concept of proof can be studied from many different perspectives. Many types of proofs have been developed throughout history such as apodictic, dialectical, formal, constructive and non-constructive proofs, proofs by visualisation, assumption-based proofs, computer-generated proofs, etc. In this paper, we develop Goguen’s general concept of proof-events and the methodology of algebraic semiotics, in order to define the concept of mathematical style, which characterizes the proofs produced by different cultures, schools or scholars. In our view, style can be defined as (...)
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  • The Role of Axioms in Mathematics.Kenny Easwaran - 2008 - Erkenntnis 68 (3):381-391.
    To answer the question of whether mathematics needs new axioms, it seems necessary to say what role axioms actually play in mathematics. A first guess is that they are inherently obvious statements that are used to guarantee the truth of theorems proved from them. However, this may neither be possible nor necessary, and it doesn’t seem to fit the historical facts. Instead, I argue that the role of axioms is to systematize uncontroversial facts that mathematicians can accept from a wide (...)
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  • Church's thesis: Prelude to a proof.Janet Folina - 1998 - Philosophia Mathematica 6 (3):302-323.
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  • Saunders Mac Lane (1909–2005): His mathematical life and philosophical works.Colin McLarty - 2005 - Philosophia Mathematica 13 (3):237-251.
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