On A.A. Markov’s Attitude towards Brouwer’s Intuitionism

The paper examines Andre A. Markov's critical attitude towards L.E.J. Brouwer's intuitionism, as is expressed in his endnotes to the Russian translation of Heyting's Intuitionism, published in Moscow in 1965. It is argued that Markov's algorithmic approach was shaped under the influence of the mathematical style and values prevailing in the Petersburg mathematical school, which is characterized by the proclaimed primacy of applications and the search for rigor and effective solutions

Proofs as Spatio-Temporal Processes

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 a semiotic meta-code that depends on the underlying mode of signification (semiosis), the selected code and the underlying semiotic space and determines the individual mode of integration (selection, combination, blending) into a narrative structure (proof). Finally, we examine certain historical types of styles of mathematical proofs, to elucidate our viewpoint

Logic and Philosophy of Science in Nancy (II)

This issue collects a selection of contributed papers presented at the 14th International Congress of Logic, Methodology and Philosophy of Science in Nancy, July 2011. These papers were originally presented within two of the main sections of the Congress. They deal with general philosophy of science (including ethical and historical aspects of philosophy of science), and philosophy of biology, physics, chemistry and economics. A first volume of contributed papers, dedicated to logic, philosophy of mathematics and cognitive science, and philosophy of technology, appeared in the last issue of Philosophia Scientiæ (18-3), 2014

Logic and Philosophy of Science in Nancy (I)

This issue collects a selection of contributed papers presented at the 14th International Congress of Logic, Methodology and Philosophy of Science in Nancy, July 2011. These papers were originally presented within three of the main sections of the Congress. They deal with logic, philosophy of mathematics and cognitive science, and philosophy of technology. A second volume of contributed papers, dedicated to general philosophy of science, and other topics in the philosophy of particular sciences, will appear in the next issue of Philosophia Scientiæ (19-1), 2015