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At the beginning of the twentieth century, among the foundational schools of mathematics appeared 'intuitionism' by Dutchman L. E. J. Brouwer, who based arithmetic on the intuition of time and all mental constructions that could be made out of it. His pupil Arend Heyting was the first populariser of intuitionism, and he repeatedly emphasised that no philosophy was required to practise intuitionism so that such mathematics could be shared by anyone. Still, stimulated by invitations to humanistic conferences, he wrote a series of notes, preserved in the State Archives, Haarlem, about solipsism. In them, he operated a series of theoretical reflections consisting of the stripping away of the patterns that are part of our consciousness and their subsequent progressive re‐introduction, in order to understand the formation of our Self as distinct from the natural world and other humans. In 1996, following a stroke, neuroscientist Jill Bolte Taylor experienced the deprivation of certain abilities in her brain and their successive regaining. In her experience there are remarkable similarities with what Heyting had hypothesised about the formation of the self. The purpose of this article is to highlight them and point out how Heyting's theoretical construct was found to be embodied in the brain. [ABSTRACT FROM AUTHOR]

The previous research attempts to reduce the influence of the belief bias on deductive thinking have often been unsuccessful and, when they succeeded, they failed to replicate. In this paper, we propose a new way to see an old problem. Instead of considering the analytical abilities of the respondent, we focus on the communicative characteristics of the experimental task. By changing the pragmatics into play through a subtle manipulation of the instruction of the syllogism problem, we obtained a strong improvement in the accuracy of the performance in both untrained and trained in logic respondents. We suggest that current models of deductive thinking should be broadened to consider also communicative understanding as part of the processing of the problem. [ABSTRACT FROM AUTHOR]

The use of the three labels (logicism, formalism, intuitionism) to denote the three foundational schools of the early twentieth century are now part of literature. Yet, neither their number nor their adoption has been stable over the twentieth century. They were not introduced by the founding fathers of each school: namely, neither Frege nor Russell spoke of 'logicism'; and even Hilbert did not use the word 'formalism' to introduce his foundational programs. At a certain point, only Brouwer used the label 'intuitionism' in his scientific production to personify his philosophy of mathematics and he used the label 'formalism' for Hilbert's foundational viewpoint. Starting with Brouwer, the origin of the use of the three labels to represent a foundational meaning, will be analysed in this paper. Thereafter, the role that Brouwer's pupil Arend Heyting had in the production and use of foundational labels will be considered. On the basis of the comparison of the attitudes of these two scholars I will finally advance the thesis that not only the creation but also the use of labels, far from being a mere gesture of academic reference to literature, can be a sign of the cultural operation each scholar wanted to do. [ABSTRACT FROM AUTHOR]

König's paradox, that he presented for the first time in 1905, preserved the same structure in all his papers: there was a number that at the same time was and was not finitely definable. Still, he changed the way for forming it, and both its consequences and its solutions changed as well. In the present paper we are going to follow the story of König's paradox, that is an intriguing mix of labelling, solving, criticising an “object” from different viewpoints and for different aims. [ABSTRACT FROM AUTHOR]

Friedrich Nietzsche and Luitzen Egbertus Jan Brouwer had strong personalities and freely expressed unconventional opinions. In particular, they dared to challenge the traditional view that considered Aristotelian logic as being absolute and intrinsic to man. Although they formed this opinion in different ways and in different contexts (Nietzsche was born in Saxony and lived in the second half of the nineteenth century, beginning his career as a classical philologist before turning to philosophy; Brouwer was a Dutch mathematician who lived from 1881 to 1966), they both based it on a view of life that considered it as a struggle for power in which logic was a weapon. Therefore, it is interesting to carry out an in-depth analysis on the origins, the core of their opinions concerning logic and the consequences. As a matter of fact, a detailed analysis and a comparison of their contributions to the philosophy of logic have not yet been carried out. In this paper, I intend to present the results of my research on this subject performed by taking into account the studies conducted by E. Steinhart, O. Schutte and S.D. Hales. [ABSTRACT FROM PUBLISHER]