Based on our research regarding the relationship between physics and mathematics in HPS, and recently on Geneva Edition of Newton's Philosophiae Naturalis Principia Mathematica (1739–42) by Thomas Le Seur (1703–70) and François Jacquier (1711–88), in this paper we present some aspects of such Edition: a combination of editorial features and scientific aims. The proof of Proposition XLIII is presented and commented as a case study.

Pierre de Fermat is known as the inventor of modern number theory. He invented–improved many methods useful in this discipline. Fermat often claimed to have proved his most difficult theorems thanks to a method of his own invention: the infinite descent. He wrote of numerous applications of this procedure. Unfortunately, he left only one almost complete demonstration and an outline of another demonstration. The outline concerns the theorem that every prime number of the form 4n + 1 is the sum (...) of two squares. In this paper, we analyse a recent proof of this theorem. It is interesting because: it follows all the elements of which Fermat wrote in his outline; it represents a good introduction to all logical nuances and mathematical variants concerning this method of which Fermat spoke. The assertions by Fermat will also be framed inside their historical context. Therefore, the aims of this paper are related to the history of mathematics and to the logic of proof-methods. (shrink)

René Girard's mimetic theory has been object of much interest in the last few years, both in the 'Continental' and in the 'English-speaking' philosophical areas. Nevertheless, Girard's thought is not always accepted in the academic circles. The main cause for this is that his theory is considered too 'philosophical' in the Human Sciences Departments, and it seems too close to cultural anthropology and literary criticism to be appreciated by philosophers. This is the reason why it could be fruitful to focus (...) the attention on the philosophical aspects of René Girard's thought. I clarify what is meant exactly by 'philosophy' within the mimetic theory of René Girard and I define the borders of the problem of the 'death of philosophy,' as it appears from Girard's work. Then, I focus on philosophical hermeneutics and its relationship with the mimetic theory. Finally, I try to answer a central question: is it still possible to speak of 'philosophy' within the Girardian universe? (shrink)

Open peer commentary on the target article “Who Conceives of Society?” by Ernst von Glasersfeld. Excerpt: While von Glasersfeld’s “epistemological model involves consciousness, memory, and some basic values” , our argument from an enactive perspective is that these axiomatic elements are not atomic and already imply the participation of those social processes they intend to ground and that this fundamental intervention happens before these processes are constituted as knowable by the individual mind they shape.

This book addresses the various systems in place for collaborative e-research and how these practices serve to enhance the quality of research across disciplines, covering new networks available through social media as well as traditional methods such as mailing lists and forums.

What principles explain or justify legal institutions or decisions, thereby transforming coercion to authority? Are there or could there be any such universal principles? Can any philosophical theory account for such principles? How, if at all, do philosophical theories of law and politics apply to particular issues? And finally, what, if any, do such practical applications tell us about general theories and principles? The essays in this volume represent the efforts of an international group of scholars to understand these general (...) aspects of legal philosophy. (shrink)

In a previous paper we investigated the extraction of proof-theoretic properties of natural deduction derivations from their impredicative translation into System F. Our key idea was to introduce an extended equational theory for System F codifying at a syntactic level some properties found in parametric models of polymorphic type theory. A different approach to extract proof-theoretic properties of natural deduction derivations was proposed in a recent series of papers on the basis of an embedding of intuitionistic propositional logic into a (...) predicative fragment of System F, called atomic System F. In this paper we show that this approach finds a general explanation within our equational study of second-order natural deduction, and a clear semantic justification in terms of parametricity. (shrink)