Synthetic Philosophy of Mathematics and Natural Sciences Conceptual analyses from a Grothendieckian Perspective

ISBN-13: 978-0692593974. Giuseppe Longo. Synthetic Philosophy of Mathematics and Natural Sciences, Conceptual analyses from a Grothendieckian Perspective, Reflections on “Synthetic Philosophy of Contemporary Mathematics” by F. Zalamea, Urbanomic (UK) and Sequence Press (USA), 2012. Invited Paper, in Speculations: Journal of Speculative Realism, Published: 12/12/2015, followed by an answer by F. Zalamea.International audienceZalamea’s book is as original as it is belated. It is indeed surprising, if we give it a moment’s thought, just how greatly behind schedule philosophical reflection on contemporary mathematics lags, especially considering the momentous changes that took place in the second half of the twentieth century. Zalamea compares this situation with that of the philosophy of physics: he mentions D’Espagnat’s work on quantum mechanics, but we could add several others who, in the last few decades, have elaborated an extremely timely philosophy of contemporary physics (see for example Bitbol 2000; Bitbol et al. 2009). As was the case in biology, philosophy – since Kant’s crucial observations in the Critique of Judgment, at least – has often “run ahead” of life sciences, exploring and opening up a space for reflections that are not derived from or integrated with its contemporary scientific practice. Some of these reflections are still very much auspicious today. And indeed, some philosophers today are saying something truly new about biology..

Topics in Programming Languages, a Philosophical Analysis through the case of Prolog

[EN]Programming languages seldom find proper anchorage in philosophy of logic, language and science. is more, philosophy of language seems to be restricted to natural languages and linguistics, and even philosophy of logic is rarely framed into programming languages topics. The logic programming paradigm and Prolog are, thus, the most adequate paradigm and programming language to work on this subject, combining natural language processing and linguistics, logic programming and constriction methodology on both algorithms and procedures, on an overall philosophizing declarative status. Not only this, but the dimension of the Fifth Generation Computer system related to strong Al wherein Prolog took a major role. and its historical frame in the very crucial dialectic between procedural and declarative paradigms, structuralist and empiricist biases, serves, in exemplar form, to treat straight ahead philosophy of logic, language and science in the contemporaneous age as well. In recounting Prolog's philosophical, mechanical and algorithmic harbingers, the opportunity is open to various routes. We herein shall exemplify some: - the mechanical-computational background explored by Pascal, Leibniz, Boole, Jacquard, Babbage, Konrad Zuse, until reaching to the ACE (Alan Turing) and EDVAC (von Neumann), offering the backbone in computer architecture, and the work of Turing, Church, Gödel, Kleene, von Neumann, Shannon, and others on computability, in parallel lines, throughly studied in detail, permit us to interpret ahead the evolving realm of programming languages. The proper line from lambda-calculus, to the Algol-family, the declarative and procedural split with the C language and Prolog, and the ensuing branching and programming languages explosion and further delimitation, are thereupon inspected as to relate them with the proper syntax, semantics and philosophical élan of logic programming and Prolog

Cassirer and structuralism of perception: an application of group theory to Gestalt psychology

Ernst Cassirer's task was to set up an account of perception as objective judgement. We can trace Cassirer's view of perception through three different accounts each of which aimed to give an answer of how perceptual judgements can be possible. These three accounts started from (1900-1923) where he presented his view depending on Functional- Relational analysis of perceptual experience. The second account started from (1923-1933) where he presented his view of perception depending on symbolic analysis of perceptual experience, and finally the third account started from (1933-1945) where the analysis of perceptual phenomena has been made depending on his apprehension of Group Theory. The main target of Cassirer in the third account was to show that there is similarity between geometry and perception with respect to the ways both of these two disciplines build up their objects. Having the same logical base, Cassirer claimed that there is similarity between geometrical determination of the object and perceptual determination of the experienced object. For Cassirer, this similarity is what allows an application of "group theory" to perception. As a result of that claim, Cassirer shifted mathematical terms such as "invariance", "frame of reference" and "transformation" from the province of geometry and reused them in the field of perception for setting up what he called psychology of thought. This thesis discusses Cassirer's first two accounts and focuses on the third account by giving examples of how the mathematical concept of "group" can be used as an analogy to provide an intrinsic explanation of the nature of the objects and their characteristics one experiences during the perceptual situation. The explanations of the perceptual phenomena represented in the perceptual experience, as given by Cassirer, based on Gestalt psychology, reflected this understanding. The ample examples created by the Gestalt psychologists and used by Cassirer indicated how both understood the object of perceptual experience as constructed and not as a thing or hic et nunc. I will show that in these three accounts, there are non-physical elements, which defined here as structural elements, involved in the perceptual experience. By the virtue of these non-physical elements, perceptual judgements are possible. Cassirer and the Gestalt psychologists emphasized that these structural elements are presupposed in every perceptual experience and this understanding will lead to the claim that both Cassirer and the Gestaltists presupposed the constructive unity of mind based on a transcendental analysis of the nature of mind and its cognitive processes