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Topology as an Issue for History of Philosophy of Science

Thomas Mormann

In Hanne Andersen, Dennis Dieks, Wenceslao J. Gonzalez, Thomas Uebel & Gregory Wheeler (eds.), New Challenges to Philosophy of Science. Springer Verlag. pp. 423--434 (2013)

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A metaphysical foundation for mathematical philosophy.Wójtowicz Krzysztof & Skowron Bartłomiej - 2022 - Synthese 200 (4):1-28.details Although mathematical philosophy is flourishing today, it remains subject to criticism, especially from non-analytical philosophers. The main concern is that even if formal tools serve to clarify reasoning, they themselves contribute nothing new or relevant to philosophy. We defend mathematical philosophy against such concerns here by appealing to its metaphysical foundations. Our thesis is that mathematical philosophy can be founded on the phenomenological theory of ideas as developed by Roman Ingarden. From this platonist perspective, the “unreasonable effectiveness of mathematics in (...) Download Export citation Bookmark
The introduction of topology into analytic philosophy: two movements and a coda.Samuel C. Fletcher & Nathan Lackey - 2022 - Synthese 200 (3):1-34.details Both early analytic philosophy and the branch of mathematics now known as topology were gestated and born in the early part of the 20th century. It is not well recognized that there was early interaction between the communities practicing and developing these fields. We trace the history of how topological ideas entered into analytic philosophy through two migrations, an earlier one conceiving of topology geometrically and a later one conceiving of topology algebraically. This allows us to reassess the influence and (...) Download Export citation Bookmark
Mathematical Aspects of Similarity and Quasi-analysis - Order, Topology, and Sheaves.Thomas Mormann - manuscriptdetails The concept of similarity has had a rather mixed reputation in philosophy and the sciences. On the one hand, philosophers such as Goodman and Quine emphasized the „logically repugnant“ and „insidious“ character of the concept of similarity that allegedly renders it inaccessible for a proper logical analysis. On the other hand, a philosopher such as Carnap assigned a central role to similarity in his constitutional theory. Moreover, the importance and perhaps even indispensibility of the concept of similarity for many empirical (...) Download Export citation Bookmark
Is There a Cultural Barrier Between Historical Epistemology and Analytic Philosophy of Science?Anastasios Brenner - 2015 - International Studies in the Philosophy of Science 29 (2):201-214.details One of the difficulties facing the philosopher of science today is the divide between historical epistemology and analytic philosophy of science. For over half a century these two traditions have followed independent and divergent paths. Historical epistemology, which originated in France in the early twentieth century, has recently been reformulated by a number of scholars such as Lorraine Daston, Ian Hacking, and Hans-Jörg Rheinberger. Elaborating novel historical methods, they seek to provide answers to major questions in the field. In the (...) Download Export citation Bookmark 7 citations
The intensional side of algebraic-topological representation theorems.Sara Negri - 2017 - Synthese 198 (Suppl 5):1121-1143.details Stone representation theorems are a central ingredient in the metatheory of philosophical logics and are used to establish modal embedding results in a general but indirect and non-constructive way. Their use in logical embeddings will be reviewed and it will be shown how they can be circumvented in favour of direct and constructive arguments through the methods of analytic proof theory, and how the intensional part of the representation results can be recovered from the syntactic proof of those embeddings. Analytic (...) Download Export citation Bookmark 1 citation

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