Paul Cohen

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I am very saddened to find out (first via Wikipedia, then by several independent confirmations) that Paul Cohendied on Friday, aged 72.

Paul Cohen is of course best known in mathematics for his Fields Medal-winning proof of the undecidability of the continuum hypothesis within the standard Zermelo-Frankel-Choice (ZFC) axioms of set theory, by introducing the now standard method of forcing in model theory. (More precisely, assuming ZFC is consistent, Cohen proved that models of ZFC exist in which the continuum hypothesis fails; Gödel had previously shown under the same assumption that models exist in which the continuum hypothesis is true.) Cohen’s method also showed that the axiom of choice was independent of ZF. The friendliest introduction to forcing is perhaps still Timothy Chow‘s “Forcing for dummies“, though I should warn that Tim has a rather stringent definition of “dummy”.

But Cohen was also a…

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Beginner’s guide to forcing

http://www-math.mit.edu/~tchow/forcing.pdf

Posted in Alain Badiou, category theory, Philosophie, Philosophie mathématique, Science-internelle, Théorie des ensembles (set theory), Théorie des topoi (topos theory) | Leave a comment

Badioustudies : Set theory ontology and The philosophy of event

Set Theory Ontology and the Philosophy of the Event

Posted in Alain Badiou, category theory, Ontologie, Philosophie, Philosophie mathématique, Science-internelle, Théorie des ensembles (set theory), Théorie des topoi (topos theory) | Leave a comment

Arkady Plotnitsky : experimenting With ontologies with Badiou and Grothendieck

http://web.ics.purdue.edu/~plotnits/PDFs/ap%20exp%20with%20ontologies.pdf

Posted in Alain Badiou, category theory, Grothendieck, Philosophie, Philosophie mathématique, Science-internelle, Théorie des ensembles (set theory), Théorie des topoi (topos theory) | Leave a comment

BadiouMathematics : Laruelle, Deleuze, Badiou : sheaf theory

http://badioumathematics.blogspot.fr/2013/09/laruelle-deleuze-badiou-sheaf-theory.html

Posted in Alain Badiou, category theory, Deleuze, Laruelle, non-philosophie, Philosophie, Philosophie mathématique, Science-internelle, Théorie des ensembles (set theory), Théorie des topoi (topos theory) | Leave a comment

Four Critiques of Badiou’s Ontology: Part 1

Larval Subjects .

20031208-flame-fractal

In a recent post, I made the claim– apparently to the ire and astonishment of some –that Peter Hallward’s critique of Meillassoux’s After Finitude applies equally to Badiou’s ontology. In the course of further remarks I also suggested that, despite his self-descriptions of his own position, Badiou’s position leads to an a prioristic idealism. This wasn’t meant as an insult to Badiou, nor is it a wholesale rejection of his thought (which has influenced and inspired me deeply), but is premised on honest disagreements and perplexities I have about his ontology. The implication seems to be that one can only appreciate or endorse Badiou by dogmatically adopting his philosophy in toto, having no point of contention with it. Knowing a thing or two about Badiou the person, I suspect this is not something he would much admire or desire. Given the apparent surprise in response to this offhand…

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Badiou, Category Theory, Vectors, and Objectiles

Larval Subjects .

basic_category1One of my great frustrations is that I lack the mathematical background to understand Category Theory as I think Badiou is really on to something in his most recent work engaging with Category Theory. If someone has a recommendation for a very rudimentary introductory text (and I already have Goldblatt) I’d be eternally grateful. I am something of a peculiarity when it comes to Badiou. When I first began reading him ten years ago I was deeply invigorated by his daring to say “Truth”. Moreover, I was struck by his claim that maths are a form of thought in the context of a philosophical academic space dominated by Heideggerian romanticism and a hostility towards all things mathematical.

Nonetheless, coming from a much more network based and systems theoretical perspective, I’ve never found myself particularly intrigued by his account of the Event or Truth-Procedures, or non-relation and subtraction, being more fascinated…

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