Comments on: Translation: Albert Lautman’s Essay on the Notions of Structure and Existence in Mathematics

By: Translation: Six Entries from Francois Laruelle’s Dictionary of Non-Philosophy « Fractal Ontology

Wed, 24 Oct 2007 23:13:21 +0000

[...] can, in my opinion, be best related to the previous translations I have posted on Alain Badiou and Albert Lautman. Badiou’s concept of model as coupling (ideological/scientific)–like Laruelle’s [...]

By: Get About Maths: Nobel, in theory and practice (Indian Express via.. » Science Discoveries . net

Wed, 17 Oct 2007 03:16:46 +0000

[...] Translation: Albert Lautman?s Essay on the Notions of Structure … This combined with the fact that they can be expressed using variables or logical constants, will provide the definition of logic or pure mathematics.? [2] Cf. Ren� Poirier, Essais sur quelques caract�res des notions d?espace et de … [...]

By: taylor27

taylor27 — Wed, 17 Oct 2007 02:01:49 +0000

Yeah, I wasn’t surprised by this work’s transversality. I am amazed though that the fifth chapter is on the mixtures of beings, which makes me think of Logic of Sense immediately. I’m going to post a quote or two from D+R to help show off Lautman as an important voice in contemporary mathematical philosophy.

By: joeofthestars

joeofthestars — Wed, 17 Oct 2007 00:52:02 +0000

This was really fascinating. I liked his identification of the two positive methods which are possible for a modern mathematical project. On the one hand, “reality can indeed be characterized by the way in which it is allowed to be apprehended and organized;” but on the other “it can also seen in an intrinsic way, from the point of view of its own structure.” Lautman points the way past deduction and psychology to a moment where there is an intrinsic characterization of real forms, which is interesting because his major claim — “mathematics thus arises as successive syntheses wherein each stage is irreducible to the former stage” — is linked inextricably to a notion of discontinuity with an earlier mode of inference; because of the non-provability of rigorous consistency, we always have to be open to the creation of new structures, new mathematical forms… It’s interesting also that he closes by following Hilbert in saying that the structure of a mathematical theory is valuable for the truth it encapsulates — he seems to say, for the meta-mathematical reality which is being simulated.

By: French Translations: Works in Progress « Fractal Ontology

French Translations: Works in Progress « Fractal Ontology — Tue, 16 Oct 2007 22:33:30 +0000

[...] Lautman – Introduction to the Essay on the Notions of Structure and Existence in Mathematics: Models of Struct… [...]