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I am looking for recent books ( say published after 2000) on the philosophy of geometry, most books on the philosophy of mathematics seem to ignore or bypass geometry at all or am I just looking with my eyes closed?

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    $\begingroup$ I suppose "Geometry Revisited" by Coxeter is apropos here. $\endgroup$ – Chris Jul 18 '17 at 7:08
  • $\begingroup$ @Chris, "Geometry Revisited" by Coxeter is from 1967 , maybe the philosophy of geometry is really a dead subject (some say the same of geometry itself) $\endgroup$ – Willemien Jul 19 '17 at 8:57
  • $\begingroup$ the book "euclidean and non-euclidean geometries" by Marvin Greenberg has a bit of philosophy in it. $\endgroup$ – Tim kinsella Jul 26 '17 at 15:13
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Interesting question. In short, I think any book on geometry is in some way philosophical. Let me explain.

Historically, mathematicians like Euclid wrote the Elements not for the final purpose of studying geometry, but in order to prepare people for the study of philosophy. Geometry was a good tool for this because any argument needs to be tight and can be spread out as several steps. This is what you need for a philosophy argument - yes you could lay your argument out in essay form, but at the core it will be a progression from one statement to the other.

Therefore, if you pick up any book on geometry which has rigour in it (for example, Geometry Revisited), you should get some insight into philosophy.

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  • $\begingroup$ the thesis "Historically, mathematicians like Euclid wrote the Elements not for the final purpose of studying geometry, but in order to prepare people for the study of philosophy" sounds very strange to me. However we knows at today that the "Euclid geometry" was known many centuries before him... so it makes more plausible the strange thesis. $\endgroup$ – Masacroso Jul 18 '17 at 7:26
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    $\begingroup$ @Masacroso Have a look at this: storyofmathematics.com/greek_plato.html : it doesn't explicitly state my thesis, but it does say that geometry was a part of philosophy $\endgroup$ – Plato Jul 18 '17 at 7:33
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    $\begingroup$ anyway the thesis is very interesting. Thank you for the link. $\endgroup$ – Masacroso Jul 18 '17 at 7:34
  • $\begingroup$ That something is useful for studying philosophy doesn't make it philosophical itself (taking it to the (to far) extreme: is learning to read realy learning philosophy?) $\endgroup$ – Willemien Jul 19 '17 at 8:50
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Francesca Biagioli: Space, Number and Geometry from Helmholtz to Cassirer. 2016. From the blurb: "This book offers a reconstruction of the debate on non-Euclidean geometry in neo-Kantianism between the second half of the nineteenth century and the first decades of the twentieth century."

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