Books on the philosophy of geometry












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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?






geometry book-recommendation big-list philosophy big-picture







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$endgroup$








  • 1




    $begingroup$
    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
















3












$begingroup$


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?






geometry book-recommendation big-list philosophy big-picture







share|cite|improve this question









$endgroup$








  • 1




    $begingroup$
    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














3












3








3


2



$begingroup$


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?






geometry book-recommendation big-list philosophy big-picture







share|cite|improve this question









$endgroup$




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?






geometry book-recommendation big-list philosophy big-picture




geometry book-recommendation big-list philosophy big-picture






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Jul 18 '17 at 6:59









WillemienWillemien

3,50032060




3,50032060








  • 1




    $begingroup$
    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














  • 1




    $begingroup$
    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








1




1




$begingroup$
I suppose "Geometry Revisited" by Coxeter is apropos here.
$endgroup$
– Chris
Jul 18 '17 at 7:08




$begingroup$
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




$begingroup$
@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




$begingroup$
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










2 Answers
2






active

oldest

votes


















4












$begingroup$

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.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    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






  • 1




    $begingroup$
    @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






  • 1




    $begingroup$
    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



















0












$begingroup$

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."






share|cite|improve this answer









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    2 Answers
    2






    active

    oldest

    votes








    2 Answers
    2






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    4












    $begingroup$

    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.






    share|cite|improve this answer









    $endgroup$













    • $begingroup$
      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






    • 1




      $begingroup$
      @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






    • 1




      $begingroup$
      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
















    4












    $begingroup$

    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.






    share|cite|improve this answer









    $endgroup$













    • $begingroup$
      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






    • 1




      $begingroup$
      @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






    • 1




      $begingroup$
      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














    4












    4








    4





    $begingroup$

    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.






    share|cite|improve this answer









    $endgroup$



    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.







    share|cite|improve this answer












    share|cite|improve this answer



    share|cite|improve this answer










    answered Jul 18 '17 at 7:13









    PlatoPlato

    1,205518




    1,205518












    • $begingroup$
      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






    • 1




      $begingroup$
      @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






    • 1




      $begingroup$
      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


















    • $begingroup$
      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






    • 1




      $begingroup$
      @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






    • 1




      $begingroup$
      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
















    $begingroup$
    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




    $begingroup$
    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




    1




    1




    $begingroup$
    @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




    $begingroup$
    @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




    1




    1




    $begingroup$
    anyway the thesis is very interesting. Thank you for the link.
    $endgroup$
    – Masacroso
    Jul 18 '17 at 7:34




    $begingroup$
    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




    $begingroup$
    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











    0












    $begingroup$

    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."






    share|cite|improve this answer









    $endgroup$


















      0












      $begingroup$

      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."






      share|cite|improve this answer









      $endgroup$
















        0












        0








        0





        $begingroup$

        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."






        share|cite|improve this answer









        $endgroup$



        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."







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Dec 19 '18 at 18:58









        Patricia A BlanchettePatricia A Blanchette

        1




        1






























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