Was Kant an Intuitionist about mathematical objects? Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern) Announcing the arrival of Valued Associate #679: Cesar Manara Unicorn Meta Zoo #1: Why another podcast?How do mathematical objects relate to the real world?Was Kant right about space and time (and wrong about knowledge)?What are the properties of Mathematical Objects?Existence of mathematical objects: how?Was Kant incorrect to assert all maths as 'a priori'?For a mathematical realist, is there a distinction between real mathematical objects and constructed mathematical objects?Modern Mathematical Objects and EmpiricismWas Kant a factor in forming Gauss's abstract view of mathematical objects?Can a physicalist be also realist about mathematical objects?Distinguishing between procedure-like and collection-like mathematical objects

Asymptotics question

License to disallow distribution in closed source software, but allow exceptions made by owner?

Should a wizard buy fine inks every time he want to copy spells into his spellbook?

How does light 'choose' between wave and particle behaviour?

How to write capital alpha?

How can I prevent/balance waiting and turtling as a response to cooldown mechanics

Where is the Next Backup Size entry on iOS 12?

Relating to the President and obstruction, were Mueller's conclusions preordained?

After Sam didn't return home in the end, were he and Al still friends?

In musical terms, what properties are varied by the human voice to produce different words / syllables?

What are the main differences between Stargate SG-1 cuts?

Resize vertical bars (absolute-value symbols)

Random body shuffle every night—can we still function?

Does the Black Tentacles spell do damage twice at the start of turn to an already restrained creature?

I can't produce songs

Why complex landing gears are used instead of simple,reliability and light weight muscle wire or shape memory alloys?

GDP with Intermediate Production

What is the difference between a "ranged attack" and a "ranged weapon attack"?

Is CEO the "profession" with the most psychopaths?

Why is std::move not [[nodiscard]] in C++20?

How can a team of shapeshifters communicate?

Are the endpoints of the domain of a function counted as critical points?

Sally's older brother

If Windows 7 doesn't support WSL, then what is "Subsystem for UNIX-based Applications"?



Was Kant an Intuitionist about mathematical objects?



Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)
Announcing the arrival of Valued Associate #679: Cesar Manara
Unicorn Meta Zoo #1: Why another podcast?How do mathematical objects relate to the real world?Was Kant right about space and time (and wrong about knowledge)?What are the properties of Mathematical Objects?Existence of mathematical objects: how?Was Kant incorrect to assert all maths as 'a priori'?For a mathematical realist, is there a distinction between real mathematical objects and constructed mathematical objects?Modern Mathematical Objects and EmpiricismWas Kant a factor in forming Gauss's abstract view of mathematical objects?Can a physicalist be also realist about mathematical objects?Distinguishing between procedure-like and collection-like mathematical objects










3















In regards to the ontology of mathematics, as far as I can understand, Kant believed that Mathematical objects existed only as features of our perception that influenced how we viewed things-in-themselves, saying that, for example, geometry was the spatial lens by which we viewed phenomena whilst number arithmetic was the temporal lens.



If so, if one were to classify this position into a contemporary position on the ontology of mathematics, would it be fair to say that he was an intuitionist (i.e. he believed mathematical objects to be human constructs)? Or was he still a platonic realist in this regard?










share|improve this question









New contributor




Aryaman Gupta is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
























    3















    In regards to the ontology of mathematics, as far as I can understand, Kant believed that Mathematical objects existed only as features of our perception that influenced how we viewed things-in-themselves, saying that, for example, geometry was the spatial lens by which we viewed phenomena whilst number arithmetic was the temporal lens.



    If so, if one were to classify this position into a contemporary position on the ontology of mathematics, would it be fair to say that he was an intuitionist (i.e. he believed mathematical objects to be human constructs)? Or was he still a platonic realist in this regard?










    share|improve this question









    New contributor




    Aryaman Gupta is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.






















      3












      3








      3








      In regards to the ontology of mathematics, as far as I can understand, Kant believed that Mathematical objects existed only as features of our perception that influenced how we viewed things-in-themselves, saying that, for example, geometry was the spatial lens by which we viewed phenomena whilst number arithmetic was the temporal lens.



      If so, if one were to classify this position into a contemporary position on the ontology of mathematics, would it be fair to say that he was an intuitionist (i.e. he believed mathematical objects to be human constructs)? Or was he still a platonic realist in this regard?










      share|improve this question









      New contributor




      Aryaman Gupta is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.












      In regards to the ontology of mathematics, as far as I can understand, Kant believed that Mathematical objects existed only as features of our perception that influenced how we viewed things-in-themselves, saying that, for example, geometry was the spatial lens by which we viewed phenomena whilst number arithmetic was the temporal lens.



      If so, if one were to classify this position into a contemporary position on the ontology of mathematics, would it be fair to say that he was an intuitionist (i.e. he believed mathematical objects to be human constructs)? Or was he still a platonic realist in this regard?







      philosophy-of-mathematics kant explanation intuitionistic-logic






      share|improve this question









      New contributor




      Aryaman Gupta is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











      share|improve this question









      New contributor




      Aryaman Gupta is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.









      share|improve this question




      share|improve this question








      edited 1 hour ago









      virmaior

      25.4k33997




      25.4k33997






      New contributor




      Aryaman Gupta is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.









      asked 8 hours ago









      Aryaman GuptaAryaman Gupta

      211




      211




      New contributor




      Aryaman Gupta is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.





      New contributor





      Aryaman Gupta is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.






      Aryaman Gupta is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.




















          1 Answer
          1






          active

          oldest

          votes


















          3














          You're right to see some resonances between intuitionism and Kant. However, there's no uncontroversial sense in which you could blithely categorize Kant as an intuitionist. I'm not sure I've ever seen anyone do it, as a matter of sociological note. More instructive, I think, than trying to get Kant to fit the intuitionist picture is to explore the subtle differences.



          First of all, it would be anachronistic to call Kant an intuitionist, since Brouwer didn't develop intuitionist mathematics until well after Kant's death. As a result, intuitionism as we know it was not an available position in Kant's time. So one would have to make the case that the anachronistic label was really warranted. This by itself, of course, does not mean that it would be inappropriate to retroactively sort Kant into the intuitionist paradigm.



          And there is some initial reason for finding this categorization attractive. Brouwer and Kant certainly agree on one really fundamental issue: namely, that mathematical truths are grounded in the nature of the mind. Certainly Brouwer and other intuitionists drew inspiration from Kant, e.g., from Kant's notion of intuition and the role that time plays in structuring intuition. In particular, Brouwer agrees with Kant that arithmetic truths are synthetic a priori. Brouwer departs strongly from Kant, though, with respect to the view of space. Brouwer denies that geometry is synthetic a priori, therefore denying the possibility of an a priori intuition of space.



          Furthermore, it is not so clear whether Kant was a constructivist about mathematics. By contrast, constructivism is at the heart of intuitionism (i.e., the position that mathematical existence can only be proven by constructing the alleged mathematical object, and not simply showing that its existence is consistent). Intuitionism is a species of constructivism, so that if Kant was not a constructivist, then you could not call him an intuitionist in any sense. It's true that Kant uses the word "construction" and claims that mathematics is in the business of constructing its concepts. But this is a potentially very misleading connection. Kant's definition of construction is:




          to construct a concept means to exhibit a priori the intuition corresponding to it (A713/B741).




          It's not at all clear that this is the notion of construction that intuitionists work with. For example, in constructing proofs the intuitionist will frequently construct an object by demonstrating an algorithm that is sufficient to construct it (this, in fact, is part of the appeal of intuitoinist logic for mathematicians interested in computability). In turn, the logic underlying intuitionism was certainly not Kant's logic; it requires a revisionary definitions of terms such as function and real number that would have certainly been alien to Kant. Let's put it this way: if Kant found himself revived from the dead and walked into a classroom where intuitionist mathematics was being taught, there would be much that he would not recognize.



          Would our revived, 21st-century Kant adopt intuitionism now that he finds it an available option? This is an intriguing question. What you'd have to do is to understand some of the subtle differences (just a couple of which I've highlighted above) and determine which of these doctrines are essential to Kant's philosophy of mathematics and which he might give up while retaining the integrity of his kernel of truth. It's also worth pointing out that several other mathematical philosophies take inspiration from the spirit, if not the letter, of Kant's own philosophy of mathematics (e.g., structuralism). This is important to note because it brings out the sense in which intuitionism certainly has no unique claim to the legacy of Kantian philosophy of mathematics, which points to the sense in which intuitionism is just one option among many that one could find implicit in the spirit of Kant's writings.



          Finally, though it is of course entirely possible to disconnect intuitionist mathematics from the idiosyncracies of its founder (Brouwer), it's also important to note that Brouwer thought of mathematics in a very different way than Kant. Brouwer held a mystical view of the mind's construction of mathematical objects that would be, to say the least, in violation of Kant's transcendental idealism.



          In short: No, Kant was not an intuitionist in any straightforward sense. However, the central resonances of Kant's view with certain general, fundamental intuitonist ideas would make an investigations of the details of the points of departure well worth studying.






          share|improve this answer

























            Your Answer








            StackExchange.ready(function()
            var channelOptions =
            tags: "".split(" "),
            id: "265"
            ;
            initTagRenderer("".split(" "), "".split(" "), channelOptions);

            StackExchange.using("externalEditor", function()
            // Have to fire editor after snippets, if snippets enabled
            if (StackExchange.settings.snippets.snippetsEnabled)
            StackExchange.using("snippets", function()
            createEditor();
            );

            else
            createEditor();

            );

            function createEditor()
            StackExchange.prepareEditor(
            heartbeatType: 'answer',
            autoActivateHeartbeat: false,
            convertImagesToLinks: false,
            noModals: true,
            showLowRepImageUploadWarning: true,
            reputationToPostImages: null,
            bindNavPrevention: true,
            postfix: "",
            imageUploader:
            brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
            contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
            allowUrls: true
            ,
            noCode: true, onDemand: true,
            discardSelector: ".discard-answer"
            ,immediatelyShowMarkdownHelp:true
            );



            );






            Aryaman Gupta is a new contributor. Be nice, and check out our Code of Conduct.









            draft saved

            draft discarded


















            StackExchange.ready(
            function ()
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fphilosophy.stackexchange.com%2fquestions%2f61995%2fwas-kant-an-intuitionist-about-mathematical-objects%23new-answer', 'question_page');

            );

            Post as a guest















            Required, but never shown

























            1 Answer
            1






            active

            oldest

            votes








            1 Answer
            1






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            3














            You're right to see some resonances between intuitionism and Kant. However, there's no uncontroversial sense in which you could blithely categorize Kant as an intuitionist. I'm not sure I've ever seen anyone do it, as a matter of sociological note. More instructive, I think, than trying to get Kant to fit the intuitionist picture is to explore the subtle differences.



            First of all, it would be anachronistic to call Kant an intuitionist, since Brouwer didn't develop intuitionist mathematics until well after Kant's death. As a result, intuitionism as we know it was not an available position in Kant's time. So one would have to make the case that the anachronistic label was really warranted. This by itself, of course, does not mean that it would be inappropriate to retroactively sort Kant into the intuitionist paradigm.



            And there is some initial reason for finding this categorization attractive. Brouwer and Kant certainly agree on one really fundamental issue: namely, that mathematical truths are grounded in the nature of the mind. Certainly Brouwer and other intuitionists drew inspiration from Kant, e.g., from Kant's notion of intuition and the role that time plays in structuring intuition. In particular, Brouwer agrees with Kant that arithmetic truths are synthetic a priori. Brouwer departs strongly from Kant, though, with respect to the view of space. Brouwer denies that geometry is synthetic a priori, therefore denying the possibility of an a priori intuition of space.



            Furthermore, it is not so clear whether Kant was a constructivist about mathematics. By contrast, constructivism is at the heart of intuitionism (i.e., the position that mathematical existence can only be proven by constructing the alleged mathematical object, and not simply showing that its existence is consistent). Intuitionism is a species of constructivism, so that if Kant was not a constructivist, then you could not call him an intuitionist in any sense. It's true that Kant uses the word "construction" and claims that mathematics is in the business of constructing its concepts. But this is a potentially very misleading connection. Kant's definition of construction is:




            to construct a concept means to exhibit a priori the intuition corresponding to it (A713/B741).




            It's not at all clear that this is the notion of construction that intuitionists work with. For example, in constructing proofs the intuitionist will frequently construct an object by demonstrating an algorithm that is sufficient to construct it (this, in fact, is part of the appeal of intuitoinist logic for mathematicians interested in computability). In turn, the logic underlying intuitionism was certainly not Kant's logic; it requires a revisionary definitions of terms such as function and real number that would have certainly been alien to Kant. Let's put it this way: if Kant found himself revived from the dead and walked into a classroom where intuitionist mathematics was being taught, there would be much that he would not recognize.



            Would our revived, 21st-century Kant adopt intuitionism now that he finds it an available option? This is an intriguing question. What you'd have to do is to understand some of the subtle differences (just a couple of which I've highlighted above) and determine which of these doctrines are essential to Kant's philosophy of mathematics and which he might give up while retaining the integrity of his kernel of truth. It's also worth pointing out that several other mathematical philosophies take inspiration from the spirit, if not the letter, of Kant's own philosophy of mathematics (e.g., structuralism). This is important to note because it brings out the sense in which intuitionism certainly has no unique claim to the legacy of Kantian philosophy of mathematics, which points to the sense in which intuitionism is just one option among many that one could find implicit in the spirit of Kant's writings.



            Finally, though it is of course entirely possible to disconnect intuitionist mathematics from the idiosyncracies of its founder (Brouwer), it's also important to note that Brouwer thought of mathematics in a very different way than Kant. Brouwer held a mystical view of the mind's construction of mathematical objects that would be, to say the least, in violation of Kant's transcendental idealism.



            In short: No, Kant was not an intuitionist in any straightforward sense. However, the central resonances of Kant's view with certain general, fundamental intuitonist ideas would make an investigations of the details of the points of departure well worth studying.






            share|improve this answer





























              3














              You're right to see some resonances between intuitionism and Kant. However, there's no uncontroversial sense in which you could blithely categorize Kant as an intuitionist. I'm not sure I've ever seen anyone do it, as a matter of sociological note. More instructive, I think, than trying to get Kant to fit the intuitionist picture is to explore the subtle differences.



              First of all, it would be anachronistic to call Kant an intuitionist, since Brouwer didn't develop intuitionist mathematics until well after Kant's death. As a result, intuitionism as we know it was not an available position in Kant's time. So one would have to make the case that the anachronistic label was really warranted. This by itself, of course, does not mean that it would be inappropriate to retroactively sort Kant into the intuitionist paradigm.



              And there is some initial reason for finding this categorization attractive. Brouwer and Kant certainly agree on one really fundamental issue: namely, that mathematical truths are grounded in the nature of the mind. Certainly Brouwer and other intuitionists drew inspiration from Kant, e.g., from Kant's notion of intuition and the role that time plays in structuring intuition. In particular, Brouwer agrees with Kant that arithmetic truths are synthetic a priori. Brouwer departs strongly from Kant, though, with respect to the view of space. Brouwer denies that geometry is synthetic a priori, therefore denying the possibility of an a priori intuition of space.



              Furthermore, it is not so clear whether Kant was a constructivist about mathematics. By contrast, constructivism is at the heart of intuitionism (i.e., the position that mathematical existence can only be proven by constructing the alleged mathematical object, and not simply showing that its existence is consistent). Intuitionism is a species of constructivism, so that if Kant was not a constructivist, then you could not call him an intuitionist in any sense. It's true that Kant uses the word "construction" and claims that mathematics is in the business of constructing its concepts. But this is a potentially very misleading connection. Kant's definition of construction is:




              to construct a concept means to exhibit a priori the intuition corresponding to it (A713/B741).




              It's not at all clear that this is the notion of construction that intuitionists work with. For example, in constructing proofs the intuitionist will frequently construct an object by demonstrating an algorithm that is sufficient to construct it (this, in fact, is part of the appeal of intuitoinist logic for mathematicians interested in computability). In turn, the logic underlying intuitionism was certainly not Kant's logic; it requires a revisionary definitions of terms such as function and real number that would have certainly been alien to Kant. Let's put it this way: if Kant found himself revived from the dead and walked into a classroom where intuitionist mathematics was being taught, there would be much that he would not recognize.



              Would our revived, 21st-century Kant adopt intuitionism now that he finds it an available option? This is an intriguing question. What you'd have to do is to understand some of the subtle differences (just a couple of which I've highlighted above) and determine which of these doctrines are essential to Kant's philosophy of mathematics and which he might give up while retaining the integrity of his kernel of truth. It's also worth pointing out that several other mathematical philosophies take inspiration from the spirit, if not the letter, of Kant's own philosophy of mathematics (e.g., structuralism). This is important to note because it brings out the sense in which intuitionism certainly has no unique claim to the legacy of Kantian philosophy of mathematics, which points to the sense in which intuitionism is just one option among many that one could find implicit in the spirit of Kant's writings.



              Finally, though it is of course entirely possible to disconnect intuitionist mathematics from the idiosyncracies of its founder (Brouwer), it's also important to note that Brouwer thought of mathematics in a very different way than Kant. Brouwer held a mystical view of the mind's construction of mathematical objects that would be, to say the least, in violation of Kant's transcendental idealism.



              In short: No, Kant was not an intuitionist in any straightforward sense. However, the central resonances of Kant's view with certain general, fundamental intuitonist ideas would make an investigations of the details of the points of departure well worth studying.






              share|improve this answer



























                3












                3








                3







                You're right to see some resonances between intuitionism and Kant. However, there's no uncontroversial sense in which you could blithely categorize Kant as an intuitionist. I'm not sure I've ever seen anyone do it, as a matter of sociological note. More instructive, I think, than trying to get Kant to fit the intuitionist picture is to explore the subtle differences.



                First of all, it would be anachronistic to call Kant an intuitionist, since Brouwer didn't develop intuitionist mathematics until well after Kant's death. As a result, intuitionism as we know it was not an available position in Kant's time. So one would have to make the case that the anachronistic label was really warranted. This by itself, of course, does not mean that it would be inappropriate to retroactively sort Kant into the intuitionist paradigm.



                And there is some initial reason for finding this categorization attractive. Brouwer and Kant certainly agree on one really fundamental issue: namely, that mathematical truths are grounded in the nature of the mind. Certainly Brouwer and other intuitionists drew inspiration from Kant, e.g., from Kant's notion of intuition and the role that time plays in structuring intuition. In particular, Brouwer agrees with Kant that arithmetic truths are synthetic a priori. Brouwer departs strongly from Kant, though, with respect to the view of space. Brouwer denies that geometry is synthetic a priori, therefore denying the possibility of an a priori intuition of space.



                Furthermore, it is not so clear whether Kant was a constructivist about mathematics. By contrast, constructivism is at the heart of intuitionism (i.e., the position that mathematical existence can only be proven by constructing the alleged mathematical object, and not simply showing that its existence is consistent). Intuitionism is a species of constructivism, so that if Kant was not a constructivist, then you could not call him an intuitionist in any sense. It's true that Kant uses the word "construction" and claims that mathematics is in the business of constructing its concepts. But this is a potentially very misleading connection. Kant's definition of construction is:




                to construct a concept means to exhibit a priori the intuition corresponding to it (A713/B741).




                It's not at all clear that this is the notion of construction that intuitionists work with. For example, in constructing proofs the intuitionist will frequently construct an object by demonstrating an algorithm that is sufficient to construct it (this, in fact, is part of the appeal of intuitoinist logic for mathematicians interested in computability). In turn, the logic underlying intuitionism was certainly not Kant's logic; it requires a revisionary definitions of terms such as function and real number that would have certainly been alien to Kant. Let's put it this way: if Kant found himself revived from the dead and walked into a classroom where intuitionist mathematics was being taught, there would be much that he would not recognize.



                Would our revived, 21st-century Kant adopt intuitionism now that he finds it an available option? This is an intriguing question. What you'd have to do is to understand some of the subtle differences (just a couple of which I've highlighted above) and determine which of these doctrines are essential to Kant's philosophy of mathematics and which he might give up while retaining the integrity of his kernel of truth. It's also worth pointing out that several other mathematical philosophies take inspiration from the spirit, if not the letter, of Kant's own philosophy of mathematics (e.g., structuralism). This is important to note because it brings out the sense in which intuitionism certainly has no unique claim to the legacy of Kantian philosophy of mathematics, which points to the sense in which intuitionism is just one option among many that one could find implicit in the spirit of Kant's writings.



                Finally, though it is of course entirely possible to disconnect intuitionist mathematics from the idiosyncracies of its founder (Brouwer), it's also important to note that Brouwer thought of mathematics in a very different way than Kant. Brouwer held a mystical view of the mind's construction of mathematical objects that would be, to say the least, in violation of Kant's transcendental idealism.



                In short: No, Kant was not an intuitionist in any straightforward sense. However, the central resonances of Kant's view with certain general, fundamental intuitonist ideas would make an investigations of the details of the points of departure well worth studying.






                share|improve this answer















                You're right to see some resonances between intuitionism and Kant. However, there's no uncontroversial sense in which you could blithely categorize Kant as an intuitionist. I'm not sure I've ever seen anyone do it, as a matter of sociological note. More instructive, I think, than trying to get Kant to fit the intuitionist picture is to explore the subtle differences.



                First of all, it would be anachronistic to call Kant an intuitionist, since Brouwer didn't develop intuitionist mathematics until well after Kant's death. As a result, intuitionism as we know it was not an available position in Kant's time. So one would have to make the case that the anachronistic label was really warranted. This by itself, of course, does not mean that it would be inappropriate to retroactively sort Kant into the intuitionist paradigm.



                And there is some initial reason for finding this categorization attractive. Brouwer and Kant certainly agree on one really fundamental issue: namely, that mathematical truths are grounded in the nature of the mind. Certainly Brouwer and other intuitionists drew inspiration from Kant, e.g., from Kant's notion of intuition and the role that time plays in structuring intuition. In particular, Brouwer agrees with Kant that arithmetic truths are synthetic a priori. Brouwer departs strongly from Kant, though, with respect to the view of space. Brouwer denies that geometry is synthetic a priori, therefore denying the possibility of an a priori intuition of space.



                Furthermore, it is not so clear whether Kant was a constructivist about mathematics. By contrast, constructivism is at the heart of intuitionism (i.e., the position that mathematical existence can only be proven by constructing the alleged mathematical object, and not simply showing that its existence is consistent). Intuitionism is a species of constructivism, so that if Kant was not a constructivist, then you could not call him an intuitionist in any sense. It's true that Kant uses the word "construction" and claims that mathematics is in the business of constructing its concepts. But this is a potentially very misleading connection. Kant's definition of construction is:




                to construct a concept means to exhibit a priori the intuition corresponding to it (A713/B741).




                It's not at all clear that this is the notion of construction that intuitionists work with. For example, in constructing proofs the intuitionist will frequently construct an object by demonstrating an algorithm that is sufficient to construct it (this, in fact, is part of the appeal of intuitoinist logic for mathematicians interested in computability). In turn, the logic underlying intuitionism was certainly not Kant's logic; it requires a revisionary definitions of terms such as function and real number that would have certainly been alien to Kant. Let's put it this way: if Kant found himself revived from the dead and walked into a classroom where intuitionist mathematics was being taught, there would be much that he would not recognize.



                Would our revived, 21st-century Kant adopt intuitionism now that he finds it an available option? This is an intriguing question. What you'd have to do is to understand some of the subtle differences (just a couple of which I've highlighted above) and determine which of these doctrines are essential to Kant's philosophy of mathematics and which he might give up while retaining the integrity of his kernel of truth. It's also worth pointing out that several other mathematical philosophies take inspiration from the spirit, if not the letter, of Kant's own philosophy of mathematics (e.g., structuralism). This is important to note because it brings out the sense in which intuitionism certainly has no unique claim to the legacy of Kantian philosophy of mathematics, which points to the sense in which intuitionism is just one option among many that one could find implicit in the spirit of Kant's writings.



                Finally, though it is of course entirely possible to disconnect intuitionist mathematics from the idiosyncracies of its founder (Brouwer), it's also important to note that Brouwer thought of mathematics in a very different way than Kant. Brouwer held a mystical view of the mind's construction of mathematical objects that would be, to say the least, in violation of Kant's transcendental idealism.



                In short: No, Kant was not an intuitionist in any straightforward sense. However, the central resonances of Kant's view with certain general, fundamental intuitonist ideas would make an investigations of the details of the points of departure well worth studying.







                share|improve this answer














                share|improve this answer



                share|improve this answer








                edited 2 hours ago

























                answered 4 hours ago









                transitionsynthesistransitionsynthesis

                75857




                75857




















                    Aryaman Gupta is a new contributor. Be nice, and check out our Code of Conduct.









                    draft saved

                    draft discarded


















                    Aryaman Gupta is a new contributor. Be nice, and check out our Code of Conduct.












                    Aryaman Gupta is a new contributor. Be nice, and check out our Code of Conduct.











                    Aryaman Gupta is a new contributor. Be nice, and check out our Code of Conduct.














                    Thanks for contributing an answer to Philosophy Stack Exchange!


                    • Please be sure to answer the question. Provide details and share your research!

                    But avoid


                    • Asking for help, clarification, or responding to other answers.

                    • Making statements based on opinion; back them up with references or personal experience.

                    To learn more, see our tips on writing great answers.




                    draft saved


                    draft discarded














                    StackExchange.ready(
                    function ()
                    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fphilosophy.stackexchange.com%2fquestions%2f61995%2fwas-kant-an-intuitionist-about-mathematical-objects%23new-answer', 'question_page');

                    );

                    Post as a guest















                    Required, but never shown





















































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown

































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown







                    Popular posts from this blog

                    Canceling a color specificationRandomly assigning color to Graphics3D objects?Default color for Filling in Mathematica 9Coloring specific elements of sets with a prime modified order in an array plotHow to pick a color differing significantly from the colors already in a given color list?Detection of the text colorColor numbers based on their valueCan color schemes for use with ColorData include opacity specification?My dynamic color schemes

                    Invision Community Contents History See also References External links Navigation menuProprietaryinvisioncommunity.comIPS Community ForumsIPS Community Forumsthis blog entry"License Changes, IP.Board 3.4, and the Future""Interview -- Matt Mecham of Ibforums""CEO Invision Power Board, Matt Mecham Is a Liar, Thief!"IPB License Explanation 1.3, 1.3.1, 2.0, and 2.1ArchivedSecurity Fixes, Updates And Enhancements For IPB 1.3.1Archived"New Demo Accounts - Invision Power Services"the original"New Default Skin"the original"Invision Power Board 3.0.0 and Applications Released"the original"Archived copy"the original"Perpetual licenses being done away with""Release Notes - Invision Power Services""Introducing: IPS Community Suite 4!"Invision Community Release Notes

                    199年 目錄 大件事 到箇年出世嗰人 到箇年死嗰人 節慶、風俗習慣 導覽選單