Oct 17, 2012

KANT’S THEORY OF KNOWLEDGE AND THE EPISTEMOLOGICAL FOUNDATION OF MATHEMATICS




By Marsigit

Kant’s view comes to dominate West European philosophy and his theory of knowledge plays a crucial role in the foundation of mathematics.



A clear understanding of his notions of would do much to elucidate his epistemological approach. Kant’s theory of knowledge seems, hitherto, to have been analyzed by post modern philosophers, and some mathematicians, and it even seems directly to rage their conjectures through incontestably certain in the ultimate concern of its consequences.

Perry R.B. retrieves that Kant’s contributions to epistemological foundation of mathematics consisted in his discovery of categories and the form of thought as the universal prerequisites of mathematical knowledge.

According to Perry , in his Prolegomena to any Future Meta¬physics, Kant exposed a question "How Is Pure Mathematics Possible?".

While Philip Kitcher in Hersh R. shows that all three foundationist gurus Frege, Hilbert, and Brouwer were Kantians; that was a consequence of the influences of Kant’s philosophy in their early milieus, and the usual tendency of research mathematicians toward an idealist vewpoint.

The publication of Kant’s great works did not put an end to the crisis in the foundation of philosophy.

On the contrary, they raged about it more furiously than ever.

As two main schools found in the philosophy of mathematics, before and after Kant, the latent elements of them were discovered and brought to the higher level.

One school considered as the sceptical promoting of the new analysis, and proceeded to build its dome furnished by its material; the other took advantage of the positions gained by the ultimate champion and developed its lines forward in the direction of transcendental claim.

Kant lays the foundations of philosophy; however, he built no structure.

He did not put one stone upon another; he declared it to be beyond the power of man to put one stone upon another.

Kant attempts to erect a temple on his foundation he repudiated.

The existence of an external world of substantial entities corresponding to our conceptions could not be demonstrated, but only logically affirmed.

References:
1 Perry, R.B., 1912, “Present Philosophical Tendencies: A Critical Survey of Naturalism Idealism Pragmatism and Realism Together with a Synopsis of the Pilosophy of William James”, New York: Longmans Green and Co. p. 139
2 Hersh, R., 1997, “What is Mathematics, Really?”, London: Jonathan Cape, p.132
3 Ibid. p. 129
4 ….., “Immanuel Kant, 1724–1804”, Retrieved 2004
5 Ibid

5 comments:

  1. Hajarul Masi Hanifatur Rohman
    S2 Pendidikan Matematika C 2016
    16709251052

    Bismillaah....
    Teori yang dikemukakan oleh Kant memang sangat berpengaruh pada filsafat pengetahuan matematika. teorinya yang terkenal yakni bahwa pengetahuan matematika merupakan pengetahuan sintetik a priori. Pada eranya, teori ini belum pernah ada, yang kemudian setelah era Kant banyak filsuf yang mengikuti aliran Kant.

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  2. Ahmad Bahauddin
    16709251058
    PPs P.Mat C 2016

    Assalamualaikum warohmatullahi wabarokatuh.
    Kant memandang pengetahuan menjadi dua unsur, yaitu unsur materi dan bentuk pengetahuan. Materi pengetahuan adalah sensasi-sensasi yang diterjemahkan oleh indera kita dari alam fenomena. Sedangkan bentuk pengetahuan adalah ikatan-ikatan pemikiran yang memberikan otoritas bagi pembentukan sensasi-sensasi sekaligus membuat penilaian.

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  3. Shelly Lubis
    17709251040
    S2 P.mat B 2017

    Assalamu'alaikum wr.wb

    As what I say before about what I have learnt in the class, I get the knowledge about the mediator philosoper, Kant, who has a great opinion about how to get the knowlwdge, taking good points from two great philosophers. and after his era, there are many philosophers follow his point of view and until now.

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  4. Nama: Hendrawansyah
    NIM: 17701251030
    S2 PEP 2017 Kelas B

    Assalamualaikum wr wb

    Terkait pandangannya Khant terhadap matematika lebih cenderung kepada filsafat eropa.Di dalam memahami konsep matematika ia menggunakan pendekatan epistimologis. Memang sangat diakui bahwa teorinya sangat melegenda dan dikenal banyak orang.Karya-karyanya memberikan konstribusi bagi para penikmat dan pecinta matematika.Meskipun demikian tapi banyak para ahli yang penganut bukan matematika murni mempertanyakan dari hasil karya-karyanya.

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  5. Wisniarti
    17709251037
    PM B Pascasarjana

    Dalam elegi ini Kant menyampaiakn bahwa landasan epistemologis matematika terdiri dari penemuan kategori dan bentuk pemikiran sebagai prasyarat universal untuk pengetahuan matematika. Dari kalimat ini, kant masih berpegang teguh dengan pernyataannya bahwa pengetahuan itu dibentu bukan hanya dari penuman kategori saja ataupun bentuk pemikiran saja. Namun lebih ari itu, yaitu pengetahuan itu dibangun dari keduanya yaitu penemuan kategori sampai bentuk pemikirannya saja.

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