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Uzay ve Zaman Teorisi Açısından Immanuel Kant’ın Matematik Felsefesi

Immanuel Kant’s Philosophy of Mathematics in Terms of His Theory of Space and Time

Journal Name:

  • Kaygı: Uludağ Üniversitesi Fen-Edebiyat Fakültesi Felsefe Dergisi

Publication Year:

  • 2012

Key Words:

Keywords (Original Language):

Author NameUniversity of AuthorFaculty of Author
Abstract (2. Language): 
At the beginning of the modern age, mathematics had a great importance for the study of Nature. Galileo claimed that ‘the book of nature was written in a kind of mathematical code, and that if we could only crack that code, we could uncover her ultimate secrets’. But, how can mathematics, consisting of necessary tautological truths that are infallible and non-informative, be regarded as the language of natural sciences, while the knowledge of natural sciences is informative, empirical and fallible? Or, is there another alternative: as Hume claimed, modern sciences only depend on empirical data deriving from our perceptions, rather than having the necessity of mathematics. Many philosophers have tried to find an adequate answer for the problem of the relationship between mathematical necessity and contingent perceptions, but the difficulty remained unsolved until Kant’s construction of his original philosophy of the nature as well as the limits of human reason. The main purpose of this study is to show how Kant overcomes this difficulty by making use of the examples of Euclidean geometry and of arithmetic: there are synthetic a priori (a priori, universal, necessary, but at the same time informative) judgments, and indeed mathematical propositions are of this kind.
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Abstract (Original Language): 
Modern çağın başlangıcında, matematik doğa çalışması için büyük bir öneme sahip olmuştur. Galileo ‘doğa kitabının bir çeşit matematiksel kodla yazıldığını,bizim ancak bu kodu kırabilmemiz durumunda, onun nihai sırlarını açığa çıkarabileceğimizi’ iddia etmiştir. Ancak, doğal bilimlerin bilgisi bilgimizi genişleten, deneysel ve yanılabilir nitelikteyken, nasıl oluyor da kesin ve bilgimizi genişletmeyen zorunlu totolojik doğruları içeren matematik, doğal bilimlerin dili olabiliyor? Ya da, Hume’un iddia ettiği gibi farklı bir seçenek mi var: modern bilimler matematiğin zorunluluğuna sahip olmaktan çok, algılarımızdan türeyen deneysel bilgiye dayanırlar. Pek çok filozof rastlantısal algılar ve matematiksel zorunluluk arasındaki ilişki problemine yeterli cevaplar bulmaya çalıştılar, ancak zorluk Kant’ın kendi orijinal tabiat ve insan bilgisinin sınırları felsefesinin oluşumuna kadar çözülmeden kaldı. Bu çalışmanın amacı Kant’ın aritmetik ve Euclid geometrisi örneklerini kullanarak bu problemin üstesinden nasıl geldiğini göstermektir: synthetic a priori (a priori, evrensel, zorunlu fakat aynı zamanda bilgimizi genişleten) yargılar vardır ve gerçekten matematiksel önermeler bu türdendir.
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  • 18
45-70
  • English

REFERENCES

References: 

‘CPR’: Kant, Critique of Pure Reason, trans. N. Kemp Smith (New York: St Martin’s, 1965).
‘CSM’: John Cottingham, Robert Stoothoff, and Dugald Murdoch (eds. and trans.), The Philosophical Writings of Descartes, vols: I & II (Cambridge: Cambridge University Press, 1985).
‘CSMK’: John Cottingham, Robert Stoothoff, Dugald Murdoch, and Anthony Kenny (eds. and trans.), vol. III (Cambridge: Cambridge University Press, 1991).
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