HİLBERT’İN BİÇİMSELLEŞTİRME PROGRAMININ FELSEFESİ

Abstract

Bu yazıda, Hilbert’in biçimselleştirme programına kadar giden matematik felsefesindeki önemli krizlerden bahsedilmiştir. Hilbert’in programının gerçekleşemeyeceğini gösteren Gödel’in eksiklik teoremi gibi programın sonuçları ve nedenleri tartışılmıştır. Daha sonra matematikteki eksikliğin neden varolduğu anlatılmaya çalışılmıştır. Son olarak, Hilbert’in programından çıkan sonuç irdelenmiştir.

Keywords

• Matematik felsefesi
• matematiksel mantık
• Gödel’in eksiklik teoremi
• Hilbert’in programı
• biçimselleştirme
• hesaplanabilirlik
• rastgelelik.

PHILOSOPHY OF HILBERT’S FORMALIZATION PROGRAM

Abstract

I discuss some of the important crises in the philosophy of mathematics which led to Hilbert’s program for formalizing mathematics. I discuss its purpose and consequences such as Gödel’s incompleteness theorems which showed that Hilbert’s program was unachievable. I also argue the reason why we have incompleteness in mathematics. Finally, I argue what followed from the failure of Hilbert’s formalization program.

Keywords

• Philosophy of mathematics
• mathematical logic
• Gödel’s incompleteness theorem
• Hilbert’s program
• formalization
• computability
• randomness.

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