HİLBERT’İN BİÇİMSELLEŞTİRME PROGRAMININ FELSEFESİ

Year 2014, Issue: 60, 265 - 280, 15.12.2014

Ahmet Çevik

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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