Nov 26, 2012

Hilbert's Program 2_Documented by Marsigit



Hilbert's Program 2


Hilbert had an anti-Kantian reaction now called formalism. The program is implemented in two steps:

2) Hilbert observed that a formal system by itself is nothing other than a set of symbols and rules for dealing with them. Symbols and rules belong to the real part of mathematics. Thus, the science of dealing with formal systems (proving properties, etc.) belongs to the real realm of mathematics. Among the properties we should be able to prove is that of consistency. Consistency implies that no contradictions will arise when dealing with the system. The method of proving consistency belongs to the real part of mathematics. The science of dealing with formal systems is called meta-mathematics. The usual way to prove consistency is to model the formal system in concrete mathematics and then show that the model was consistent.




1 comment:

  1. Syahrial
    16701251015
    S2 PEP kelas B 2016
    Hilbert mengamati bahwa sistem formal dengan sendirinya tidak lain dari satu set simbol dan aturan untuk berurusan dengan mereka. Simbol dan aturan milik bagian nyata dari matematika. Dengan demikian, ilmu berurusan dengan sistem formal (membuktikan sifat, dll) milik ranah nyata matematika. Di antara sifat-sifat tersebut kita harus bisa membuktikan bahwa konsistensi. Konsistensi berarti bahwa tidak ada kontradiksi akan muncul ketika berhadapan dengan sistem. Metode membuktikan konsistensi milik bagian nyata dari matematika. Ilmu berurusan dengan sistem formal disebut meta-matematika.

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