Resultaten voor 'ernest nagel'

1. Ernest , Nagel

Principles of the Theory of Probability

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1. Ernest , Nagel
2. James , R. Newman

Gödel Kanitlamasi

20. yüzyil matematiksel mantik tarihinin en önemli olayi Kurt Gödelin matematigin temelleri hakkinda kanitladigi teoremlerdir. Kesinlik, tutarlilik, tamlik gibi niteliklerin matematige yüklenmesinin en önemli nedeni, matematigin aksiyomlardan türetilen dogru önermelerinin, yani teoremlerin kesin olarak kanitlanabilir olmasiydi. Böylece dogruluk ve kanitlanabilirlik örtüstürülüyordu. Matematigin teoremlerinin dogru iseler dogruluklari kesinlikle kanitlanabilen, dogru degilseler yine dogru olmadiklari kesin olarak kanitlanabilen önermeler olduklari, dolayisiyla matematikte kesinlik ve tutarliligin tam olarak egemen oldugu kabul edilmisti. Gödel bu kabullerin ve beklentilerin sanildigi gibi saglam olmadigini yine matematikten yola cikarak kesin olarak kanitlamistir. Whitehead ve Russellin matematigin mantiksal temelleri konusundaki anitsal calismasi olan Principia Mathematicayi ele alarak, temellerin hep eksik kalacagini göstermistir. Gödel, dogal sayilar aritmetigini kapsayan bir bicimsel dizgede, karar verilemeyen önermeler oldugunu kanitlamistir; yani bu önermeler ne kanitlanabilirler ne de bunlarin bicimsel degillemeleri kanitlanabilir. Ama öte yandan, bu karar verilemeyen önermelerin dogru olduklari üst-matematiksel akil yürütmelerle gösterilebilir. Ayrica Gödel, dogal sayilar aritmetigini kapsayan bir bicimsel dizgenin tutarliliginin, bu dizgenin icinde kanitlanamayacagini da kanitlamistir. Gödelin calismalarinin sonuclari matematigin kendi icsel sinirliliklari oldugunu ortaya koymustur. Hic kusku yok ki, benim ortaya cikardigim calisma bir yaniyla, Nagel ve Newmanin kitabindan kaynaklanmistir.-Douglas R. Hofstadter, Gödel, Escher, Bachin yazariGödelin kanitlamasi üzerine yazilmis en iyi kitap. -Scientific AmericanOlaganüstü bir yorumlama. -Nature K

1. Ernest , Nagel

Teleology Revisited and Other Essays in the Philosophy and History of Science

1. Ernest Nagel
2. James R. Newman

Godel's Proof

'Nagel and Newman accomplish the wondrous task of clarifying the argumentative outline of Kurt Godel's celebrated logic bomb.' – The Guardian In 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of physicist Albert Einstein, his theorem proved that mathematics was partly based on propositions not provable within the mathematical system. The importance of Godel's Proof rests upon its radical implications and has echoed throughout many fields, from maths to science to philosophy, computer design, artificial intelligence, even religion and psychology. While others such as Douglas Hofstadter and Roger Penrose have published bestsellers based on Godel’s theorem, this is the first book to present a readable explanation to both scholars and non-specialists alike. A gripping combination of science and accessibility, Godel’s Proof by Nagel and Newman is for both mathematicians and the idly curious, offering those with a taste for logic and philosophy the chance to satisfy their intellectual curiosity. Kurt Godel (1906 – 1978) Born in Brunn, he was a colleague of physicist Albert Einstein and professor at the Institute for Advanced Study in Princeton, N.J.

1. Ernest Nagel
2. James R. Newman

Gödel's Proof

In 1931 Kurt Godel published his fundamental paper, On Formally Undecidable Propositions of Principia Mathematica and Related Systems. This revolutionary paper challenged certain basic assumptions underlying much research in mathematics and logic. The authors provide an explanation of the main ideas and broad implications of Godel's discovery.

1. Ernest Nagel

Structure of Science

"Structure of Science: Problems in the Logic of Scientific Explanation - 2nd Edition".