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axiomatize

2023-07-02 13:50 作者:木玉光  | 我要投稿

到20世紀(jì)初,有很多人試圖將熱力學(xué)公理化。我認(rèn)為這不是一個(gè)很有用的東西。物理學(xué)是關(guān)于現(xiàn)實(shí)的,而現(xiàn)實(shí)是非常復(fù)雜的,它不像歐幾里德幾何那樣可以被公理化。如果你真的想要絕對(duì)合乎邏輯,你必須在完全確定之前陳述很多很多事情。所以,在我看來(lái),公理化物理學(xué)的想法是沒(méi)有用的。之所以有公理化熱力學(xué)的討論,是由于在數(shù)學(xué)發(fā)展到了十九世紀(jì)末二十世紀(jì)初的時(shí)候,出現(xiàn)了將數(shù)學(xué)公理化的想法,大數(shù)學(xué)家希爾伯特的厥功至偉。希爾伯特在1900年就23個(gè)重要的數(shù)學(xué)問(wèn)題發(fā)表了著名的演講,對(duì)20世紀(jì)的數(shù)學(xué)產(chǎn)生了巨大的影響。這23個(gè)問(wèn)題中,有一個(gè)是將物理學(xué)公理化。在我看來(lái),這不是正確的方向。大約在1930年,一位名叫哥德爾的年輕數(shù)學(xué)家證明,將整個(gè)數(shù)學(xué)公理化的想法并不是完全正確的事情,這導(dǎo)致了數(shù)學(xué)、數(shù)理邏輯和哲學(xué)的偉大進(jìn)步。然后,在沒(méi)有實(shí)現(xiàn)物理公理化的情況下,人們對(duì)這個(gè)希爾伯特問(wèn)題失去了興趣,直到1950年代。20世紀(jì)50年代,基本粒子物理學(xué)進(jìn)入了一個(gè)探索未來(lái)的時(shí)期,一些人,尤其是德國(guó)的很多人,在某種意義上復(fù)興了這種公理化物理學(xué)的想法。當(dāng)時(shí)國(guó)際上有許多人去跟風(fēng),發(fā)展出來(lái)一個(gè)叫作公理化場(chǎng)論的領(lǐng)域,但是到了1970年代,這個(gè)領(lǐng)域也走到了盡頭。今天,在這樣的方向上進(jìn)行這種努力并不被認(rèn)為是推動(dòng)物理學(xué)向前發(fā)展的有用嘗試。我們?cè)谟懻撐锢韺W(xué)時(shí)應(yīng)當(dāng)努力成為物理學(xué)家而不是邏輯學(xué)家。 原文: By the beginning of the 20th century, there were many people who try to axiomatize thermodynamics. 我認(rèn)為it’s not a very useful thing. Physics is about reality, and reality is very complicated. It’s not like Euclidian geometry you can axiomatize. If you want really to be absolutely logical, you have to state many many things before you can be completely sure. So the idea axiomatizing physics, in my opinion, is a useless thing. The reason there were discussions of axiomatizing thermodynamics was because, at the end of the 19th century and the beginning of the 20th century in mathematics, through, especially, the leadership of the great mathematician Hilbert, there was an idea to axiomatize mathematics in his 23 problems. Hilbert in the year 1900 gave a famous speech about 23 important problems in mathematics, and that caused the tremendous influence on 20th century mathematics. One of these 23 was to axiomatize physics, in my opinion, that is not the right direction. Around 1930 there was a young mathematician named G?del who showed that the whole idea of axiomatizing the whole mathematics is not quite right thing to do, that's a great development in mathematics, in mathematical logic and in philosophy. Then without having achieved the axiomatization of physics, they lost of interest about this Hilbert problem until the 1950s. In the 1950s elementary particle physics entered into a period of searching for the future, some people, especially many people in Germany, in some senses were reviving this idea of axiomatizing physics, and that was picked up by a number of people over the world. So it became a field called the axiomatic field theory, but by the 1970s that died again. It's today such kind of effort in such a direction is not considered to be a useful way to push physics forward. So we are trying to be physicists and not logicians in discussing physics.

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