Post #766

Видимо, постоянная рубрика канала: интуиционизм, но не конструктивизм 1. Mathematical reasoning [...] is no logical reasoning [...;] it uses the connectives of logic only because of the poverty of language, and thus may perhaps keep alive the language accompaniment even after the human intellect has already long ago outgrown the logical argument. For, far from the fact that it would be a "strange company" that does not reason logically, I believe that it is only a matter of inertia, that the words that go with it [i.e., logic] as yetstill exist in modern languages. A pure use of these words hardly occurs, and [in] impure [form] they are used in daily life, where they have led to all kinds of misunderstanding and dogmatism [..]. Those misconceptions arose, not because of insufficient mathematical insight, but because mathematics, lacking a pure language, makes do with the language of logical reasoning, although its thoughts reason not logically, but mathematically, which is something totally different. Brower in the letter to Kroteweg, 21.01.1907 2. How can we talk of a mathematical 'nature' possessing joints to carve? But this, in essence, is how many mathematicians do talk. Rather than anything contained within the doctrine currently referred to as 'Platonism', the sense they have is that something much stronger than logic offers resistance to their efforts, and that when they view matters 'correctly' things fit into place. Whereas Hopf algebra theory is an established part of real mathematics, snook theory is not, they would say, because it is not the result of carving 'conceptual reality' at the joints. Towards a philosophy of real mathematics, D. Corfield Мегаполис — Из жизни планет