Intuitionism Quotes

“The process by which [a logical theorem] is deduced shows us that it does not differ essentially from mathematical theorems; it is only more general, e.g. in the same sense that “addition of integers is commutative” is a more general statement than “2 + 3 = 3 + 2”. This is the case for every logical theorem: it is but a mathematical theorem of extreme generality; that is to say, logic is a part of mathematics, and can by no means serve as a foundation for it.”
― Arend Heyting, Intuitionism: An introduction

“If really the formalization of language is the trend of science, then intuitionistic mathematics does not belong to science in this sense of the word. It is rather a phenomenon of life, a natural activity of man, which itself is open to study by scientific methods; it has actually been studied by such methods, namely that of formalizing intuitionistic reasoning and the signific method, but it is obvious that this study does not belong to intuitionistic mathematics, nor do its results. That such a scientific examination of intuitionistic mathematics will never produce a complete and definite description of it, no more than a complete theory of other phenomena is attainable, is clearly to be seen.”
― Arend Heyting, Intuitionism: An introduction