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In classical mathematics, a mathematical model of an object is devised and the notion of the exact solution of this model is determined.
Indeed, as will be explained below, the mathematical implications of the second act of intuitionism contradict classical mathematics, and therefore do not hold in most constructive theories, since these are in general part of classical mathematics.
In the first decades of the twentieth century, parts of the mathematical community were sympathetic to the intuitionistic critique of classical mathematics and to the alternative that it proposed.
Its first part, Logic Sets, and Numbers, shows how mathematical logic is used to develop the number structures of classical mathematics.
Nonetheless, most practicing mathematicians prefer to stick to classical mathematics.
Because many important theorems in classical mathematics depend for their proof upon the principles affected, large parts of classical mathematics are called into question.
Arguably, it could now express all parts of classical mathematics.
Assume that the methodology of classical mathematics is justified.
Of course, this is not the case for classical mathematics.
There is an analogy with classical mathematics on this point.
Only as far as the latter is concerned, intuitionism becomes incomparable with classical mathematics.
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