On the Interpretation of Intuitionistic Logic

Alongside theoretical logic, which systematises the proof schemata of theoretical truths, one can systematise the schemata of problem-solving, e.g. those of geometric construction problems. Then, corresponding to the principle of the syllogism, we find for example, the following principle: If we can reduce the solution of b to that of a, and reduce the solution of c to that of b, then we can also reduce the solution of c to that of a.