The analysis given in the previous chapters of the different functions of our intellect shows that the requirements for a legitimate use of the intellect, whether with a view to theory or to practice, are as follows: (1) The accurate, intuitive grasp of the real things under consideration and all their essential characteristics and relations, which is to say all the data. (2) The formation of accurate concepts from these, which is to say the unification of those characteristics under the correct abstractions, which now become the material for subsequent thinking. (3) The comparison of these concepts, sometimes with what is intuited, sometimes with each other, sometimes with the rest of the supply of concepts; so as to generate accurate and exhaustive judgments that are relevant to the matter at hand and deal with it comprehensively; that is, correct judging of the matter. (4) The compilation or combination of these judgments into the premises of syllogisms: these can turn out very differently according to the selection and arrangement of the judgments, yet this is the primary determinant of the real result of the whole operation. This should entail that the process of free deliberation will come across precisely the most useful and decisive of the many possible combinations of different judgments relevant to the issue. – But if any essential point is overlooked in the first function, which is to say with the intuitive grasping of things and relations, the accuracy of all subsequent intellectual operations cannot prevent a false result: because this is where the data are found, the material of the whole investigation. Without the certainty that these are all correct and complete, one should abstain from any definitive decision in important matters. –

A concept is correct; a judgment is true; a body is real; a relation is evident. – A propositiona that is immediately certain is an axiom.Only the principles of logic and those of mathematics that are drawn a priori from intuition, and finally the law of causality as well – only these have immediate certainty. – A proposition that is indirectly certain is a theorem, and what brings about this certainty is the proof.