For this reason we cannot look to Kant for a satisfactory theory of philosophical method. What he has to teach us on that subject will fall into two parts which he tries, but without success, to keep in two watertight compartments: one relating to the principles and methods of transcendental philosophy and taught chiefly by example, the other to those of metaphysics, taught by precept in the concluding chapters of the Critique.(from intro. to An Essy on Philosophical Method by R.G. Collingwood )
Bearing this in mind, we may turn to these chapters in order to see how Kant, at the end of his critical inquiry, sums up his conclusions as to the
method of metaphysics. At once we see that his aim is not so much to controvert but rather to correct Descartes, by a careful distinction between philosophical and mathematical thinking. He argues in detail that, of the special marks of mathematical science, not one is to be found in philosophy, and that the adoption of mathematical methods there
can do nothing but harm.1 Philosophy knows no definitions: or rather, their place in philosophy is not at the beginning of an inquiry but at the end; for we can philosophize without them, and if this were not so we could not philosophize at all.2 Philosophy knows no axioms: no truths, there, are self-evident, any two concepts must be discursively connected by means of a third.3 Philosophy knows no demonstrations : its proofs are not demonstrative but acroamatic; in other words, the difference between mathematical proof and philosophical is that in the former you proceed from point to point in a chain of grounds and consequents, in the latter you must always be ready to go back and revise your premises
when errors, undetected in them, reveal themselves in the conclusion.