The difference between a proof and the conviction it ought to generate poses a special problem in an age conditioned to the proofs which exact science can deliver. About those proofs it is easily overlooked that all too often they amount to mere identity relations, dressed as they can be in the language of mathematical physics. Its equation signs readily convince because the two sides they connect contain no real novelty with respect to one another. Thus the conviction which those proofs or demonstrations generate comes forth almost automatically. Taken by themselves, they are of little help to convince one about the reality to which they supposedly refer. For no equation sign can be set up between the mind, swayed as it can be by the identity relations of logic or mathematics, and external reality.

That even the fact, let alone the nature, of external reality, however ordinary, cannot be proven by mere logic or mathematical formulas does not make one's immediate registering of external reality a less than fully rational process. To know the existence of things is in fact the very first step in reasoning. Any “critical” knowledge or philosophy which does not accept this will remain a mere criticism of criticism and not a criticism of the external reality one registers, and not even of one's registering it.

This should be acknowledged even by rigid idealists insofar as they want to communicate to others their claim that it is possible to start with mere ideas.