“One can never really give a proof of the reality of anything; reality is not something open to proof, it is something established. It is established just because proof is not enough. It is this characteristic of language, at once indispensable and inadequate, which shows the reality of the external world. Most people hardly ever realize this, because it is rare that the very same man thinks and puts his thought into action.”

“If we leave that general descriptive talk where everything which looks like a poem can be called a poem and turn instead to normative talk, we will of course not recognize as a poem everything that looks like a poem. A real poem has to be a successful poem, a successful speech act. In approximately the same way that only a mathematical proof which really proves something can be called a mathematical proof. It is not enough that it looks like a proof. The proof has to prove. For the poem it is not enough to look like a poem. It has to achieve something.”

“Still, there's no harm in putting a full stop to one's disagreeable thoughts by looking at a mark on the wall... Here is something definite, something real. thus, waking from a midnight dream of horror, one hastily turns on the light and lies quiescent, worshipping the chest of drawers, worshipping solidity, worshipping reality, worshipping the impersonal world which is proof of some existence other than ours.”

“It is an unfortunate fact that proofs can be very misleading. Proofs exist to establish once and for all, according to very high standards, that certain mathematical statements are irrefutable facts. What is unfortunate about this is that a proof, in spite of the fact that it is perfectly correct, does not in any way have to be enlightening. Thus, mathematicians, and mathematics students, are faced with two problems: the generation of proofs, and the generation of internal enlightenment. To understand a theorem requires enlightenment. If one has enlightenment, one knows in one's soul why a particular theorem must be true.”

“The empiricist assumes without any evidence or proof that his experiences somehow give him a magical access to reality. So completely does he identify experience and reality that he cannot liberate himself from thinking of the two as one and the same. In equating experience and reality, he is making a huge and unwarranted leap. But this breakdown of reason is not easy for him or us to recognize because our human minds have a built-in disposition toward illusion – the illusion that reality must be exactly the way we experience it. The irony is that many of the people who proceed in this irrational way think of themselves as following strictly along the pathways of reason.”

“I searched everywhere for a proof of reality, when all the while I understood quite well that the standard of reality had changed”