How we cite our quotes: Citations follow this format: (Part.Chapter.Paragraph). We used Constance Garnett's translation.
Quote #7
…give [man] economic prosperity, such that he should have nothing else to do but sleep, eat cakes and busy himself with the continuation of his species, and even then out of sheer ingratitude, sheer spite, man would play you some nasty trick. He would even risk his cakes and would deliberately desire the most fatal rubbish, the most uneconomical absurdity, simply to introduce into all this positive good sense his fatal fantastic element. lt is just his fantastic dreams, his vulgar folly that he will desire to retain, simply in order to prove to himself […] that men still are men and not the keys of a piano, which the laws of nature threaten to control so completely that soon one will be able to desire nothing but by the calendar. And that is not all: even if man really were nothing but a piano-key, even if this were proved to him by natural science and mathematics, even then he would not become reasonable, but would purposely do something perverse out of simple ingratitude, simply to gain his point. (1.8.4)
Hmm…who is this mysterious and theoretical "man"? Because it sounds to us like the Underground Man is talking about himself. Man "would purposely do something perverse"…like live in a hole underground? Like bang his head against the stone wall of 2+2=4? Exactly.
Quote #8
Good heavens, gentlemen, what sort of free will is left when we come to tabulation and arithmetic, when it will all be a case of twice two make four? Twice two makes four without my will. As if free will meant that! (1.8.5-6)
This is the Underground Man's attempt to prove that reason is incompatible with free will. If all of our actions were based on reason, then we would always want 2+2 to equal 4. But if we were limited to only wanting reasonable things, then the concept "free will" wouldn't have any meaning.
Quote #9
But yet mathematical certainty is after all, something insufferable. Twice two makes four seems to me simply a piece of insolence. Twice two makes four is a pert coxcomb who stands with arms akimbo barring your path and spitting. I admit that twice two makes four is an excellent thing, but if we are to give everything its due, twice two makes five is sometimes a very charming thing too. (1.9.2)
This seems purely an issue of ego and pride. It would certainly be simpler for the Underground Man to desire that 2+2=4. In that case, his free will would be satisfied. But he is, alas, both stubborn and principled.