Quote 1
To know and not to know, to be conscious of complete truthfulness while telling carefully constructed lies, to hold simultaneously two opinions which cancelled out, knowing them to be contradictory and believing in both of them, to use logic against logic, to repudiate morality while laying claim to it, to believe that democracy was impossible and that the Party was the guardian of democracy, to forget whatever it was necessary to forget, then to draw it back into memory again at the moment when it was needed, and then promptly to forget it again: and above all, to apply the same process to the process itself. That was the ultimate subtlety: consciously to induce unconsciousness, and then, once again, to become unconscious of the act of hypnosis you had just performed. Even to understand the word "doublethink" involved the use of doublethink. (1.3.20)
The Party’s concept of doublethink is contrary to reason, logic, and the workings of the brain. It takes a great effort for Winston to engage in doublethink.
Quote 2
Until they become conscious they will never rebel, and until after they have rebelled they cannot become conscious. (1.7.4)
At reaching a metaphysical paradox, Winston has arrived at a conclusion he does not wish to believe: the proles will never gain the consciousness required for them to effectively rebel.
Thought 2: For the proles, consciousness is as necessary for rebellion as the latter is for consciousness. This paradox is the proles’ futile plight.
Quote 3
It was as though some huge force were pressing down upon you – something that penetrated inside your skull, battering against your brain, frightening you out of your beliefs, persuading you, almost, to deny the evidence of your senses. In the end the Party would announce that two and two made five, and you would have to believe it. It was inevitable that they should make that claim sooner or later: the logic of their position demanded it. Not merely the validity of experience, but the very existence of external reality, was tacitly denied by their philosophy. The heresy of heresies was common sense. And what was terrifying was not that they would kill you for thinking otherwise, but that they might be right. For, after all, how do we know that two and two make four? Or that the force of gravity works? Or that the past is unchangeable? If both the past and the external world exist only in the mind, and if the mind itself is controllable…what then? (1.7.27)
Deathly afraid of the Party’s proposition that there exists no external reality independent of the mind, Winston feels despair – not because of the doctrine itself, but because he may be subject to the truth of that doctrine.