secure absolute control over people's thoughts, the Party constructs its own parallel universe in which, according to the blatantly contradictory slogans put out by the Party, “War is Peace,” “Freedom is Slavery,” and “Ignorance is Strength.”

If anyone is to secure freedom from the Party's control, they need to be able to think for themselves. This means accepting that there's a world of fact where the Party's writ does not run. In this world, two plus two equals four. It always has and it always will, irrespective of what the Party says. But in the totalitarian dystopia of Oceania, if the Party says that two plus two equals five, then everyone is automatically expected to agree.

Winston understands that for people to have freedom, there needs to be a world of fact that is independent of what we or anyone else might think; a realm of truth that cannot be subverted by political or religious dogma. Mathematical equations form part of this world, and the ability to assert their absolute, unwavering truth, irrespective of what the Party might say, is an essential part of what it means to be free.

When Winston Smith writes this line in his secret diary, he is saying that freedom means having the ability to assert objective truths. The made-up Ingsoc ideology that 2+2=5 represents the way that the Party controls people’s minds. To people like us, 2+2=4 is an objective truth based upon our universally accepted understanding of how math works. If the United States government was to all of the sudden say that 2+2=5, people living in the United States would be able to safely refute this claim with the objective truth. To Winston, this ability is what constitutes freedom. If a person has the ability to state and do what they know is right without fear of suppression or control, they are a truly free person. But people do not have this freedom in Oceania.

The Party has made truths like 2+2=4 obsolete in their effort for total social control. Winston understands that refusing to follow the Party’s logic is the door to true freedom, but his awareness of how the Party uses mechanisms like newspeak and doublethink to limit free thought is dangerous. The Party has such a tight grip on people’s freedoms that even though Winston believes that he is getting away with free thinking, the Party is on to him all along. In the end, after Winston is tortured in the Ministry of Love, he traces 2+2=5 in dust on a table. This is an important moment because it represents that even though Winston understood how the Party maintained control through manipulating truth, the Party was so powerful it ended up controlling his mind too.

Winston recognizes that the Party will accept nothing less than complete orthodoxy and expects citizens to believe that two plus two equals five. Defying logic in order to subscribe to the Party's view is the ultimate form of control. Winston expresses the importance of independent, rational thought, which is necessary to challenge the Party's authority, by writing in his diary,

Freedom is the freedom to say that two plus two make four. If that is granted, all else follows.

He is saying that autonomous free-thinkers will have the power to undermine the authoritarian regime if they do not conform to the Party's doctrine and think independently.

Deep inside the Ministry of Love, O'Brien tortures and brainwashes Winston until he transforms into an orthodox Party member. At one point, he holds up his hand and demands that Winston state that he has four fingers. As an independent thinker and rational man, Winston cannot exercise doublethink and reject logic. It is only after Winston faces his worst fear that he completely submits to the Party and accepts their skewed version of reality.

In the Ministry of Truth, where Winston Smith works, his job is to manipulate information constantly so that everything that is disseminated unfailingly supports the Party’s view of events—a view that changes by the minute, not just by the day. Truth, in this frame of reference, becomes meaningless: there are no facts, just an endless supply of changes. Winston longs for some solid ground under his feet. Although he knows that mathematical and physical certainties cannot really be altered, his entire occupational responsibility makes him claim the opposite.

Winston is not saying that two and two do not make four. He wants the freedom to be able to oppose the Party’s total control of information. In part, he means that he wishes he could quit his job and not be complicit in supporting the unceasing distortion of information. Winston learns the hard way that there are facts: the main fact is that the Party will never allow anyone the opportunity to challenge its control. The most important word in his statement thus becomes the “if,” because the freedom to state a fact is not available to the people. People do not even have the intellectual freedom to state mathematical truths.

O’Brien is trying to force the Party’s own logic on Winston; more specifically, he is trying to control and reshape Winston’s reality—what he knows to be true—into whatever will suit the purpose of the Party.  If Winston has the right to insist on his version of the truth—which is a truth that stands independent of ideology—then he can hold on some vestige of being human and determine at least that much of his life for himself. “You believe reality is something objective,” says O’Brien to Winston, but “reality …only in the mind of the Party…Whatever the Party holds to be truth is truth.”  For Winston, if two plus two equals four, then reality is objective, and if this is true he can still seek objective truths and discount the double think of the Party.

In the novel, the government has complete control and may censor anything it likes. The government decides what is true, and if it feels, it may change what is true and make sure all believe their new truth has always been true.

Take Winston's job at the Ministry of Truth. His job to go through documents and edit or change documents to match the current version of truth according to the government. Winston also knows that going against these accepted "truths" may mean disappearing without a trace. Therefore, if the government says 2+2=5, than it is true. Even if an individual knows it to be incorrect, he or she must accept it as true. For example, Winston starts to realize more and more that things  put out by Big Brother are falsehoods and brazen lies, but he does not have the freedom to deny their claims, let alone protest against them.

George Orwell, in his 1946 essay, "Politics and the English Language", argues for an inherent connection between political freedom and clear language. In many ways, Orwell's ideas derive from John Stuart Mill's essay "On Liberty`which argues that the most important form of liberty is free speech, because it is only in an open marketplace of ideas, where viewpoints are questioned and tested against one another that truth can emerge. Improvements in society, whether political, ethical, or commerical all depend on the ability of citizens to put forth new ideas and discuss them openly; where there is no free speech, there is only stagnation and tyranny. Orwell adds to Mills concept of free speech the addition of clear speech. In an era with increasing power of mass media, Orwell sees that the putative freedom of speech possessed by citizens in mass culture was illusory of part of the debate was framed in speech so unclear that the fundamental mechanisms of liberty, those of open debate, were undermined by language so obfuscatory that those in control of the media could constantly reframe the grounds of debate to reinforce their own power, as do the rulers in 1984. Mass communication  shifts the locus of power in the novel to those who control the means of communication.

Winston Smith lives in the dystopian nation of Oceania, where the totalitarian government controls nearly every aspect of society through effective propaganda, extensive surveillance, fear, and manipulation. Newspeak, doublethink, and the mutability of the past are the primary principles of Ingsoc, which enable the regime to oppress and control the entire population. By utilizing these three principles, Big Brother effectively controls reality and creates a narrative that corresponds to the regime's current policies. Doublethink is the difficult mental exercise that allows a person to simultaneously believe two contradicting ideas. In order to be completely orthodox, Party members must be able to exercise doublethink, which allows them to fully accept and believe anything the government says.

In addition to doublethink, the Party continually alters the past and even fabricates events and people to coincide with their current political agenda. Between the mutability of the past and doublethink, the Party effectively controls reality as well as human history. Citizens have no way of challenging the regime and cannot prove that the Party is lying or manipulating the population without a point of reference. Since the Party controls reality, they can state that two plus two equals five, which is an illogical concept. However, the orthodox population will digest the information using doublethink and believe it without question. In his secret diary, Winston writes,

Freedom is the freedom to say that two plus two make four. If that is granted, all else follows.

Essentially, Winston is saying that freedom is the ability to use logic against the Party and refuse to exercise doublethink. By rejecting doubethink, Party members would be acting independently, embracing their humanity, and freeing themselves from the oppressive regime. If citizens were to reject Big Brother's propaganda, they would easily rebel against the Party and change the culture of Oceania.

The idea presented in this quote is that freedom means being able to interpret the facts of the world around you for yourself. You can look at the equation 2+2 and rightly deduce for yourself the answer. In other words, you are allowed the freedom to make your own decisions, come to the right conclusions, and rely on your own senses. In the world of the novel, Big Brother controls all the information. Because of this, there is no freedom to discern the truth.

In the context of the novel, the phrase “2+2=5” is used to represent the lies the government is propagating on the people. While it is self evident that the result of that equation is 4, the government has forced upon the citizens their version of the truth—that the answer is 5. So, Winston is saying that freedom is the ability to make your own conclusions, even when the government doesn’t want you to know the truth.

In Oceania, only the Party gets to decide what's true and what isn't. If the Party says that 2+2=5, then it is. The truth as understood by all sane, rational individuals—that 2+2 is actually four—is subversive because it challenges the power of the Party to construct truth and reality for all its subjects. Stating that 2+2=4 is an expression of freedom, because it shows that individuals are using their capacity to think for themselves, to get to the truth of the matter without the assistance of the Party. Once people start thinking for themselves, they don't need the Party to think for them. This makes them dangerous, a serious threat to the Party's total grip on power. For once the people realize that the truth exists independently of the Party's perspective, there'll be a domino effect, with all other aspects of the one-party state called into question. Then it can only be a matter of time before the Party loses power.

This quote is taken from Part One, Chapter Seven of 1984 when Winston is talking about the nature of the Party's power over the people of Oceania. He tells us that the Party insist that people "reject the evidence of your ears and eyes" and to believe only what Big Brother tells you to believe. In other words, the Party controls how people interpret truth and reality. So, for Winston, being able to say that two plus two equals four is significant because it represents true freedom and the ability to say whatever one wants to say without fear of violence.

The idea that two plus two equals five is also linked to this concept of true freedom. It suggests that people are so brainwashed by the Party that they will believe anything they are told, even something which is obviously wrong, like that two plus two equals five. By accepting the Party's version of truth, people are forced to give up their freedom, and this is how the Party maintains absolute power.

In the book, the party is trying to force people to see it as the only source of truth.  It manipulates and changes the truth so that people don't have any way to know what's real.  It's in this context that you need to think of this quote.

The quote comes at the end of Part 1, Chapter 7.  Winston is thinking that the Party is too strong for him to oppose.  But then he thinks that as long as he can hold onto a truth like 2+2=4 then he has a foundation of reality and can resist the Party's attempts to tell him lies.

The connection to the other equation is that later on when Winston is being tortured, he is reminded of this diary entry and is tortured to try to push him toward being able to see that 2+2=5 (which would mean that he would be giving up any hope of having an independent mind).