War is Peace: The only thing constant in Winston's world is change, and constant war is a part of it. Perpetual and changing battles, alliances, and treaties maintain a status quo which guarantees (in a paradoxical way) a certain predicability on the part of the people and stability to the party. That is its concept of "peace."
Freedom is Slavery: There is no place for the individual or for individual choices in Oceania; people only exist via corporate identity. Anyone outside of this realm of conformity is ostracized. 'Freedom' (free will) is now 'slavery' (being bound up to oneself; alienation) according to the current value system.
Ignorance is Strength: This is the force of denial (individual and collective) in overdrive! Going along with it is the idea that what somebody doesn't know won't hurt him. Ignoring what is even evident and molding one's thoughts to fit society's mind-frame reinforces (strengthens) the group.
The Party has three central tenets upon which it rules. They are 1) War is Peace 2) Freedom is Slavery and 3) Ignorance is Strength.
The first, the philosophy that says "War is Peace," is explained in Chapter Three. The world is divided into three separate states: Eurasia, Oceania, and Eastasia. The Inner Party convinces the Outer Party that war is the natural state outside of the borders of Oceania. Everywhere except in their home country, war continually wages, but if they maintain a peaceful state in Oceania proper, everyone must be on the same side, ready to fight all threats from the outside. Maintaining peace at home, the party leaders contend, is dependent on wars taking place elsewhere.
The second tenet, "Freedom is Slavery," is explained by O'Brien, also in Chapter Three. O'Brien argues that when there is too much choice, people are vulnerable:
The first thing you must realize is that power is collective. The individual only has power in so far as he ceases to be an individual. You know the Party slogan "Freedom is Slavery." Has it ever occurred to you that it is reversible? Slavery is freedom. Alone— free— the human being is always defeated. It must be so, because every human being is doomed to die, which is the greatest of all failures. But if he can make complete, utter submission, if he can escape from his identity, if he can merge himself in the Party so that he is the Party, then he is all-powerful and immortal. The second thing for you to realize is that power is power over human beings. Over the body— but, above all, over the mind. Power over matter— external reality, as you would call it— is not important. Already our control over matter is absolute.
The third slogan, "Ignorance is Strength" is founded on the basic principle that those who are kept in the dark are not capable of revealing secrets and endangering the homeland. The party believes in a strict class system, which, it argues, has forever been in place:
Throughout recorded time, and probably since the end of the Neolithic Age, there have been three kinds of people in the world, the High, the Middle, and the Low. They have been subdivided in many ways, they have borne countless different names, and their relative numbers, as well as their attitude towards one another, have varied from age to age: but the essential structure of society has never altered. Even after enormous upheavals and seemingly irrevocable changes, the same pattern has always reasserted itself, just as a gyroscope will always return to equilibrium, however far it is pushed one way or the other.
In these three ways, keeping the masses in the belief that war is necessary, that freedom is to be feared,
and that one has an assigned place in society, the Party is able to maintain absolute power and the ability
to control its citizens.
In the mind of the Party, they are not paradoxes.
"War is Peace." -This world is full of troubles and most of the time we don't even know what or where they are. When we have an enemy in plain sight, we are confident in our ability to fight him. Therefore, with that confidence we feel at peace. We've taken action. We are doing something. In times of peace, we know there's an enemy somewhere... On top of that, war often brings economic benefits (e.g. World War II bringing the country out of the Great Depression).
"Freedom is Slavery." - When you are free, you are responsible for yourself. No one will take care of you or look out for your welfare. You are tied to the struggle to survive. If the government provides for your needs, you are free to pursue other pleasures.
"Knowledge is Ignorance." - As the saying goes, "The more you learn, the more you realize the less you know." Without knowledge, you are freed from responsibility. "Ignorance is bliss." So in a way, you can also say "Ignorance is Freedom."
The three paradoxical slogans of the Inner Party, which are posted in elegant lettering on the Ministry of Truth, or Minitrue, are:
WAR IS PEACE
FREEDOM IS SLAVERY
IGNORANCE IS STRENGTH
The three slogans:
War is peace
Freedom is slavery
Ignorance is strength
This quote is also the reader’s first encounter with the idea of double think, the party process of weakening an individual mind’s strength and independence and forcing them to live in a constant state of propaganda induced fear. Through double think, the government is able to force its people to willingly accept basically anything they say, even if it makes no sense whatsoever. For instance, the Ministry of Peace is in charge of waging war, the Ministry of Love is in charge of political torture, and the Ministry of Truth is in charge of doctoring history books to reflect the Party’s ideology. This slogan is an important symbol which shows the hidden power of the government over its people by saying that even though the slogan is completely illogical, the people are psychologically so influenced by the government that they turn a blind eye toward anything else. In other words, the government is able to convince people that “war is peace” by telling the people that having a common enemy helps keep the country together in many ways, but it was mostly because of the fact that since there is war, everyone will be afraid which will allow the government to control them easier resulting in peace. With “freedom is slavery” they explain that they will succeed only if they are united, if they try to go off on their own, then they will fail. By the same token, “Slavery Is Freedom,” because the man subjected to the collective will is free from danger and want. And “ignorance is strength” because the more people ignore the contradictions of their slogan, the more powerful the governments power gets over its people.
War is Peace.--This is to unite the people against a constant enemy that exists and threatens the safety of Oceania. Thus the people are limited to uniting to solve a threat and will have to show consistent support for the Party.
Freedom is Slavery-- This is portrayed when Winston visits the poorer parts of Oceania, where the people are not as well of and have not much influence to sway the people against the Party. Although they are constrained to items like the lottery, they are more instinctive, have common sense, as they could detect when and where the bomb would explode in the book.
Knowledge is Ignorance--By knowing more, you realize you know less. That is probably the way to make sense of it.