Examine the party's three slogans: "War is peace. Freedom is slavery. Ignorance is strength." What do you think they mean?

THese are all paradoxical slogans. There is a lot to this but here is a simple explanation,

War is Peace- While the country is fighting, people within the country are on the same side hence the Party enjoys uncontested power. Nobody questions their government while at war...It's that sort of thing.

Ignorance is strength- If people remain ignorant, they will not question the Party hence making the country "stronger".

Freedom is slavery- If people are free to do things and express ideas contrary to party doctrine, everybody is made weak. They are slaves to their own ideas and not strong under one idea from the Party.

These are all paradoxical slogans. There is a lot to this but here is a simple explanation,

War is Peace- While the country is fighting, people within the country are on the same side hence the Party enjoys uncontested power. Nobody questions their government while at war...It's that sort of thing.

Ignorance is strength- If people remain ignorant, they will not question the Party hence making the country "stronger".

Freedom is slavery- If people are free to do things and express ideas contrary to party doctrine, everybody is made weak. They are slaves to their own ideas and not strong under one idea from the Party.

War is Peace. In their society, keeping the masses believing that constant war is being waged is actually a way of maintaining peace. War elicits great patriotism and devotion to country; it also promotes sacrifice and giving to the community over oneself. So, if there is constant war, the people are constantly giving, sacrificing, and pledging devotion to their government. This keeps the people in check and in control, and hence, peaceful. That is how the Party uses that slogan. The people think it just means that world peace is maintained through war. Without war, their security would be threatened.

Freedom is slavery is more tricky. The people probably believe that to mean that having total freedom is actually a way to become enslaved to your senses, weaknesses and vices. For example, the Party encourages young women to remain virtuous and restrict themselves from being romantically involved or sentimental in any way. The society has firm beliefs about sex and relationships--there is very little freedom there, because they feel that sex and relationships enslave people. If you are constantly embroiled in relationships, you are subject to the turmoil and unhappiness that they sometimes cause, and are constantly thinking about it. That is not freedom, according to them. So, to the people and the masses, they have been taught that freedom to act, and sometimes act poorly, actually tends to enslave one to sentimental and unessential vices and emotions. To the Party, a free people represents the removal of their power. So, the people must not be free in order to remain in power.

To the masses, being ignorant about the true condition of things is actually beneficial, because it helps them to remain happy and optimistic, and thus strong. To the workers within the Party, like Winston, their entire jobs rely on keeping the people ignorant of true facts and statistics. Essentially, lie to keep the people in the dark, and then the Party--and their jobs--will always be strong. The people's ignorance gives the Party strength; if they really knew the true state of things and how they had been manipulated, they would rebel, and take away the Party's power.

In the end, it all comes down to the Party creating slogans that ensure the continuation of their power and contro

With all due respect, you're all missing the point a bit here. The broad strokes of what's going on here is one of the ongoing themes in 1984.

The use and corruption of language by power structures as a form of mind control is a very important theme in his work. These are mantras. The only logic to them is that they are supposed to destroy the meaning of words, and break down the positive or negative associations people have with those words. It's an excersise in thought control. They aren't supposed to make sense, and that's precisely the point. By invoking a paradox, you destroy meaning and control thought.

You can see exactly this happening in the modern world. Progressives are Nazis. Freedom fighters are terrorists if they're foriegn, but "disturbed" if they're domestic. "Fake News" and the most Orwellian phrase I've ever heard used in modern politics: "Alternate Facts".

It's fairly obvious that the slogans in 1984 are forms of propaganda. But there are plenty of other examples of the idea at work elsewphere. There's the baffling "newspeak", designed to soothe and obfruscate meaning, and the interigation methods designed to re-condition and reprogram thought.

“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 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 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.” [1984 p31]