A Quote by Alonzo Church
The only thing that might have annoyed some mathematicians was the presumption of assuming that maybe the axiom of choice could fail, and that we should look into contrary assumptions.
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School is an institution built on the axiom that learning is the result of teaching. And institutional wisdom continues to accept this axiom, despite overwhelming evidence to the contrary.
Another advantage of a mathematical statement is that it is so definite that it might be definitely wrong; and if it is found to be wrong, there is a plenteous choice of amendments ready in the mathematicians' stock of formulae. Some verbal statements have not this merit; they are so vague that they could hardly be wrong, and are correspondingly useless.
There will be some fundamental assumptions which adherents of all the variant systems within the epoch unconsciously presuppose. Such assumptions appear so obvious that people do not know what they are assuming because no other way of putting things has ever occurred to them. With these assumptions a certain limited number of types of philosophic systems are possible, and this group of systems constitutes the philosophy of the epoch.
To choose one sock from each of infinitely many pairs of socks requires the Axiom of Choice, but for shoes the Axiom is not needed.
It's only when you look back sometimes and you look at some people in your life and you're like, Oh my god, there was something so pure about that. The thing that kind of bugged me, maybe, is the thing that's so unique.
[On the] question of why we might want to look at images even more than the real thing: I think there is some quality when you look at an image of, not only seeing this thing, whether it's the horse or the sky, but you are seeing somebody point at it and say, Look!
Annoyed?” said Sophie. “Why should I be annoyed? Someone only filled the castle with rotten aspic, and deafened everyone in Porthaven, and scared Calcifer to a cinder, and broke a few hundred hearts. Why should that annoy me?
In my [Impossibility] theorem I'm assuming that the information is a ranking. Each voter can say of any two candidates, I prefer this one to this one. So then we have essentially a ranking. It's a list saying this is my first choice. This is my second choice. Each voter, in principle, could be asked to give that entire piece of information. In the ordinary Plurality Voting, say as used in electing Congressmen, we generally only ask for the first choice. But, in principle, we could ask for more choices.
The one thing - apart from assumptions about German - that I have to challenge frequently is people assuming that lexicographers are fierce protectors of the language when in fact our job is not to put a lid on it.
It was unfair that people could pretend to be one thing when they were really something else. That they would get you on their side and then do nothing but fail, and fail, and fail again. People should come with warnings, like cigarette packs: involvement would kill you over time.
Assuming if there's such a thing as reality, if you have a false relationship with it, how can you do anything but fail?
Contrary to common belief, the presumption of innocence applies only inside a courtroom. It has no applicability elsewhere, although the media do not seem to be aware of this.
You had a choice: you could either strain and look at things that appeared in front of you in the fog, painful as it might be, or you could relax and lose yourself
Truth was funny, because it was an insistent thing, maybe as powerful and insistent as some force of nature, the push of water or wind. You could keep it out only so long, but it had its own will and its own needs, and maybe you could keep it at bay with lies, but not for long, not for always.
Some mathematicians didn't even perceive of the possibility of a picture being helpful. To the contrary, I went into an orgy of looking at pictures by the hundreds; the machines became a little bit better.
When you are annoyed at someone's mistake, immediately look at yourself and reflect how you also fail; for example, in thinking that good equals money, or pleasure, or a bit of fame. By being mindful of this you'll quickly forget your anger, especially if you realize that the person was under stress, and could do little else. And, if you can, find a way to alleviate that stress.
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