thomblake comments on Beauty quips, "I'd shut up and multiply!" - Less Wrong

6 Post author: neq1 07 May 2010 02:34PM

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Comment author: thomblake 07 May 2010 07:11:13PM 1 point [-]

If smart people are saying "2+2=5" and I point out it's 4, would you say "what matters is why you want to know what 2+2 is"?

Yes. For example, let's take a clearer mathematical statement, "3 is prime". It seems that's true whatever people say. However, if you come across some mathematicians who are having a discussion that assumes 3 is not prime, then you should think you're missing some context rather than that they are bad at math.

I chose this example because I once constructed an integer-like system based on half-steps (the successor function adds .5). The system has a notion of primality, and 3 is not prime.

Comment author: Vladimir_Nesov 07 May 2010 08:57:42PM * 1 point [-]

What you should say when asked "What is 2+2?" is a separate question from what is 2+2. 2+2 is 4, but you should probably say something else if the situation calls to that. The circumstances that could force you to say something in response to a given question are unrelated to what the answer to that question really is. The truth of the answer to a question is implicit in the question, not in the question-answering situation, unless the question is about the question-answering situation.

Comment author: thomblake comment score below threshold [+] (5 children)

Comment author: Vladimir_Nesov 07 May 2010 09:43:07PM 4 points [-]

"Should" refers to moral value of the outcome, and if someone is holding a gun to a puppy's head and says "if you say that 2+2=4, the puppy will die!", you shouldn't answer "4" to the question, even though it's correct that the answer is 4. Correctness is a concept separate from shouldness.

Comment author: thomblake comment score below threshold [+] (3 children)

Comment author: Vladimir_Nesov 07 May 2010 10:05:27PM * 3 points [-]

You are disputing definitions. You seem to include "should" among the possible meanings of "correct". When you say, "in this situation, the correct answer is 5", you refer to the "correctness" of the answer "5", not to the correctness of 2+2 being 5. Thus, we are talking about an action, not about the truth of 2+2. The action can, for example, be judged according to moral value of its outcome, which is what you seem to mean by "correct" [action].

Thus, in this terminology, "5" is the correct answer, while it's also correct that the [true] answer is 4. When I say just "the answer is 4", this is a shorthand for "the true answer is 4", and doesn't refer to the actual action, for which it's true that "the [actual] answer is 5".

Comment author: thomblake 08 May 2010 02:34:02AM 0 points [-]

Right, so for some arbitrary formal system, you can derive "4" from "2+2", and for some other one, you can derive "5" from "2+2", and in other situations, the correct response to "2+2" is "tacos".

Comment author: Vladimir_Nesov 08 May 2010 10:42:21AM * 1 point [-]

When you ask "What is 2+2?", you mean a specific class of formal systems, not an "arbitrary formal system". The subject matter is fixed by the question, the truth of its answer doesn't refer to the circumstances of answering it, to situations where you decide what utterance to produce in response.

The truth might be a strategy conditional on the situation in which you answer it, one that could be correctly followed given the specific situation, but that strategy is itself fixed by the question.

For example, I might ask "What should you say when asked the value of 2+2, taking into account the possibility of being threatened by puppy's death if you say something other than 5?" The correct answer to that question is a strategy where you say "4" unless puppy's life is in danger, in which case you say "5". Note that the strategy is still fixed by the question, even though your action differs with situation in which you carry it out; your action correctly brings about the truth of the answer to the question.

Comment author: JoshuaZ 07 May 2010 07:30:52PM 1 point [-]

If you want a standard system where 3 is not prime consider Z[omega] where omega^3=1 and omega is not 1. That is, the set of numbers formed by taking all sums, differences, and products of 1 and omega.

thomblake comments on Beauty quips, "I'd shut up and multiply!" - Less Wrong

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