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Say that someone asks you "What's the difference between those curves (see image below)?"

enter image description here

Given the definition of a curve as being "a line or outline which gradually deviates from being straight for some or all of its length".

Can you formally answer with "One is orange and the other is blue."? Or because the color isn't a part of the definition of the curve such an answer is invalid?

Joe
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  • Is this your attempt to re-ask this ( http://philosophy.stackexchange.com/questions/29510/understanding-the-definition-of-a-definition ) question? if so, it would be preferable for you to delete that earlier one. – Dave Nov 10 '15 at 18:03
  • @Dave It looks to me as if this is a follow up based on the answers to the previous question. – Chris Sunami Nov 10 '15 at 19:45

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Every formal question presupposes a domain of discourse from which valid answers can be drawn. Whether or not it is made explicit, a question like this appears to be seeking a mathematical answer. Giving a color-based answer violates the implied domain of discourse, and suggests that the person answering has either accidentally or deliberately misinterpreted the question.

Of course, there are situations where "outside the box" thinking is required, or desirable. In such a case the implied domain of discourse is the "box" and ignoring it is "thinking outside of it."

Formal questions, however, restrict the realm of possible answers by necessity. In a formal system, every recognized condition must be well-defined within that system. That cannot be guaranteed without a restricted domain.

Chris Sunami
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  • "Whether or not it is made explicit, a question like this appears to be seeking a mathematical answer." How do you formally speaking, determine that this question is seeking (obviously) a mathematical answer? – Joe Nov 10 '15 at 20:33
  • @Joe We don't usually make that determination formally. As with anything else, we judge by context and experience. Informally, there is generally understood to be a social compact whereby people support communication by making the best available good faith assumptions about intention. Would it be possible to give a computer exact rules for distinguishing a mathematical question from a non-mathematical question? Quite possibly, but in practice, that's not the way we do it. – Chris Sunami Nov 11 '15 at 03:31
  • @Joe for this question, the definition of curve that you provided in the OP sets the context -- that definition clearly focuses on the geometrical aspects. – Dave Nov 11 '15 at 13:24
  • @Dave You're right, one might argue that since the subject of the definition is a concept originated from the geometry, the context must therefore be geometry unless explicitly stated otherwise. I suggest that in cases alike every deduction of context is appropriate as long as one can logically explain why it has been chosen this way. This is of course much different that just choosing on a whim, as logical deduction sets a straight line of reasoning. A random choice is a point which could originate from anywhere and go wherever. – Joe Nov 11 '15 at 17:37
  • @Dave If we would allow choices on a whim, then their validity couldn't be established. And since both sides would be allowed to make arbitrary choices without any clarification, a situation could occur where both sides would enter a perpetual loop of blindly dumping information without ever crossing on mutual understanding. – Joe Nov 11 '15 at 17:45
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My answer would be: Both curves are phase-delayed. The blue one has a phase plus 1.6 unit with respect to the brown one.

Added. Just to give also an answer to your literal question: Yes, of course one can answer "One is orange and the other is blue." But this answer misses the characteristic differences between both curves from a mathematical point of view.

Jo Wehler
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  • This answers the question within the question, not the actual question. – Chris Sunami Nov 10 '15 at 19:53
  • My comment cross-posted with your edit! However, I still think this reply doesn't illuminate the OP's actual question --you now mention what is wrong, but not why it is wrong. – Chris Sunami Nov 10 '15 at 19:55
  • @Chris Sunami The domain of discourse for the OP question is given implicitly: It is the sine curve and the concept of phase-delay. It is not to learn the colours. - Hence the answer "One is orange and the other is blue." misses the domain of discourse. Therefore it is wrong. – Jo Wehler Nov 10 '15 at 20:02