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what is special about mathematics

What, if anything, is special about mathematics? Perhaps mathematics lays exclusive claim to a certain class of questions and answers?

Are Vincent van Gogh's paintings of sunflowers beautiful? As much as we may want to say "yes", in all fairness, we must admit that this is, in some sense, a subjective view.

Was Vincent van Gogh born in 1853? The answer here is "yes" (although it could be "no" or "I don't know"), but there is no reason for this other than the vicissitudes of fate.

Is [Unable to write template]? The correct answer is "yes". Like the previous question, the correct answer depends on knowledge, but this time, there is not just a reason for the answer to be correct (or not) – this time, we feel there is a reason for the answer itself*.

The first question is a matter of opinion. It might be made the subject of a scientific investigation, but as such, it has no correct answer. The second question is a matter of factual knowledge – data about the real world. You may have to check a few sources to be sure of the fact, but you can't figure it abstractly. The third question is one of procedural knowledge. Anyone who has learned how to subtract integers can figure out the answer.

If, as we've heard, "knowledge is power", then surely procedural knowledge carries more power than factual knowledge: facts alone don't do anything. Procedural knowledge alone may not convey the ability to do: the circumstances must be right. But it is a good start.