“Mathematics and logic are collections of norms”, says David Bloor. “The ontological status of logic and mathematics is the same as that of an institution. They are social in nature.” [1] Now, if that is meant to convey the idea that the symbols and conventions of logic and mathematics, and the uses to which we put them, are ontologically subjective, being that they depend upon us for their existence, then it is a banal point. If, on the other hand, it is meant to convey something more radical, namely, that the ontological status of logic and mathematics is as subjective as the ontological status of a dress code or a bill of rights, then it is absurd; for then the claim is that propositions such as “twice two is four” or “A and not-A are contradictory” express nothing more independent of social convention than propositions such as “wrong hat, Gerald” or “citizens are permitted to bear arms on the first Tuesday of every month”. If such is true, and if furthermore there are many and diverse conventions by which we might fruitfully live our lives, then we might fruitfully think that twice two is five or nineteen or sixty thousand, without adverse consequences, being that there is no ontologically objective world by which we would be constrained in thinking one way or another. Everything is social, apparently. That, I presume, is Professor Bloor’s point. He is only a sociologist, after all.
[1] David Bloor, “Wittgenstein and Mannheim on the Sociology of Mathematics”, in Studies in History and Philosophy of Science, Vol.4:2, p.189.
[1] David Bloor, “Wittgenstein and Mannheim on the Sociology of Mathematics”, in Studies in History and Philosophy of Science, Vol.4:2, p.189.
3 comments:
And yet you know that he wouldn't dream of driving a car designed using any other maths than the pukka stuff. He is, therefore, a fool or a knave.
P.S. that's not the exclusive "or" I was using there.
Academics can be so amusing sometimes.
Like one philosopher said: So many philosophers doubt the existence of themselves or of other things, wondering whether it exists or not. But none of them would stand in the path of a moving car, even though they'll still prattle on whether it exists or not.
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