weebecka: Shall we just accept that you see maths as being an objective reality and I see it as being a personal, social and contextual reality (or something like that, I'm not sure I've expressed it very well)? To be honest, no, I don't think you have. I like to think I'm well read, and a little knowledgeable about the people you mention - Kuhn, Popper, et al - and yes, they have points, but I'm certain they'd agree that Mathematics - the proven, concrete stuff, that's been around since man first learned to scribe on a clay tablet - is objective. The whole scientific falliablity, paradigm shift stuff is such because science is applied mathematics - like poetry is applied language - and hence is open to interpretation. But Mathematics itself certainly isn't. The difference between pure mathematics and applied mathematics is this - Pure just simply 'is'; Applied takes the agreed, proven statements of Pure Mathematics and uses them to solve problems in context. Creating social constructs is all well and good as you have rules in which to do so, but if you don't have the rules in the first place, then how can you play the game?
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