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Posted By: AngusI didn't say that mathematics exists in the material world. I said it has some sort of existence in addition to the material world.
Both mathematics and the material world are there to explore but are not created by us.
I disagree that mathematics is a construct. Though sure you can build bathematical constructs just as you can build material ones.
[strike]The parallel between mathematics and language is false. Language lacks a consistency requirement. You can say anything and there is no way within language to evaluate its validity. Hence unicorns.[/strike]
Hmmm. That is not correct. I left it in so you can see what I've gone away to think about.
it simply doesn't exist outside of a mind- the nub of the discussion. I asked earlier if there would be three of anything if there were no people. Was there three of anything before apes learned to speak? For me “threeness” is a primordial part of the extended universe that contains the material and the mathematical worlds. I draw support from the infinite elaboration that the idea of counting can unveil if a creature has developed enough mind to appreciate the mathematical world.
Posted By: AsterixWould it be a stretch to say that mathematics started out as a way to conduct business? As in, "I will give you three clams for that fish."
Posted By: loremanMathematics exists in the “material world”. The distinction between the “material world” and some esoteric mental world is a false one. It’s like saying that tv programs don’t exist.
Posted By: loremanWhat is a “product of the mind”? Maths, when being performed - or discovered, is a series of electro-chemical impulses (and that’s at a gross level, further down the turtles it’s a series of spins and probabilities) with the irony being that the physical expression of thinking about mathematics conforms with the relationships and rules which mathematics is used to describe.
Posted By: loremanNo, it’s not hard determinism, because my understanding is that QM won’t allow for that. The Universe is probabilistic but not pre-determined.
However, everything that happens within it, including “thought” has a physical component, involving interactions between different bits of space-time. It would be really interesting to know whether, in a group of people thinking about a particular mathematical process at the same time, their brains light up in similar ways.
Posted By: AngusPosted By: AsterixWould it be a stretch to say that mathematics started out as a way to conduct business? As in, "I will give you three clams for that fish."
Not a stretch. Just wrong, depending on what you mean by mathematics. If you mean "the human discovery of mathematical relationships" then I'll accept it. If you mean "mathematical relationships", then I won't.
Posted By: pcstruPosted By: loremanNo, it’s not hard determinism, because my understanding is that QM won’t allow for that. The Universe is probabilistic but not pre-determined.
I'm not at all clear about that; it looks like another turtle - quite squashed by all the turtles above and squashing the turtles below.
If your 'freewill' is just a product that rises up from 'random' collapses of waveforms, then you have no control over that. Your free will is just as illusory; you have no way to effect any control over that collapse.
However, everything that happens within it, including “thought” has a physical component, involving interactions between different bits of space-time. It would be really interesting to know whether, in a group of people thinking about a particular mathematical process at the same time, their brains light up in similar ways.
Sure, everything is predicated on the material world as a substrate. The central question then is whether there is such a thing as strong emergence - processes that are essentially identity independent of the substrate from which things emerge that cannot be predicted in principle by the physical models of that substrate. You can't have unicorns without a substrate that supports a mind and the operational mind, but you won't find or predict the existence of unicorns by looking at our models of the material world.