I saw this great video about the philosophy of mathematics with James Brown.
http://www.ideasroadshow.com/issues/jam ... 2013-04-12
After watching it I was more convinced of the veracity platonic idea of Forms only in so far as it relates to mathematical concepts. But I'm still wrestling with the question 'if someone discovers a mathematical truth, what do they really discover?' does it have a distinct existence ontologically distinct from human beings?
Thought experiments
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The Voice of Time
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Re: Thought experiments
I find two questions here: what is a mathematical truth?
and the one you put more directly: does it have a distinct existence ontologically distinct from human beings?
I have two simple answers for both. A mathematical truth, is in practice, the restraints and abilities put upon patterned change. It says what are the limits of this kind of pattern? What are the possibilities? Mathematics is all about pushing boundaries and see how far you can take a single thread of pattern recognition, or in other words how far you can go on recognizing new patterns without reaching a restraint that is irrespective of the nature of the thing itself except its pattern.
To the second direct one: when you try out the restraint or possibility does it exist? Is it actually possible for you to see 6 apples by taking two apples from two different baskets? Or do you see the restraint of 2+2=4? In computer science this is all much more clear, because here it's all a matter of: at what conditions is it possible to make the machine produce this-x and this-y and this-z result? The computer, while working on compatible matter, will only produce a given result if a series of patterned conditions are met. It does not really matter what kind of materials you use to make it... it's technically possible to make calculators out of wood or steel machinery or water-buckets for that sake, and likely somebody has done them all although I've never heard of anybody who cared to do it (especially when you can go and just buy a calculator saving time, space and efficiency).
and the one you put more directly: does it have a distinct existence ontologically distinct from human beings?
I have two simple answers for both. A mathematical truth, is in practice, the restraints and abilities put upon patterned change. It says what are the limits of this kind of pattern? What are the possibilities? Mathematics is all about pushing boundaries and see how far you can take a single thread of pattern recognition, or in other words how far you can go on recognizing new patterns without reaching a restraint that is irrespective of the nature of the thing itself except its pattern.
To the second direct one: when you try out the restraint or possibility does it exist? Is it actually possible for you to see 6 apples by taking two apples from two different baskets? Or do you see the restraint of 2+2=4? In computer science this is all much more clear, because here it's all a matter of: at what conditions is it possible to make the machine produce this-x and this-y and this-z result? The computer, while working on compatible matter, will only produce a given result if a series of patterned conditions are met. It does not really matter what kind of materials you use to make it... it's technically possible to make calculators out of wood or steel machinery or water-buckets for that sake, and likely somebody has done them all although I've never heard of anybody who cared to do it (especially when you can go and just buy a calculator saving time, space and efficiency).
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tillingborn
- Posts: 1314
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Re: Thought experiments
To be honest, I haven't looked at the link, but on the general point of the ontological status of mathematical truths I'm particularly fond of Einstein's saying: 'As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality'.tdecelles wrote:I saw this great video about the philosophy of mathematics with James Brown.
http://www.ideasroadshow.com/issues/jam ... 2013-04-12
After watching it I was more convinced of the veracity platonic idea of Forms only in so far as it relates to mathematical concepts. But I'm still wrestling with the question 'if someone discovers a mathematical truth, what do they really discover?' does it have a distinct existence ontologically distinct from human beings?
Does it make any sense to claim that a tautology such as 2+2=4 'exists'? What about the 10^500 (thanks to whoever pointed that out to me) solutions to string theory, or Cantor's argument that there is an infinity of infinities? I concede that it is a more compelling idea if the maths in question is QED say, but for all it's staggering accuracy, is it actually 'true'?
Personally, I think that although the universe is very big, it is dwarfed by mathematics. I take the universe to be everything that 'is real', therefore, maths doesn't fit.
Re: Thought experiments
Oh, that James Brown.
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Impenitent
- Posts: 4368
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Re: Thought experiments
It's a man's world...John K wrote:Oh, that James Brown.
-Imp
Re: Thought experiments
It would be a fictional fact.a mathmatical truth is a fictional fact.zero being a fact.