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Math: Created or discovered?

 
 
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eudemonia
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16 April 2008 07:04
 

arildno

K, guess you win then. Whatever that means. Just some thoughts.

 
 
 
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burt
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16 April 2008 20:13
 
McCreason - 16 April 2008 12:38 AM

Was mathematics made up by people, incorporated into culture and society and then handed down through the generations? Ideas are memes. Is not mathematics an idea? It is an invented explanation and intrepetation of the abstract, no? 2 plus 2 equals 4. Only if we say so and believe it and tell our kids it is so.

This is an uninformed (I don’t mean that in a negative sense, just that it slides over many issues) gloss of a view of mathematics that has come up over the past 30 - 40 years generally going under the heading of social constructivism.  It is rooted in Wittgenstein’s views of language and mathematics.  The basic issue has to do with the reality of mathematical objects and the universality of mathematical truths.  When you say that mathematics is made up by people, there is an ambiguity: we make up symbolic systems and formal rules for symbol manipulation—those are human constructions but, as with language, do the constructs (in this case the definitions, axioms, and theorems) refer to something out there in an independent reality, or are they simply made up playthings?  Is the Pythagorean theorem universally true, or is it just a human construction that might be false in some other part of the universe?  In the former case, saying that mathematics is a meme is like saying Mount Everest is a meme and ignoring the real physical mountain.

 
Ecurb Noselrub
 
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Ecurb Noselrub
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17 April 2008 11:02
 

If mathematics did not have an independent existence apart from the human mind, there would not be as much order as there is in the universe, and by order I mean that physical things operate according to a set of laws or principles. The symbols and language of mathematics and physics are the descriptions of those laws and principles. We make up the symbols, but the principles are universal. The information that resulted in those laws and principles was inherent and contained in whatever it was that went Bang 13.7 billion years ago.

 
 
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eudemonia
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17 April 2008 14:22
 

Bruce said better and more eloquently what I was trying to say. We apply symbols and language to mathematics for explanation and understanding. The principles of mathematics exist on their own of course. Now, are not human contrived symbols and language for explanations… passed on..as..memes? A meme can be either true or not true in principle correct? Somebody call Dawkins. grin

 
 
 
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burt
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17 April 2008 23:54
 
McCreason - 17 April 2008 06:22 PM

Bruce said better and more eloquently what I was trying to say. We apply symbols and language to mathematics for explanation and understanding. The principles of mathematics exist on their own of course. Now, are not human contrived symbols and language for explanations… passed on..as..memes? A meme can be either true or not true in principle correct? Somebody call Dawkins. grin

I think you are confusing ontology with epistemology.  The symbols and the rules for mathematical operations and deductions are epistemological, they are, as it were, the telescope through which we see the mountain.  The objects and principles of mathematics themselves are ontological.  If one is into memetics then you can say that the epistemological instruments are memetic in nature, but not everybody would agree—the idea of a meme is not clearly defined and not that many people buy into it as other than a term that is much overused.

 
 
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arildno
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18 April 2008 02:12
 
Bruce Burleson - 17 April 2008 03:02 PM

If mathematics did not have an independent existence apart from the human mind, there would not be as much order as there is in the universe, and by order I mean that physical things operate according to a set of laws or principles.

A mere assertion.

The symbols and language of mathematics and physics are the descriptions of those laws and principles.

1. Why mix the empirical science of physics into this??
2. You can make perfectly valid maths that bears no resemblance to natural phenomena.
3. It remains conjectural that “standard” maths is an “adequate” description of the natural world.
It seems so, but this is just an empirical question, not having any relevance whatsoever to the mathematics per se.

 
Oolon Colluphid
 
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Oolon Colluphid
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03 June 2008 08:38
 

Mathematics is a language invented by humans to describe properties that already exist in nature.  We didn’t invent the universe but we invented ways of describing it with ever increasing accuracy.

 
 
 
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burt
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03 June 2008 14:02
 
Flerndip - 03 June 2008 12:38 PM

Mathematics is a language invented by humans to describe properties that already exist in nature.  We didn’t invent the universe but we invented ways of describing it with ever increasing accuracy.

But there are areas of mathematics that seem to have no connection to anything in nature (the multiple differential structures that can be defined on exotic spheres, for example).

 
 
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arildno
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05 June 2008 09:12
 
Flerndip - 03 June 2008 12:38 PM

Mathematics is a language invented by humans

Correct.

to describe properties that already exist in nature.

Only partially correct, and hence false. While it is true enough that the impulse to formation of maths has been practical concerns, that does not mean that the primary concern of maths is practically oriented, or world-descriptive.

We didn’t invent the universe

but we invented ways of describing it with ever increasing accuracy.

True enough, but that is not the essence of maths.

 
 
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GAD
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05 June 2008 10:32
 

Math is a way to describe things, that some people use it to describe what they imagine does not make what they imagine anymore of a reality in and of it self then the math they used to describe it.

 
 
 
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burt
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07 June 2008 14:40
 
GAD - 05 June 2008 02:32 PM

Math is a way to describe things, that some people use it to describe what they imagine does not make what they imagine anymore of a reality in and of it self then the math they used to describe it.

You are confusing epistemology (description of things) with ontology (the reality or non-reality of the things indicated by the means of description).  I can, for example, give a mathematical description of the behavior of the Earth as it orbits the Sun.  I can do this using Newtonian gravitational theory, or using general relativity.  Both of these are descriptions, and both are quite accurate but they are not the thing described and the mathematical objects that are involved in constructing the descriptions are not the notational symbols use to indicate them.  Math provides a means of constructing descriptions of things, but math itself, as a human activity, is more like the study of possible patterns and relationships.

 
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