Math's existence?

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Some schools of thought seem to teach that math is a product of our ability to reason.

Some schools, Russell is one that comes to mind, seem to teach that math has its own existence.

Any helpful thoughts.

How does Russell, if he does, explain that math has its own existence?

Thanks!
 
Jim_Baur said:
Some schools of thought seem to teach that math is a product of our ability to reason.

Some schools, Russell is one that comes to mind, seem to teach that math has its own existence.

Any helpful thoughts.

How does Russell, if he does, explain that math has its own existence?

Thanks!
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i just read a book called “the mathematical experience”. it speaks to this topic and is very interesting, but what i took away from it is that the foundations of math are a bit of a mystery to everyone. it is far from a settled matter even now.

you might pick up a copy and give it the once over.🙂
 
Hi Jim,

You have touched upon a highly contested issue of philosophy. On the one hand, it does seem that mathematical axioms and so forth do exist in some sense. 2+2=4, I take it, would be true even if there were no humans around. On the other hand, what kind of existence is this? Most philosophers would consider mathematical laws and axioms to be abstract objects. Whether abstract objects of any type can be said to “exist” is itself contested. There are basically three schools of thought, although each of these can be divided into sub-categories:
  1. Nominalism: Abstract objects are just human conventions. The truth of math and logic is contingent upon language, and indeed, is built into the fundamental rules of language.
  2. Realism: Abstract objects exist a se, independently of human thoughts.
  3. Conceptualism: This is sort of a middle ground. Abstract objects do, in fact, exist, but only as thoughts or concepts of the mind.
Of course, I have oversimplified each of these views. There are many nuances to consider. For example, Plato and Aristotle were both Realists, but their views were significantly different.
 
Here is just one example of an argument that both realists and conceptualists might use:

“P: There is no possible world such that there are no things that are not self-identical”

From P, it follows that there are 0 number of things that are not self-identical. So, we might say, the number 0 exists. Now, 0 is exactly one thing, so the number 1 also exists. This means that 0 and 1 both exist, so two things exist. You can probably see where I’m going with this. 🙂 An infinite cardinality can be deduced if, in fact, numbers actually exist.

The interesting question for me is whether these numbers are concepts of the mind or not. If they are, then they cannot be concepts of just any mind, since a finite mind cannot be the ground of an infinite cardinality. If conceptualism is true, then in conjunction with the reality of the set of all real numbers, it follows that numbers are grounded in an infinite mind, e.g. God.
 
For those philosphers that hold math exists on its own, do they explain how?

Please do not laugh as these simple questions, do they explain how pi exists on its own?

Is math alive?

If living, will it die?

Is math inanimate?

How many threes are there?

I think that some physical scientists believed math ran the physcial world, if so, how?

Does math animate the natural physcial laws? How?

Or, what is the ontological nature of mathematics?

Did it evolve?

Did math evolve and then physcial matter?

Did math evolve and then the physical laws evolve?

Is math eternal?

How do they handle such questions?

Again, I am sorry if these questions are rather silly, I hold them dearly.

Thanks!
 
Jim_Baur said:
Some schools of thought seem to teach that math is a product of our ability to reason.

Some schools, Russell is one that comes to mind, seem to teach that math has its own existence.

Any helpful thoughts.
Click to expand...
Jim
Here is what Leopold Kronecker, the famous 19th century mathematician had to say about the question:

“God made the integers; all else is the work of man”

Kronecker, who was at one time Gregor Cantor’s mentor, became Cantor’s antagonist.

Yppop
 
Jim_Baur said:
For those philosphers that hold math exists on its own, do they explain how?

Please do not laugh as these simple questions, do they explain how pi exists on its own?

Is math alive?

If living, will it die?

Is math inanimate?

How many threes are there?

I think that some physical scientists believed math ran the physcial world, if so, how?

Does math animate the natural physcial laws? How?

Or, what is the ontological nature of mathematics?

Did it evolve?

Did math evolve and then physcial matter?

Did math evolve and then the physical laws evolve?

Is math eternal?

How do they handle such questions?

Again, I am sorry if these questions are rather silly, I hold them dearly.

Thanks!
Click to expand...
Who addresses these kinds of questions?

Have they been addressed?
 
Jim, for a unique theistic spin on mathematical realism, you might consider reading this article by John Byl: Theism and Mathematical Realism.

In short, belief in a God who orders all things makes mathematical realism (or conceptualism) a viable option. The reverse is also true, I think.

Quine and Putnam are well-respected sources who defend mathematical realism. Here is a handy summary on one of the arguments for this view from the Stanford Encyclopedia of Philosophy: Indispensability Arguments in the Philosophy of Mathematics.

Hope this helps!
 
There are many books that address these issues. A while back, I found one that expressed something close to what I personally think, but I can’t find it now. But anyway, one such book is Philosophy of Mathematics: An Anthology by Dale Jacquette (see here). There are many others.
 
Found it - the essay “Is Mathematical Truth Time-Dependent?” by Judith Grabiner in New Directions in the Philosophy of Mathematics: An Anthology edited by Thomas Tymoczko (see here).
 
Thanks for all of the help!

I will take all of the help that any others would like to offer.
 
Just_Lurking said:
Found it - the essay “Is Mathematical Truth Time-Dependent?” by Judith Grabiner in New Directions in the Philosophy of Mathematics: An Anthology edited by Thomas Tymoczko (see here).
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i wondered when you were going to show. how have you been?, havent seen you in a while
 
Just_Lurking said:
Same old, same old. Anything new with you?
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not really, just delving deeper and deeper into things i dont really understand:p
Another book: 18 Unconventional Essays on the Nature of Mathematics by Reuben Hersh (see here).
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i got to say, “the mathematical experience” is fascinating. im inspired.🙂
 
Take a look at Morris Kline’s Mathematics: The Loss of Certainty. It is an excellent popular account of mathematical history and the philosophical problems raised by the intuitionist, formalist, logicalist schools of the early 20th century.
 
Jim_Baur said:
For those philosphers that hold math exists on its own, do they explain how?

Please do not laugh as these simple questions, do they explain how pi exists on its own?

Is math alive?

If living, will it die?

Is math inanimate?

How many threes are there?

I think that some physical scientists believed math ran the physcial world, if so, how?

Does math animate the natural physcial laws? How?

Or, what is the ontological nature of mathematics?

Did it evolve?

Did math evolve and then physcial matter?

Did math evolve and then the physical laws evolve?

Is math eternal?

How do they handle such questions?

Again, I am sorry if these questions are rather silly, I hold them dearly.

Thanks!
Click to expand...
Jim

Listen closely to these math students, and you may find the answers you are looking for.

youtube.com/watch?v=UTby_e4-Rhg

yppop
 
These suggestions are absolutely helpful.

Thanks!

I do not have the time or energy as of now to read entire works.

Does philosophy give definitive answers to them questions?

I am not being silly, I hope.

Are there an unending number of threes, fours, and pis?

I know that Kepler actually held the idea that triangles and cubes actually exist outside our minds, was he correct or incorrect?

Does philosophy answer such questions definitvely?

If any person can address these actual questions, I would be most thankful.

I am, already, thankful for all of the help I have thus far received, and the works which were suggested will be read some day in the future.

Again, thanks!
 
Jim_Baur said:
Does philosophy answer such questions definitvely?
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No, there aren’t any definitive answers to these questions. There are various philosophical factions that each have their own different answers.

I’m not even sure most working mathematicians find such philosophical speculation useful, much less definitive.
 
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