Is there a materialist explanation of mathematics?

[inocente]

Let’s consider intangible entities rather than abstract processes. Do materialists deny the existence of intangible entities? I imagine that it might depend on the materialist. Some people might deny that they are materialists, while also denying the existence of intangible entities.

Are there facts about intangible entities that might be discovered in future, even though those facts are not deductive consequences of any statement that anybody has ever thought of? Alternatively, does a system of axioms merely create the rules for a game, so that seeking truth is self-deception, unless the search for truth occurs inside the box?

The bottom line for all materialists is that matter precedes all non-material things, including any intangible entities, including whatever anyone may imagine or may exist.

Regarding materialists and knowable truths, I think Hume’s Fork probably sums it up, with its distinction between statements about ideas (analytic, necessary, a priori) and statements about the world (synthetic, contingent, a posteriori). - en.wikipedia.org/wiki/Hume%27s_fork

There is that word: “everything.” Do materialists believe that material reality arises out of matter, and are you describing what you think materialists believe, while yourself not being able to conceive of anything that is both real and non-material?

Yes, the common thread in materialism is the claim that without matter there would be no reality, all arises out of the physical. For instance, see en.wikipedia.org/wiki/Emergence

I wouldn’t call myself a materialist - I don’t see how any theist could since it would mean matter preexists God (perhaps along the lines of God being formed in our image rather than we being formed in His).

Indeed, most might call themselves physicalists instead.
What difference does it make? In the days when all of the evidence about the great length of geological time-spans that had been accumulated by geologists was dismissed by the physicist Lord Kelvin, on the grounds that a chemical reaction in something the size of the Sun that produces energy at the rate that the Sun produces energy could not be sustained for millions of years, materialists could have called themselves “Young Earth Physicalists.”

The intro and section 1 of the SEP article I linked explains the distinction - plato.stanford.edu/entries/physicalism/

In other words, mathematics is merely a tool used in physics, chemistry, etc? Can you direct my attention to a particular conjecture in number theory that was “invented to represent and abstract various kinds of order in matter”? It sounds as though either you are excluding number theory, or speaking in such vague terms that it is impossible to determine what is meant.

I explained it badly, apologies. My intention was to say that math expresses order, and to the materialist math could not exist unless there was order in the material world. In a chaotic world, no persons could evolve or otherwise exist to invent math, thus the existence of math is contingent on the prior existence of order. So conjectures don’t necessarily say anything about our world but could not exist without our world. Not sure if that’s a better explanation or not.

 

[inocente]

In that case, I am neither a materialist nor an idealist. I believe that 42 exists as an intangible entity. I believe that I also have an idea of 42, but that there is a difference between 42 itself and my idea of 42, just as there is a difference between a finger or toe and my perception of a finger or toe.

Sounds like you’re a dualist, most folk are probably dualists of one school or another.

 

[GaryTaylor]

Bottom line

The bottom line for all materialists is that matter precedes all non-material things,

Then they need explain…

The matter didn’t sit motionless nor did something come from nothing.

Bottom line

 

[inocente]

Did you look at what I was responding to?
forums.catholic-questions.org/showpost.php?p=12758802&postcount=11

PseuTonym:
It is obvious that if some people are experiencing difficulty in learning elementary facts about fractions of positive integers, then it would be no solution for them to try to study neuroscience and electro-chemical reactions in the brains of people who are thinking about fractions.

Tomdstone:
Neuroscience and electro-chemical reactions are not, strictly speaking, mathematical subjects.

PseuTonym:
According to materialist philosophy, there are no such things as positive integers. Of course, it is not possible to study what does not exist. Therefore, according to materialist philosophy, the best that one could do is to study the thoughts of people who are thinking about positive integers or other mathematical objects.

But according to materialism there are positive integers, it’s just that positive integers don’t have a separate existence beyond the world.

Plato thought the number 42 and a perfect circle and so on exist perfectly in a separate plane, in a preexisting world of ideas, and that our material world only contains imperfect copies. Materialists say no, ideas only exist as a result of matter, there is no separate world of ideas. So, for instance, a perfect circle exists as the generalized form of all things we call circles, in the equation of the circle.

 

[PseuTonym]

Originally Posted by PseuTonym:
*Let’s consider intangible entities rather than abstract processes. Do materialists deny the existence of intangible entities? I imagine that it might depend on the materialist. Some people might deny that they are materialists, while also denying the existence of intangible entities.

Are there facts about intangible entities that might be discovered in future, even though those facts are not deductive consequences of any statement that anybody has ever thought of? Alternatively, does a system of axioms merely create the rules for a game, so that seeking truth is self-deception, unless the search for truth occurs inside the box?
The bottom line for all materialists is that matter precedes all non-material things, including any intangible entities, including whatever anyone may imagine or may exist.
*

Regarding materialists and knowable truths, I think Hume’s Fork probably sums it up, with its distinction between statements about ideas (analytic, necessary, a priori) and statements about the world (synthetic, contingent, a posteriori). - en.wikipedia.org/wiki/Hume%27s_fork

I followed your link and the explanation seems to be that truths of number theory can be deduced from logic, but that is simply not true, unless you expand the concept of “logic” to include all future axioms of number theory that anybody discovers or invents, and possibly much more.

 

[Tomdstone]

I followed your link and the explanation seems to be that truths of number theory can be deduced from logic, but that is simply not true, unless you expand the concept of “logic” to include all future axioms of number theory that anybody discovers or invents, and possibly much more.

You have to have some definitions in place to prove anything. Take for example Euclid’s proof that there are an infinite number of prime numbers. You need to known what a prime number is and from there it is a logical deduction based on showing that assuming the opposite leads to a contradiction.

 

[inocente]

I followed your link and the explanation seems to be that truths of number theory can be deduced from logic, but that is simply not true, unless you expand the concept of “logic” to include all future axioms of number theory that anybody discovers or invents, and possibly much more.

You don’t discover axioms. You invent a set of axioms then manipulate them to get theorems. A true theorem follows from the axioms, a false theorem doesn’t, but the axioms are always just inventions.

 

[PseuTonym]

You don’t discover axioms. You invent a set of axioms then manipulate them to get theorems. A true theorem follows from the axioms, a false theorem doesn’t

I quoted up to and including the one statement that I want to examine:
“A true theorem follows from the axioms, a false theorem doesn’t.”

That statement is not clear enough for me to work with, so with your permission I would like to consider the following:

“Every true statement in number theory is a logical consequence of the axioms, and no false statement in number theory is a logical consequence of the axioms.”

Is that something that you might have asserted, or do you disagree with that statement?

---

In the meantime …

First,

Do you acknowledge that a conjecture can be discovered? For example, somebody considers adding consecutive odd numbers: 1+3 = 4, 1+3+5 = 9, 1+3+5+7 = 16, and notices that the results are squares. Quite quickly, a conjecture can be formulated. What is it that you believe prevents a generalization that is discovered via examples from being given the label “axiom”? After all, if you think that all axioms must be “justified logically” by deducing them from other axioms, then you will simply find yourself trapped in circular reasoning.

Second,

What distinction between discovery and invention do you have in mind? Insofar as intellectual property rights are concerned, I believe it is an established matter of law that an axiom cannot be patented.

 

[Rhubarb]

I don’t mean to cloud the waters further, but there has been serious debate as to what the very nature of what an “axiom” even is. Frege and Hilbert disagreed about what an axiom is, and they shared vigorous correspondence on the subject.

 

[Charlemagne_III]

Since animals have consciousness and are able to think and perform elementary mathematical processes, and they do not have souls, and are therefore purely material beings, it follows that there is a materialist basis for mathematics.

There is a materialist basis for mathematics, since mathematics corresponds to the rules of nature, as in E= mc2. However, the mental operation is not thereby reduced to a purely material operation. Whether animals can perform elementary mathematical processes is dubious to say the least, regardless of claims to the contrary. My dog natural knows the difference between 1 and 3 dog biscuits without it following that he is a mathematician.

 

[Charlemagne_III]

[SIGN][/SIGN]

An appeal to a soul, or God can certainly fix the problem for the realist. But then the Realist who chooses that path owes an account of soul, and God. And I get that most people here are going to grant the soul and God. But that has its own philosophical problems, one of which is accessibility again. Volumes could be written fighting back and forth so I’m nit going to touch it except to say that it’s not going to be a savory answer for those that won’t grant them.

This is not an agnostic website so I don’t think your conclusion follows except for agnostics, atheists, deists, etc., of which there are only a few lurking here.

 

[PseuTonym]

I don’t mean to cloud the waters further, but there has been serious debate as to what the very nature of what an “axiom” even is. Frege and Hilbert disagreed about what an axiom is, and they shared vigorous correspondence on the subject.

If you have any specific questions to ask or comments to make about the nature of axioms, then I recommend posting them in the following (relatively new) thread:

The search for truth in mathematics
forums.catholic-questions.org/showthread.php?t=947163

 

[Rhubarb]

This is not an agnostic website so I don’t think your conclusion follows except for agnostics, atheists, deists, etc., of which there are only a few lurking here.

I don’t expect anyone to see every philosophical problem the same way I do. But people who take philosophy seriously should at least be able to recognize where there ARE philosophical problems.

For example, I take it we both believe in free will. But there are numerous philosophical problems with it. But I don’t want to derail the thread - I only brought it up to give a common objection to a realist account of mathematical objects. (And universals in general)

 

[Tomdstone]

My dog natural knows the difference between 1 and 3 dog biscuits without it following that he is a mathematician.

Is it a purely materialistic process which enables mental process of your dog to know the difference between 1 and 3?

 

[Tomdstone]

I don’t expect anyone to see every philosophical problem the same way I do. But people who take philosophy seriously should at least be able to recognize where there ARE philosophical problems.

For example, I take it we both believe in free will. But there are numerous philosophical problems with it. But I don’t want to derail the thread - I only brought it up to give a common objection to a realist account of mathematical objects. (And universals in general)

Philosophy might be an interesting gloss on some historical aspects of mathematics. But I don’t see where philosophy has added to the bank of mathematical results. What information does philosophy give you about the Cauchy Goursat theorem?

 

[Rhubarb]

Philosophy might be an interesting gloss on some historical aspects of mathematics. But I don’t see where philosophy has added to the bank of mathematical results. What information does philosophy give you about the Cauchy Goursat theorem?

Philosophers are often mathematicians. Descartes created the Cartesian coordinate system and used it in his account of space, for example. I don’t know enough about pure math to comment specifically about the current literature on the subject. Philosophy of mathematics is less about doing math itself but what the nature of math itself is. These are fundamental questions. Now, for example, my professor in Phil-Math had her BS and MS in pure math, and only her PhD in philosophy. She was well versed in math.

 

[ThinkingSapien]

Bottom line

The bottom line for all materialists is that matter precedes all non-material things,

There are books on the topic. But the information is too much be posted here. You’d have to check out the books.

Here are a couple of titles:

• Where Mathematics comes From
• Calculus: An Intuitive and PhysicalApproach

 

[Charlemagne_III]

Is it a purely materialistic process which enables mental process of your dog to know the difference between 1 and 3?

Probably. The material scent of three dog biscuits may be stronger than the scent of one.

 

[Charlemagne_III]

Philosophy might be an interesting gloss on some historical aspects of mathematics. But I don’t see where philosophy has added to the bank of mathematical results. What information does philosophy give you about the Cauchy Goursat theorem?

Philosophy historically precedes math in all probability. If math is derived from philosophy it is derived from the branch of philosophy called Logic. As logic is the mother of mathematics, it is unlikely there would be any mathematics without logic struggling heroically to give birth.

plato.stanford.edu/entries/philosophy-mathematics/

Philosophy of mathematics discussed.

 

[Tomdstone]

Philosophy historically precedes math in all probability. If math is derived from philosophy it is derived from the branch of philosophy called Logic. As logic is the mother of mathematics, it is unlikely there would be any mathematics without logic struggling heroically to give birth.

plato.stanford.edu/entries/philosophy-mathematics/

Philosophy of mathematics discussed.

I found this article no help at all in trying to understand the philosophy behind the Cauchy-Goursat theorem.