Is there a materialist explanation of mathematics?

[PseuTonym]

Even though these concepts may have been developed at least partially without reference to the real world, in the end, mathematics has been shown to have great power in explaining materialist phenomena.

Below is a revised version of your words:

Even though these concepts may have been developed at least partially without reference to the material world, in the end, mathematics has been shown to have great power in explaining material phenomena.

I agree with the revised version.

I would like to emphasize that mathematics is about reality. However, mathematics is about intangible or non-material aspects of reality. Thus, the power of mathematics in explaining material phenomena is a demonstration of how knowledge of some intangible aspects of reality can assist people in gaining knowledge of, and power over, other aspects of reality.

My conclusion is that “intangible” does not imply unreal or unimportant. Some intangible things are both real and important. However, there is plenty of propaganda suggesting the exact opposite: that material phenomena are the only phenomena, and that progress in science and technology are a result of focusing attention on material phenomena, and on denying the existence of anything else.

 

[PseuTonym]

3]Therefore, gravity is immaterial.

There are at least two approaches to handle that problem.

One approach is indicated here:
“Researchers propose a new way to detect the elusive graviton”

Among the four fundamental forces of nature, only gravity has not had a basic unit, or quanta, detected. Physicists expect that gravitational force is transmitted by an elementary particle called a graviton, just as the electromagnetic force is carried by the photon.

Read more via link:
asunews.asu.edu/20140303-graviton-research

Another approach to simply expand “material” to include whatever entities physicists propose in their attempts to explain phenomena of physics.

Chomsky wrote about this very explicitly in the following book:
New Horizons in the Study of Language and Mind

In Chomsky’s writings that are available online, you can find some hints about these matters:

One can say that the dualism introduced by empiricist dogma is methodological rather than substantive. That is to say, it is taken for granted that the body must be studied by the ordinary methods of science but, in the case of the mind, certain preconceptions have been imposed which have virtually removed this study from the domain of scientific inquiry.

Newton showed that Cartesian mechanics could not account for the movement of heavenly bodies. To explain this movement he postulated a new force: gravity, attraction at a distance; that is, a force which by the criteria of his time was considered to be occult, mystical, because action at a distance violated basic assumptions of mechanics. Newton showed that in this way one could account for the facts, though he too was quite uncomfortable with the “occult force” he was postulating. This postulate became the common sense of following generations, with Laplace and others. An inconceivable idea for pre-Newtonian physics subsequently became part of science because of its remarkable explanatory power.

It might turn out that we are led to new principles when we inquire into the nature of the mind. It is conceivable, though not demonstrated, that principles entirely different from those of contemporary physics enter into the explanation of mental phenomena. In all these matters one must guard against dogmatism.

From:
Empiricism and Rationalism
Excerpted from Language and Responsibility, Pantheon, 1977

Link:
chomsky.info/books/responsibility02.htm

 

[GaryTaylor]

There are at least two approaches to handle that problem.

One approach is indicated here:
“Researchers propose a new way to detect the elusive graviton”

Another approach to simply expand “material” to include whatever entities physicists propose in their attempts to explain phenomena of physics.

Chomsky wrote about this very explicitly in the following book:
New Horizons in the Study of Language and Mind

In Chomsky’s writings that are available online, you can find some hints about these matters:

From:
Empiricism and Rationalism
Excerpted from Language and Responsibility, Pantheon, 1977

Link:
chomsky.info/books/responsibility02.htm

I’ve seen it. I rarely think of things in material terms, I see the connection. If there was no material to drop off the table we would never have even understood the law of gravity. I look at matter from a symbol point of view M.

You know I’m not ever sure a good deal of these are all right and frankly I’d have to see the math. But a photon reduced can’t be measured, whats measured is the energy-frequency. I “assume” the matter still exists as do others to participate in the continued work. Which is why I think there is two points of view, whats remaining may indeed be energy and frequency with a magnetic field. Course theories vary one way or the other.

 

[Rhubarb]

Is there an account of mathematics that a materialist would accept? Sure. A materialist could accept an anti-realist position on math.

Is there an account of math that relies on materialism? I’ve read of a few, but they are hard to defend with what I know. A philosopher of mathematics might be able to give some of the current and historic arguments.

 

[GaryTaylor]

A philosopher of mathematics might be able to give some of the current and historic arguments.

What is the importance of the argument in the end, I mean whats the punchline, matter always existed and from that we came to be?

 

[Charlemagne_III]

On the assumption that the only actually existing things are such material or physical entities as matter, energy, space, time, etc., how does one explain what a mathematical fact is? Similarly, given a materialist framework of philosophy, how does one explain how people acquire knowledge of mathematical facts, in the sense of original research and not merely study of the results of research that was conducted by others?

This is what I understood to be the original question in your thread.

My answer was predicated on the belief that intellect is not material, and therefore neither is math, though of course math refers to physical entities and even entities that can hardly be described as physical, but must be inferred to exist nevertheless.

I believe our individual minds are created and constructed to operate, however limited they do so, as modeled on the mind of God. Our minds are real, and are impacted by the physical world of our brains, but only as a bridge to the mind of God.

 

[Tomdstone]

Is there an account of math that relies on materialism?

My answer was predicated on the belief that intellect is not material,…

Do animals have an immortal soul or are they purely material beings? In catechism, the nun taught us that animals do not have a soul and they do not go to heaven. Would that not imply that animals are purely material beings? Then how would you explain the number crunching abilities of many animals except that mathematics has a material foundation? How is it that many animals understand number and their ordinal relations? “Recent experiments by psychologists Elizabeth Brannon and Herb Terrace of Columbia University show that captive rhesus monkeys can understand the ordinal relations among the numbers one to nine.”
americanscientist.org/issues/pub/what-do-animals-think-about-numbers/1

 

[GaryTaylor]

Do animals have an immortal soul or are they purely material beings? In catechism, the nun taught us that animals do not have a soul and they do not go to heaven. Would that not imply that animals are purely material beings? Then how would you explain the number crunching abilities of many animals except that mathematics has a material foundation? How is it that many animals understand number and their ordinal relations? “Recent experiments by psychologists Elizabeth Brannon and Herb Terrace of Columbia University show that captive rhesus monkeys can understand the ordinal relations among the numbers one to nine.”
americanscientist.org/issues/pub/what-do-animals-think-about-numbers/1

Can you prove they don’t have a soul mathematically? We are talking material and math? What do you have on this? It should be easy for the materialist

 

[Tomdstone]

Can you prove they don’t have a soul mathematically?

The nun in our catechism class said that they do not have a soul and that they do not go to heaven. Do you disagree with her?

 

[GaryTaylor]

The nun in our catechism class said that they do not have a soul and that they do not go to heaven. Do you disagree with her?

I wasn’t there. Nor do I study animals. Since you bought it up I guess you’ll elaborate on souls and animals and the theory of principle of quantum superposition . And tell us how it applies to both humans and animals. Or is your point to check to see if I’m following the Church.

 

[Charlemagne_III]

The nun in our catechism class said that they do not have a soul and that they do not go to heaven. Do you disagree with her?

I would certainly agree with her. Animals also do not have a conscience to follow that would merit them immortal life in heaven or hell. Animals run on instinct, not morals. When my dog steals the bacon off my kitchen counter top he does not fear the pains of hell.

Would that he did!

No doubt monkeys can distinguish between the advantage of nine bananas over one banana, but does that make them mathematicians?

 

[Tomdstone]

I would certainly agree with her. Animals also do not have a conscience to follow that would merit them immortal life in heaven or hell. Animals run on instinct, not morals. When my dog steals the bacon off my kitchen counter top he does not fear the pains of hell.

Would that he did!

No doubt monkeys can distinguish between the advantage of nine bananas over one banana, but does that make them mathematicians?

Since animals do not have immaterial souls, that would mean that they are completely material beings, would it not? And yet they have elementary number crunching abilities and are understand the ordinal relations among numbers.

 

[PseuTonym]

The use of an infinity sign in a mathematical expression

Thank you for the explanation. I see the connection with calculus and what you are getting at. However, this seems to me to be a red herring.

It is necessary to warn students that they will reach contradictions if they try to compute limits by performing algebraic manipulations with infinity as though it were a member of the set of real numbers. Also, infinity was taboo in mathematics for many centuries, and the taboo lingers, so it seems that one can kill two birds with one stone by convincing students that there are two kinds of infinity: a dangerous kind and a safe kind. Thus, there is a motivation to tell students that the 8 symbol on its side that they see in calculus is not dangerous. There is temptation to continue the old tradition of attempting to distinguish between the potentially infinite and the actual infinite, and to deny the existence of the actually infinite.

However, it is enough to contemplate a sequence of inscribed and circumscribed polygons that become arbitrarily good approximations of a circle. If it is an infinite sequence of polygons, then infinity is involved. Archimedes would have understood this train of thought, because he invented it.

 

[yppop]

If by “materialist explanation” the OP means “the belief that there is no spiritual component to reality only matter” then the answer is NO.

Mathematics requires abstract thought and matter can’t think because without a spiritual component there is no mind… The mind is the interface between the material brain and the spiritual substance of the soul… The brain may be necessary to thought but not sufficient. Even though animals, especially mammals, have both brains and psychical components they cannot think because they don’t have minds (or souls) and, hence can’t do math (no matter what some animal psychologists want to believe) because thinking requires a special brain, namely, one with a language capability. By language I mean not only words but symbols in general, which would also include numbers.
Yppop

 

[Tomdstone]

If by “materialist explanation” the OP means “the belief that there is no spiritual component to reality only matter” then the answer is NO.

Mathematics requires abstract thought and matter can’t think because without a spiritual component there is no mind… The mind is the interface between the material brain and the spiritual substance of the soul… The brain may be necessary to thought but not sufficient. Even though animals, especially mammals, have both brains and psychical components they cannot think because they don’t have minds (or souls) and, hence can’t do math (no matter what some animal psychologists want to believe) because thinking requires a special brain, namely, one with a language capability. By language I mean not only words but symbols in general, which would also include numbers.
Yppop

With respect to whether or not animals can think, I am not sure that I agree with you. It seems to me that dogs can think to some primitive extent, and experiments by scientists show that some animals are capable of rudimentary thought.
What is your definition of thought or to think?

 

[GaryTaylor]

With respect to whether or not animals can think, I am not sure that I agree with you. It seems to me that dogs can think to some primitive extent, and experiments by scientists show that some animals are capable of rudimentary thought.
What is your definition of thought or to think?

Think

to believe that something is true, that a particular situation exists, that something will happen, etc.

: to have an opinion about someone or something

: to form or have (a particular thought) in your mind

See some point of contention here with the animals and people? Tom animals and people can think. But you know that. So whats the point of dialogue Tom?

So what is materialists mathematical view of the start of the Universe…Tom. Unless you want to talk about puppies some more.

 

[GaryTaylor]

“mounting evidence indicates that, in contrast to Darwin’s theory of a continuity of mind between humans and other species, a profound gap separates our intellect from the animal kind.”

Hauser and his colleagues have identified four abilities of the human mind that they believe to be the essence of our “humaniqueness” mental traits and abilities that distinguish us from our fellow Earthlings. They are: generative computation, promiscuous combination of ideas, the use of mental symbols, and abstract thought. [Read: Top 10 Mysteries of the Mind]

1. Generative computation

Humans can generate a practically limitless variety of words and concepts. We do so through two modes of operation recursive and combinatorial. The recursive operation allows us to apply a learned rule to create new expressions. In combinatorial operations, we mix different learned elements to create a new concept.

1. Promiscuous combination of ideas

“Promiscuous combination of ideas,” Hauser explained, “allows the mingling of different domains of knowledge such as art, sex, space, causality and friendship thereby generating new laws, social relationships and technologies.”

1. Mental symbols

Mental symbols are our way of encoding sensory experiences. They form the basis of our complex systems of language and communication. We may choose to keep our mental symbols to ourselves, or represent them to others using words or pictures.

1. Abstract thought

Abstract thought is the contemplation of things beyond what we can sense.

google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja&uact=8&ved=0CCcQFjAB&url=http%3A%2F%2Fwww.livescience.com%2F33376-humans-other-animals-distinguishing-mental-abilities.html&ei=B2HkVIemMYGDgwTekYNg&usg=AFQjCNFB2XIfIyuO5i9MJ67N9qd_ncMY7A

google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0CCEQFjAA&url=http%3A%2F%2Frealtruth.org%2Farticles%2F090806-002-science.html&ei=B2HkVIemMYGDgwTekYNg&usg=AFQjCNH6QaLdkvF1uNjfzLY4DHTx1-kVnA

 

[inocente]

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.

Interesting thread but to some extent I think you’re tilting at windmills, since these days materialists don’t deny abstract processes but claim instead that everything arises out of matter. Indeed, most might call themselves physicalists instead.

Thus, the materialist says, we couldn’t exist if matter behaved totally randomly. The fact that we exist implies some kind of orderliness in the matter. Math is the collection of systems we invented to represent and abstract those various kinds of order.

The materialist does not deny non-material things such as gravity, math or consciousness but claims they couldn’t exist in the absence of matter.

global.britannica.com/EBchecked/topic/369034/materialism
plato.stanford.edu/entries/physicalism/
en.wikipedia.org/wiki/Materialism

 

[ThinkingSapien]

Thank you for the explanation. I see the connection with calculus and what you are getting at. However, this seems to me to be a red herring.

I think it’s relevant to the apparent “problem” in the message to which I had replied.

It is necessary to warn students that they will reach contradictions if they try to compute limits by performing algebraic manipulations with infinity as though it were a member of the set of real numbers.

I think the mathematical models we build of reality are approximations and their isomprphic qualities are good within ranges.For example, Newtonian mechanics is pretty good for the things we usually observe here on the surface of the earth. Not so good for things on a quantum or some astronomical scales. But no, Infinity isn’t expressive if a specific quantity any more than NaN is. But they are very useful for symbolic computation.

 

[GaryTaylor]

Simply put a universe without matter would have no observer and measurement would not be possible. Very old fact of science. The question really comes back to todays work and the relationship of mass-energy-gravity. Its a chicken-egg conundrum and of course we couldn’t exist if matter behaved totally randomly. But it behaves as its does do to energy which is the activity. And comprises of 96% of the universe. To which the remaining 4% NASA is reluctant to even call this strictly “matter”. All facts.