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Charlemagne_III
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I think they go further than that by insisting consciousness itself is a material operation.
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Charlemagne_III
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It is because animals do not have immortal souls that they cannot read the mind of God any more than they can read the Ten Commandments.
God gives all his creatures instincts to follow. They all follow them more or less.
Only man goes beyond his instincts to explore why God gave him the potential to think like God.
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Tomdstone
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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.
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GaryTaylor
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No science for that?
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PseuTonym
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How about using the set of finite von Neumann ordinals as a model of the set of non-negative integers?
The approach is as follows:
First, the empty set corresponds to the number zero.
Then, for a given set m in our hierarchy, we define the successor of m to be (m union its singleton). For example, the successor of the empty set is simply the set that has exactly one member, that one member being the empty set. That follows from the definition of successor because, for any set x, (empty set union x) = x.
Do you accept that as an example?
I can imagine that, because the integers are non-physical, you might not accept my example. However, I agree that the positive integers are not physical entities. The crux of the matter is whether or not, starting from the assumption that some entities are non-physical, we can arrive at the conclusion that they are not part of reality.
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inocente
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Perhaps some do, but I was responding to a claim that “according to materialist philosophy, there are no such things as positive integers”.
That’s not the case though. In both idealism and materialism the number 42 exists, and it exists as an idea.
The difference is that while the materialist holds that ideas are not the basis of reality, that ideas are secondary to matter, the idealist holds the opposite, that matter is not the basis of reality, matter is secondary to ideas.
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PseuTonym
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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?
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?
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.”
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.
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PseuTonym
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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.
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yppop
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I use a very narrow definition of the word “thinking” , namely, “thinking is the use of symbols to create thoughts”. IMO, Dogs certainly have thoughts which are generated by signs. However, I will concede the use of the word “thinking” to describe the creation of thoughts that have been created by either signs or symbols. I have no problem with the belief that dogs can think when describing a dog’s correct response to a word “sit” because in such an instance"sit" is used as a sign. My narrow definition more correctly should have bee called “abstract thinking” to contrast to your “thinking to some primitive extent”. On this I believe we can agree. One of my daughters has a border collie whose command vocabulary is a bit more than primitive.
Thanks anyway for a thoughtful question. I seldom get those.
Yppop
Now here I open a other door to a discussion of the difference between “signs” and “symbols”.
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Tomdstone
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The differential calculus is built on the assumption of the continuity of the real line, and yet AFAIK, matter is discrete and not continuous. therefore the math model is in this case an approximation.
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PseuTonym
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What is the continuity of the real line? I am familiar with the concept of a continuous function, but not the concept of a continuous space. Of course, it is possible to consider a function space. In other words, we can use a set of functions to define some kind of space, with each point in the space corresponding to some function. However, we usually make a conceptual distinction between functions and spaces. Are you making reference to what is often described as the “least upper bound property” or “completeness property” of the set of real numbers?
Why are you making reference to the discreteness of matter, rather than to the discreteness of space?
This conclusion was already reached for three-dimensional space based on the curvature of the physical space-time continuum. Perhaps it would be interesting to attempt to construct a one-dimensional space having curvature.
You responded to my post about a kind of set-theoretic construction of the non-negative integers. The non-negative integers are ordinarily conceptualized as spread out as discrete points along the real line. So it is not clear to me why you selected that post to respond to.
My post (in this thread) about infinities that arise in connection with the set of real numbers includes the following:
Read the full post via this link:
forums.catholic-questions.org/showpost.php?p=12759829&postcount=33
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Rhubarb
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Well, I mean, there are lots of projects that try to account for mathematics without having to appeal to a realist explanation - like saying that numbers exist and give truth value to mathematical propositions. Benacerraf pointed to the problem that realism and anti-realism seem to have. There’s Logicism, Nominalism, Formalism, I think Conceptualism (or Structionism, I always get the two confused) all try to give a complete account of mathematics in ways that do not rely on any sort of insubstantial thing like “a number.” But then, these anti-realist positions have problems too.
The realist has to deal with accessibility. If mathematical objects exist outside of space and time, in some realm, and act as a referent to mathematical objects then it seems strange that we can come to know about them - our senses are IN space and time. This is the problem of universals. The anti-realist has to deal with applicability. Mathematics seems necessary, and maps onto things in the real world - we can use it to make extremely accurate predictions and descriptions. This seems strange if math is just a language we invent. These anti-realist positions, I think, would cohere with a materialist position.
Philosophy of Math is super fascinating. I really wish I had the patience to learn more straight math so I could make sense of it at a deeper level.
The realist has to deal with accessibility. If mathematical objects exist outside of space and time, in some realm, and act as a referent to mathematical objects then it seems strange that we can come to know about them - our senses are IN space and time. This is the problem of universals. The anti-realist has to deal with applicability. Mathematics seems necessary, and maps onto things in the real world - we can use it to make extremely accurate predictions and descriptions. This seems strange if math is just a language we invent. These anti-realist positions, I think, would cohere with a materialist position.
Philosophy of Math is super fascinating. I really wish I had the patience to learn more straight math so I could make sense of it at a deeper level.
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Charlemagne_III
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This is the same as the problem of explaining the realm of intellect as separate from the physical realm of the brain. If our intellect survives our body with our soul, we have to admit that it exists in another realm thus far in tangible or knowable. Mathematics exists in the intellect and so also participates in that other world.
“God is a mathematician of a very high order and He used advanced mathematics in constructing the universe.” Paul Dirac, Mathematician.
Is there a clue here?
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GaryTaylor
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Its one dimensional thinking.
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Tomdstone
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Oh, I see what you mean. Since the usual, but not always, independent variable in differential calculus is time, the question is whether or not time is discrete.
I am not sure whether or not space or time is discrete. It is possible, I suppose. In any case, the real line is not discrete in a mathematical sense, since between any two points on the real line, you can find one in between. This would not be true AFAIK with a thin rod.
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PseuTonym
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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.
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Tomdstone
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Can you give a reference for this statement? I am not that familiar with materialist philosophy.
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Tomdstone
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As a specific example, take the function which gives the temperature of a rod at a point. Generally, this is taken to be a continuous function, but since matter is discrete, it really is not so. But the approximation to continuity is good enough for almost all applications (except possibly on the quantum level).
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Rhubarb
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[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.
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GaryTaylor
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How so? The matter didn’t sit motionless nor did something come from nothing. The universe is practically all energy. Gravitons don’t exist, can’t fine one [never], see one, and further relativity indicates a zero start point which the graviton phenomsciencetheroists would like to conclude they will “have to change” to fit there other unproven theory, To what they have is no idea. We are talking massless particles at this point.
Something set the sequence in process through energy. The energy is the invisible paradigm which interconnects the universe and holds it together through the gravity energy-force which is created by the EM force-energy. Both forces have infinite range and travel at the speed of light. They differ in that Energy creates the EM force and matter creates the gravity, matter can be converted to energy and visa-versa. And energy cannot be destroyed only displaced. The EM force is where we are at with photons. We simply do not know, the photons through the work of energy and its further implications such as frequency, reduced the photon to what appears to be pure energy. But it is still observable as matter like a red hot ball, and they produce s string of interconnected photons which vibrate, then the gravity is assumed to be connected through the graviton. Thats the dilemma in simple terms and the basic relationship of two major forces in the universe EM and gravity.
I’m waiting for the materialist theory, I already took the math class.
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