Are Really Big Numbers Real, Exploring Materialism’s Necessary Implications

This is a dialog from a blog thread yesterday, if it continues I’ll add that at the bottom. Note, this is with “Dan L.” who shouldn’t be confused with my frequent opponent “ Dan S.” Also note, I give the definition of “materialism” at the beginning which has always been what I understood the ideology to consist of. I didn’t realize Dan L is a mathematician before posing the question to him, I did know he was defending materialism. I had earlier said that I didn’t think that we could limit the universe to materialism and that, while I thought the biggest reason for rejecting Dualism was that it was unfashionable, I could see no inherent problem with the idea, though I don’t take that position or Idealism either.

AM — I'll pose a problem to you that I posed elsewhere. If by "materialism" you mean the belief that only those things within the material universe are real, consider this. Think of a number, let's say in the set of Real numbers, that is a trillion, trillion powers bigger than the number of individual entities in the physical universe, every subatomic particle, every everything. A number a trillion, trillion times bigger than whatever number that is. Is that number contained within the material universe? In what way is it contained in the material universe? Is it real? Is there a number even larger than that which, eventually, even you could not account for being in the material universe? Please explain in a way that will convince a skeptic of materialism as opposed to a true believer.

And there are other barriers to clarity on the issue of materialism. That's just one

Dan L.---- I think the anxiety and confusion such questions cause actually comes down to the fact that words like "exist" and "real" are notoriously hard to define. For example, the assertion, "I exist" is terribly problematic whatever Descartes might have to say about it. The atoms in my body are constantly recycled, as are the cells. New memories are constantly being added, and my beliefs and desires change as a function of new experiences in my life. To borrow from Nietzsche, "to be" is not the correct verb - it is "to become." This is connected to what I was saying to Mike about problems with intuitive notions of causality.

Another example: the U.S.S Constitution, moored right across the harbor from me, has at most one piece of wood left of the original ship. Is it still the same ship it was during the Revolutionary War? It has the same name and the hull was refurbished one board at a time as needed. I say there is a sense in which it is the same thing (the U.S.S Constitution) and a sense in which it is not (the physical matter of which it is composed has been recycled).

Similarly, there is a sense in which numbers exist and a sense in which they don't exist. Think about trying to make a perfect circle from a material substrate. Since the substrate is composed of a finite number of atoms, you can never get the ratio of the circumference to the diameter to be pi. It will always be a rational number. There is a sense in which pi exists and a sense in which it does not - we can calculate its value to an arbitrary degree of precision in principle, but in practice we actually can't.

As I've been trying to get across, I'm not really a reductionist. See my example in my response to Mike above - I don't believe knowledge can in principle be reduced to statements about subatomic particles. But I don't think the fact that we can talk intelligibly about abstractions makes souls, deities, or the flying spaghetti monster any more coherent as elements of causal models.

AM ---- What do you mean by "materailism" if it isn't that classic definition? Is there a coherent definition for "materialism", one that would be self-apparent to a reasonable person who was given that definition? If there isn't, then I'd contend that materialism wasn't real in any but a subjective sense, which wouldn't bother me but I'd imagine some materialists might have a rather strong emotional reaction to the idea.

Is there a number so large that there would exceed a definable one-to-one correspondence with the actual number of physical entities in the material universe? Would that number be a part of the material universe? Would that number be real? You know, when I really want to be a pain, I make it a rational number and then ask how it could be represented as a ratio. I've never actually had to duck after doing that yet.

I'd like an explanation of why that question isn't a valid one.

I believe the FSM is copyrighted and maybe even trademarked, and I do believe the creator of it is known. I don't think any souls and no supernatural deities have such a clear historical foundation. Gogol notwithstanding.

Dan L. — There's no coherent definition for "materialism" any more than there is for "dualism," which is usually taken to include various forms of animism and similarly "primitive" beliefs despite the fact that such beliefs bear little resemblance to scholastic Christianity. The categories are fuzzy. My philosophical beliefs are largely influenced by Dennett, but I don't agree with him on everything either.

The core of it, though, is that I reject dualism. I reject causal explanations that invoke immaterial causes. I have several reasons for doing so, but the most obvious is something that occurred to me by the age of twelve: that if the supernatural actually exists, then it is part of nature and therefore natural. If human intelligence is really mediated through a soul, then that soul must be able to transfer or transduce energy either by applying a force or through other means.

And there is no evidence that such a thing happens, or that it is a necessary element of any explanation of human behavior or any other natural event. Positing such things is completely extraneous to the goal of actually learning about how things work. Either you posit an entity whose existence we can verify through falsifiable experimental hypotheses, or you posit an entity that is by definition impossible to study. The latter is not science; it cannot be science; it is, in fact, antithetical to science.

Is there a number so large that there would exceed a definable one-to-one correspondence with the actual number of physical entities in the material universe? Would that number be a part of the material universe? Would that number be real? You know, when I really want to be a pain, I make it a rational number and then ask how it could be represented as a ratio. I've never actually had to duck after doing that yet.

Asking whether numbers exist is, to me, like asking whether I could put a particular build of Microsoft Windows in the freezer. Microsoft Windows isn't a thing; it's a pattern of behaviors that occur within an electronic device of a particular architecture. It does not exist corporeally, it exists functionally. To ask me to put it in a freezer is a simple category mistake. There is an abstract sense of existence, in which we can talk perfectly coherently about unicorns, and then there is an actual state of existence in which there is no such thing as unicorns. Likewise, we can talk about pi, the ratio of the circumference of a perfect circle to its diameter, even though there is no such thing as a perfect circle. And again, none of this implies the existence of a soul or a god or anything else "supernatural."

AM – @ Dan L. Asking whether numbers exist is, to me, like asking whether I could put a particular build of Microsoft Windows in the freezer. Microsoft Windows isn't a thing; it's a pattern of behaviors that occur within an electronic device of a particular architecture. It does not exist corporeally, it exists functionally. To ask me to put it in a freezer is a simple category mistake. Dan L.

So we have non-corporeal entities that seem to be relevant to the material universe, I'd imagine you would agree, at least to the extent that you can explain physical phenomena with math, in fact, science is about entirely dependent on doing so, at times with great accuracy. I'd guess you wouldn't hazard to explain that interaction between the material and the non-corporeal, would you? Would the numbers exist without the material universe? But if they can't then that makes my big numbers question all the more relevant. Does that number exist and if it doesn't wouldn't that mean that there are a finite number of numbers? Maybe that property of the numbers system is just an invented myth? Do you really want to go there?

I've never thought of this before, has anyone ever described a computer program as an artificial natural law? One that governs forces towards a, one hopes, relatively fixed end? Maybe the role that numbers play in those might help, or maybe not, since those are artificial and not natural but a merely mimic the actual universe. Maybe "phony natural laws" would be a better term.

Come to think of it "actual universe" might be a more inclusive term than "natural universe". Who knows? Maybe it might get some materialists out of a rut?

- There is an abstract sense of existence, in which we can talk perfectly coherently about unicorns, and then there is an actual state of existence in which there is no such thing as unicorns.

Unicorns were alleged to exist in the physical world, you were supposed to be able to trap one because they would put their head in the lap of a virgin. They were not alleged to be suprenatural or abstract. And now you're giving me two senses of existence, though I don't see how unicorns are at all relevant to numbers, what properties do they share in common? Certainly not in that one is a made up story and the other is rather useful to science and other areas of real life.

- Likewise, we can talk about pi, the ratio of the circumference of a perfect circle to its diameter, even though there is no such thing as a perfect circle. And again, none of this implies the existence of a soul or a god or anything else "supernatural."

I haven't implied that numbers are implications of the existence of a supernatural, as far as I know, our only means of knowing them is in relation to the natural part of that "actual universe" that I'm liking more as this comment develops. I don't think we have any idea if numbers would be relevant to the supernatural, just as we would have no reason to insist that logic or science would be relevant to it. There is absolutely no evidence that any of those would apply. All I wanted to do is explore the idea of real things that aren't contained in the material universe and I'm doubting numbers are the more I think about it. At least unless they got that infinity thing wrong. Wouldn't that be fun.

- Logic is prior to mathematics because you cannot do mathematics without logic.

Logic is the product of human experience of the material universe. In his Swathmore Lecture, Eddington said, "Mind is the first and most direct thing in our experience; all else is remote inference." Logic is the product of the human experience of the world. It has no known existence outside of us, we have no idea of any other animals in the universe use logic, it could be peculiar to us, a peculiar feature of our minds using our brains to reach and interact with the outside world. Maybe we're just interfaces, hum?

- If human intelligence is really mediated through a soul, then that soul must be able to transfer or transduce energy either by applying a force or through other means.

Why not? as I said there isn't any reason to believe that what we know about physical laws would govern any supernatural, there isn't any reason to believe that would be a necessity in the supernatural. There isn't any reason to think that a supernatural wouldn't be able to apply force to the material world. Many religions assert that what we do in the physical world has an effect on our souls in the supernatural, after all.

- Positing such things is completely extraneous to the goal of actually learning about how things work.

I'm not entirely sure what you mean by "learning how things work". I don't see that this is an absolutely necessary conclusion. Maybe it's, actually, intrinsic to the way in which we, as individual beings, are conscious in the material universe. No one has ever explained how we are conscious of the physical universe, we don't just reflect what's out there like a mirror.

- Either you posit an entity whose existence we can verify through falsifiable experimental hypotheses, or you posit an entity that is by definition impossible to study. The latter is not science; it cannot be science; it is, in fact, antithetical to science.

I never thought it was science, I'd say it's outside of the proper subject matter of science, the material universe being the only thing that science was invented to study. I think you've got the cart before the horse, too. Falsifiability is a tool of science to test ideas, it's not a test of usefulness or even the existence of something, it's a tool to test the usefulness of an idea about things.

If I wasn't tired I'd think of a dozen things that couldn't be falsified that you'd really rather not do without, actual existence, for a starter, though the separation of church and state is one of my favorites in this argument and the foundation of the entirety of civil rights and democratic government. And I think you might want to take up Exobiology and Evo-psy in that regard, in which case prepare yourself to do battle with, I'd guess, the larger part of the world council of new atheism. Certainly the blog contingent. Remember to be sufficiently pious while you're debunking them or you'll catch it.