Do ideal objects mean existence of soul?

I have recently heard a shiur by one rabbi which is a one of a five-part series called "Philosophical Evidence for Soul". This shiur was part 2 or 3, and the argument of the shiur can be briefly summarized as following:

We have access to knowledge of ideal objects. Those include numbers, imagined colors which we have never observed in real life, geometrical objects, and in general abstract ideas and logical concepts. 

All those things are not a part of the physical world, even though they can have a relationship with the physical world (e.g., objects can be counted using numbers). On the other hand, they do exist, and some of them (e.g., numbers, relationships between shapes) are necessarily true. So, if all there is to our mind is that it's a physical brain, then how can something physical know about something non-physical? Clearly, we need an organ that itself would be non-physical and allow us to know of non-physical (ideal) phenomena. Such as, for instance, soul.

I think this argument is flawed. Not that I disagree with the outcome, but I certainly disagree with the logic.

There are obvious immediate problems with this argument (why soul? why not another mysterious organ?), but I want to focus on the biggest problem with this argument: it misrepresents what ideal objects are.

I am going to spare you of a lengthy discussion of the history of this topic's philosophy and an outline of all the different views. I will just give you my own view, and you can judge yourself what you think of it. I will note that my description is limited to those things that we can observe with out own eyes and that everyone has knowledge of. I am not going to talk about angels, parallel worlds, souls, and other phenomena that I think exist but are not a part of our everyday experience. After all, the argument above states that we can deduce from our everyday experience that materialism is wrong.

The essence of my argument is that something physical can know about something non-physical. And there are things besides our brains that do so all the time. But, first things first:

It is true that physical objects are not the only phenomena out there. Or, rather, it is true that matter is not all there is to physical reality. There is also space. There is time. There are properties of matter, which consist of the ways that pieces of matter behave in space and time and the ways they are arranged. Let us call all those aspects of reality ideal phenomena. (I am just giving a definition.)

A few things immediately should be noted:

1. Ideal phenomena do not exist independently of matter. One can have mushrooms arranged in a circle, or chairs arranged in a circle, but there must be something arranged in a circle. (Now, I know that philosophers claim that there are circles existing as a part of our mind. And as ideal objects in Platonic sense. I am not talking about those right now. Actually, I will touch on the former soon. But, for now, I am just talking about physical phenomena as we think they exist objectively, by themselves, as a part of reality.)

2. Ideal phenomena are not the same thing as matter. As evidenced by the fact that I can arrange different pieces of matter in the same set of arrangement (e.g., I can arrange keys in a circle or mushrooms in a circle).

3. Ideal phenomena are not strictly nominalistic: they are not merely our own descriptions of the world out there. It is crucial to understand what exactly I mean:

• I do not mean that circular and triangular arrangement are really "out there", the way we perceive them. I don't know what's really "out there", and I do not think it is a meaningful way to talk about the reality at all. I cannot know what's "out there" except through the way I perceive it in my mind. (Although I could compare my views of what's out there with others, including, potentially, aliens who may see reality completely differently from us. But then I would just know one or more ways of perceiving the reality, not the reality "itself".)
• I do mean that there is something out there, independent of my mind, which I perceive in my mind as a "triangular arrangement" or "color of blue" or "a particular sequence of nucleotides of DNA". That something is distinct from my perception of it. And that something is distinct from the matter that I perceive it consists of.
  
  The proof that I have is that objects interact with each other independently of my mind, and can even use what we call information: DNA is the best example. Millions of cells in our body use the information of their DNA interactively and have done so before we came to exist. They used patterns of matter of their DNA molecules as a crucial aspect of their survival. They have evolved and continue to do so (micro, macro, whatever) using DNA.
  
  So, it's silly to say that properties of objects are only in our mind. Our perceptions of them are only in our mind. But whatever caused those perceptions is real, and it is really separate from whatever causes our perception of its matter.

So, what about our mind? What about ideal objects that the rabbi claims we perceive: the numbers, the imaginary colors, the geometrical objects? Well, in my opinion those are nominalistic. They are models of reality that exist in the patterns of our brain matter's arrangement and patterns of its behavior in space in time: what we can collectively call "mind".

To explain:

First, let us acknowledge again that information can exist outside of our consciousness. Computers store, use, and share information. So do living cells (including the non-neural ones).

Information is a representation of some ideal phenomena using another set of ideal phenomena. So, for instance, a specific kind of amino-acids that make up a protein is the protein's property, one ideal phenomenon that is associated with the protein's matter due to its matter's peculiar arrangement.

That property is represented in a sequence of nucleotides on a DNA (or RNA) molecule: a completely different set of matter arranged in a completely different way, but such that the arrangement can be used by the cell's machinery to build the protein. That specific arrangement of pieces of matter on a DNA molecule is information about the protein.

This example allows us to understand what mind is and how physical matter of the brain can "know" about the non-physical ideal phenomena of the world. It can do so by arranging itself in such a way as to represent those phenomena (the same way that nucleotides of the DNA are arranged to represent the sequence of amino-acids of a protein). That arrangement is itself an ideal phenomenon, an information.

That arrangement can be further used to do other things. Unlike DNA (to our knowledge), the brain is capable of making new information (new arrangements of matter) based on the patterns of old information which it used to represent the world's ideal phenomena. It does so to model the world and predict it.

That's what the brain does when it imagines a color that would be between two shades which it observed. It has three types of information stored in it:

a) color A: the representation of the ideal phenomenon that the brain perceived from the world outside

b) color B: ditto

c) color C: a modeled representation of what a color between A and B would look like if it were to exist

It is true that color C was never perceived from the "outside". But we should not say that it existed "somewhere" in some ideal realm. It was invented by the brain.

The same is true for numbers. Numbers are models that brains use to make sense of reality. To say that there are three apples on the table is not a statement about objective reality. It is a statement about our internal model of the objective reality. We perceived a bunch of matter out there and grouped it into separate apples. And we made sense of it by assigning the concept of "three" to the peculiar way in which we grouped the apples.

This is why children need to be taught math, even basic counting. Because it is not something that they perceive as a part of the world naturally, from birth. It is a way that they can model the world in their brains, and this particular way is useful for making all kinds of predictions about the world.

So, the "logical truths" and numbers and geometric objects all come from "within", not from without: neither from the physical world nor from some ideal, spiritual Platonic parallel universe. The reason we can share that information freely with each other (and why Mathematicians get paid salaries) is because our brains are similar enough that, with enough basic training, arranging and modelling our perceptions of the world into numbers or abstract geometric shapes comes easy to us. (Some of it. Some people have very difficult time understanding higher-level mathematical concepts. Which is why most people don't use algebra, calculus, differential equations, or multi-dimensional topology in their everyday lives. Only certain professionals do.) The fact that our brain is so flexible in its modeling of reality and imagining different concepts (some having nothing to do with reality) is probably to blame.

Also, although it is quite mysterious that mathematics is so useful for predicting the reality,
we must realize that:

1) mathematics really merely organizes our internal representations of the reality (i.e., 2+2 always equals 4, because our brains are consistent in how they use the concepts of "2", "4" and "+" and how they apply those to understanding of reality),

2) the specific form of mathematics we have chosen is one that predicts reality well. We may have chosen other systems.

A better question is: how come our mind can predict reality so well, using the systems of abstraction that it creates? But that's another issue. (Isaac Newton would say that the answer is that the world was created by a rational G-d who imparted some of that rationality onto us, creating us in His image. But some people today would say that the brains simply evolved to do so in their environment.)

This is not to say that souls don't exist. I believe that souls exist, but that they belong to a third class of phenomena (besides the matter and the ideal phenomena): the spiritual "objects" (again, it's just a working definition). And that is another story.

And this is not to say that our knowledge about the brain and the physical/ideal objects explains consciousness. I don't think it does (yet). And that (which is part 1 of the rabbi's series) is a valid critique of materialism. But that is also another story.