Wow, thanks.
You're welcome!
I respect your thoughts on these issues and admire your writing ability.
Let me try to work through this, because it may simply be a limitation of the way I think about this subject.
Concepts as far as we can tell are always the result of neuron activity. We speak about them as though they have a separate immaterial existence, but I think this is one of those instances where we are fooled by using a noun for number rather than a verb. When we think about anything we are doing something; when we think about numbers we should maybe conceive that as 'numbering' or some other verb.
This argument doesn't work for me. It seems that although the use of symbolic references is properly consider an action, the symbols themselves are generally considered objects, not actions. What is difficult with mathematics is that the symbols necessarily represent intangible rather than physical things, thus they don't appear to be composed of the same 'substance' as physical objects. I don't see that why this implies that such concepts should be considered actions, not objects unless you first assume monism as a premise.
If number was an immaterial concept I can see no way that it could possibly interact with the material world; this is one of the problems that Plato and Descartes encountered though it was later critics who pointed out the problem.
Don't dualists insist that their souls interact with their physical bodies? What evidence do you have that if dualism were true, no interaction would not be possible between concepts such as numbers and physical objects such as human beings?
It seems to me that numbers clearly interact with and affect our material world through the instantiation and manipulation of those concepts in human thought. I still don't understand why this doesn't qualify as interaction between the intangible concepts of numbers and the physical world.
The way that I envision the issue of the physical and mental in materialism and idealism is this:
Idealism -- fundamental substance is mind and its actions are the 'material world'
Materialism -- fundamental substance is matter and mind is created by matter's actions (our brains)
Yes, you have a point. If Idealism is true and matter is created via immaterial thoughts, then intangible concepts and the symbols representing them would be composed of the same 'substance' as matter. But I find this argument to be the idealist version of the above argument that concepts are formed of matter because all known instantiations of them can be so considered. While it's certainly a possibility, I don't consider the argument conclusive enough to establish monism as true.
If we think in terms of the radical absence of humans (which is impossible for us because when we think we inject ourselves into all situations), I think it is easier to imagine number not being a fundamental 'thing'. A bunch of rocks on the ground is just a bunch of rocks on the ground. It only becomes five rocks when someone is there to think of them in that way.
The relationships among those rocks and the basic relationships in the universe will continue in our radical absence; but that does not seem to create any more reality for these concepts.
So five rocks are five rocks whether anyone is there to observe them or not. We don't presume that physical objects such as rocks don't exist when noone is there to observe them, so why presume that numbers don't exist when noone is there to observe them? Again, it seems to me that this argument depends on how you define certain terms, such as 'exist', which in turn seems to depend on underlying assumptions about the world, such as monism.
The ratio of the circumference to diameter of a circle will always be the same whether we exist or not; but that does not mean that pi exists independent of us. Pi, as that ratio, exists because someone conceived of it as a ratio.
Whereas it seems to me that the ratio does exist independently of humans since any other being, human or not, that concieved of that ratio would observe the same value. (Actually, I am making an assumption that non-humans would arrive at the same value for that ratio even though the symbols they would use to represent it would be different. But that does seems a reasonable assumption to me.)
The way we establish whether something exists independently of ourselves is through the consistency of observations by different human beings. That is, if an object was observed to have the same properties regardless of who observed it, then it can be assumed that that object has an existance independent of those humans who examined it. When the descriptions differ significantly from one person to another, such as for gods and ghosts, we don't feel as confident because the disparate observations alter what conclusions can drawn from them.
In general, the more people that independently observe something and the more those observations agree regarding the properties of that thing, the greater the confidence we have that the object exists separately from ourselves. Using that same criteria, it's reasonable to conclude numbers, such as pi, have an existance independent of the humans who examine them.
