Soul

[Neo-Scholastic]

The problem is that you assume that concepts which are innately tied to material objects can exist separately of material objects. ...The immaterial number is nothing more than a helpful representation.

Not exactly. What he is saying, and correct me Tex if I'm wrong, is this. Numbers are formal features of reality that have fixed meanings in a way that no set of physical objects can.

A heifer and her calf walk by a farmer and his son. The son says to his father, "I guess that means Bessie gave birth." The farmer in response says, "I think it means you left the gate open."

Here we have an physical system being interpreted with two meanings. In actually, the sight of a heifer and her calf can have innumerable meanings assigned to it, one of which could be the value of 2. Physical systems have no definite meaning. In contrast to this, the number 2, as an immaterial object of thought, has a very definite meaning independent of any physical system that it could describe as conforming to its value.

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How does this purported soul power itself? How does this soul physically move the ions to make the impulses of thought in the brain. We know how much energy it takes to fire a neuron so where does the soul get this energy?

...and where exactly does a mass of neurons get its qualitative content? How does the expenditure of energy produces the feeling of pain or the memory of your grandmother?

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Furthermore, unlike anything, ever, which is actually immaterial, quantities are not open to interpretation. The integer 3 is always the integer 3. You cannot interpret the integer 3 as being the integer 2 unless you modify the integer 3 in some way that it is no longer the integer 3, such as subtracting the integer 1 from it. This is an artifact of the innately material nature of numbers.

Actually, you are proving Tex's point. Because integers are not open to interpretation, i.e. they have fixed formal properties, they do not depend on any particular set of physical facts. Therefore they exist independently of the things they describe.