Juggernaut,

Here is a reply to your post of Jul 2. Forgive the long time it took me. I felt like we were talking past each other and couldn't figure out a way to connect our intellectual universes. But I want to try again.

In math only one, as a number has meaning, and there is only one 'number' necessary in concept.

What is the intellectual content of this statement? What do you mean by one "having meaning"? How do you define that?

Meaning, as I understand it, is built up from a web of defining associations and distinctions. For instance, one has meaning as a concept because (for example) I can tell you when you have put one quarter in front of me, and when you have not. Because I can use the concept to analyze and structure my world, the concept has meaning. But the same is true of two, three, sqrt(2), pi, and 0.9[bar]. It's just that the analysis and structuring I can perform with them is a bit more complex.

I agree with you that in some sense, we construct all of our numbers from one. Or at least that's one approach you can take -- traditionally you use a set-theoretic construction and start with the empty set (which is "one" object). But I don't understand how you can define "meaning" in such a way that only the number one has meaning, unless you have something radically unusual in mind when you say "meaning".

Since all other numbers get their meaning based upon one, they are signs, and one is the concept.

Again, explain this statement. How does numbers "getting their meaning based upon one" make numbers "signs", while only "one" is a true concept? What do you mean by sign and concept that you make statements like this? They have no concrete meaning to me whatsoever, and seem like just so much hot air.

In one of these dictionaries around here Idea was in part defined as: one thing. If this is so then the conceptual duck is a single duck having the qualities of all ducks.

Again, what does this mean concretely? Suppose I were to take this statement as written. Then I could go to a pond, point out a duck, and tell my friend "since this duck is a duck, it has the qualities of all ducks, hence it is a 'conceptual' duck!"

How can my friend understand this? Is he to just stand and nod solemnly in agreement? What is the intellectual meat of this sentence?

Now, there are many phenomena that seem to have meaning even though as infinites they cannot be concieved of. We all sort of give a subjective value to existence, or the cosmos, or to God; but we cannot measure the meaning against the reality...With finite reality we stand on firmer ground, and I think it is for that reason, in part, that people sometimes thought the concept preceeded the reality. It is because every concept represents a measure of perfection that reality does not.

Again, does this have a concrete meaning? Do the nouns and verbs refer to anything specific at all?

Every conceptual one is equal, and no real one is equal.

Okay, at this point I'll leave off asking you to get specific and try to guess your meaning. Although the request still stands.

If only 'conceptual' ones are equal, then why not interpret math as referring to only conceptual ones?

In saying 3-2 approximates 1, it is because only in math does one equal one.

So are you saying 3-2 = 1 but only "in math", or are you saying 3-2 only approximates 1 even in math? And what would it mean to work with 3-2 and 1 "outside of math"? They are mathematical concepts, there is no way to speak about them outside math. For example, what does it mean for numbers to approximate each other outside of math?

It is not something that can be demonstrated.

Demonstrated where, to what standards, how, why? What do you mean by demonstrate?

Rather you need the insight to realize how futile is math at giving an exact picture of reality.

I never said math can give an exact picture of reality. Math is an exact analysis of a system of abstract ideas which approximate or resemble certain parts of reality.

If you must think of math in a real-world context, don't think of it as giving approximate answers to real-world questions. Instead, it is giving exact answers to abstract questions, questions which approximate or resemble certain real-world questions in useful ways. For example:

Math question:

Q: What is 3-2?

A: 1.

Approximate real-world question:

Q: If I have three oranges and John steals two oranges from me, how many do I have left?

A: One orange.

If you derive the answer to the real-world question by doing math rather than looking in your current orange stock, you risk missing out on key facts. For example, maybe John felt some remorse and brought the oranges back, so you really still have three oranges. Or (as was discussed in the 1+1=24 thread) one could mess up the conversion of the real-world data to/from math, and get a nonsense answer that way.

These errors come about not because math is inexact, but because the conceptual resemblance between math and the real world is incomplete or incorrectly conceived by the math user.To summarize, the process of applying math to the real world can be modeled as a flow-chart:

real-world question --(approximately model as)--> math question --(solve exactly)--> math answer --(approximately model as)--> real-world answer.

This is why it makes no sense to say that 3-2 "approximately" equals 1. The approximation steps occur outside the domain of math, purely in the domain of modeling. There is no such thing as 1 or 3-2 "in the real world". They are purely mathematical objects. 1 orange is a real object, but 1 and 1 orange are not the same. 1 is an abstract mathematical object, 1 orange is a real physical sensible orange. The moment you add a quantitative modifier to a real-world noun, you have engaged in the process of approximate mathematical modeling and have thus left the strict domain of exact, pure mathematics.