Trying to reinvent all of ontology, semiotics, mathematics from scratch is an honorable endeavor. It's however also rather foolish.
It's like you're reinventing the wheel and haven't even gotten to the point where you realize that it, maybe, shouldn't be square.
It is a symbol for a specific value withing a predefined value system.
It refers to one value.
...which is, for what feels like the 200th time, in contradiction to the claim that it doesn't refer to
anything. The two claims can both be false, or both undefined, but they cannot possibly both be right.
It does not refer to anything else.
It does not refer to 6/2. This is two values and an operation.
It may not
refer to 6/2 (though it does), but the value it refers to can still be the same as the value "6/2" refers to, or produces if you prefer. You could be right about this, and your conclusion still wouldn't follow.
In context means within a predefined value system.
So 3 has one value in some system. And 0.3 has a different value because it is within a different context.
The other symbols are your context.
3 has no other symbols to consider.
The string "3.0" can refer to an integer 3
The value scheme known as the "integers" is a specifically defined scheme.
3 has one place in that scheme. Adding any amount of zero's after the decimal does not change the value within that predefined scheme.
...it can be shorthand for 3.0+/-0.05 when talking imprecise measurements....
That is not a value. It is an infinite amount of values.
It may not be a value for whatever definition of
value you have in mind, but it
is a potential meaning and indeed frequent meaning of the string "3.0" so whatever else this may or may not show, it shows that you're wrong to claim that "it doesn't refer to anything else".
And it is not saying the value of 3.0 in the scheme is 3+/- 0.05.
It is saying a measurement of 3.0 in the scheme is assigned the value of 3.0 +/- 0.05.
You just said that 3.0 +/- 0.05 is not a value. Now it is? I guess you were using two different definitions of
value then and now?
The pattern is merely what the mind recognizes.
That may be so, but it doesn't make the pixels go away.
Utterly meaningless point.
You are not experiencing pixels. You are experiencing what your brain creates from the illuminated pixels.
You can't experience a pixel. Your mind has no pixels.
If that is so, it doesn't matter. They're their whether or not I "experience" them, for whatever definition of "experience", and for whatever reason you thought it worthwhile to bring this up in the first place.
But you can experience and recognize a pattern. To a mind "3" is only a recognizable pattern.
So, substituting your definition, we get: Once assigned within a system the one to one correspondence is nothing else. That's not a meaningful statement.
How is something full of meaning meaningless?
Within some scheme "3" corresponds to a specific value.
It does not refer to any other value within that scheme.
And it is not referring to any other scheme of values. It exists withing one. Period.
Saying 1/3 is shorthand for 1 divided by 3 makes no sense to you?
Sure it does. It doesn't however make it so that the operation rather than the value it produces is the only thing it refers to and it certainly doesn't make it so that that value must and not shared by other representations, or as the result of other operations.
Performing an operation on two values gives you a different value.
The different value is derived by the operation.
Being derived is very different from "referring to".
Hey, maybe we should try a different approach. Let's replace all references to "3" with references to "dog", and all references to "abstract value" or "number" with "animal". It's a simple sanity check for the things you claim about labels and their referents. If your claims don't make sense for the one were we can directly assess them, your theory of ontology and/or semiotics must be broken. We can tell that much even without pinpointing where it is broken.
So I understand you're claiming 3 refers to a specific abstract value and nothing else within a scheme, 1 is a different abstract value in that scheme, and operation involving those two values doesn't refer at all, and its product is necessarily something distinct from the value of any other pattern within the scheme, and an operation using values x and y is distinct from an operation using values z and w (therefore, 1/3 and 5/15 are distinct entities). Is that a fair paraphrase? If not, where did I go wrong?
So let's translate this: "dog" refers to an animal species and nothing else within the scheme of the English language, "comodo dragon" refers to a different species, and "buffalo" and "rattlesnake" are yet other species. Each operation involving any two of these species is a separate entity, neither identical to any other like operation, nor co-referent with any other symbol within the scheme. Take for example, the operation: "determine the latest common ancestor of X and Y, and project its living descendants". It follows that "the extant descendants of the latest common ancestor of buffalo and comodo dragons" and "the extant descendants of the latest common ancestor of dogs and rattlesnakes" have to express two different sets, neither of which can be co-referent with the term "amniotes".
Since this is obvious nonsense, there must be a bug
somewhere in your logic. If you won't take my hints as to where to find it, go ahead and waste your time finding it yourself.