First of all, when I addressed numbers and math as being a universal absolute earlier in this thread, I pointed out that as such it is the same and works the same despite cultures, despite location and despite time. Ancient civilizations created the exact same math independent of one another. Language, on the other hand, is not a universal absolute. Different cultures have different languages, and a language has limitations and errors, and a language changes over time.
I don’t know what a “universal absolute” is. I am thinking of the speed of light,
c, that is, so far as we know, a constant across all space/time, although there is some evidence from research in past years that even that may “wiggle” by a small amount.
But we say that is universal because a million different measurements now align with *c *being isotropic, everywhere, under all conditions. It’s an empirical conclusion that supports “universal” as scope.
Numbers, though, are something different. I understand it’s hard to use the mind to separate the mind from the non-mind, but this is the glory of the human meta-representational brain, to be able to “stand above” and idea and consider it provisionally. If you do that with numbers, it turns out that “humans” or “minds” (perhaps chimps think in terms of numbers, too, for example) are the limits of our scope. Numbers are not extended in space/time, they do not have physical effects or dynamics. If we eliminate all minds from the universe, we would expect numbers to be a perfect nothing, not even a false concept, because there are no concepts at that point.
So, I think your ‘universal absolute’ is quite small, and limited to the “universe” of minds. Numbers certainly are real features of natural minds, but beyond that, they are an utter nothing in the universe. To say that
pi is a number is to confuse, map and territory, to say that the
representation of the physical property is physical property.
Yes, there is a subjective quality to math because language factors into our understanding of it. We fashion different words to represent the numbers and mathematical processes, but that is as far as it goes. Other than this, math works the same way for everyone. Therefore, it is a very big leap to consider that and then simply conclude that because one tiny aspect of our understanding of math is subjective, then the rest of it must be subjective as well.
I don’t need any of the subjectivity of language to make my point. If humans could communicate “telepathically”, somehow, without explicit languaguage, just exchanging infra-linguistic concepts between one another, all this would work out the same way. It is the
concept which is ephemeral, natural, transitory, mental. It is the cognitive construct that places subjects and objects in relation to each other – and this process subsumes the whole of math – that “subjectifies” math, along with all other concepts. Those concepts may be very good models for objective reality, but they are, finally, concepts and models, parts of the map, not the territory.
Language is not the basis for the subjectivity of math. The underlying concepts are the basis.
Secondly, your use of the term “extramental reality which just is what it is” is simply another way of saying that there is an objective reality. The question at hand is whether or not quantity is a characteristic of objective reality or a characteristic solely of subjective perception. To address that I will cut & paste what I posted to AT previously:
Let’s take a moment to consider particles. Despite our concepts of boundaries and unity (i.e., is the machine in my garage “one car” or “large assortment of automotive parts”?), if we break down the universe into the simplest of components, there would still be a finite amount of particles. After all, does science say that anything within creation is infinite? No.
That’s not clear. Time, for example, is considered to be infinite in the forward direction. Our universe, according to our best performing models, will expand forever, for an infinite amount of time. But no matter, that – these are still map features we are talking about. The territory admits of no such feature. It is what it is, and “finite” is a mental construct we apply.
Did the Big Bang start with an infinite amount of material? No.
Unknown. The physics model makes for a singularity – mathematically – in which energy/mass become infinite, because energy and mass are dynamically related to space/time which is posited to have been infinitely small. But that’s a good example of the value of distinguishing map and territory. That may be something we can accurately model mathematically, but most physicists I read regard that as a boundary problem, where the size isn’t actually zero and the energy isn’t infinite. But this remains an unknown.
-TS