Recently, I've been realizing more and more the importance of differentiating between objects and our linguistic labels for them. In fact, there are many words that we use for things that have no corresponding physical reality.
The number 2, for instance. You can't point to it. You can't touch it. You can't see it. 2 is a word we use to describe a particular grouping, real or imagined, of other objects.
Infinity, also. You can't point to it, touch it, more memorize it. It's defined as something that doesn't end. But because of our inherently limited nature, we can't measure or see anything without end.
Random. Many things we think of as random are not in fact random, but determined by variables we don't know. Randomness, then, would be better understood as "Something I can't put into a pattern."
Imaginary numbers. Not really any more imaginary than real numbers. Again, just a label we use to stick in our formulas. There are no "square roots" in reality, much less any "negative numbers." These are linguistic labels we use to manipulate algebraic formulae.
An idea. We have ideas all the time, and speak of them as though they are real. But you can't touch or feel an idea.
Dimensions. You can't touch or see dimensions. They are just labels we use to describe the universe in which we live. And the big X,Y, and Z are not the only, nor even the best means of describing reality. Non-Euclidean geometries can also describe the universe equally effectively, if not more effectively. Dimensions are just language, not reality.
Seems like the most viscious philosophical arguments are usually over the definitions of these words without any physical correspondending reality.
And what's REALLY weird are the folks (like Pythagoras, Plato, Anselm, and Descartes) who treat these labels as though they are real -- or even, more real than reality. Pythagoros went as far as to worship numbers. Plato thought the form of "greenness" was more real than anything green on the Earth. Anselm thought that because God was defined as the being than which no greater can be conceived, that he must, therefore, exist in reality. And Descartes had his own ontological argument.
All these people made the same fundamental mistake -- treating a label as though it were real -- and in some cases, more real than reality itself.
The ambiguity between label and reality caused a lot of unnecessary struggles more me, particularly in the area of math. As I got higher in math, it seemed more and more like the teachers and books were treating things like probability and integrals like they were something real -- and I was trying to conceptualize them that way. But they're not. Probability is just a label we put on our degrees of ignorance. If we knew all the variables that went into determining the outcome, there wouldn't be any probability. The same problem with calculus. You can't point to or touch an "integral." It's a mathematical game we play to bridge ourselves from physical reality to physical reality quickly and conveniently.
My math and stats teachers, I think, didn't get that. They insisted on treating math as though it were something real -- as though it had some corresponding REALITY to it -- which, of course, it does not. They were just making the same mistake Pythagorus did.
It also caused me to struggle with philosophical discussions about "essence." Philosophers spoke (and speak) of "essence" as though it has some reality it it. But "essence" is really just a definition we put on what we see.
I come to realize that all this means is that I'm thoroughly nominalist and existentialist in my philosophy without knowing it. But now by knowing it, I'm much better able to understand what they meant with all that "essence" stuff.
I wonder what it is about people that makes some of them want to treat labels like reality.