(September 14, 2018 at 9:36 am)RoadRunner79 Wrote:(September 14, 2018 at 9:27 am)polymath257 Wrote: Ahh...but my examples are NOT just different languages. They are different fundamentally and are *all* definitions of the *number* 4 in different contexts.
I am hung up on language because mathematics *is* a language. And the number 4 is word in that language. It doesn't have an independent existence: it is a language construct. And, in math, different aspects of the language have wildly different *definitions* of the *number* 4.
Using a language construct doesn't mean that what you are describing is subjective in it's nature. We use language to convey things. Perhaps sometimes that language is not a precise as we would like, or a word can have multiple meanings which we have to discern. I'm not talking about the language (and I don't think the others are either).
Again, what we are describing is what is objective. But we are describing the trees, not the number 4. In fact, at no point did you actually describe the number 4. And there is a good reason for that. The reason is that 4 is a language construct, not something external (and objective).