Furthermore: What can mathematics inform you of if I tell you that I either am or am not thinking of a number that may or may not be imaginary, negative, irrational, rational, positive, complex, whole, or real. Please illustrate.
I don’t think mathematics claims that it can answer that question. It is more focused on answering questions like “what does 1 + 2 = 3 mean, and why do we think it is true?”
but folks here at LW seem to disagree when I assert that mathematics lacks empirical content.
That’s a curious notion. I’m about ready to believe just about anything of the LW commenter community nowadays, though. I’ve been thoroughly disabused of several notions regarding this site’s populace over the last two monhs. <_<
That being said; it might help if I explain how I parse “real” from “exists”. To my definitions, “real” covers anything which is a proscriptive restriction on the behaviors of that which exists. “Exists” is anything that directly interacts with something else (or conceivably could / did). I categorize “numbers” in the same ‘area’ as I do ‘the laws of logic’—they are real, but do not exist. Mostly these things can be treated as “definitionally true”; we define 2 as “1+1” and we define “1″ as “a single thing”.
(Side note: this neatly resolves the Transcendental Argument for God, by the way. “Resolves” in the sense I am an atheist.)
I don’t think mathematics claims that it can answer that question. It is more focused on answering questions like “what does 1 + 2 = 3 mean, and why do we think it is true?”
Then you agree with my position over that of wedrifid’s.
But I think “1 + 2 = 3” is true outside our lightcone.
And what information does this allow us to derive about what is outside of our lightcone?
Remember: “1 + 2 = 3” is definitionally true. It would remain true even if the universe did not exist; it is a non-contingent / non-local truth.
Fair enough. I should have reference the Pythagorean theorem.
I don’t disagree with this statement, but folks here at LW seem to disagree when I assert that mathematics lacks empirical content.
That’s a curious notion. I’m about ready to believe just about anything of the LW commenter community nowadays, though. I’ve been thoroughly disabused of several notions regarding this site’s populace over the last two monhs. <_<
That being said; it might help if I explain how I parse “real” from “exists”. To my definitions, “real” covers anything which is a proscriptive restriction on the behaviors of that which exists. “Exists” is anything that directly interacts with something else (or conceivably could / did). I categorize “numbers” in the same ‘area’ as I do ‘the laws of logic’—they are real, but do not exist. Mostly these things can be treated as “definitionally true”; we define 2 as “1+1” and we define “1″ as “a single thing”.
(Side note: this neatly resolves the Transcendental Argument for God, by the way. “Resolves” in the sense I am an atheist.)