> It isn't. It's the same idea expressed with different words.
But one is "backwards" and one is not?
> is that there is a finite number of equivalence classes that the physical things can be unambiguously mapped to.
Unambigious is quite a claim.
Is 3.0 and 3 the same symbol on your view? Depending on context they might denote the same idea (the number three). Other times maybe 3 is an integer and 3.0 is a float and their types are important.
Sometimes my computer spits out 10 to mean the sixtenth natural number, sometimes the second natural number, sometimes the tenth natural number. Its all the same physical thing, however what other physical things its equivalent to depends on context.
No, it's not. The symbol systems used for math are deliberately engineered to make this true.
> Is 3.0 and 3 the same symbol on your view? Depending on context
Exactly. It depends on the context. Sometimes "A" and "a" ArE tHe SaMe SyMbOl, SoMeTiMeS tHeY aReN't. (Sometimes "Y" and "TH" are the same symbol! [1]) Likewise, sometimes "3.0" and "3" are the same symbol, sometimes they aren't. But within a given context, in order to qualify as math, the mapping has to be unambiguous.
But one is "backwards" and one is not?
> is that there is a finite number of equivalence classes that the physical things can be unambiguously mapped to.
Unambigious is quite a claim.
Is 3.0 and 3 the same symbol on your view? Depending on context they might denote the same idea (the number three). Other times maybe 3 is an integer and 3.0 is a float and their types are important.
Sometimes my computer spits out 10 to mean the sixtenth natural number, sometimes the second natural number, sometimes the tenth natural number. Its all the same physical thing, however what other physical things its equivalent to depends on context.