>> Your calculator does have a representation of arithmetic too. It's those bits is
moves around in registers, which are very much isomorphic to the relevant
arithmetic.
Hm. Strictly speaking I believe my pocket calculator has an FPGA, a
general-purpose architecture that in my calculator happens to be programmed for
arithmetic, specifically. So I think it's accurate for me to say that, although
the calculator has a program and that program certainly is a representation of
arithmetic, I have to provide the interpretation of the program and reify the
representation as arithmetic.
In other words, the program is a representation of arithmetic to me, not to the calculator. The calculator might as well be programmed to randomly beep, and it wouldn't have any way to know the difference.
(But that'd be a cruel thing to do to the poor calculator).
Hm. Strictly speaking I believe my pocket calculator has an FPGA, a general-purpose architecture that in my calculator happens to be programmed for arithmetic, specifically. So I think it's accurate for me to say that, although the calculator has a program and that program certainly is a representation of arithmetic, I have to provide the interpretation of the program and reify the representation as arithmetic.
In other words, the program is a representation of arithmetic to me, not to the calculator. The calculator might as well be programmed to randomly beep, and it wouldn't have any way to know the difference.
(But that'd be a cruel thing to do to the poor calculator).