All the premises necessary to prove that 2+2=4 can be found in the definitions of 2, 4, + and =. Add in some definitions from set theory, and you get sizeof(X)=2 && sizeof(Y)=2 and disjoint(X,Y) |- sizeof(X u Y)=4. The trickier assumptions are in converting from operations on apples to operations on sets. This isomorphism is entailed by the counting algorithm; if there’s no person around to count them, then when we said “there are two apples” we were talking about a counterfactual in which something did run the counting algorithm. (Note that the abstract counting algorithm assumes a perfectly-reliable tagging of counted and not-counted-yet objects, and a perfectly reliable incrementing number; a count made by a human has neither of these things, so sometimes counted_as(25,000)+counted_as(25,000gp) = counted_as(50,001).)
This doesn’t seem directly relevant to the meditation. Are you saying that, yes, it is an assumption, because it’s an argument from definition? Because I guess that would be responsive, but the more interesting question is whether or not those definitions of 2, 4, +, and = can be known to correspond to the external world through more than just our assumptions.
All the premises necessary to prove that 2+2=4 can be found in the definitions of 2, 4, + and =. Add in some definitions from set theory, and you get sizeof(X)=2 && sizeof(Y)=2 and disjoint(X,Y) |- sizeof(X u Y)=4. The trickier assumptions are in converting from operations on apples to operations on sets. This isomorphism is entailed by the counting algorithm; if there’s no person around to count them, then when we said “there are two apples” we were talking about a counterfactual in which something did run the counting algorithm. (Note that the abstract counting algorithm assumes a perfectly-reliable tagging of counted and not-counted-yet objects, and a perfectly reliable incrementing number; a count made by a human has neither of these things, so sometimes counted_as(25,000)+counted_as(25,000gp) = counted_as(50,001).)
This doesn’t seem directly relevant to the meditation. Are you saying that, yes, it is an assumption, because it’s an argument from definition? Because I guess that would be responsive, but the more interesting question is whether or not those definitions of 2, 4, +, and = can be known to correspond to the external world through more than just our assumptions.