I don’t see how “For all X, X is contained by a Y” and “For all Y, Y is contained by an X” can both be true [implicitly assuming that X is not the same as Y, I am guessing].
And what do you mean here by “true”, in an instrumental sense? Do you mean the mathematical truth (i.e. a well-formed finite string, given some set of rules), or the measurable truth (i.e. a model giving accurate predictions)? If it’s the latter, how would you test for it?
Just to be clear, are you suggesting that on your account I have no grounds for treating “All red boxes are contained by blue boxes AND all blue boxes are contained by red boxes” differently from “All red boxes are contained by blue boxes AND some blue boxes are contained by red boxes” in the way I discussed?
If you are suggesting that, then I don’t quite know how to proceed. Suggestions welcomed.
If you are not suggesting that, then perhaps it would help to clarify what grounds I have for treating those statements differently, which might more generally clarify how to address logical contradiction in an instrumentalist framework
And what do you mean here by “true”, in an instrumental sense? Do you mean the mathematical truth (i.e. a well-formed finite string, given some set of rules), or the measurable truth (i.e. a model giving accurate predictions)? If it’s the latter, how would you test for it?
Beats me.
Just to be clear, are you suggesting that on your account I have no grounds for treating “All red boxes are contained by blue boxes AND all blue boxes are contained by red boxes” differently from “All red boxes are contained by blue boxes AND some blue boxes are contained by red boxes” in the way I discussed?
If you are suggesting that, then I don’t quite know how to proceed. Suggestions welcomed.
If you are not suggesting that, then perhaps it would help to clarify what grounds I have for treating those statements differently, which might more generally clarify how to address logical contradiction in an instrumentalist framework