3 ms·
How do you go about testing the hypothesis that 1 + 1 = 2? Not just showing that a particular physical representation obeys the logical laws of arithmetic, but
by icen 10y ago
How do you go about testing the hypothesis that 1 + 1 = 2? Not just showing that a particular physical representation obeys the logical laws of arithmetic, but to test the actual laws themselves.
- jamesrcole 10y agoThe point is that it's not a hypothesis. Or, at least there are views about maths where it's not a hypothesis.
- icen 10y agoSo it's something that's not a scientific hypothesis, but is considered knowledge! (Or, if as in the other comment chain, 1+1=2 is too obvious, you can take any sufficiently non-trivial theorem of your choosing).
- jamesrcole 10y agoUnder the view I'm describing any statement like that is a kind of definition, not something that is true or false. You can investigate whether it is consistent with other definitions. I believe that doing so is empirical work, which I think is consistent with a broad notion of science
- acover 10y agoI could be wrong but if you wanted to test the hypothesis: given the rules of addition show that 1 + 1 = 2 can be deduced. The experiment would be to go about the deduction. It is falsifiable.
- kijin 10y agoWhen we talk about falsification in modern science, we usually mean falsification through empirical experiment. It must involve data from the real world. If you include thought experiments based on nothing but arbitrary axioms, a lot of crazy claims about supernatural beings and other metaphysical curiosities would also qualify as falsifiable. I'm not sure whether you'd like to go down that rabbit hole. Science is about understanding the actual physical world that we live in -- not some fantasy world no matter how internally consistent it might be.