Wednesday, April 3, 2024

If 4 weren’t even, would it be a prime number?

This counterfactual conditional, you may think, is a little hard to evaluate. The counterfactual, you might say, is underdefined by its very nature. You might even go so far as to say that 4’s not being even, being a contradiction, could authorize any conclusion. It might be a teacup.

Yet, it is surely, in general, good practice in evaluating a counterfactual conditional to consider the closest cases to reality. “If not for the long freight at the railroad crossing, I would have gotten to work on time.” We may well think this is likely true because, in possible worlds closest in content to this one, I would have gotten to work on time in that I had plenty of time when I got to the crossing and nothing else seems to have been in the offing that would have delayed me.

The closest ways that 4 might fail to be even are that it be 3 or 5; certainly not 9 or a teacup. So, it is true that if 4 were not even it would be prime.

This, of course, is nonsense. Your initial instinct was right that there is no evaluating a counterfactual beginning:  “If 4 were not even . . .” 

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