Sunday, October 10, 2010

Revisiting that pesky material implication

Consider this:




(1) If I roll an even number, it will land 6.





Presuming an unbiased conventional die, it seems appropriate to attribute my degree of confidence as 1/3, since there are only 3 instances of even number and only 1 of those 3 is a 6.



But now consider (1) as a material conditional. There are now only 2 ways which (1) can be false (from the die landing on 2 or 4). Thus, we say the degree of confidence in its truth is 4/6, which yields 2/3.



1/3 vs. 2/3



Two different degrees of confidence for a single statement. Is this a problem for the material implication?

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