Keith’s Conundrums: Semantics and Epistemology of “if”.

Keith Douglas

Recap:
Last month I used Bunge’s analysis of the 11 aspects of rationality to look inside and outside at current AI discussions and found them wanting. Nobody has as yet responded, so I move on.

New stuff:
This month we are going to do some semantics and epistemology of “if”. This word has a traditional analysis in elementary logic as the so-called material conditional. It is said that this is false when the consequent C is false and the antecedent A true in “if A then C” and all other circumstances is true. If you are new to this sort of area of investigation, this might seem a bit strange. If you are old hat at it, you will have seen this but may also find it strange as you will have hopefully reflected on what you know here. Only those of you who have seen it and not reflected much on it may not find it unusual. However, this month’s column is to shake your complacency regardless. In later months we will do other connectives. (Even “and” is problematic.)

Consider the following sentences, broadly construed, and in particular their truth conditions. State what it would take to determine which are true, which are false, which are something else (supposing there is a something else), etc.

1. If I go to the library, I will meet a friend.
2. If I take an aspirin, I will cure my headache.
3. If I dip an aspirin in prussic acid and then take it, I will cure my headache.
4. If a prime number greater than 2 is even, it will be divisible by 2.
5. If the sky were blue, Aristotle would have been a philosopher.
6. If the sky were green, Aristotle would have been a photographer.
7. If wishes were horses, beggars would ride.
8. If I drop this bowling ball above a lane on earth it will dent the surface of the lane.
9. If I drop this bowling ball above a lane on the Moon it will dent the surface of the lane.
10. If if I will go to the store then I will meet a friend then I will meet a friend.
11. I will go if and only if Don goes.
12. If the sky is green, Aristotle was a philosopher.
13. If the sky is blue, Aristotle was a chemist.
14. If the sky is green, Aristotle was a chemist.
15. If a man has 0 hairs on his head, then he is bald. If a man has 1 hair on his head he is bald.
    (Repeat the apparent pattern until something funny happens.)
16. If you want to have ice cream, eat your sandwich.
17. You may eat ice cream only if you eat your sandwich.
18. If I invent a time machine in the future then I would already know it.
19. If 2+2=4, then 3+3=6
20. If 2+2=5, then 4+1=0
21. If colourless green ideas sleep furiously, then 1+1=2
22. If 1+1=2, then colourless green ideas sleep furiously.
23. If 1+1 were 3, then 2+2 would be 6.
24. If it is true that there is a sea battle tomorrow, then the future is not contingent.
25. “If I did it” – title of a book by OJ Simpson to analyze.
26. If you wish to stay within the law, act carefully.
27. If god commands you to do X, then you must do X!
28. If the Ramsey test for conditionals were correct, then this statement would be true.
29. If the Ramsey test for conditionals is correct, then this statement would be true.
30. If the probability of A given B is X, then the probability of the conditional “if A then B is 1-X”.
31. If Gene Roddenberry did not create Star Trek then who did?