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

Keith Douglas

Previously I asked about “if.” Alex B. and Steve W. graciously contributed some analysis and discussion. Thank you! However, one thing I noticed from both answers is how hard it was for both of them to justify their decisions; sometimes we got appeal to standard views, for example. This is not very surprising. The justification of the truth conditions of anything are hard, and arguably the various versions of “if” are challenging indeed. I likely started with the hardest case.

Considering “Or”

For your last Conundrums of the year, the exercise is the same as last time, but we will focus on “or.” Thus: 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. Terry is old or young.
2. Berries are sweet or sour.
3. You may have sour berries or sweet berries.
4. You may have ice cream or pie for dessert.
5. You may have ice cream or you may have pie for dessert.
6. It will rain or it won’t.
7. There is a sequence of the digits 7777777777777777777777777 somewhere in the expansion of π or there isn’t.
8. All the zeroes of the Riemann zeta function are at the negative even integers and all complex numbers with real part = 1/2 or they are not.
9. The continuum hypothesis is true or false.
10. “Aristotle was a philosopher” is true or false.
11. Aristotle is a philosopher or Aristotle is a photographer.
12. God exists or god does not exist.
13. Either Superman or Sherlock Holmes solved the crime.
14. My sister is older than me or my sister is younger than me.
15. Russell fut un philosophe célèbre ou Heidegger fut un Nazi.
16. You must P, for all P your commanding officer tells you, or go to military prison.
17. All natural numbers are either prime or composite.
18. The electron in a double slit experiment either goes through slit A or it goes through slit B.
19. Not A and not B, therefore not A or B. 
20. Not A or not B, therefore not A and B.