Keith’s Conundrums: And Now?

Keith Douglas

Last time we talked about “or.” Thanks to Alex for reading. To steelman what he has said, perhaps he is suggesting we adopt a five-valued logic for some purposes. There are suggestions in the literature that get a lot of attention for a four-valued one, so what’s one more? This is a serious joke. There are many parameters that are implicit in classical logic that people have claimed are worthy of change for various reasons. Ordinary language semantics is one of them. Interestingly, use of similar formal tools in electrical and computer engineering does lead to a logic that includes values called “don’t care,” very similar to Alex’s “Who cares anyway?”

And Now?

This time we’ll do an investigation of “and,” to continue on our semantics and epistemology of ordinary language. As usual, the goal is to prepare critical discussion of the so-called large language models that are all over the news. The task is to discuss the meaning of “and” in each of the supplied statements. Note: I have greatly simplified this discussion. It seems to me that it is much easier to understand that “or” and “if” come in many varieties in ordinary language, but the problems with “and” are harder to get good examples of.

1. Mary is a good scholar and Ahmed is a good footballer.
2. Ahmed is a good scholar and footballer.
3. Mary and Ahmed and Caroline and Jason and Fung and Barry and Laura are going out.
4. And that’s the end of that chapter!
5. It is possible to make no mistakes and still lose.
6. Can you lift the barbell and whistle?
7. I get out of bed every morning and shower.
8. Lottery ticket 1 won’t win and lottery ticket 2 won’t win and … and lottery ticket n won’t win. 
9. You may have cake and pie.
10. You may have pie and a coffee.
11. It is raining and snowing.
12. It is raining and not raining.
13. The universe is infinite in past time and finite in past time.
14. Spock and Data solved the scientific mystery.
15. You must P for all P your commanding officer tells you, and promptly.
16. Not A or not B, therefore not A and B.
17. Not A and not B, therefore not A or B.
18. Richard Dean And Erson was the star of MacGyver. 
19. Betty and Lisa are going out.
20. Aristotle in the Rhetoric and Euclid in the Elements praise good use of language.
21. All’s fair in love and war.
22. Whales are mammals and whales are mammals.
23. John will succeed if and only if Ahmed helps him.
24. John will succeed and Lisa will help John instead.
25. Lisa will help John but he will succeed.
26. John and Lisa will succeed.
27. John will succeed and Lisa will succeed.

Looking Forward

During our gap in publication we’ve also lost a friend and CFIC community member — Kevin Brown. I will (I hope!) write a formal “in memory of” Conundrum next time. It proved too challenging to figure out exactly how to write the one I had in mind for this month. To tease, I intend to ask a question about methods in history.