Скачать или смотреть What is COMMUTATIVITY? (plus a problem for Boolean AND)

To say that an operator is commutative is to say that order doesn't matter. But even such deceptively simple commutative operators like "AND" can behave in surprising ways that seem to undermine their commutativity.

Here is the issue: compare the following two statements:

"The king has died of a heart attack, AND a republic has been declared"
"A republic has been declared, AND the king has died of a heart attack"

The second of these appears to say that the declaration caused the heart attack. So perhaps "AND" is not commutative after all—something very inconvenient for our thinking about "AND".

What to do? Grice the problem away! The apparent non-commutativity of "AND" is cancellable. That is, we can say:

"A republic has been declared, AND the king has died of a heart attack—but I don't mean to say that the declaration caused the heart attack!"

Since this statement is not self-contradictory, it is clear that the non-commutative meaning we attributed to the second statement was not part of its literal meaning, but instead a conversational implicature.

(For more on conversational implicature, see the video about Grice:    • What is conversational IMPLICATURE? ⟨09,03⟩  )

0:00 What is commutativity?
0:30 A natural-language problem
1:05 Cancellation to the rescue

The death of the king example, and the Gricean solution, are discussed in L. Jonathan Cohen, "Some Remarks on Grice's Views about the Logical Particles of Natural Language", Pragmatics of Natural Languages, ed. Yehoshua Bar-Hillel (Dordrecht: Reidel, 1971), 50–68.

This video is brought to you by the FWO, as a part of a project on indirect proof and assertion. You can see a brief overview of the project here: https://research.kuleuven.be/portal/e...

For information about the FWO, see: https://www.fwo.be/en/
For information about the FWO's junior postdoc (the one that I hold), see: https://www.fwo.be/en/support-program...

Special thanks to the folks at Café Carlisse in Leuven, for letting me film in their bar!