Notes and Homework from Methods of Logic, 1.3

The Conditional
Notes:

Given common language, the ascription of truth or falsity to a conditional statement in the event that its antecedent is false is, says Quine, "rather more arbitrary". Usually when people make conditional statements they mean to communicate a proposition concerning the consequent that holds only in the case that the antecedent holds. They don't mean to communicate anything about what is the case when the antecedent is not the case.

The most "convenient" decision, says Quine, is to regard all conditionals with false antecedents as true. This makes enough sense to me. This decision seems at least to be kindlier towards regular speaker intentions than regarding such conditionals as false.

The contrafactual conditional ought not to be construed in the fashion of the material conditional. This is because the speaker's intention in making such a conditional claim already assumes the falsehood of the antecedent, but still thinks that something is being communicated of interest by the compound. Such a conditional is not automatically verified by the falsehood of the antecedent.

The contrafactual conditional is not truth-functional. Some c-conditionals that have false antecedents and true consequents are true, while some c-conditionals that have false antecedents and false consequents are true. It is not the truth or falsity of the antecedents and consequents themselves that make the compounds true or false, hence such compounds are not truth-functional.

Interesting that Quine seems to doubt the viability of any coherent theory of contrafactual conditionals. I wonder whether Lewis has anything particular to offer here.

Material conditionals seem irrelevant, since the following statements come out true given its truth-conditions:
* If France is in Europe then the sea is salt.
* If France is in Australia then the sea is salt.
* If France is in Australia then the sea is sweet.

Quine notes, in a kindred spirit to my earlier comment, that it would not seem any less strange to attribute falsity to the statements. He says that rather "the strangeness is intrinsic to the statements themselves."

Homework:

Pretty happy about this. It asks me to translate 'p ↔ q' into terms purely of alternation and negation.

I came up with the following answer:
'-[-(-pVq)V-(pV-q)'

which, incidentally, I think can be translated to (-pVq)V(pV-q).

Anyway, I checked the back of the book, and they gave as an answer:
'-(pVq)V-(-pV-q)'

This deflated me. I felt lousy. I thought I had gotten it right. BUT THEN, just in case, I tested the two for logical equivalence, and found out by dint of tedious work that '-[-(-pVq)V-(pV-q)' is in fact logically equivalent to '-(pVq)V-(-pV-q)'. So, my answer was right after all...you can simply dock me points for lack of concision in my notation (which, I understand, is important. Nevertheless, I technically did what the question asked, and so am happy.