Meeting Date Change

Hi Folks,

I'm out of town and won't be back till next week. Let's meet the following Tuesday, June 20, @ 8pm in the philosophy department conference room.

--ID

The Paradox of Indicative Conditionals?

Let's review the reading for last time (Jackson, 1-16).

Jackson presents four principles that, he claims, can't be true together. (Jackson, 4ff.)

(P1) Truth-Functionality Principle: The standard truth-functional account of conjunction, disjunction and negation best analyzes English conjunction, disjunction and negation.

(P2) Uncontested Principle: Any conditional with a true antecedent and a false consequent is false.
This principle bifurcates. First, the falsity of a material conditional is sufficient to guarantee the falsity of the corresponding indicative conditional.

(A) If (P É Q) is false, then (P → Q) is false too.

Second, the truth of an indicative conditional is a necessary condition of the truth of the corresponding material conditional.

(B) If (P É Q) is true, then (P → Q) is true too.

(P3) Passage Principle: From (P or Q), infer, validly (~P → Q). (We'll focus on the disjunction only, but there is a conjunctive form of the passage principle as well.) In English: From, "Either the butler or the maid stole the vase," we can infer, "If it wasn't the butler, it was the maid who stole the vase."

(P4) Principle of the Paradoxes of Material Implication: The following inferences are invalid.
(1) ~P, therefore, (P → Q)
(2) Q, therefore, (P → Q)

From the invalidity of (1) and (2) we get:

(3) (P → Q) ≠ (P É Q)

Now we can get see the Paradox.

Consider an English disjunction, (~P or Q).
From (~P or Q), by P3, infer (P → Q).
By P1, (~P or Q) = (P É Q).
Hence, from (P É Q), one can infer (P → Q).
But, by P2, (P → Q) entails (P É Q).
Therefore:
(3') (P → Q) = (P É Q)

So, which of the principles must we reject? We can't bite the bullet and accept the results because the results are explicilty contradictory (I'm assuming we aren't Australian or Brazilian and hence aren't paraconsistentists or dialetheists).

Put your choice (and a brief explanation of your choice) for the pricnicple you would reject in a comment. Your explanation should clarify why the principle you reject, though false, seems true.

--ID

The Use of Symbols

Do you know html? If you do, then you will have no problem distinguishing material conditionals from indicative contitionals in your posts, for example. If you don't know html, you have (at least) two options. First, you could learn just enough html to allow you to insert symbols into your posts. Second, you can try to use alternative keyboard elements for arrows and horsehoes ...

I prefer the first option.

Isn't it nice to have arrows, horseshoes, negations, etc. at your disposal?

Consider:

(a) p → q

(b) p ⊃ q

(c) ¬ p

--ID