[Guest]

As everyone with basic knowledge of sentential logic knows, the disjunction pVq is equivalent to the conditional

-P --> q.

The reading is

p or q is equivalent to if not p, then q

Now, there is a completely acceptable, and commonly used utterance, namely

Either i don't remember him, or i don't know him -P v -Q

According to the above equivalence, it is equivalent to the utterance/sentence

If I remember him, then I don't know him... [for it holds that (-PV-Q) <-> (P --> -Q) ]

Nevertheless, the latter sentence of course contravenes our intuitions, and knowledge of language, as well as of the world.

How such an equivalence comes?

[Guest]

As everyone with basic knowledge of sentential logic knows, the disjunction pVq is equivalent to the conditional

-P --> q.

The reading is

p or q is equivalent to if not p, then q

Now, there is a completely acceptable, and commonly used utterance, namely

Either i don't remember him, or i don't know him -P v -Q

According to the above equivalence, it is equivalent to the utterance/sentence

If I remember him, then I don't know him... [for it holds that (-PV-Q) <-> (P --> -Q) ]

Nevertheless, the latter sentence of course contravenes our intuitions, and knowledge of language, as well as of the world.

How such an equivalence comes?

I haven't considered this overly much, but I think the problem involves syntax and semantics and the limitations of sentential logic.

You are working with "P = I remember him" and "Q = I know him." These are syntactically correct sentences in sentential logic, but they don't represent independent events semantically. In order for someone to "remember" someone, they actually have to "know" them first. You have left that as an implied assumption in your construct (otherwise you wouldn't have the question that you do), but if we add that in: P --> Q, then the system will be inconsistent in the case where P is true.

So while the sentence, "If I remember him, then I don't know him" doesn't make much sense looking at it in a purely semantic sense, it will hold true for the two consistent solutions, when P = F and Q = T/F.

P   Q   P --> Q   P --> -Q   Consistent?

T   T      T         F           no

T   F      F         T           no

F   T      T         T           yes

F   F      T         T           yes

Does that make sense? I sort of made up my argument as I went along...

[Guest]

I am glad you made that sentential calculus analysis. Although i agree with your relative observations, the point hre is not to consider the issue in terms of --> alone. For what is more significant, and may be more puzzling is the equivalence of a disjunction with a conditional, which, albeit quite logical, is counter-intuitive here. So, you have to consider things in the light of disjunction, as well.