Paradox

Ken writes:

If God does not exist, then it’s not the case that if I pray my prayers will be answered. I do not pray. Therefore God exists.

I came across this today in discussion of the paradoxes of material implication. The interpretation of the conditional ‘if I pray, my prayers will be answered’ is at issue. Is it equivalent to ‘either I won’t pray or my prayers will be answered’ or is there a more intimately conditional meaning? If the conditional is treated strictly conservatively and in accordance with classical logic, then the argument is valid. So the soundness turns on whether the premise is true. It looks plausible though, doesn’t it?

Advertisements

5 thoughts on “Paradox

  1. Murray

    It seems that the argument “If God does not exist, then it’s not the case that if I pray my prayers will be answered. I do not pray. Therefore God exists” may be interpreted in two ways:

    Version 1:
    “If God does not exist, then it’s not the case that if Ken prays his prayers will be answered.
    Ken does not pray. Therefore God exists” For this version the first premise is not convincing because the following 3 statements are equivalent

    > not(if Ken prays his prayers will be answered)
    >not(either Ken does not pray or Ken’s prayers are answered)
    >Ken prays and his prayers are not answered

    So the first premise of the argument is equivalent to
    “If God does not exist, then Ken prays and his prayers are not answered”.

    Now this premise does not seem evident so the argument fails.

    Version 2:
    “If God does not exist, then it’s not the case that
    (for all x) if x prays, x’s prayers will be answered.
    Ken does not pray. Therefore God exists.”

    The following 3 statements are equivalent:

    > not( (for all x) if x prays, x’s prayers will be answered )
    > (there exists x) not(if x prays, x’s prayers will be answered )
    > (there exists x) x prays and x’s prayers will not be answered

    Now the first premise becomes something like “If God does not exist, some person’s prayers will not be answered.” This seems at least plausible but together with the assertion that Ken does not pray, does not seem to imply the conclusion.

  2. kenanddot

    It doesn’t resolve matters to find two closely similar arguments that aren’t successful. Is the original argument successful?

    Ken’s identity is not important to the argument. It would be interesting if God’s existence could be established whenever anyone thought the argument through themselves (where the first person pronoun referred to whoever was thinking it through).

    Perhaps the problem is that the premises are in a certain pragmatic tension in that someone in a position to believe the first premise would for that reason not be in a position to believe the second. If one thought “If God does not exist, then I pray and my prayers go unanswered” one would not also think “I don’t pray”.

    1. Murray

      Let me try a more linguistic tack. It seems that the “I” in the two premises does not mean the same thing. In the first premise it seems to stand for “one” or an arbitrary person. In the second it is the statement of a particular person who may as well be Ken. The paradox seems to be generated by the shifting interpretation of “I”.

  3. kenanddot

    Maybe the ‘if’ in the consequent of the first premise isn’t the material conditional, but a subjunctive one? It doesn’t sound right to say the first premise means exactly the same as “If God doesn’t exist, then I (ken/one/everyone) prays and the prayers go unanswered”. The premise is closer to: If God doesn’t exist, then if I were to pray, it wouldn’t be answered.

    Re: your linguistic solution. How would it cope with:
    1/ If G doesn’t exist, then if anyone prays, it will go unanswered.
    2/ no one prays.
    Therefore G exists.
    OK you might think the second premise is false, but that doesn’t really diagnose what is wrong with the argument. This version, though, doesn’t equivocate on the meaning of ‘I’.

    1. Murray

      Well I think the revised first premise is false as well. If God does not exist someone’s prayer might well appear to be answered.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s