Re: Martin Gardner's New Prediction Paradox


Gene Ledbetter wrote:
> If I were A, I would write the following, and then I would return the
> card to Martin Gardner:
>
> Dear Martin,
>
> I regret that I am unable to comply with your request.

Exactly.
That is not, as you so arrogantly claim, a refutation of
the paradox or a reduction of it FROM the lofty status
of "paradox" TO the dungheap of "wordy nonsense".
It is rather simply your realization and admission that the
paradox is a paradox.

Of course, given that the proof that this predicition paradox is
paradoxical is so short, the question arises, could the person
making this request have reasonably failed to know that it was
paradoxical? Gardner himself is bragging that he DID know.
Requesting that a person perform a speech act that you know
he cannot perform, arguably, isn't so much paradoxical as malicious.

This one is entirely analogous to "Just tell me simply, yes or no,
will the next word out of your mouth be "no"?"
The fact that no response to this question is "correct" is intended
to be analogous to the fact that no possible assignment of truth-
values or "interpretations" to the logical sub-parts of a certain
kind of logical sentence can make the sentence true. That kind
of sentence is called a contradiction. Or, if it occurs at the higher
natural/meta-language level, a paradox.

In formal languages (as opposed to informal or natural ones), one
can continue somewhat satisfactorily from this starting
point by simply failing to answer the question at all, ever. You just
leave
the malicious questioner waiting, for his answer, forever. Serves him
right.

.

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