Best Answer bonanova, 18 February 2013 - 09:50 PM

It is paradoxical because it concerns both (a) facts and (b) truth values of statements about facts.

There are standard ways to deal with self-referential paradoxes.

Tarski eliminated conflict by permitting statements that did only (a) or (b) but not both.

Thus, a statement can either address facts, OR the truth values of statements, but not both.

**<edit>**

- It's more restrictive than that, or course.

Conflict arises when a statement refers to the

truth value of its own statement about a fact.

**<end edit>**

For this particular question, here's my two-cents:

First, "correct" needs to be defined. I can think of four ways:

- The chosen answer is "correct" if it follow the instructions for making a choice.

That is, if it is chosen at random.

Correct means correctly following the OP instructions.

In this sense any random choice is correct.

The number associated with that choice is irrelevant to its "correctness" as a choice.

- The chosen answer is "correct" if the number I choose gives the probability that I chose it.

The chosen answer is correct therefore if my choice is (a) or (d).

- The chosen answer is "correct" by the previous analysis if I choose (a) or (d).

The probability of choosing {(a) or (d)} is 50%.

If 25% must be the probability that I chose {(a) OR (d)}, then {(a) OR (d)} is not the correct answer.

- Alternately, if (a) or (d) is the "correct" answer, then (b) is the correct choice.

When more than one condition applies, there is the possibility of conflict.

In cases 3 and 4, this happens; thus the classical self-referential paradox.

By the way, my choice of definition for "correct" is the most literal one: the first.

OK.

So I went ahead and made a choice at random; therefore it was a "correct" choice.

What was my choice?

(b) 100%