The phrase 'I'm not going to dignify that with a response'
Is a classic example of the liar paradox. Discuss [20 marks]
(BelladonnaAnodyne Melissa's gonna wet herself, I swear..., Tue 11 Jan 2011, 10:12, 1 reply, 15 years ago)

OK
The problem of the liar paradox is that it seems to show that common beliefs about truth and falsity actually lead to a contradiction. Sentences can be constructed that cannot consistently be assigned a truth value even though they are completely in accord with grammar and semantic rules.
The simplest version of the paradox is the sentence:
This statement is false. (A)
If the statement is true, everything asserted in it must be true. However, because the statement asserts that it is itself false, it must be false. So the hypothesis that it is true leads to the contradiction that it is false. Yet the sentence cannot be false for that hypothesis also leads to contradiction. If the statement is false, then what it says about itself is not true. Hence, it is true. Under either hypothesis, the statement is both true and false.
However, that the liar sentence can be shown to be true if it is false and false if it is true has led some to conclude that it is neither true nor false. This response to the paradox is, in effect, to reject the common beliefs about truth and falsity: the claim that every statement has to abide by the principle of bivalence, a concept related to the law of the excluded middle.
The proposal that the statement is neither true nor false has given rise to the following, strengthened version of the paradox:
This statement is not true. (B)
If (B) is neither true nor false, then it must be not true. Since this is what (B) itself states, it means that (B) must be true and so one is led to another paradox.
Another reaction to the paradox of (A) is to posit, as Graham Priest has, that the statement follows paraconsistent logic and is both true and false. Nevertheless, even Priest's analysis is susceptible to the following version of the liar:
This statement is only false. (C)
If (C) is both true and false then it must be false. This means that (C) is only false, since that is what it says, but then it cannot be true, creating another paradox.
There are also multi-sentence versions of the liar paradox, which are essentially logical arguments. The following is the two-sentence version:
The following statement is true. (D1)
The preceding statement is false. (D2)
Assume (D1) is true. Then (D2) is true. This would mean that (D1) is false, and hence (D2) is false. This in turn means that (D1) is true, and this continues infinitely, creating a paradox.
The argument version of the liar paradox generalizes to any circular sequence of such statements (wherein the last statement asserts the truth/falsity of the first statement), provided there are an odd number of statements asserting the falsity of their successor. E.g., the following is a three-sentence version, with each statement asserting the falsity of its successor:
D2 is false. (D1)
D3 is false. (D2)
D1 is false. (D3)
Assume (D1) is true. Then (D2) is false. This would mean that (D3) is true, and hence (D1) is false, leading to a contradiction. Instead, assume (D1) is false. Then (D2) is true, which means (D3) is false. This would mean (D1) is true, again leading to a contradiction, and hence the paradox.
( disasterprone "Pyjamas caused the Holocaust", Tue 11 Jan 2011, 10:14, Reply)

I would give you 10 marks for that (you failed to address the statement in the question)
But I'm taking all your points away for obviously copying and pasting.

You get a U.
(BelladonnaAnodyne Melissa's gonna wet herself, I swear..., Tue 11 Jan 2011, 10:17, Reply)

I thought that was how modern day students did things
I was trying to be down with the kids.
( disasterprone "Pyjamas caused the Holocaust", Tue 11 Jan 2011, 10:19, Reply)

Nah, they've got software to stop you doing that now.
Which was a bit annoying.
(BelladonnaAnodyne Melissa's gonna wet herself, I swear..., Tue 11 Jan 2011, 10:21, Reply)

Good! I'm glad to hear it.
GCSEs and A-Levels are easy now, Degrees should be hard so they remain a real achievement.
( disasterprone "Pyjamas caused the Holocaust", Tue 11 Jan 2011, 10:28, Reply)