For those interested in the Liar Paradox and would like to read an interesting solution, my thesis supervisor Nick Smith has written a paper.? It can be read here .
? Section 2 can be skipped by those with no formal training in logic and semantics.? The rest of the paper is quite readable – although if anyone wants any help or explanation, I am happy to provide it in the comments section of this post.? Ask away!
4 Comments
I can’t read that whole pdf!
Anyway, what happens if you write:
A: Sentence B is true
B: Sentence A is false
or
A: Sentence B is false
B: Sentence A is false
Could you ask Nick about this please?
I believe it gets around the problem of what the sentence is refering to. The first situation may actually be possible, thinking about it.
Gah. My brain hurts.
Hi Alex – great to see you back.
Your first two sentences reproduce the liar paradox. If sentence A is true, then sentence B must be true. But if sentence B is true, then sentence A is false – contradicting our hypothesis. A contradiction similarly occurs if we assume A is false.
As you point out – this example is used to point out that paradox is not caused by self-reference. Hence other solutions must be found that do not deny self-reference.
Your second two sentences aren’t paradoxical and have perfectly understandable truth conditions. If sentence A is true, then B must be false. If B is false, then A is true – which is what we started with – so that’s fine. Similarly, if A is false, then B is true and B says that A is false, so that’s also what we started with. Similar reasoning applies if you start with B in each case.
Ah, I see about the second set. So it is, in a way, a quantum statement; both are both true and false at the same time. -.- was reading about quantum stuff in New Scientist a few weeks back.
I was thinking about the paradox, when to my sudden amazement, I no longer understood what the sentence actually meant. Seriously, I could not comprehend either what the sentence meant, or what the paradox was! Wierd. The answer that I then came with was: “this sentence does not exist, it is an impossibility and does not mean anything”.
Thinking about this stuff really does have that effect. Part of it has to do with the plausibility of the truth-conditional theory of meaning – that we only understand a sentence once we understand what conditions would have to obtain for the sentence to be made true. But once we reflect on liar sentences we realise we really don’t understand their truth conditions. We then end up where you are and conclude that it is just meaningless.
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