I’m highly sympathetic to the intuition that the liar sentence is devoid of meaning in some important respect, but I don’t think we can just declare the liar sentence meaningless and then call it a day. Because in another respect, it definitely seems meaningful. I understand what a sentence is, and I feel like I understand what it is for a sentence to be true or false. If someone wrote on a blackboard “The thing written on the blackboard of room 428 is false,” I feel like I would understand what this is saying before I went to check out room 428. Hence I must understand the sentence if it turns out that we’re in room 428 already.
Also consider the Strengthened Liar: “This sentence is not true.” According to your solution, that sentence should also be dismissed as meaningless, right? But surely meaningless sentences a fortiori aren’t true. But that’s precisely what the sentence asserts, hence it is true.
A sharper formulation of the paradox just came to my mind. Consider the statements X = “X is not true” and Y = “X isn’t true”. (The difference in spelling is intentional.) If X is meaningless, then X isn’t true, therefore Y is true. But it’s a very weird state of affairs if replacing “isn’t” by “is not” can make a true sentence meaningless!
Good point. I take the claim that a sentence S is meaningless as equivalent to the claim that S has no truth-conditions. Let A be any schema for the conditions on which a sentence has truth-conditions, so that for each English sentence S, A(S) is true iff S is meaningful/has truth-conditions. Let S be the sentence ~A(S). Then S has truth-conditions iff A(S) iff ~~A(S) iff ~S. Contradiction. Nowhere was it assumed that the contradictory sentence was meaningful.
When you state A(S) iff ~S, you are formally substituting S for ~A(S), but the meaning of “A(S) iff ~S” is “the set of truth-conditions for ~~A(S) is the same as the set of truth-conditions for ~S”. But this assumes that there exists a set of truth-conditions for ~S, which assumes that there exists a set of truth-conditions for S, i.e. that S is meaningful, by your definition.
I’m highly sympathetic to the intuition that the liar sentence is devoid of meaning in some important respect, but I don’t think we can just declare the liar sentence meaningless and then call it a day. Because in another respect, it definitely seems meaningful. I understand what a sentence is, and I feel like I understand what it is for a sentence to be true or false. If someone wrote on a blackboard “The thing written on the blackboard of room 428 is false,” I feel like I would understand what this is saying before I went to check out room 428. Hence I must understand the sentence if it turns out that we’re in room 428 already.
Also consider the Strengthened Liar: “This sentence is not true.” According to your solution, that sentence should also be dismissed as meaningless, right? But surely meaningless sentences a fortiori aren’t true. But that’s precisely what the sentence asserts, hence it is true.
If it’s meaningless, it doesn’t assert anything.
A sharper formulation of the paradox just came to my mind. Consider the statements X = “X is not true” and Y = “X isn’t true”. (The difference in spelling is intentional.) If X is meaningless, then X isn’t true, therefore Y is true. But it’s a very weird state of affairs if replacing “isn’t” by “is not” can make a true sentence meaningless!
The apostrophe in this sentence isn’t needed for comprehension.
Good point. I take the claim that a sentence S is meaningless as equivalent to the claim that S has no truth-conditions. Let A be any schema for the conditions on which a sentence has truth-conditions, so that for each English sentence S, A(S) is true iff S is meaningful/has truth-conditions. Let S be the sentence ~A(S). Then S has truth-conditions iff A(S) iff ~~A(S) iff ~S. Contradiction. Nowhere was it assumed that the contradictory sentence was meaningful.
When you state A(S) iff ~S, you are formally substituting S for ~A(S), but the meaning of “A(S) iff ~S” is “the set of truth-conditions for ~~A(S) is the same as the set of truth-conditions for ~S”. But this assumes that there exists a set of truth-conditions for ~S, which assumes that there exists a set of truth-conditions for S, i.e. that S is meaningful, by your definition.
O.K., I don’t know how to italicize here.
Next time you comment, try the Help link (lower right).
Ah, thanks.