Can a sentence without a truth value be true?

Question

I was doing some very, super, light reading on self reference.

It seems to me that the statement

• nothing that I say is true

both:

• cannot be understood with the T-schema;
• is self referential.

- Everything that Bill believes is true.

Heath argues that analyzing this sentence using T-schema generates the sentence fragment—“everything that Bill believes”—on the righthand side of the Logical biconditional.

Is that the case?

It also seems the sentence is both:

• ungrounded, as it can't be categorically true; but
• not analytic, because if it is false we can't tell from the sentence alone.

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I wondered if this meant the sentence could be true, but that this cannot be formalised into any "truth value".

Answer 1

I'd say no - it's not clear what it means for something which can't be assigned a truth value to be true. If it can't be assigned a truth value, then isn't it "nonsense"?

But the reverse might be so: that which "cannot be assigned a truth value" can be assigned a value of "false", as "nonsense" is not "true". And that which is not true, is false.