The sentence theory of truth bearers – problems with cognitively meaninglessness and logical implication

In a sentence theory of truth bearers, what it means to say that a sentence is cognitively meaningful is that it is true or false. To say that it is not cognitively meaningful (i.e. cognitively meaningless) means that it is not true or false.

In contrast, in a proposition theory of truth bearers, what it means to say that a sentence is cognitively meaningful is that it expresses a proposition. To say that a sentence is cognitively meaningless means that it does not express a proposition.1

I wonder if there is some problem with cognitively meaningfulness, logical implication and a sentence theory of truth bearers. Consider:

P. Colorless green ideas sleep furiously.

Q. The Earth is spherical.

Now consider a sentence that is about a logical implication from (P) to (Q):

S. That colorless green ideas sleep furiously logically implies that the Earth is spherical.

Now, it seems to me that if (P) is cognitively meaningless, then any sentence of which (P) is an antecedent or consequent, is cognitively meaningless too.

But now recall how a logical implication is defined. P implies Q iff there is no possible world in which Q is false and P true. But this is the case above. (P) is not true in any possible world at all2 and so any logical implication in which it is the antecedent is true. (Also where it is a consequent.) Thus, (S) is true. Contradiction. Something is terribly amiss.

Maybe some other definition of logical implication is needed. Suppose we stop defining it in terms of truth and falsity, and use the “is the case” phrase instead. Logical implication can then be defined as this: P logically implies Q iff there is no possible world in which P is the case and Q is not the case. Presumably all cognitive meaningless sentences are not the case. They are not false either because the semantic truth relations only hold for cognitively meaningful sentences. Now given the definition of logical implication all logical implications with a cognitively meaningless sentence as the antecedent are true. Again contradiction.

Notes

1By “means” I literally mean “means”. Not to be confused with an implication interpretation. I do not want to imply that some pluralistic proposition theory of truth bearers is false.

2Ignore potential problems with sentences meaning something else in a possible world.

This Post Has 4 Comments

  1. Simen

    The straightforward fix is to note that implication is only defined for sentences that have a truth value. If not both X and Y are either true or false, then X implies Y is cognitively meaningless. Another way to say it is that cognitive meaninglessness is infectious: any sentence built out of one or more c. meaningless elements is itself c. meaningless. It’s part of the definition of implication that the elements it’s built of are meaningful. “Boo! implies Fuck!” is neither true nor false, for obvious reasons.

  2. Emil Kirkegaard

    Indeed, that fixes it.

    But cognitive meaninglessness is not completely infectious. That’s the problem. Consider this sentence: “The sentence “bla bla aha aha” is cognitively meaningless.”. Is that sentence not “build out of” at least one c. meaningless elements? Yes it is. But it is not c. meaningless.

  3. Simen

    The sentence is quoted, and thus “quarantined”. Even if you left off the quote marks, so long as they could be inferred from context, they are still part of the sentence’s meaning. In a programming language, things like “1 + #@!æadfgg” would be a syntax error, but “1 + ‘#@!æadfgg'” wouldn’t. Same thing. So I’d maintain that any unquoted (i.e., quoted neither explicitly nor implicitly, through context) parts that are c. meaningless render the full sentence c. meaningless. Or do you have a counter-example that isn’t based on quotation?

  4. Emil Kirkegaard

    No, I don’t have any counter-examples to that right now. I came up with a similar solution to you.

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