When you say “Hello.” is it true or false? Of course it's neither – we can only assign a truth value to propositions and there are many uses of language that don't form propositions, so it should be no surprise that speech acts that are neither true nor false exist.
J. L. Austin, a philosopher of language, calls sentences that can have a truth value “constative utterance” and the others “performative utterance”. Furthermore, he claims that speech acts have at least two facets:
- the locutary act, which basically means “what the sentence says grammatically”
- the illocutary act, or what you want to achieve with that utterance
Wikipedia lists a few good examples of performative utterances: [src]
- “You're fired!” expresses both the employment status of the individual in question, as well as the action by which said person's employment is ended.
- “I hereby appoint you as chairman” expresses both the status of the individual as chairman, and is the action which promotes the individual to this position.
- “We ask that you extinguish your cigarettes at this time, and bring your tray tables and seatbacks to an upright position.” This statement describes the requirements of the current location, such as an airplane, while also issuing the command to stop smoking and to sit up straight.
Some of these sentences could be judged for truthness based solely on their grammatical content. For example “You're fired!” might be considered false if the boss changed their opinion immediately and the employee wasn't in fact fired. But that would be missing the point – these sentences are not intended as factual statements.
By now, I hope to have demonstrated that truthness of sentences (and the quality of having a truth value) cannot be decided by analysing the grammatical structure alone. Context and intent are crutial.
Now let's return to propositions. The way Wikipedia [src] paraphrases the Stanford Encyclopedia of Philosophy: [src]
A proposition is the meaning of a declarative sentence, where "meaning" is understood to be a non-linguistic entity which is shared by all sentences with the same meaning.
This clearly isn't the only possible definition, if you want a more in-depth analysis, I suggest reading the entry in the Stanford Encyclopedia. For my answer, this definition will suffice.
Clearly, a simple analysis of the gramatics of the sentence isn't enough even here – a clear “meaning” is needed. This is obvious even with seemingly innocent sentences like “A mouse is on the table.” It clearly can be true, or false. But are you talking about the rodent, or a computer mouse? The sentence can encode two different propositions and can only be evaluated if we know the intent of the speaker. In a sense, the sentence itself isn't true or false, its meaning is.
The teeth of crows are pearly white.
This looks like a constantive utterance without doubt. If we take the sentence literally and don't consider it a metaphor for anything, then it forms a perfectly valid proposition. These universal propositions are generally quite hard to prove, but if we assume that there is truly not a single crow with teeth, then the proposition is true. Really, it's negation would be “There exists at least one crow whose teeth are not pearly white.“ And we know there isn't such a crow. For a more in-depth discussion, see this question.
(Actually, crows are said to collect various small objects (whether or not that is true), so some crow might actualy have someone else's teeth. See, this is the problem of judging sentences without context.)
This university has legs.
This is exactly the type of sentence that is impossible to judge without context. Did the speaker mean something specific? Then the proposition is formed by that intent. Did they say it because it sounded like nonsense to them? Then it served some other illocutary act and it's a performative utterance, not a constative one.
I am immortal.
This seems like a non-controversial constantive utterance to me. If the speaker meant literally immortal, they will be eventually proven wrong. (Even if they might not live long enough to find out haha.) If they meant immortal in some figurative or metaphysical way, it depends on various thing and it might be a non-trivial statement. Either way, it would be a valid proposition, being either true, false, or independent of our “world-model”.