I'll try to add something to this from the field of semantics within linguistics. I'm not a semantics expert, so if anyone with more experience wants to correct me, please do. (This is also probably why this answer is so painfully syntax/grammaticalization-focused.)
First, I'll attempt to answer the question as posed for well-formed sentences.
There's actually a theory of semantics that tries to carry out this hypothesis, called truth-conditional semantics (this is actually the theory that I learned in class). It's implemented in a far subtler manner than your question frames, however.
In truth-conditional semantics, everything is a function from tuples of entities (people, places, things, ideas, truth values, abstract 137-dimensional entities, whatever) to truth values. Nouns, verbs, adjectives, everything:
- Nouns are functions that map everything they describe to
True, and everything else to
False. For example, "sandwich" is a function that maps every thing you can call a "sandwich" to
True, and everything else to
False. Two pieces of bread with mayonnaise between them? If you want to call that a sandwich, the function denoted by "sandwich" maps to
True for you. A drawing of a sandwich? If you want to call that a sandwich, that maps to
True for you. A pop tart? If you want to call that a sandwich, you'll burn in hell for infinite infinities, but that maps to
True for you.
- Verbs that can take a direct or indirect object are the reason why the definition says "tuples of entities" rather than just "entities". For example, "removes" is a verb that maps triples (or pairs) of things to a truth value; "x removes y from z" returns a truth value that is only true when all of x, y, and z fit this situation. Therefore, the triple (a shovel, dirt, the ground) gets mapped to true, but (the ground, a shovel, dirt) does not.
(Wait, aren't nouns functions too?)
(Yes. Functions can be applied to functions. Long story.)
And what about entire sentences? In both syntax and semantics, sentences can be written in a tree structure:
English comes with rules about how to compose each node from its children -- for example, the QP's value is the outcome of the function in the D node applied to the function in the NP node -- and the sentence's (the S node's) value is the outcome of the VP function applied to the QP function.
Since VPs return truth values, this means sentences *are* truth values.
What about questions and commands? A Google Scholar search was unfruitful, so I'm only speculating here. A common theory of syntax says that both are actually normal declarative sentences in disguise, with some transformations to make it into a question or command due to an invisible word influencing the sentence. This isn't really a complete answer; we don't know what that invisible word does with the truth condition.
As a very unsophisticated hypothesis, consider the following:
(1) I wonder if it will rain tomorrow.
(2) I wonder, will it rain tomorrow?
(3) *I wonder it will rain tomorrow.
In (1), "wonder" takes ("I", "if it will rain tomorrow") as its argument tuple. In (2), it takes ("I", "will it rain tomorrow?") as its argument tuple. This may be evidence that "will it rain tomorrow?" and "if it will rain tomorrow" have the same value, and neither of these values are truth conditions. Further supporting that questions and the if-clause in (1) aren't truth conditions, (3), where we plugged in a truth condition, is ungrammatical.
I can't come up with a similar example for commands. But, since the asker was asking about a statement about all sentences, it should be enough to show that some well-formed sentences don't have truth conditions as their values.
Next, I'll address some issues in your rebuttals to why questions are still truth values.
what I just uttered has come out of the truth hood which indicates that I don't know your name, so in this case, the sentence I uttered is a by product of the truth I have
Ooh, juicy, we're flipping straight from the most formal of semantics into pragmatics. The study of conversational implicatures takes care of this -- conversational implicatures are ideas that aren't directly implied by what you say (e.g. "X is a square" must always imply "X is a rectangle"), but rather by what you say if you're obeying certain social rules about conversation. I can totally ask someone "what is your name?" and already know their name; if I do, however, I'm either joking or being weird. As far as linguists studying the meaning of a sentence are concerned, that social consequence doesn't matter in determining the semantics of the sentence itself.
If in your own personal philosophical ventures, however, you would like to count that social consequence as a valid contributor to meaning, I would agree that everything that can ever be said has a truth value attached to it. These social rules about conversation are so well-ingrained in our ideas that we make legal decisions based off of them, and therefore, you can't say a single thing without implying other things that must have truth values about the situation in which you're saying them -- at the very least, the truth that it's appropriate to say the thing you say.