Propositions are the building blocks of logic. A proposition is defined as a declarative sentence that is either true or false. That every meaningful declarative sentence must bear a truth value is a matter of a priori knowledge. We cannot have access to all propositions at once to examine whether they bear truth values; this is a matter of analytical reasoning. It lies in the very nature of a declarative sentence that it either asserts what the case is or it does not. If it asserts what the case is, it is true; if it does not, it is false. Thus, the statement “every proposition is either true or false” is itself an analytical proposition.
However, it is interesting to note that there are certain declarative sentences that appear to bear truth values but fail the test upon closer inspection. Let us begin with such a sentence: "This sentence is false" (the liar's paradox). It is a declarative sentence that seems to escape the condition of bearing a definite truth value. If the sentence is true, then what it says must hold — that it is false — which is a contradiction. If it is false, then what it says is not the case — i.e., it is not false, so it must be true — again a contradiction. Thus, the truth value of the sentence is indeterminate: it is neither true nor false. In fact, the sentence is meaningless in the logical sense.
Consider another example: "The current king of France is bald." As there is no monarchy in France at present, there is no current king. Thus, the subject term refers to a non-existent entity, rendering the sentence logically meaningless. Some may argue that the sentence is false rather than meaningless. But on reflection, this is not safe to assume. If the sentence were false, its negation — "The current king of France is not bald" — should be true. Are we ready to accept this negative assertion? It is no better than the affirmative one. If there is no current king, then saying he is bald or not bald is equally absurd. Thus, the sentence fails to meet the requirements of a proposition.
Interestingly, in Indian philosophy, Advaitins give a very similar example: "The barren woman's son is tall." On analysis, it becomes clear that this sentence too is neither true nor false. Maya (cosmic nescience) in Advaita Vedanta is similarly described — as neither real nor unreal. To justify this, Advaitins offer such examples of sentences that are neither true nor false. For some, this defies the law of the excluded middle. If we divide individuals into two groups — bald and not bald — the current king of France does not belong to either group.
To address this, Bertrand Russell proposed that the sentence "The current king of France is bald" is false, but this assumes it is meaningful. Russell pointed out that its negation is ambiguous and may express two distinct propositions:

1. There is no current king of France (and therefore he is not bald).
2. There is a current king of France who is not bald.

Of these, the first is true, while the second is false. Russell interpreted the sentence as asserting the second. According to him, the sentence is a conjunction of three propositions:

(i) There exists an x such that x is the current king of France.
(ii) There is only one such x.
(iii) x is bald.

Symbolically:
∃x (K(x) ∧ ∀y (K(y) → y = x) ∧ B(x))
For a sentence to qualify as a proposition, it must be meaningful. Therefore, while every proposition is a declarative sentence, not every declarative sentence qualifies as a proposition. A significant case of meaninglessness arises from category mistakes. Consider the sentence: "Prime numbers are hungry." On the surface, it may seem false, but calling it false gives it undeserved status. False statements are still meaningful; if a statement is false, its negation should be true. However, the negation of "Prime numbers are hungry" — namely, "Prime numbers are not hungry" — is equally meaningless. Hence, the original sentence is not merely false but meaningless.
In language, some words are used not in their primary (denotative) sense but in a secondary (indicative or associative) sense. For example: "The Crown was very kind to him." Here, the word 'crown' does not refer to an ornamental headgear but to royal authority. The meaning shifts from the physical object to the institution it symbolizes. Clearly, the primary meaning is not in use here, as otherwise it would result in a category mistake. Yet, without any confusion, the word ‘crown’ is understood to mean ‘royalty’.
Similarly, in legislative contexts, we hear: "I want to place this resolution with the permission of the honourable chair." Here, 'chair' refers to the presiding officer of the house. Such expressions are context-sensitive and convey metonymic meanings within specific contexts. According to Russell, Frege, and formal logic, metonymic terms are disallowed from forming propositions, while only terms referring to their primary meaning are permitted.
However, I believe some metonymic expressions have transcended their context dependence. Words like ‘Crown’ (for royalty) and ‘White House’ (for the American administration) have acquired stable, context-independent referents. For instance, in the sentence: "The White House announced new measures to protect the country," the word clearly refers to the U.S. administration. Such words are recognized as metonymy in English. While ‘chair’ remains context-bound, ‘crown’ and ‘White House’ have evolved to function as primary terms. Language evolves. Sometimes meanings broaden, as with the word "run," which originally referred to the flow of liquids but now denotes movement in general.
Thus, it becomes clear that the line between primary and secondary meanings is not rigid. There are many sentences whose surface form deviates from standard propositional structure, but whose intention clearly reveals a proposition. For example: "Am I your servant?" is interrogative in form but expresses the proposition: "I am not your servant." This shows that intention plays a vital role in determining whether something functions as a proposition.
Frege, Russell, early Wittgenstein, and logical positivists emphasized the need for precise and unambiguous language so that it could serve scientific inquiry. This is why they avoided implied, suggestive, or figurative language. However, even science deals with different layers of reality. What is true in classical physics may not hold in quantum physics. Terms like ‘particle’ or ‘wave’ may not signify the same thing in both contexts. Niels Bohr warned: “When it comes to atoms, language can be used only as in poetry.” Even in science, multiple levels of language are needed. Mathematics is considered the most appropriate language for quantum physics, yet even here, there are layers: the language of infinitesimals, for instance, differs from that of standard calculus. A part of a line segment can contain as many points as the entire segment — a counterintuitive idea defying normal intuitions of part-whole relations.
Certain statements are treated differently in everyday language and scientific contexts. "Tomatoes are vegetables" is true in culinary language but false in botanical terms, where a tomato is classified as a fruit. "Leaves are green" is another common proposition. In ordinary language, greenness seems inherent to leaves, but physical science explains that leaves appear green because they reflect green light and absorb other wavelengths. So greenness does not inhere in the leaf. These are examples of context-sensitive propositions.
In drama, actors may say: "I am the king of Mithila." Within the dramatic context, the statement is true, though false in reality. This parallels the doctrine of Anekāntavāda in Jainism and sheds light on the Dvaita–Advaita debate. Advaitins argue that the rope-snake illusion is neither real nor unreal. If it were unreal like a circular triangle, it wouldn’t be perceived; if it were real, it wouldn’t be negated later. Hence, it is anirvacanīya — indescribable. Dvaitins respond by analogy to drama: the actor's claim is true within the play, false outside it. Similarly, the rope-snake is true from the standpoint of illusion, false in the real world.
Fiction offers more examples of context-bound truths. "James Bond was a British intelligence agent" is true within Ian Fleming’s novels but not in historical reality. Again, we encounter context-driven truth. In Indian poetics, "Moonlight is cool" is a valid expression. Literally, moonlight may not lower temperature, but poetically it evokes a certain sentiment. Thus, poetic and factual language may yield different propositions.
Can a statement laden with suggestive meaning generate a suggestive proposition? I believe it can. When an employee says, "It is six p.m. now," he may not merely be reporting the time; he may be implying that the workday is over. The literal content differs from the implied intention.
In conclusion, just as reality has many layers — imagination, fiction, drama, empirical experience, classical physics, quantum physics — so too must language operate on multiple levels. We should not insist on propositions relying only on the primary meanings of words. To some extent, this view is supported by thinkers like Grice, Searle, and classical Indian philosophers.