Proposition — In logic and philosophy of language, a proposition is the declarative content of a statement — what is said when one makes an assertion, and which can be true or false. A fundamental distinction: the sentence is the linguistic expression (a sequence of words in a particular language), while the proposition is the content that the sentence expresses. Two sentences in different languages (“Snow is white” / “La neige est blanche”) express the same proposition; the same sentence may express different propositions in different contexts (“I am hungry” — said by different people).
Frege: Propositions as Thoughts
Gottlob Frege, in “Der Gedanke: Eine logische Untersuchung” (1918, Beiträge zur Philosophie des deutschen Idealismus; translated as “The Thought: A Logical Inquiry”), calls propositions Gedanken (thoughts). A thought is not a subjective mental content (the psychological state of an individual) but an objective and atemporal content — something that can be grasped by several subjects, that exists independently of any mind, and that is the primary bearer of truth value. Frege rigorously distinguishes: (a) the sentence (linguistic sign); (b) the sense of the sentence (Sinn), which is the thought; and (c) the reference of the sentence (Bedeutung), which is its truth value (the True or the False, treated as logical objects).
Russell: Structured Propositions
Bertrand Russell, in his realist phase (prior to 1905), proposed that propositions are structured entities containing the very objects and relations as constituents. A proposition about Mont Blanc contains Mont Blanc. In “On Denoting” (1905), Russell reformulated the theory through the theory of descriptions — so-called “definite descriptions” such as “the present King of France” have no referent, but can nonetheless appear in coherent propositions through logical analysis. The Russellian theory of structured propositions was revived and systematised in contemporary analytic philosophy by philosophers such as Nathan Salmon and Scott Soames.
Propositions as Sets of Possible Worlds
An influential alternative, developed in the context of possible-worlds semantics, identifies propositions with sets of possible worlds: the proposition expressed by a sentence is the set of all possible worlds in which the sentence is true. This approach, associated with Stalnaker, Lewis, and the formal semantics of the 1970s–1980s, is mathematically elegant but faces objections: it renders all necessary propositions (such as mathematical theorems) identical to the set of all possible worlds — which means that “2+2=4” and “the square of 4 is 16” would express the same proposition, which seems counterintuitive (the problem of hyperintensional propositions).
Propositional Attitudes
Propositions are indispensable for the analysis of propositional attitudes — mental states such as belief, desire, hope, and fear, which are always states about something: believing that it will rain tomorrow, desiring that the team wins. The logical structure of such attitudes is S believes that p, where p designates a proposition. The debate about the nature of propositions therefore has direct consequences for the philosophy of mind and the theory of intentionality.
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