© Peter H. Roosen-Runge, 1999
Daniel Dennett, in The Intentional Stance (p. 121), presents "three quite general characterizations of propositions" to be found in the philosophical literature. It is interesting that, from the Tractarian perspective, each of these are fundamentally faulty.
(1) Propositions are sentence-like, constructed from parts according to a syntax.
No. Propositions are more abstract than sentences (which are propositional signs). Propositions are (instantiated) logical forms, a logical form being an abstract data structure which, when instantiated, associates an entity with a set of relations and functions describing its structure and contents. For example, an array has an associated size value n and a function from a set of n integers to a set of values, which when applied to one of the integers i gives the value of the ith entry in the array.
The Tractatus took one logical form to be basic: the functional form used extensively in mathematics and computer science, which associates with a proposition a functor naming a predicate or relation (the predicate or relation "symbol"), an arity giving the number n of arguments of the functor, and a list of arguments of length n. In mathematical notation, (which is quite independent of the actual sign), the form of a proposition is usually represented as
For example, the sentence "John loves Mary" has, taken as a proposition, the logical form 'loves'('William', 'Margaret'), where 'loves', 'John", and 'Mary' are pieces of notation used to designate the functor and arguments of this particular form. In another language, the same form might have been written 'liebt'('Wilhelm', 'Margarete').
Propositional forms have no syntax, although the notation used to express them does. Syntax is an aspect of an inscription, which is a state of a medium interpreted linguistically. Propositional signs are inscriptions used to express or state propositions.
Parts are objects: entities with states; and what can be constructed from parts is another part. Propositions, not having states, are not parts and cannot be constructed from them. Propositional signs aren't constructed from parts either; they are states of parts (the media in which they are inscribed.) The structure or syntax of a propositional sign can be described in terms of the states of parts of the medium in which it is inscribed, by describing a configuration.
(2) Propositions are possible worlds.
This doesn't work, at least not without a coherent concept of 'possible world'. (None is known to me. See Worlds.) If "worlds" are equated with "states of affairs", then equating them with propositions is just to use the word 'proposition' for the (Tractarian) sense of a sentence, the sense being the state of affairs in which the (Tractarian) proposition is true. This leaves unexplained the connection between the structure of the sentence (the propositional sign) and the proposition (the sense).
(3) Propositions are arrangements of objects and properties. That is, a proposition is identified with the "fact" that the expression of the proposition as a sentence describes.
This attempts to repair the missing connection between sign and proposition in (2), and is closer to a workable concept, although the facticity is irrelevant.
Dennett correctly notes the connection between this idea and the "correspondence theory of truth". For (in the Tractarian view), a proposition, as a logical form, has a structure which corresponds to a configuration which, in turn, structures a state of affairs = the sense of the proposition. What's wrong about (3) in Tractarian terms, is the identification of propositions with configurations. A configuration of objects and properties is (or, is the structure of) a state of affairs, and a proposition (as a logical form) is not a state of affairs; it is about a state of affairs. A propositional sign is a state of affairs, and indeed, the correspondence between a proposition and its sense is constructed via a correspondence between a configuration (syntactic structure) as a structuring of the state of affairs which constitutes the propositional sign, and a configuration which structures the state of affairs that constitutes the sense of the proposition.