Propositions and Other Abstracta

Beyond numbers and sets lies a third family of abstract entities, posited not by mathematics but by the theory of meaning: propositions, the things sentences express, beliefs are directed at, and truth attaches to. They are joined by a looser collection — word types, musical works, novels, the game of chess — which are abstract by the usual tests yet came into existence at a definite time through human activity, and so fit badly into any scheme that makes abstracta eternal.

The case for propositions

Propositions are posited for the work they do, and the arguments are all of the form "here is something we say; what could make it true?"

• Same content, different sentences. "Snow is white" and "Schnee ist weiß" say the same thing. That thing is not either sentence.
• Objects of attitudes. Belief, doubt, and hope relate a person to something, and two people can believe the same thing while sharing no words.
• Bearers of truth. Truth attaches primarily to what is said rather than to the utterance, which is why the same sentence can be true in one mouth and false in another.
• Quantification over them. "Everything he said is true," "there is something we both believe but cannot express." Ordinary talk quantifies over these things, and by the criterion of commitment that is prima facie commitment.

The sceptic replies that each job might be done by sentences plus a relation of synonymy, or by mental states with content but no objects. Quine, characteristically, held that propositions are creatures of darkness with no criterion of identity — when is the proposition expressed by one sentence the same as that expressed by another? — and that "no entity without identity" disqualifies them.

Two accounts, and the granularity problem

Propositions as sets of possible worlds. A proposition is the set of worlds at which it is true. Elegant, well-behaved, and integrates with the semantics of modality: entailment becomes subset inclusion, consistency becomes non-emptiness.

Its defect is granularity. All necessarily true propositions are true at all worlds, so all are the same set — so believing that $2+2=4$ is believing that every group of prime order is cyclic, and nobody who believes one thereby believes the other. The account cannot distinguish any two necessarily equivalent contents, which makes it useless for the attitudes it was partly introduced to explain.

Structured propositions. A proposition has constituents in an arrangement, so that Brutus killed Caesar and Caesar killed Brutus differ by structure even where the constituents match. Two versions:

• Russellian: the constituents are the objects and properties themselves. Brutus — the man — is literally a part of the proposition. Handles necessary equivalence and de re belief; but then the proposition about Brutus did not exist before Brutus did, and abstracta acquire a surprising contingency.
• Fregean: the constituents are senses, modes of presentation, rather than the referents. Handles the classic puzzles (believing Hesperus is bright without believing Phosphorus is), at the cost of an additional layer of entities with their own identity conditions — exactly what Quine complained of.

Structured accounts face the difficulty already met twice in this section: the unity of the proposition. A proposition is not a list of its constituents; Brutus, killing, Caesar as a mere collection is not the claim that Brutus killed Caesar. What unifies them? Any answer that adds a further constituent invites Bradley's regress. The recurrence is not a coincidence: it is the same problem about how structure can be more than aggregation, whether the item structured is a fact, a state of affairs, or a proposition.

Types and tokens

Peirce's distinction is indispensable and independently interesting. The word "the" occurs three times in this sentence — three tokens, one type. The token is a concrete mark or sound; the type is the repeatable pattern.

Types look like abstracta and behave like universals, and the same options recur: a type may be a universal instantiated by its tokens, a set of tokens, or a resemblance class. The set option is unattractive for the familiar reason that a word type would then vary with how many times it happened to be written, and would cease to exist if all its tokens were destroyed — but we want to say that a word can be lost, which presupposes it survived long enough to be lost.

The distinction generalises to a class of entities that make trouble for tidy schemes:

• Musical works. Beethoven's Fifth is not any of its performances or scores, yet it was composed in 1808. It is abstract and created — which the Negative Way says is impossible, since a timeless entity has no date of origin.
• Novels and games. Moby-Dick is not any copy; chess is not any board. Both are abstract artifacts with an origin and, plausibly, conditions under which they could cease to exist.
• Fictional characters. Holmes is either an abstract artifact created by Conan Doyle, or nothing at all — a dispute belonging with nonexistent objects rather than here.

Created abstracta are the theoretically interesting case. If Thomasson is right that such entities exist and depend for their existence on human activity, then abstractness does not imply eternity or independence, and one of the standard contrasts between abstract and concrete dissolves. If she is wrong, then either the works are concrete — implausible, since no performance is the symphony — or they are eternal and Beethoven discovered the Fifth, which is a hard saying.

Where these abstracta sit

This family bears on the category question by supplying the counterexamples that keep the abstract/concrete distinction from settling down. Impure sets were awkward for the Negative Way; created abstracta are worse, because they have origins, dependencies, and possibly ends, while remaining unlocated and causally inert.

They bear on the inventory question through the theory of meaning rather than through science, which makes them methodologically distinctive: the argument for propositions is not that physics needs them but that semantics does. Whether that is as good a reason is exactly the question the indispensability argument raises about mathematics, and the two cases should be judged by the same standard. The book's treatment of the underlying semantic issues — reference, truth-conditions, and what a theory of meaning must deliver — is in the remark on semantics and the theory of meaning.