Facts and States of Affairs

"The world is the totality of facts, not of things." Wittgenstein's opening claim in the Tractatus proposes that the basic furniture of reality is not objects but their being arranged as they are — that what exists fundamentally is not the cat and the mat but the cat's being on the mat.

The motivation is the same one that produced Armstrong's realism: objects and properties can each exist without the object having the property, so something further is needed to account for the difference between a world where it does and one where it does not.

Logical atomism

Russell's version, developed alongside Wittgenstein's, holds that the world consists of atomic facts — simple particulars having simple properties or standing in simple relations — with complex facts built by logical combination. Language mirrors this: atomic propositions correspond to atomic facts, and the truth of complex propositions is a function of theirs.

The programme raised immediate difficulties about which facts are needed as truthmakers for which sentences, and those difficulties are still the shape of the debate:

Negative facts. What makes "the cat is not on the mat" true? Russell reluctantly accepted negative facts and reported that his Harvard audience nearly rioted. The alternatives are to appeal to incompatibility — the cat's being on the sofa excludes its being on the mat — or to totality facts, below.
General facts. "All ravens are black" is not made true by the individual ravens, since they could all be black and there be a further raven. Something must add that these are all the ravens.
Totality facts. Armstrong's device for both: a higher-order fact that a given collection is all the facts of its kind. This handles negatives and generals at once, at the cost of a strange entity whose constituents include everything.

Armstrong's states of affairs

The most developed modern version makes states of affairs the fundamental category, with particulars and universals as abstractions from them rather than independent building blocks. The argument is the truthmaker argument, and its structure is worth setting out because so much depends on it:

" $a$ is $F$ " is true.
Something must exist in virtue of which it is true.
$a$ alone will not do: $a$ can exist without being $F$ .
$F$ alone will not do: $F$ can exist without $a$ having it.
The pair ${a, F}$ will not do either: the pair exists whenever both members do, including when $a$ is not $F$ .
So something further is required — the state of affairs $a$ 's being $F$ , whose existence entails the truth.

Step 5 is the crucial one, and it explains why the state of affairs is not simply the mereological sum or set of its constituents. A state of affairs is a non-mereological composition: it has $a$ and $F$ as constituents, but two states of affairs can share all constituents and differ — $a$ 's loving $b$ and $b$ 's loving $a$ — which classical mereology cannot represent. That is a substantial addition to the formal apparatus, and the difficulty of it is the same as the unity problem that generates Bradley's regress.

The slingshot

The strongest argument against facts is the slingshot, in versions due to Church, Gödel, and Davidson. Its conclusion is that if facts are what true sentences correspond to, there is only one of them.

The argument assumes two principles, each independently plausible:

(L) Logically equivalent sentences correspond to the same fact.
(S) Substituting co-referring singular terms preserves the fact corresponded to.

Now take any two true sentences $p$ and $q$ . Using definite descriptions built with the aid of $p$ :

$p \equiv (ι x (x = \emptyset \land p)) = \emptyset$

— that is, $p$ is logically equivalent to the claim that the unique object identical to $\emptyset$ and such that $p$ is $\emptyset$ . By (L) these correspond to the same fact. Since $p$ and $q$ are both true, the descriptions $ι x (x = \emptyset \land p)$ and $ι x (x = \emptyset \land q)$ denote the same object, namely $\emptyset$ . So by (S) we may substitute, obtaining a sentence corresponding to the same fact but logically equivalent to $q$ . By (L) again, $p$ and $q$ correspond to the same fact.

Since $p$ and $q$ were arbitrary, all true sentences correspond to one Great Fact. Facts, so understood, cannot do the work of distinguishing truths.

The responses are all denials of a premise, and each is a substantive commitment:

Reject (S). Deny that co-referring descriptions can be substituted in fact-contexts — that is, treat "the fact that…" as referentially opaque, like belief contexts. Natural, but it makes facts less like worldly items and more like ways of representing.
Reject (L). Deny that logical equivalence preserves the fact. This requires a structured conception on which facts have constituents in an arrangement, so that $p$ and its baroque equivalent correspond to different facts even though neither can be true without the other. This is the standard Armstrongian reply, and it means facts must be individuated more finely than by their truth-conditions.
Deny that facts correspond to whole sentences. Restrict truthmaking to atomic sentences and treat the rest by composition.

The slingshot is thus not a refutation but a constraint: it shows that a fact ontology must be structured and must give up unrestricted substitution.

Do we need them?

The sceptical position is that facts are an unnecessary shadow of true sentences. On this view "the fact that the cat is on the mat" is simply a nominalisation, adding nothing to "the cat is on the mat"; the appearance of an entity comes from the grammar of the phrase, which is exactly the slide the problem of universals page warns against.

The ostrich makes the same reply here as there: what makes it true that the cat is on the mat is that the cat is on the mat, and no entity beyond the cat and the mat is required. Whether this is an answer or a refusal depends entirely on the truthmaker principle — which is the subject of the next page.

Where facts sit

This is a category question with an unusual feature: the proposed category is one whose members have other entities as constituents, so accepting it changes the structure of the scheme rather than merely lengthening it. If states of affairs are fundamental, then objects and properties are abstractions, and the substance and universals debates are debates about derivative items.

Everything on this page turns on the demand made in step 2 of the argument above — that a truth needs something in the world in virtue of which it is true. That demand is stated and examined directly on the truthmakers page.