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This chapter outlines a theory of facts, according to which facts are combinations of particulars and universals. The discussion proceeds as follows. Section 1 discusses the relation between the theory of facts and Realism, the traditional metaphysical doctrine of universals. Section 2 places at the centre of the theory of facts and universals the relation of combination, a multigrade relation taking a variable number of terms. Section 3 discusses the ‘vector logic’ of multigrade relations. Section 4 introduces ‘the problem of the unity of the proposition’, i.e., the problem of why it is impossible to judge ‘nonsense’. This turns out to be the same as the problem of the distinction between particulars and universals. Section 5 rejects solutions that invoke extra entities such as propositions or states of affairs. Section 6 offers a solution via the theory of negative facts. Section 7 extends the theory of negative facts to other complex facts, namely conjunctive and general facts. Section 8 further extends the theory of complex facts to allow it to cope with multiple generality, without the need to resort either to ‘logical forms’ or to ‘variables’. Section 9 suggests that an adequate semantic theory for the Predicate Calculus can be developed within the theory of facts.

With the Descriptive Constraint discussed in Ch. 9 at hand, Ch. 11 examines diverse theories of facts with a view to establishing how viable they are, and then turns to claims about the semantics of causal statements that have been used to motivate ontologies of facts and events. Neale makes the point that there is considerable confusion in the literature on the matter of whether causal statements are extensional, but shows that once the clarifications effected in earlier chapters are brought to bear, almost all of the confusion can be eradicated and decisive results obtained. There are still some extensional causal statements, and these can be delimited on the basis of their superficial grammatical forms, but there are other causal statements for which it is, as far as Neale can ascertain, still an open question whether extensional or non‐extensional treatments are to be preferred, much turning on the position taken on the overall shape of a semantic theory. If non‐extensional treatments prove appealing, the resulting theories will have to satisfy the strictures imposed by the Descriptive Constraint. The six sections of the chapter are: Identity Connectives; Fact Identity; Events; Events and Causes; Facts and Causes; and Fact Identity Again.

Examines the work of Bertrand Russell. It looks at Russell's idea that true sentences stand for facts (rather than truth‐values) and the philosophical and formal details of his Theory of Facts (the theory of facts as complexes) and Theory of Descriptions, both of which Neale describes as being poorly understood to this day. The six sections of the chapter are: Facts and their Parts; Representing Russellian Facts; The Theory of Descriptions; Abbreviation; Scope; Quantification and Notation. An appendix to the book looks further at Russell's definition of descriptions as incomplete symbols.

Sets out Kurt Gödel's slingshot (collapsing) argument. The original argument—or, at least, the premisses of the argument that Neale attributes to Gödel—can be found in a fleeting footnote to a discussion of the relationship between Bertrand Russell's Theory of Descriptions and Theory of Facts. Usually each theory is viewed as quite independent of the other, but Gödel argues otherwise: that the viability of the latter depends upon the viability of the former (or at least upon the viability of some non‐referential theory of descriptions). Neale summarizes Gödel's standpoint as follows: ‘if a true sentence stands for a fact, then in order to avoid the collapse of all facts into one, the friend of facts must give up either (a) an intuitive and straightforward Fregean Principle of Composition or (b) the idea that definite descriptions are expressions that purport to stand for things.’ The sections of the chapter are: Elimination (linguistic and ontological); Facts and Descriptions; Identities in the Matrix; and The Eleatic One (the collapse of all facts into one).

Introduces the criticisms put forward by philosophers such as Donald Davidson and Richard Rorty to the idea that one thing might represent another: that thoughts, utterances, and inscriptions are said to have content by virtue of their power to represent reality; and that those that do the job accurately are true, they correspond to the facts, or mirror reality—they are representations of reality. The author then outlines the deductive proof that he will present in the book to show that Davidson's and Rorty's criticisms are unfounded. The content of the proof is based on the work of Kurt Gödel and W. V. Quine, and demonstrates conclusively that (i) any supposedly non‐truth‐functional operation must satisfy an exacting logical condition in order to avoid collapsing into a truth‐function, and (ii) any theory of facts, states of affairs, situations, or propositions must satisfy a corresponding condition if such entities are not to collapse into a unity. The three main sections of the chapter: examine the case against representations made by Davidson and Rorty, including Davidson's notorious argument against facts; discuss Rorty's critique of representational philosophy (his anti‐representationalism); and consider collapsing (or slingshot) arguments that discredit the existence of facts (and are used in the critique of the fact–representation distinction), as put forward by Gottlob Frege, and developed by Alonzo Church, Quine, Davidson, and Gödel. The last section of the chapter outlines the structure of the book.