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The notion of a truthmaker is introduced, and the importance of the notion for metaphysics is stressed. Russell was a pioneer. All truth is a matter of correspondence of a proposition to reality, so truthmaker Maximalism should be accepted. It need not be a one—one correspondence. ‘What are your truthmakers?’ is superior to Quine's question ‘What do you quantify over?’ Minimalist theories of truth, descending from Frank Ramsey, are rejected. Minimal truthmakers, however, are not rejected except in the case of infinities. The relation of truths to their truthmakers is an internal one, depending solely on the terms involved, truth and truthmaker. Truthbearers, that is truths, are true propositions, but propositions are no more than what is believed, supposes that, entertains that, etc., what philosophers call ‘intentional objects’. They can include impossibilities. There is no realm of propositions. The important Entailment Principle says that if a proposition entails some further proposition, then a truthmaker for the premise is also truthmaker for the conclusion. This casts significant light on the nature of valid argument.

Logical and mathematical truths differ from the empirical sciences in being necessary; they can be discovered a priori and in general can be proved (contra Quine). How is this possible? This problem is partly met by recognizing that the rational sciences are sciences of the possible. Only the mathematical structures that are instantiated in space‐time are existents. Furthermore, using the Entailment Principle, it is seen that only the logico‐mathematical axioms require truthmakers. We should recognize laws in these sciences, but laws that are necessary. Such laws will be truthmakers for truths about uninstantiated structures, for instance large infinite numbers. What is the source of these necessary laws? Perhaps it is a necessity in the nature of things.

The problem to be discussed is the logical problem of experience, which focuses on three inconsistent theses: there are experiential truths; if there are experiential truths, every truth is entailed by, or supervenes on, some non-experiential truth; and if there are experiential truths, not every truth is entailed by, or supervenes on, some non-experiential truth. This problem is distinguished from two others: the empirical problem and the traditional mind-body problem.

This chapter shows that once we have accepted the solution to the negation problem from Chapter 4, this leads immediately to solutions to analogous problems about conjunction and disjunction, and in fact to a constructive semantics for a very simple normative language with the expressive power of propositional logic. The semantics for this simple language is outlined, and inconsistency, entailment, and validity are defined. It is proven, given very simple assumptions, that the semantics yields the correct results about which sentences are inconsistent with which. Logical inconsistency is distinguished from ordinary inconsistency and given a precise definition, and it is shown why Geach's original moral modus ponens argument is logically valid. Finally, a loose end about the inconsistency of ‘murdering is wrong’ and ‘not murdering is wrong’ is set aside.

This chapter discusses the question of how modern model-theoretic methods should be assessed from a Fregean point of view. It is argued that while the central features of mathematical theories, from a post-Fregean point of view, have essentially to do with features of those theories’ classes of models, this is not the case from Frege’s point of view. Given a Fregean starting-point, from which logical relations are borne not by sentences but by thoughts, and from which conceptual analysis is relevant to the discovery of logical relations, classes of models are not sensitive to the crucial logically-significant features of theories. Hence the important logical properties of theories as Frege understands them cannot be cashed out in standard modern terms. For similar reasons, model-theoretic entailment in a sufficiently rich language will diverge from logical entailment as understood by Frege

Causal redundancy arguments allege that all the causal work attributed to ordinary macroscopic objects is really performed (jointly) by their microscopic parts, making ordinary objects epiphenomenal. Trenton Merricks holds that this shows there are no such things, since, if there were ordinary objects such as baseballs, they would be causally efficacious. It is argued, however, that Merricks' argument is either invalid or unsound, depending on how one understands “overdetermination”. This chapter makes the case that standard prohibitions against overdetermination do not apply where there are analytic entailments between the causal claims, so we can accept the causal claims of, for example, a baseball and of simples arranged baseballwise, without them being rivals in claims to causal efficacy or yielding redundant “double causation”.

This chapter surveys the semantic motivations of ‘split’ case marking of intransitive subjects in several genetically unrelated languages in terms of Dowty's proto-role entailments. It is argued that it is not the overall balance of entailments but a single entailment grammaticalized in a given language which determines case marking.

This chapter begins with a brief history of the idea of conventional implicatures (CIs) and a close look at Grice’s original definition. It compares and contrasts CIs with conversational implicatures, at-issue entailments, presuppositions, and intonational meanings, concluding that CIs, as Grice defined them, are distinct from all of them. The chapter then considers the linguistic consequences of Grice’s specifications. CIs should be scopeless, they should determine their own dimension of meaning, they should introduce new (but backgrounded) information, and they should serve as a kind of commentary on the main content of the sentence that contains them.

This chapter offers a critique of mainstream formal semantics. It begins with a statement of widely assumed adequacy conditions: namely, that a good semantic theory must (i) explain relations of entailment; (ii) show how the meanings of complex expressions are ‘composed’ from the meanings of their parts; and (iii) characterize facts of meaning in truth-theoretic terms (it may be supposed, for example, that the meaning of a sentence, s, is the set of possible worlds in which s is true). The chapter then proceeds to criticize the orthodox conception of semantics that is articulated in these three desiderata. This critique is followed by a sketch of an alternative conception — involving desiderata that are more in tune with the empirical objectives of linguistics. Finally, the chapter proposes and defends a specific theoretical approach — use based rather than truth based — that is suggested by that alternative conception.

For a present propositional attitude token to stand in a memory‐relation to a past propositional attitude token, the contents of both tokens need not be type‐identical but only sufficiently similar. This view flies in the face of the widespread identity theory of memory which demands type‐identity of diachronic content tokens and attitude tokens. This chapter determines to what extent two diachronic propositional attitude tokens may differ from one another and one of them still count as sufficiently similar to the other so as to be memory‐related to it. The chapter starts out by distinguishing two aspects of the veridicality constraint on memory: authenticity and truth. The truth of a memory report has to do with the memory content correctly representing objective reality. Authenticity, on the other hand, is an internal criterion concerning the accuracy of the reproduction of a past propositional attitude (true or false). The mark of authentic content representation is entailment: a present propositional attitude token is memory‐related to a past propositional attitude token only if the content of the present token is entailed by the content of the past token. One of the consequences of the entailment thesis is that it is possible that the content of a memory state is entertained for the first time at the time of recollection. This view is compared and contrasted with Plato's theory of recollection whereby all learning is nothing but remembering. Finally, the chapter addresses the question of when two diachronic attitude tokens are of the same kind and proposes a functionalist answer. The notion of attitude‐similarity is spelled out in terms of sameness of direction of fit and polarity.

The significance and utility of the concept of truthmaking are discussed. The suggestion that truthmaking is entailment (truths entail truthmakers) is found wanting, as is the apparently innocent slogan that ‘truth supervenes on being’. Truthmaking is said to be an internal relation holding between a truth bearer — a representation that the world is some way — and the world’s being that way. Quine’s criterion of ontological commitment and its implications for the determination of what exists are discussed and found to be ontologically unilluminating. The question whether every truth has a truthmaker is addressed, and the suggestion that truths of logic and mathematics ‘require nothing of the world’, hence need no truthmakers (‘trivialism’), is regarded with favor. The possibility that reality, being itself, has a definite nature, is defended.

Gappy semantics is used to model indeterminacy with ‘upwards falsity-preservation’ emphasized as much as downwards truth-preservation. This two-way idea is generalized to multiple premiss/multiple conclusion rules in a ‘neo-classical’ characterization of entailment; it is shown that this notion is non-transitive, though simple transitivity of entailment holds. A sound proof theory is set out, and it is shown how excluded middle fails. Quantifiers are interpreted as infinitary conjunctions and disjunctions and ‘classical recapture’ demonstrated for a negation-complete Peano-Arithmetic in the infinitary logic. This negation-completeness is extended to the simple theory of types, and to a set theory based on a schema whose instances are infinitary generalizations of the pair set axiom. It is acknowledged this is highly artificial, and not a modeling of real mathematics. The chapter concludes with a comparison of these formal theories and ‘really existing’ set theory and with a discussion of the legitimacy of classical reasoning in the latter.

I deal with the cognitive states expressed by de dicto logically complex sentences–those that are expressives, such as negations, disjunctions, universal noun phrase sentences, and adverbs of generality. I also articulate more clearly STA’s expressivism about semantic norms and its psychologism: the account of how sentences express cognitive states is integral to the semantics that STA gives of them.

The chapter surveys the recent and fast‐growing literature on the aggregation of logically interrelated propositions, following List and Pettit's formalization of the “doctrinal paradox”. The classical preference aggregation problem is a special case in which propositions take the form of binary preference judgments (“alternative x is better than alternative y”). The first part of the chapter focuses on aggregation methods that satisfy an Arrowian independence condition (“propositionwise aggregation”). In the independent case, the literature has produced a number of general characterization results that precisely demarcate the circumstances in which satisfactory aggregation is possible from those in which it is not Arrow's impossibility theorem and Gibbards oligarchy theorem are special cases of these results. The independence condition is, however, not uncontroversial and the second part of the chapter considers various relaxations of it. Judgment aggregation is still a very active field and the chapter concludes with an outlook on what we believe are important topics for future research.

This chapter considers the contrasts that are drawn between dispositions and occurrences, structures and categorical properties. The second section presents the first objection to the orthodox view of ascriptions of dispositions. It holds that disposition ascriptions do not uniquely entail conditionals. The third section discusses Elizabeth Prior's unsuccessful reply against Mellor's triangularity. The fourth section considers the problem in Mellor's position. The sixth section presents a functionalist response to the first objection. The seventh section presents the second attack on distinction. It holds that not even disposition ascriptions entail conditionals. The eighth section proposes another reply supporting the account of dispositions using a functionalist account which ultimately fails. The ninth section describes the context of ideal conditions. The last section presents a defence of realism.

While this chapter attempts to explain the construction of one kind of post-Gricean presupposition pragmatic theory, it also looks into the possible substantive problems that may be encountered regarding issues on presupposition. In doing so, the author focuses on one type of post-Gricean theory of pragmatism and extracts the aspects of entailment and generalized conversational inferenda from the notion of presupposition. Also, the author attempts to explore Grice's endeavor to come up with the same reduction through making use not of the notion of semantical nonspecificity but of the notion of ambiguity. Lastly, the author discusses his belief that Stalnaker and Grice altered the use of the concept of common ground, and that “accommodation” may pave the way for the reconstruction of theories that concern presupposition.