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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.

The formal ontological concept of an object is explicated and contrasted with that of a property. F. P. Ramsey’s objections to this distinction are challenged. The sense in which objects possess an individuality not exhibited by entities of certain other types is discussed. The object/property distinction is distinguished from that between universals and particulars. The ontological status of events and processes, and that of abstract entities such as numbers, are examined. Gottlob Frege’s treatment of number and his object/concept distinction are criticized, and an alternative account of the ontological status of concepts is advanced.

F. P. Ramsey’s objections to the universal/particular distinction, especially as advocated by Bertrand Russell, are examined in depth and rebutted. At the same time, certain important lessons are drawn from his arguments concerning how best to articulate the distinction. In response to related arguments recently directed against the four-category ontology by Fraser MacBride, it is shown how each of the four categories can be uniquely identified in terms of the characteristic pattern of ontological dependence relations that its members bear to members of other ontological categories.

This chapter develops an epistemic theory of causality. The origins of such a theory may be found in the writings of Kant and Ramsey. According to the epistemic theory, we think in terms of cause and effect because it is convenient to do so, not because our causal claims latch on to a physical causal connection. A formal causal epistemology is put forward, and it is argued that this approach provides a synthesis of the hypothetico-deductive and inductive accounts of causal discovery. Analogies between epistemic causality and objective Bayesianism are highlighted.

This chapter presents several constructions of ω₁-like models with interesting second order properties. The list includes: recursively saturated rather classless models, rigid recursively saturated models, models whose additive reducts are isomorphic but whose multiplicative reducts are not, and very similar but nonisomorphic models. The chapter also presents two constructions used in completeness theorems for Peano Arithmetic with the Ramsey quantifier and the stationary quantifier.

This chapter makes use of an induced version of Ramsey's Theorem to prove several results: the Abramson-Harrington theorem on omitting large indiscernible sets and Hanf numbers for models of arithmetic; a theorem characterizing the possible automorphism groups of models; and a theorem based on countable recursively saturated models being generated by a set of indiscernibles.

Frank Ramsey was involved in preparing the English translation of the Tractatus as an undergraduate at Cambridge. He developed an account of the theory of types which avoided the difficulties associated with the axiom of reducibility by following what he took to be Wittgensteinian principles. In December 1924, he wrote an essay which was eventually published under the title ‘The foundations of mathematics’. The material in the essay that is relevant here falls into three distinct parts: in the first Ramsey showed how to develop a theory of types on Wittgensteinian principles that had no need of the problematic axiom of reducibility; in the second he dealt with the derivation of the theory of classes from the theory of types; and in the third he addressed the problematic dependence of the theory on the axiom of infinity.

This concluding chapter summarizes the discussion in the preceding chapters. The book sought an answer to the question: can we give an account of arithmetic which does not make it depend for its truth on the way the world is? And if so, what constrains the world to conform to arithmetic? All the accounts we have considered have turned out to be flawed. But what is striking is how often an account was rejected not for philosophical reasons but for technical ones. It is shown that since the problem of arithmetic participates in the larger puzzle of the relationship between thought, language, experience, and the world, we can distinguish accounts that look to each of these to supply the content we require.

This chapter presents the main argument in favor of a positive discount rate. In a growing economy, future generations will consume more goods and services than we do. In this context, investing for the future is equivalent to asking poor consumers to sacrifice more of their consumption for the benefit for wealthier people. Because of inequality aversion, one would be ready to do so only if the rate of return of these investment projects is large enough to compensate for the increased intertemporal inequalities that these projects would generate. The Ramsey rule quantifies this wealth effect. In fact, several experts have used the Ramsey rule to make recommendations on the choice of the discount rate to evaluate public policies, in particular toward climate change.

This chapter develops F. P. Ramsey's theory of truth. Everyone knows that Ramsey had a theory of truth. Rather fewer people know that the theory came in two significantly different versions, and that the later and less famous version is more fertile than its predecessor. The more famous version is, of course, Ramsey's redundancy theory of truth, which he expounded in his great paper of 1927, ‘Facts and Propositions’. The Ramsey–Prior theory, contra Ramsey's original approach, confirms that the word ‘true’ has a determinate sense. It does so by specifying the contribution that the word makes to what is expressed by a statement that contains it. That specification vindicates the common-sense view that ‘true’ is grammatically and semantically a predicate.

Rules for setting Ramsey (1927) optimal commodity taxes are derived in this chapter using the conventional welfare analysis presented in Ch. 6. When these tax rules apply, Diamond and Mirrlees (1971) and Stiglitz and Dasgupta (1971) prove that the producer prices can be used as shadow prices in project evaluation if private profits are eliminated from consumer incomes. This result is demonstrated using shadow prices to value the changes in economic activity from a marginal tax change. It provides economic intuition that can be used, together with the generalized Hatta decomposition, to extend a number of the familiar optimal tax rules to economies with variable prices.

Maurice Frank Wiles (1923–2005), a Fellow of the British Academy, was an Anglican theologian who was able within that tradition to develop the field of ‘doctrinal criticism’. He began his career concentrating on the period of the early Fathers of the Church, and it was this grounding that sowed the seeds of his later work on modern doctrine. Arianism would remain a particular interest. Yet Wiles retained a profound respect for tradition and, like the Fathers, constantly measured his doctrinal critique against the experience of believers in life and worship, regarding theology as second-order discourse – reflection on the significance of what was primary for Christianity, such as the experience of salvation. During his student days two people particularly influenced him: Ian Ramsey, who was Chaplain of his college and his first Theology tutor; and Henry Chadwick, who encouraged his early research in the Church Fathers. The evolution of Wiles' thinking is perhaps best observed in the collection published as Working Papers in Doctrine.

Excise taxes, broadly defined, are important revenue instruments. Their distinguishing features are selectivity in coverage, discrimination in intent, and often some form of quantitative measurement in determining the tax liability. The main objectives of excise taxation are to raise revenue for general purposes (Ramsey rule), to reflect external cost (Pigou prescription), to discourage consumption, and to charge road users for government-provided services. Some of the main issues in excise tax design concern the choice between specific and ad valorem rates and the trade-offs between taxes, tradable permits, and command-and-control regulations. Other issues are the proper coordination between excise taxes and value-added taxes and the desirable degree of harmonization in a single market.

For accommodating defective utterances within compositional semantics, truth-value gaps (Kleene's 3-valued logic) and gluts (Priest's LP) are equally efficient, but in terms of classical logic gaps yield harmless incompleteness, whereas gluts precipitate collapse; ex contradictione quodlibet. The discrepancy is less deep than first appears, however. A dialetheist dual to van Fraassen's supervaluationism, implicit in Ramsey's ‘Theories,’ counts sentences true if they are true in at least one acceptable model. Divergent illucutionary norms compensate for differing semantics. Subvaluationists (so-called by Varzi) replace the supervaluationist maxim, ‘Do not assert what is untrue,’ by ‘Do not assert what is false.’ Both predict the same verbal behavior.

A brief history of early magnetic resonance methods is given. In 1938, Rabi published the description of the first successful magnetic resonance experiment which he had used with collaborators to measure the nuclear magnetic moments in LiCl. With other collaborators, it became clear that the method provided precision radio-frequency and microwave spectroscopy. The theory of the method and the calculations of transition probabilities are given in detail. Although Rabi's method gives more accurate results than any previous method, the accuracy is limited by the fact that the accuracy increases with the length of the apparatus, but the length can not exceed ½ a wavelength of the oscillatory radiation without getting cancellations from the opposite phases. In 1949, Ramsey pointed out that this problem could be overcome by using two separated oscillatory field regions with each one less than ½ a wavelength long, but with the two regions being many wave lengths apart and with the oscillations in the two regions being coherently driven. This method (often called the Ramsey method) works well and provides resonances that can be hundreds of times narrower than that by Rabi's method. Sometimes the intensity of the resonances are increased by added space focusing or by the use of very slow molecules. Possible distortions of molecular beam resonances and means for preventing them are discussed.

In success semantics the notion of representation is linked to that of successful action. This chapter dissents from one popular way of expounding the connection, and suggests a different one making a fuller use of decompositional semantics.