If we wish to formulate an axiomatic truth-theory interpreting a modal language and treat the symbol of necessity as a sentential operator and not as a quantifier over possible worlds, there arise various problems. These are due partly to the fact that words could have meant something other than what they actually mean and partly to certain principles of modal metaphysics. One of those principles is existentialism about propositions: a proposition that is expressed in a sentence containing a non-empty name could not exist if the referent of the name did not exist. The paper explains how the problems arise. It also explains how we can avoid them using substitutional quantification in the metalanguage. The truth-theory we can construct in that way is compositional and homophonic, and its theorems interpreting the various sentences of the modal language are derived in a straightforward way. The paper develops one such theory for a propositional modal language and one for a first-order modal language. The first-order case involves a number of intricacies that are discussed.

How should we treat the liar and kindred paradoxes? A Theory of Truth argues that we should diverge from classical logic, and presents a new formal theory of truth. The theory does not incorporate contradictions and is not substructural, but deviates from classical logic significantly. It endorses principles like ‘No sentence is both true and false’ and ‘No sentence is neither true nor false’.The book starts with an introduction to the paradoxes, suitable for newcomers to the subject, before presenting its approach. Four versions of the theory are covered, extending the theory to a determinacy operator and to a full first-order language with quantifiers. Each includes all Tarskian biconditionals that can be formulated in its language. The author uses original methods to prove the consistency of each version and compares the theory to alternative non-classical theories, including Field’s paracomplete approach, Ripley’s nontransitive system and Zardini’s contraction-free calculus.

Some authors have suggested that, contrary to what is usually thought, ‘actually’ and similar expressions (‘in fact’, ‘in reality’, etc.) cannot effect a return to the actual world when used in a context generated by a different modal operator, and so are quite unlike the actuality operator of modal logic. I argue that they can induce such a return. The argument involves comparing them with other devices that can play a similar role, such as scope and mood, and examining the effect of ‘actually’ and the like in a range of different sentences.

Existentialism about propositions is the view that a proposition expressed in a sentence containing a nonempty name or indexical depends ontologically on the referent of the name or indexical: the proposition could not exist if the referent did not. The paper focuses on names. It discusses some arguments for existentialism and then presents a novel one. That argument does not presuppose that propositions have constituents, and it could be accepted by those who hold broadly Fregean views about names. It shows that, for example, if Aristotle had not existed, no sentence could have meant that Aristotle is a philosopher. The paper also touches on the consequences of existentialism.

The liar and kindred paradoxes show that we can derive contradictions when we reason in accordance with classical logic from the schema (T) about truth: S is true iff p, where ‘p’ is to be replaced with a sentence and ‘S’ with a name of that sentence. The paper presents two arguments to the effect that the blame lies not with (T) but with classical logic. The arguments derive contradictions using classical logic, but instead of appealing to (T), they invoke semantic claims that seem even harder to reject. The first argument relies on two standard semantic principles that are not disquotational and on the claim that if there is such a thing as the property of being true, then ‘true’ expresses that property. The second argument relies on a schema about meaning: S means that p, where ‘S’ and ‘p’ are to be replaced as before.

The liar and kindred paradoxes show that we can derive contradictions if our language possesses sentences lending themselves to paradox and we reason classically from schema (T) about truth: S is true iff p, where the letter p is to be replaced with a sentence and the letter S with a name of that sentence. This article presents a theory of truth that keeps (T) at the expense of classical logic. The theory is couched in a language that possesses paradoxical sentences. It incorporates all the instances of the analogue of (T) for that language and also includes other platitudes about truth. The theory avoids contradiction because its logical framework is an appropriately constructed nonclassical propositional logic. The logic and the theory are different from others that have been proposed for keeping (T), and the methods used in the main proofs are novel.

The liar and kindred paradoxes make it difficult to construct a consistent and plausible formal theory of truth. One approach is to tackle them not by restricting the principles about truth that pre-theoretically seem correct, but by deviating from classical logic. I outline a nonclassical propositional logic I have constructed within that approach, as well as a theory of truth embedded in the framework of the logic. (Preliminary presentation of some of the material that eventually became the paper 'A propositional theory of truth'.)

The paper is an investigation into the concept of actuality from the standpoint of the philosophy of language. It is argued that expressions such as ‘actually’ and ‘in fact’ are not indexicals like ‘here’ and ‘now’; when e.g. ‘Snow is actually white’ is uttered in a world, what proposition is conveyed does not depend on the world. Nor are such expressions ambiguous. The paper makes a suggestion about the role that ‘actually’ and its cognates do play. It is also argued that the sentence ⌜Actually S⌝ expresses a necessary truth only if S itself expresses one. In order to capture the necessitation of the proposition expressed in ⌜Actually S⌝ , it is not sufficient to prefix the word ‘necessarily’.

Serious actualism is the principle that, for every entity x and every property φ, it could not have been that x did not exist but had φ. The principle was called ‘serious actualism’ by A. Plantinga, who argued for it. Accepting it has serious consequences about how it is philosophically preferable to develop first-order modal logic. In the paper I show why some alleged counterexamples to the principle should not convince us, and then I offer three arguments for serious actualism and for the corresponding principle about relations. According to the first, by accepting those doctrines we avoid a serious difficulty when we try to explain when two properties, or two relations, coincide in extension. The second argument relies on some tenets about sets. The third improves upon Plantinga’s reasoning in favour of serious actualism. I then draw some conclusions about when a linguistic expression ought to be regarded as a predicate from a logical and semantic point of view. Finally, I discuss certain principles about time and space that are analogous to serious actualism.

In this paper the language of first-order modal logic is enriched with an operator @ (‘actually’) such that, in any model, the evaluation of a formula @A at a possible world depends on the evaluation of A at the actual world. The models have world-variable domains. All the logics that are discussed extend the classical predicate calculus, with or without identity, and conform to the philosophical principle known as serious actualism. The basic logic relies on the system K, whereas others correspond to various properties that the actual world may have. All the logics are axiomatized.

After an introduction to the issue of indexicals, the paper adumbrates the approaches of certain philosophers, mainly D. Kaplan and G. Evans. After criticizing some aspects of those approaches and agreeing with others, it puts forward a view that can be characterized as Fregean. According to that view, whenever an indexical is uttered, the content (or sense) of the utterance is bipolar: it consists partly in the entity referred to and partly in a way in which one can think of the entity and which involves the particular utterance. As the way of thinking involves the utterance, the content is different whenever an indexical is used, whether the indexical is the same or not. On the other hand, as the content includes the reference, it does not coincide with the content of any definite description; the reference of a definite description is not part of its content.

The paper discusses several first-order modal logics that extend the classical predicate calculus. The model theory involves possible worlds with world-variable domains. The logics rely on the philosophical tenet known as serious actualism in that within modal contexts they allow existential generalization from atomic formulas. The language may or may not have a sign of identity, includes no primitive existence predicate, and has individual constants. Some logics correspond to various standard constraints on the accessibility relation, whereas others correspond to various constraints on the domains of the worlds. Soundness and strong completeness are proved in every case; a novel method is used for proving completeness.

The word ‘actually’ often refers to what is in fact the case, but it also often points to what would have been the case in a possible situation that is being envisaged. To capture such nuances, the formal languages discussed in the paper add subscripts to modal operators; in the model theory the subscripts allow an actuality operator to turn the evaluation of a formula to a world introduced by a preceding possibility or necessity operator having the same subscript. The paper covers both propositional and predicate logic and proves the completeness of axiomatizations that extend standard modal systems beginning with K.

The paper argues, varying Cantor’s well-known set-theoretic reasoning, that the principle “(It is possible that p) iff (in some possible world, p)” leads to a paradoxical conclusion regarding how many possible worlds there are. The argument justifies some scepticism about whether there are possible worlds in any of the philosophical senses of the term (as opposed to the sense in which we talk about possible worlds in modal logic and which is minimally laden from a metaphysical viewpoint).

Take a formula of first-order logic which is a logical consequence of some other formulae according to model theory, and in all those formulae replace schematic letters with English expressions. Is the argument resulting from the replacement valid in the sense that the premisses could not have been true without the conclusion also being true? Can we reason from the model-theoretic concept of logical consequence to the modal concept of validity? Yes, if the model theory is the standard one for sentential logic; no, if it is the standard one for the predicate calculus; and yes, if it is a certain model theory for free logic. These conclusions rely inter alia on some assumptions about possible worlds, which are mapped into the models of model theory. Plural quantification is used in the last section, while part of the reasoning is relegated to an appendix that includes a proof of completeness for a version of free logic.

This paper shows that some plausible assumptions about any object that has a name lead to the conclusion that the object could not have failed to exist. Considering the conclusion wrong, I argue that the source of the error is the principle “If something is the case, it could not have been impossible”, which occurs in some systems of modal logic; if an object did not exist, it would not be possible for it to exist.

The paper is an analysis of Plato's "proof" of the immortality of the soul in Phaedrus 245c-246a. It points out that the "proof" consists of two arguments: one intended to show that, as long as it exists, the soul does not cease to be alive, and one meant to demonstrate that the soul never ceases to exist.