Counterpossibles, story prefix and trivialism

The aim of this paper is to argue in favor of the view that some counterpossibles are false. This is done indirectly by showing that accepting the opposite view, i.e., one that ascribes truth to each and every counterpossible, results in the claim that every necessarily false theory has exactly the same consequences. Accordingly, it is shown that taking every counterpossible to be true not only undermines the value of debates over various alternative theories and their consequences, but also puts into question the very possibility of such debates. In order to explicate this thesis, the close bond between counterpossibles and the so-called story prefix (i.e., the sentential operator ‘According to fiction F, P’) is explored. A number of possible responses to this criticism are also presented, and it is argued that none of them address the main problem.

Ontology Deflated

Kit Fine (Fine, 2009) rejects the standard Quinean quantificational account of ontological questions and favours an account of a very different kind on which existence or reality is expressed not by quantifiers but by a predicate ‘exists’ or ‘is real’, itself ultimately to be explained in terms of a sentential operator. Although primarily directed against the quantificational account, Fine’s criticisms apply equally to the account favoured by Hale, which rejects much of Quine’s view but agrees with him on a fundamental point: ‘The mark of our commitment to entities of a given kind is our acceptance, as strictly and literally true, of statements embedding expressions which, if they have reference at all, have entities of that kind as their referents, or semantic values.’ The chapter’s aim here is to explain why Hale finds Fine’s criticisms to be unsound.

An Occurrence at Owl Creek Bridge

This chapter presents a Radical Fictionalist analysis of talk about fiction, as in my utterances of ‘Fahrquhar was a well to do planter’ or of ‘according to Bierce’s Occurrence, Fahrquhar was a well to do planter’. According to this chapter’s favourite approach, namely the Way of Retelling, the former sentence does not encode a proposition, and the latter does not involve a sentential operator. The central sections of this chapter justify the sense in which these sentences are not in the business of truth, and are rather to be assessed according to the normative dimension of faithfulness. The final sections of this chapter present an alternative to the Way of Retelling, namely the Way of Truth. This hypothesis remains consistent with the premises of Radical Fictionalism, but it satisfies those who insist that fiction talk is to be analysed as elliptical talk concerned with actual truth.

Clause-final negation

Negation in a number of Austronesian and Papuan languages with SVO order is expressed by a rather rigid clause-final position of the negative adverb. Some typological generalizations for negation are reviewed and the distribution of this trait in languages of different stocks is discussed, arguing that it most likely originates in Papuan languages. Some proposals for different types of negation, such as whether it is a verbal (or VP) operator, a constituent operator or a sentential operator are considered. The problem of determining the scope of negation is discussed, with the conclusion that hard and fast semantic meanings for NEG at different structural levels cannot be posited, suggesting that perhaps a solution can be found in the application of some universal pragmatic principles.

Two incomplete anti-realist modal epistemic logics

Many phrases have been used to express what are sometimes called anti-realist conceptions of truth: ‘verifiability’, ‘knowability’, ‘rational acceptability’, ‘warranted assertability’. In spite of their obvious differences, all four of these phrases have a common form; each is a cognitive attitude modified by ‘-ability’. They speak of the possibility of verification, knowledge, rational acceptance or warranted assertion. Schematically, it seems to be claimed that it is true that A if and only if it is possible that it is E'd that A, where ‘E’ is to be replaced by some cognitive verb and ‘A’ by any indicative sentence of the class to which the anti-realist conception is being claimed to apply. Since truth is redundant as a sentential operator, this boils down to the following thesis, where ‘p’ is a propositional variable and ‘M’ expresses the appropriate kind of possibility:(*) also formalizes views such as Putnam's: ‘To claim a statement is true is to claim it could be justified’ [11, p. 56]. It is no doubt a crude model for anti-realism, but one has to start somewhere; by seeing how and why more sophisticated versions of anti-realism differ from (*) one should be able to understand them better too. Moreover, if an anti-realist rejects the equation of truth with, say, warranted assertibility, arguing that truth is rather to be identified with the possibility of getting into a position in which one's warrant to assert somehow cannot be overturned, the form of (*) is preserved, for truth is still being identified with the possibility of something.

A natural extension of natural deduction

One of the main ideas of calculi of natural deduction, as introduced by Jaśkowski and Gentzen, is that assumptions may be discharged in the course of a derivation. As regards sentential logic, this conception will be extended in so far as not only formulas but also rules may serve as assumptions which can be discharged. The resulting calculi and derivations with rules of any finite level are informally introduced in §1, while §§2 and 3 state formal definitions of the concepts involved and basic lemmata. Within this framework, a standard form for introduction and elimination rules for arbitrary n-ary sentential operators is motivated in §4, understood as a contribution to the theory of meaning for logical signs. §5 proves that the set {&, ∨, ⊃, ⋏} of standard intuitionistic connectives is complete, i.e. &, ∨, ⊃, and ⋏ suffice to express each n-ary sentential operator having rules of the standard form given in §4. §6 makes some remarks on related approaches. For an extension of the conception presented here to quantifier logic, see [11].