Alethic pluralism holds that there are many ways of being true. The view has been accused of being unable to do justice to the traditional account of logical validity, understood as necessary truth preservation. In this paper I reformulate the debate in terms of the naturalness of generic truth, and discuss some notable consequences of this more careful reformulation. I show not only that some alleged solutions, like the resort to plural quantification, are ineffective, but also that the problem is (...) not really posed by mixed inferences, as usually thought. Finally, I argue that the traditional account of logical validity does carry a commitment to generic truth, so that a strong version of alethic pluralism can hardly vindicate it. (shrink)

In this paper, we shall give another proof of the faithfulness of Blass translation of the propositional fragment \ of Leśniewski’s ontology in the modal logic \ by means of Hintikka formula. And we extend the result to von Wright-type deontic logics, i.e., ten Smiley-Hanson systems of monadic deontic logic. As a result of observing the proofs we shall give general theorems on the faithfulness of B-translation with respect to normal modal logics complete to certain sets of well-known accessibility relations (...) with a restriction that transitivity and symmetry are not set at the same time. As an application of the theorems, for example, B-translation is faithful for the provability logic \ ), that is, \ \ \ \supset \Box \phi \). The faithfulness also holds for normal modal logics, e.g., \, \, \, \. We shall conclude this paper with the section of some open problems and conjectures. (shrink)

In Mathematics is megethology Lewis reconstructs set theory combining mereology with plural quantification. He introduces megethology, a powerful framework in which one can formulate strong assumptions about the size of the universe of individuals. Within this framework, Lewis develops a structuralist class theory, in which the role of classes is played by individuals. Thus, if mereology and plural quantification are ontologically innocent, as Lewis maintains, he achieves an ontological reduction of classes to individuals. Lewis’work is very attractive. However, the alleged (...) innocence of mereology and plural quantification is highly controversial and has been criticized by several authors. In the present paper we propose a new approach to megethology based on the theory of plural reference developed in To be is to be the object of a possible act of choice. Our approach shows how megethology can be grounded on plural reference without the help of mereology. (shrink)

Plural Logic is an extension of First-Order Logic with plural terms and quantifiers. When its plural terms are interpreted as denoting more than one object at once, Plural Logic is usually taken to be ontologically innocent: plural quantifiers do not require a domain of their own, but range plurally over the first-order domain of quantification. Given that Plural Logic is equi-interpretable with Monadic Second-Order Logic, it gives us its expressive power at the low ontological cost of a first-order language. This (...) makes it a valuable tool in various areas of philosophy. Some authors believe that Plural Logic can be extended into an even more expressive logic, Higher-Level Plural Logic, by adding higher-level plural terms and quantifiers to it. The basic idea is that second-level plurals stand to plurals like plurals stand to singulars. Allegedly, Higher-Level Plural Logic enjoys the expressive power of type theory while, again, committing us only to the austere ontology of a first-order language. Were this really the case, Higher-Level Plural Logic would be a very useful tool, extending and strengthening some of the applications of Plural Logic. However, while the notions of plural reference and quantification enjoy widespread acceptance today, their higher-level counterparts have been received with scepticism. The main objection raised against them is that higher-level plural reference is unintelligible. This has been argued, among others, on the grounds that there are no higher-level plurals in natural language and that, if there were any, they could be eliminated. In this thesis, after introducing the debate on plurals in Chapters 1 and 2, I turn to defending the legitimacy of the notion of higher-level plural reference. To this end, in Chapter 3, I present and elucidate the notion. Next, in Chapter 4, I show that some natural languages clearly contain these expressions and that they do so in an ineliminable manner. Finally, in Chapters 5 and 6, I develop a semantics for higher-level plurals that employs only devices previously well-understood by English speakers. To finish, in Chapter 7, I describe an application of Higher-level Plural Logic: a strengthening of the neo-Fregean programme. After describing my proposal, I turn to the issue of the logical status of this formalism and defend an optimistic take on the matter. (shrink)