Moving up and down in the generic multiverse

We give a brief account of the modal logic of the generic multiverse, which is a bimodal logic with operators corresponding to the relations "is a forcing extension of" and "is a ground model of". The fragment of the first relation is called the modal logic of forcing and was studied by us in earlier work. The fragment of the second relation is called the modal logic of grounds and will be studied here for the first time. In addition, we discuss which combinations of modal logics are possible for the two fragments.Comment: 10 pages. Extended abstract. Questions and commentary concerning this article can be made at http://jdh.hamkins.org/up-and-down-in-the-generic-multiverse

Agency and fictional truth: a formal study on fiction-making

Fictional truth, or truth in fiction/pretense, has been the object of extended scrutiny among philosophers and logicians in recent decades. Comparatively little attention, however, has been paid to its inferential relationships with time and with certain deliberate and contingent human activities, namely, the creation of fictional works. The aim of the paper is to contribute to filling the gap. Toward this goal, a formal framework is outlined that is consistent with a variety of conceptions of fictional truth and based upon a specific formal treatment of time and agency, that of so-called stit logics. Moreover, a complete axiomatic theory of fiction-making TFM is defined, where fiction-making is understood as the exercise of agency and choice in time over what is fictionally true. The language L of TFM is an extension of the language of propositional logic, with the addition of temporal and modal operators. A distinctive feature of L with respect to other modal languages is a variety of operators having to do with fictional truth, including a \u2018fictionality\u2019 operator M (to be read as \u201cit is a fictional truth that\u201d). Some applications of TFM are outlined, and some interesting linguistic and inferential phenomena, which are not so easily dealt with in other frameworks, are accounted for

The Contextual Character of Modal Interpretations of Quantum Mechanics

In this article we discuss the contextual character of quantum mechanics in the framework of modal interpretations. We investigate its historical origin and relate contemporary modal interpretations to those proposed by M. Born and W. Heisenberg. We present then a general characterization of what we consider to be a modal interpretation. Following previous papers in which we have introduced modalities in the Kochen-Specker theorem, we investigate the consequences of these theorems in relation to the modal interpretations of quantum mechanics.Comment: 21 pages, no figures, preprint submitted to SHPM

Specificity distinction

This paper is concerned with semantic noun phrase typology, focusing on the question of how to draw fine-grained distinctions necessary for an accurate account of natural language phenomena. In the extensive literature on this topic, the most commonly encountered parameters of classification concern the semantic type of the denotation of the noun phrase, the familiarity or novelty of its referent, the quantificational/nonquantificational distinction (connected to the weak/strong dichotomy), as well as, more recently, the question of whether the noun phrase is choice-functional or not (see Reinhart 1997, Winter 1997, Kratzer 1998, Matthewson 1999). In the discussion that follows I will attempt to make the following general points: (i) phenomena involving the behavior of noun phrases both within and across languages point to the need of establishing further distinctions that are too fine-grained to be caught in the net of these typologies; (ii) some of the relevant distinctions can be captured in terms of conditions on assignment functions; (iii) distribution and scopal peculiarities of noun phrases may result from constraints they impose on the way variables they introduce are to be assigned values. Section 2 reviews the typology of definite noun phrases introduced in Farkas 2000 and the way it provides support for the general points above. Section 3 examines some of the problems raised by recognizing the rich variety of 'indefinite' noun phrases found in natural language and by attempting to capture their distribution and interpretation. Common to the typologies discussed in the two sections is the issue of marking different types of variation in the interpretation of a noun phrase. In the light of this discussion, specificity turns out to be an epiphenomenon connected to a family of distinctions that are marked differently in different languages

Disquotationalism and the Compositional Principles

What Bar-On and Simmons call 'Conceptual Deflationism' is the thesis that truth is a 'thin' concept in the sense that it is not suited to play any explanatory role in our scientific theorizing. One obvious place it might play such a role is in semantics, so disquotationalists have been widely concerned to argued that 'compositional principles', such as (C) A conjunction is true iff its conjuncts are true are ultimately quite trivial and, more generally, that semantic theorists have misconceived the relation between truth, meaning, and logic. This paper argues, to the contrary, that even such simple compositional principles as (C) have substantial content that cannot be captured by deflationist 'proofs' of them. The key thought is that (C) is supposed, among other things, to affirm the truth-functionality of conjunction and that disquotationalists cannot, ultimately, make sense of truth-functionality. This paper is something of a companion to "The Logical Strength of Compositional Principles"

Structural Relativity and Informal Rigour

Informal rigour is the process by which we come to understand particular mathematical structures and then manifest this rigour through axiomatisations. Structural relativity is the idea that the kinds of structures we isolate are dependent upon the logic we employ. We bring together these ideas by considering the level of informal rigour exhibited by our set-theoretic discourse, and argue that different foundational programmes should countenance different underlying logics (intermediate between first- and second-order) for formulating set theory. By bringing considerations of perturbations in modal space to bear on the debate, we will suggest that a promising option for representing current set-theoretic thought is given by formulating set theory using quasi-weak second-order logic. These observations indicate that the usual division of structures into \particular (e.g. the natural number structure) and general (e.g. the group structure) is perhaps too coarse grained; we should also make a distinction between intentionally and unintentionally general structures