Quantified Modal Logic (QML)

1. Overview & Major Debates


Frege (and Russell) devised an ingenious procedure for regimenting binary quantifiers like “every” and “some” in terms of unary quantifiers like “everything” and “something”: they formalized sentences of the form ⌜⌜Some A is B⌝⌝ and ⌜⌜Every A is B⌝⌝ as ∃x(Ax∧Bx) and ∀x(Ax→Bx), respectively. They analyzed a sentence like “some apples are delicious” in terms of the sentence “something is an apple and delicious”, whereas they parsed the sentence “every material object is extended” as “everything is extended, if it is a material object”.

2. Simplest QML


3. Resources

3.1 Websites

Modern Origins of Modal Logic, Stanford Philosophy

Transworld Identity in Modal Logic, Stanford Philosophy

Lewis, David (1968) Counterpart Theory and Modal Logic

3.2 Books

von Bentham, Johan Modal Logic for Open Minds

Chellas (1980) Modal Logic: An Introduction

Goldblatt (1992) Logics of Time and Computation

Hughes and Cresswell (1996) A New Introduction to Modal Logic (replaces earlier editions).

Kripke, Saul Naming and Necessity

Lewis, David On the Plurality of Worlds

Pacuit, Eric Notes on Modal Logic

Williamson, Timothy (2013) Modal Logic as Metaphysics

Zalta: The most useful brief tutorial on QML that I have found.

3.3 PDFs

Goldblatt (2003) History of Modal Logic

Liao (2012) What are Centered Worlds?

Linsky and Zalta (1996) In Defense of the Contingently Nonconcrete

  • Very important for me, since in my interpretation of SR, all worlds must have a common domain of quantification.
  • “Unlike Kripke semantics, in which each world may have a different domain, our interpretation employs models with a single domain of quantification, the objects of which have different properties at different worlds.”
  • They defend this article against a critique by Karen Bennett

McDaniels, Kris (2004) Modal Realism with Overlap.

  • Abstract: In this paper, I formulate, elucidate, and defend a version of modal realism with overlap, the view that objects are literally present at more than one possible world. The version that I defend has several interesting features: (i) it is committed to an ontological distinction between regions of spacetime and material objects; (ii) it is committed to compositional pluralism, which is the doctrine that there is more than one fundamental part-whole relation; and (iii) it is the modal analogue of endurantism, which is the doctrine that objects persist through time by being wholly present at each moment they are located.
  • Useful to me because it is consistent with the notion of reference frames providing unique views of a common underlying physical reality

McDaniels, Kris (2006) Modal Realisms

Smith, Quentin (2001) The Metaphysical Necessity of Natural Laws

  • “In this paper I will defend the thesis that natural laws are metaphysically necessary, i.e. obtain in every possible world. Metaphysical necessity and possibility are the unrestricted modalities in the semantical interpretation of the modal logic system S5, which I adopt in this paper. I shall defend the following definition of a law of nature: (D1) L is a natural law if and only if (i) L obtains in every possible world (ii) L is synthetic (iii) L is a posteriori (iv) L is a universal generalization (v) L mentions no times, places or particular things or events. (vi) L entails corresponding counterfactuals.
  • A good example of a very sensibly written philosophy paper

Williamson, Timothy (2016) Modal Science

3.4 Professors/Online Classes

Bennet and Sider Bibliography on Modality and Possible Worlds. Annotated selectively.

Garson: Author of the excellent Modal for Philosophers  jgarson@uh.edu

MIT course on Modal Logic

Zalta: The most useful brief tutorial on QML that I have found is the class notes of Zalta, PDF here.