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
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
- Ted Sider First Review of Williamson
- Ted Sider Second Review of Williamson
- Yagisawa Review of Williamson for Notre Dame
Zalta: The most useful brief tutorial on QML that I have found.
- 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
- 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
- “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
3.4 Professors/Online Classes
Bennet and Sider Bibliography on Modality and Possible Worlds. Annotated selectively.
Garson: Author of the excellent Modal for Philosophers email@example.com