# Teaching & Learning Guide for: Problems with Temporary Existence in Tense Logic

## Abstract

This guide accompanies the following article(s): Meghan Sullivan, ‘Problems with Temporary Existence in Tense Logic’. Philosophy Compass 7/1 (2012): 43–57. doi: 10.1111/j.1747-9991.2011.00457.x

### Author’s Introduction

Over the past century, there has been considerable debate over whether and how anything changes with respect to existence. Most A-theorists of time (presentists, growing block theorists, and branch theorists) think things come to exist or cease to exist. B-theorists of time (four-dimensionalists, in particular) think objects do not change with respect to existence. In my Compass article, I outline a serious difficulty that A-theorists face in trying to reason about temporary existents. The most straightforward logics for time and existence entail that nothing exists merely temporarily. The problem arises from a set of theorems of the simplest temporal logic – the converse Barcan formulas. But attempts to fix the logic to get rid of the Barcan formulas pressure A-theorists to abandon an intuitive and widespread assumption about existence. I survey the logical and metaphysical options for solving the problem.

### Author Recommends

Burgess, John P. Philosophical Logic. Princeton: Princeton University Press, 2009.

An introductory textbook in philosophical logic. Chapter 2 focuses on temporal logic and motivates a logic-based response to problems with the temporal Barcan schemas.

Prior, A. N. Past, Present, and Future. Oxford: Oxford University Press, 1967.

The first attempt to rigorously formulate propositional and quantified tense logic. Chapter 8 especially provides philosophical insight into problems with change in existence. Prior uses Polish notation for his proofs and formalism, which requires a bit of background to translate.

Sider, Theodore. Four-Dimensionalism. Oxford: Oxford University Press, 2001.

Provides a useful background on the debates in the philosophy of time. The first three chapters that precisely define the different theories are especially relevant.

Sider, Theodore. Logic for Philosophy. Oxford: Oxford University Press, 2010.

A useful guide to the semantics and proof theory of modal and temporal logics.

van Inwagen, Peter. ‘Meta-Ontology.’Erkenntnis 48 (1998):233–50.

Gives an explanation and defense of neo-Quinean assumptions.

Williamson, Timothy. ‘Bare Possibilia.’Erkenntnis 48 (1998):257–73.

Provides a logic-based argument for necessary, permanent existence and gives an A-theory-friendly model for explaining change on such an ontology.

Zimmerman, Dean W. ‘Temporary Intrinsics and Presentism.’Metaphysics: The Big Questions. Eds. Peter van Inwagen and Dean W. Zimmerman. Oxford: Blackwell, 1998.

Surveys a problem in formulating presentist theories of change and motivates the need for tense operators.

### Sample Syllabus:

Here is a sample syllabus for a course on time in metaphysics and logic:

Week I: Introduction: A-Theories and B-Theories

We will consider precise ways of differentiating A-theories of time and B-theories of time, looking in particular at how A-theorists and B-theorists think of intrinsic properties.

•  Chap 4.2., Lewis, David. On the Plurality of Worlds. Oxford: Blackwell, 1986.
•  Zimmerman, Dean W. ‘Temporary Intrinsics and Presentism.’Metaphysics: The Big Questions. Eds. Peter van Inwagen and Dean W. Zimmerman. Oxford: Blackwell, 1998.
•  Chap 2, Sider, Theodore. Four-Dimensionalism. Oxford: Oxford University Press, 2001.

Week II: The Bug: Temporary Existence in Tense Logic

We will consider why A-theorists use tense logics to express their views, and we will look at the difficulties A-theorists have expressing temporary existence in tense logic.

•  Sullivan, Meghan. ‘Problems for Temporary Existence in Tense Logic.’Philosophy Compass.
•  Chap 8, Prior, A. N. Past, Present, and Future. Oxford: Oxford University Press, 1967.

Week III: Option 1: Rewire Tense Logic?

We will learn about Kripke’s solution to the parallel problem in modal logic, consider how it might be applied to tense logic, and then consider philosophical difficulties for the proposal.

•  Chap 2, Burgess, John P. Philosophical Logic. Princeton: Princeton University Press. 2009.
•  Kripke, Saul. ‘Semantical Considerations in Modal Logic.’Reference and Modality. Ed. Bernard Linsky. Oxford: Oxford University Press, 1971.
•  Optional: Chap 10, Sider, Theodore. Logic for Philosophy. Oxford: Oxford University Press, 2010.

Week IV: Option 2: Believe in Permanent Existence?

Williamson does not think we should revise our quantification theory. Instead, he argues that we should believe all objects necessarily, always exist. We will consider possible justifications for permanent existence.

•  Williamson, Timothy. ‘Bare Possibilia.’Erkenntnis 48 (1998): 25773.
•  Williamson, Timothy. ‘Necessary Existents.’Logic, Thought and Language. Ed. Anthony O’Hear. Cambridge: Cambridge University Press, 2002.
•  Sullivan, Meghan. ‘The Minimal A-Theory.’Philosophical Studies (forthcoming).

Week V: Deflate the Debate (Drop Neo-Quineanism)?

We might think the logical problem only arises because we assume there is a single logic for existence. This assumption looks silly if we think there is no metaphysically privileged sense of existence. Deflationists argue for this solution to the presentist/eternalist debate. We’ll see if it provides attractive options for the more general debate over temporary existence.

•  Hirsch, Eli. ‘Ontology and Alternative Languages.’Metametaphysics: New Essays in the Foundations of Ontology. Eds. David J. Chalmers, David Manley, and Ryan Wasserman. Oxford: Oxford University Press, 2009.
•  Hofweber, Thomas. ‘The Meta-Problem of Change.’Nous 2 (2009): 286314.
•  van Inwagen, Peter. ‘Meta-Ontology.’Erkenntnis 48 (1998): 23350.

### Focus Questions

•  Are A-theorists right to draw a close distinction between the past and future and merely possible worlds? To what extent is the analogy apt? What are some reasons the analogy might be misleading?
•  Test your familiarity with QTLK. Which of the following are theorems? Can you prove them? If they are not theorems, can you provide countermodels in the formal semantics? Feel free to include diagrams for countermodels.
• (a)∀xF(Sx) → ∃xF(Sx)
• (b)∃xF(Sx) → ∃xH(Sx)
• (c)∃xP¬∃y(x = y) → P∃x¬∃y(x = y)
•  “A-theorists who use Kripke’s semantics and free tense logic are forced to have a non-Quinean theory of existence.” How would someone argue for this claim? Do you agree?
•  “Williamson’s ontology gives up what is most important about Neo-Quineanism.” How would someone argue for this claim? Do you agree?