Teaching & Learning Guide for: Problems withTemporary Existence in Tense Logic

Meghan SullivanUniversity of Notre Dame

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 any-thing changes with respect to existence. Most A-theorists of time (presentists, growingblock theorists, and branch theorists) think things come to exist or cease to exist. B-theo-rists of time (four-dimensionalists, in particular) think objects do not change with respectto existence. In my Compass article, I outline a serious difficulty that A-theorists face intrying to reason about temporary existents. The most straightforward logics for time andexistence entail that nothing exists merely temporarily. The problem arises from a set oftheorems of the simplest temporal logic – the converse Barcan formulas. But attempts tofix the logic to get rid of the Barcan formulas pressure A-theorists to abandon an intuitiveand widespread assumption about existence. I survey the logical and metaphysical optionsfor 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 logicand 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. Chapter8 especially provides philosophical insight into problems with change in existence. Prioruses Polish notation for his proofs and formalism, which requires a bit of background totranslate.

Sider, Theodore. Four-Dimensionalism. Oxford: Oxford University Press, 2001.Provides a useful background on the debates in the philosophy of time. The first threechapters 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.

Philosophy Compass 7/4 (2012): 290–292, 10.1111/j.1747-9991.2011.00461.x

ª 2012 The AuthorPhilosophy Compass ª 2012 Blackwell Publishing Ltd

Williamson, Timothy. ‘Bare Possibilia.’ Erkenntnis 48 (1998):257–73.Provides a logic-based argument for necessary, permanent existence and gives anA-theory-friendly model for explaining change on such an ontology.

Zimmerman, Dean W. ‘Temporary Intrinsics and Presentism.’ Metaphysics: The BigQuestions. Eds. Peter van Inwagen and Dean W. Zimmerman. Oxford: Blackwell, 1998.Surveys a problem in formulating presentist theories of change and motivates the needfor 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-TheoriesWe will consider precise ways of differentiating A-theories of time and B-theories of time, looking inparticular at how A-theorists and B-theorists think of intrinsic properties.

Reading:• 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 LogicWe will consider why A-theorists use tense logics to express their views, and we will look at thedifficulties A-theorists have expressing temporary existence in tense logic.

Reading:• 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 mightbe applied to tense logic, and then consider philosophical difficulties for the proposal.

Reading:• 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 weshould believe all objects necessarily, always exist. We will consider possible justifications for perma-nent existence.

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ª 2012 The Author Philosophy Compass 7/4 (2012): 290–292, 10.1111/j.1747-9991.2011.00461.xPhilosophy Compass ª 2012 Blackwell Publishing Ltd

Reading:• Williamson, Timothy. ‘Bare Possibilia.’ Erkenntnis 48 (1998): 257–73.• 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 exis-tence. 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 attrac-tive options for the more general debate over temporary existence.

Reading:• 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): 286–314.• van Inwagen, Peter. ‘Meta-Ontology.’ Erkenntnis 48 (1998): 233–50.

Focus Questions

• Are A-theorists right to draw a close distinction between the past and future and merelypossible worlds? To what extent is the analogy apt? What are some reasons the analogymight be misleading?

• Test your familiarity with QTLK. Which of the following are theorems? Can youprove them? If they are not theorems, can you provide countermodels in the formalsemantics? Feel free to include diagrams for countermodels.(a) "xF(Sx) fi $xF(Sx)(b) $xF(Sx) fi $xH(Sx)(c) $xP�$y(x = y) fi 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 youagree?

• ‘‘Williamson’s ontology gives up what is most important about Neo-Quineanism.’’How would someone argue for this claim? Do you agree?

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ª 2012 The Author Philosophy Compass 7/4 (2012): 290–292, 10.1111/j.1747-9991.2011.00461.xPhilosophy Compass ª 2012 Blackwell Publishing Ltd