Infinity, causation, and paradox / Alexander R. Pruss

Author:: Pruss, Alexander R.
Published:: Oxford : Oxford University Press, 2018.
Edition:: First edition.
Physical Description:: 1 online resource : illustrations (black and white)

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Contents:

Machine generated contents note: 1.Infinity, Paradox, and Mathematics -- 1.Paradox and Causal Finitism -- 2.Some Mathematical and Logical Notes -- 3.Modality -- 3.1.Metaphysical possibility and necessity -- 3.2.Rearrangement principles -- 3.2.1.Defeasibility -- 3.2.2.Causal powers -- 4.Finitism: An Alternate Hypothesis -- 4.1.Time and finitism -- 4.2.Non-causal paradoxes: An advantage? -- 4.3.Mathematics: A disadvantage -- 4.3.1.Infinitely many primes -- 4.3.2.Potential infinity -- 4.3.3.*If-thenism -- 4.4.Future infinities -- 5.*Defining the Finite and the Countable -- 5.1.The finite -- 5.2.Acceptable models for the axioms of arithmetic -- 6.Evaluation -- Appendix: *Counting Future Things -- 2.Infinite Regresses -- 1.How to Violate Causal Finitism -- 2.Infinite Causal Regresses -- 3.Type (i): Uncaused Regresses -- 3.1.Viciousness -- 3.2.Vicious regresses and the Hume-Edwards Principle -- 3.3.Regresses and explanatory loops -- 4.Type (ii): Causation Passing through Infinitely Many Steps -- 5.Type (iii): Outside Cause Directly Causing Each Item -- 5.1.Options -- 5.2.Regresses with outside overdetermination -- 6.*Analogy with Axiom of Regularity -- 7.Evaluation -- Appendix: *Two Kinds of Violations of Causal Finitism -- 3.Supertasks and Deterministic Paradoxes -- 1.Introduction -- 2.Thomson's Lamp Revisited -- 2.1.Introduction -- 2.2.Causal finitism -- 2.3.Non-standard analysis -- 2.4.Special Relativity -- 2.5.Benacerraf s solution and the Principle of Sufficient Reason -- 2.6.Two counterfactuals -- 2.7.Evaluation -- 3.Grim Reapers -- 3.1.Introduction -- 3.2.Causal finitism -- 3.3.The absurd conclusion objection -- 3.4.A rearrangement objection -- 3.5.The mereological objection -- 3.5.1.Fusion -- 3.5.2.Necessary emergence of organic wholes -- 3.6.Uncaused lighting -- 3.6.1.Objection -- 3.6.2.The Causal Principle is true -- 3.6.3.Is the lamp lighting really uncaused? -- 3.6.4.A mysterious correlation -- 3.7.Discrete time -- 3.8.Evaluation -- 4.Infinite Newtonian Universes -- 4.1.An argument against causal finitism and a riposte -- 4.2.Smullyan's rod -- 4.3.The conditional -- 5.Another Eternal Life -- 6.Time Travel and Causal Loops -- 6.1.Grandfathers and togglers -- 6.2.Time travel and backwards causation without causal loops -- 7.Evaluation -- 4.Paradoxical Lotteries -- 1.Introduction -- 2.Countably Infinite Fair Lotteries -- 2.1.Background -- 2.2.Expected surprise -- 2.3.A guessing game -- 2.4.Symmetry -- 2.4.1.Symmetry and lotteries -- 2.4.2.*Symmetry and expected utility -- 2.5.Bayesian manipulation -- 2.5.1.The paradox -- 2.5.2.*A switchover point? -- 2.5.3.*Countable additivity and conglomerability -- 2.6.Improving everyone's chances -- 3.Constructing Paradoxical Lotteries -- 3.1.Fairness and paradoxicality -- 3.2.Lucky coin-flip sequences -- 3.3.What it is to construct a countably infinite fair lottery -- 3.4.*Coin-flips and the Axiom of Choice -- 3.5.Random walks -- 4.Objections -- 4.1.Infinite lotteries and uniform distributions -- 4.1.1.The problem -- 4.1.2.Response I: No continuous distributions -- 4.1.3.Response II: Measurement of infinite precision data -- 4.1.4.Response III: The use of the Axiom of Choice -- 4.2.*A non-normalizable quantum state -- 4.3.Limitations on our reasoning -- 5.Evaluation -- 5.Probability and Decision Theory -- 1.Introduction -- 2.Guessing with Finitely Many Errors -- 2.1.Doing a little better than one can -- 2.2.A contradiction -- 2.3.Doing much better than one can -- 2.4.*Construction of strategy guaranteeing at most finitely many errors -- 2.5.A multipersonal synchronic version -- 2.5.1.An angelic announcement -- 2.5.2.An objection and a tweak -- 2.5.3.*Making the paradox robust -- 2.6.A parody? -- 2.6.1.The story -- 2.6.2.Evaluating the parody -- 3.Satan's Apple -- 3.1.The story -- 3.2.Synchronic version -- 3.3.Diachronic version -- 3.4.Objection: Scores, desires, and promises -- 3.5.Evaluation -- 4.Beam's Paradox -- 4.1.*The mathematical formulation -- 4.2.*Synchronic version -- 4.3.*Diachronic infinite future version -- 4.4.*Diachronic supertask version -- 4.5.Evaluation of Beam's paradox -- 5.Evaluation of Decision-Theoretic Paradoxes -- Appendix: *Proof of the Theorem from Section 2.1 -- 6.The Axiom of Choice Machine -- 1.Less Technical Introduction -- 2.*The Axiom of Choice for Countable Collections of Reals -- 3.*Paradoxes of ACCR -- 3.1.Die-guessing games -- 3.2.Non-measurable sets -- 3.3.Banach-Tarski paradox -- 4.*An Argument for ACCR -- 5.*A Choice Machine -- 5.1.Strange mathematics and paradox -- 5.2.Coin-flips and Dutch Books -- 5.3.How to construct a Choice Machine -- 5.3.1.Angels -- 5.3.2.A four-dimensional machine -- 5.3.2.1.Making the machine -- 5.3.2.2.Using the machine -- 5.3.2.3.Causal infinitism and verifying the machine's match -- 5.3.3.A three-dimensional machine -- 5.3.4.**Is AC needed? -- 5.3.5.Luck -- 6.Evaluation -- Appendix: **Details of Coin-Toss Rearrangement -- 7.Refinement, Alternatives, and Extensions -- 1.Introduction -- 2.Refinement -- 2.1.Event and trope individuation -- 2.2.Histories generated by partial causal relations -- 2.3.A closer look at Grim Reapers -- 2.4.Objections to causal finitism involving partial causation -- 2.5.Absences and omissions -- 3.Some Competitors to Causal Finitism -- 3.1.Finitism -- 3.2.No infinite regresses -- 3.3.No past infinities -- 3.4.No infinite intensive magnitudes -- 3.4.1.The basic theory -- 3.4.2.Some infinite intensive magnitudes -- 3.4.2.1.Center of mass and moments of inertia -- 3.4.2.2.Mental life -- 3.4.2.3.Black holes -- 3.4.2.4.Particles -- 3.4.3.Huemer's intensive magnitudes -- 3.4.3.1.Speed, Thomson's Lamp, and Hilbert's Hotel -- 3.4.3.2.*Smullyan's rod -- 3.4.3.3.Immaterial minds -- 3.4.4.Evaluation -- 3.5.No room -- 4.Why is Causal Finitism True? -- 4.1.The question -- 4.2.Some explanatory suggestions -- 5.Further Extensions -- 5.1.Causal loops -- 5.2.Explanatory relations -- 6.Overall Evaluation -- 8.Discrete Time and Space -- 1.Introduction -- 2.Causal Finitism and Discreteness -- 2.1.The basic argument -- 2.2.From discrete time to discrete space? -- 3.Two Kinds of Discreteness -- 3.1.Subdivisibility and fixeity -- 3.2.Refining the Aristotelian picture -- 3.2.1.An objection to Aristotelian discreteness -- 3.2.2.Internal and external discreteness -- 4.Physics -- 4.1.An objection to causal finitism -- 4.2.Causation and physics -- 4.3.Quantum collapse -- 4.3.1.Some background -- 4.3.2.Causation -- 4.3.3.Back to discrete time -- 5.Fields and Discrete Space -- 6.Evaluation -- 9.A First Cause -- 1.Introduction -- 2.An Uncaused Cause -- 2.1.The quick argument -- 2.2.Towards a necessary being -- 2.3.Support for the Causal Principle -- 2.4.The Kalam argument -- 3.Compatibility with Theism? -- 3.1.Theism -- 3.2.Divine motivation -- 3.3.Divine knowledge -- 3.4.Divine action -- 3.5.Limits on metaphysical possibility -- 4.Evaluation -- 10.Conclusions.

Summary:

Alexander R. Pruss examines a large family of paradoxes to do with infinity - ranging from deterministic supertasks to infinite lotteries and decision theory. Having identified their common structure, Pruss considers at length how these paradoxes can be resolved by embracing causal finitism.

Subject(s):

ISBN:

9780191847325 (ebook)

Audience Notes:

Specialized.

Note:

This edition previously issued in print: 2018.

Bibliography Note:

Includes bibliographical references and index.

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