Macroscopic Ontology in Everettian Quantum Mechanics

Wilson, Alastair

doi:10.1111/j.1467-9213.2010.675.x

Cited by 17 publications

(14 citation statements)

References 19 publications

(17 reference statements)

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“…We contribute to this tradition by showing that it makes openness compatible with a standard Kaplanian picture of context and illuminates the division of labour between the semantics and the metaphysics of the open future. A close relative of our point of view is Wilson's (2011) Kaplanian interpretation of the proposal in Saunders & Wallace (2008). As Wilson puts it (p. 364), Saunders and Wallace's background assumptions 'entail that where there are multiple complete branches, there are multiple contexts and hence multiple distinct utterances'.…”

Section: Epistemic Readings Of Willmentioning

confidence: 99%

Will done Better: Selection Semantics, Future Credence, and Indeterminacy

Cariani¹,

Santorio

2017

Mind

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Statements about the future are central in everyday conversation and reasoning. How should we understand their meaning? The received view among philosophers treats will as a tense: in 'Cynthia will pass her exam', will shifts the reference time forward. Linguists, however, have produced substantial evidence for the view that will is a modal, on a par with must and would. The different accounts are designed to satisfy different theoretical constraints, apparently pulling in opposite directions. We show that these constraints are jointly satisfied by a novel modal account of will. On this account, will is a modal but doesn't work as a quantifier over worlds. Rather, the meaning of will involves a selection function similar to the one used by Stalnaker in his semantics for conditionals. The resulting theory yields a plausible semantics and logic for will and vindicates our intuitive views about the attitudes that rational agents should have towards future-directed contents.

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Section: Epistemic Readings Of Willmentioning

confidence: 99%

Will done Better: Selection Semantics, Future Credence, and Indeterminacy

Cariani¹,

Santorio

2017

Mind

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“…If the indeterminacy evinced by entangled states is interpreted as inconsistency, then the computational properties at issue might further have to be defined on a distribution of epistemic possibilities which permit of hyperin-This section examines the philosophical significance of the Boolean-valued models of set-theoretic languages and the modal coalgebraic automata to which they are dually isomorphic. I argue that, similarly to second-order logical consequence, (i) the 'mathematical entanglement' of Ω-logical validity does not undermine its status as a relation of pure logic; and (ii) both the modal profile and model-theoretic characterization of Ω-logical consequence provide a guide13 The nature of the indeterminacy in question is examined inSaunders and Wallace (2008),Deutsch (2010),Hawthorne (2010),Wilson (2011), Wallace (2012,Lewis (2016: 277-278), and Khudairi (ms). For a thorough examination of approaches to the ontology of quantum mechanics, seeArntzenius (2012: ch.…”

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confidence: 97%

Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism

Khudairi

2019

Philosophical Studies Series

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This essay examines the philosophical significance of Ω-logic in Zermelo-Fraenkel set theory with choice (ZFC). The dual isomorphism between algebra and coalgebra permits Boolean-valued algebraic models of ZFC to be interpreted as coalgebras. The modal profile of Ω-logical validity can then be countenanced within a coalgebraic logic, and Ω-logical validity can be defined via deterministic automata. I argue that the philosophical significance of the foregoing is two-fold. First, because the epistemic and modal profiles of Ω-logical validity correspond to those of second-order logical consequence, Ω-logical validity is genuinely logical, and thus vindicates a neo-logicist conception of mathematical truth in the set-theoretic multiverse. Second, the foregoing provides a modal-computational account of the interpretation of mathematical vocabulary, adducing in favor of a realist conception of the cumulative hierarchy of sets. * Forthcoming in d'Alfonso and Berkich (eds),'On the Cognitive, Ethical, and Scientific Dimensions of Artificial Intelligence -Themes from IACAP 2016' (Springer: 2018). further be defined via automata. In Section 3, I examine how models of epistemic modal algebras to which modal coalgebraic automata are dually isomorphic are availed of in the computational theory of mind. Finally, in Section 4, the philosophical significance of the characterization of the modal profile of Ωlogical validity for the philosophy of mathematics is examined. I argue (i) that it vindicates a type of neo-logicism with regard to mathematical truth in the set-theoretic multiverse, and (ii) that it provides a modal and computational account of formal grasp of the concept of 'set', adducing in favor of a realist conception of the cumulative hierarchy of sets. Section 5 provides concluding remarks.

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“…If such a continuant performs an experiment, then it overlaps either a spin-up outcome or a spin-down outcome, but not both. However, Wilson [2010] argues that this proposal breaks down when it is applied to objective uncertainty about events which occur after our own deaths: as a result, it is not capable of grounding probabilities for future outcomes in full generality.…”

Section: Motivating Branching-time Semantics Via Physicsmentioning

confidence: 99%

Everettian quantum mechanics without branching time

Wilson

2011

Synthese

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ABSTRACT:In this paper I assess the prospects for combining contemporary Everettian quantum mechanics (EQM) with branching-time semantics in the tradition of Kripke, Prior, Thomason and Belnap. I begin by outlining the salient features of 'decoherence-based' EQM, and of the 'consistent histories' formalism that is particularly apt for conceptual discussions in EQM. This formalism permits of both 'branching worlds' and 'parallel worlds' interpretations; the metaphysics of EQM is in this sense underdetermined by the physics. A prominent argument due to David Lewis [1986] supports the non-branching interpretation. Belnap et al. [2001] refer to Lewis' argument as the 'Assertion problem', and propose a pragmatic response to it. I argue that their response is unattractively ad hoc and complex, and that it prevents an Everettian who adopts branching-time semantics from making clear sense of objective probability. The upshot is that Everettians are better off without branching-time semantics. I conclude by discussing and rejecting an alternative possible motivation for branching time.

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Macroscopic Ontology in Everettian Quantum Mechanics

Cited by 17 publications

References 19 publications

Will done Better: Selection Semantics, Future Credence, and Indeterminacy

Will done Better: Selection Semantics, Future Credence, and Indeterminacy

Modal Ω-Logic: Automata, Neo-Logicism, and Set-Theoretic Realism

Everettian quantum mechanics without branching time

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