Gregory Wheeler

Selected Articles

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  Machine Epistemology and Big Data
  The Routledge Companion to Philosophy of Social Science, forthcoming.
  

  @inbook{BigData:2017,
  title = {The Routledge Companion to Philosophy of Social Science},
  editor = {Lee McIntyre and Alex Rosenberg},
  publisher = {Routledge},
  year = {2017},
  author = {Gregory Wheeler},
  chapter = {Machine Epistemology and Big Data}
  }

  [ bib| preprint]
  

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  Resolving Peer Disagreements Through Imprecise Probabilities (w/ Lee Elkin)
  Noûs, forthcoming.
  

  Two compelling principles, the Reasonable Range Principle and the Preservation of Irrelevant Evidence Principle, are necessary conditions that any response to peer disagreements ought to abide by. The Reasonable Range Principle maintains that a resolution to a peer disagreement should not fall outside the range of views expressed by the peers in their dispute, whereas the Preservation of Irrelevant Evidence (PIE) Principle maintains that a resolution strategy should be able to preserve unanimous judgments of evidential irrelevance among the peers. No conciliatory Bayesian resolution strategy satisfies the PIE Principle, however, and we give a sure loss argument in support of PIE and against Bayes. The theory of imprecise probability allows one to satisfy both principles, and we introduce the notion of a set-based credal judgment to frame and address a range of subtle issues that arise in peer disagreements.

  @article{ip-peer:2015,
  title = {Resolving Peer Disagreements Through Imprecise Probabilities},
  author = {Lee Elkin and Gregory Wheeler},
  journal = {No{\^{u}}s},
  year = {forthcoming}
  }

  [abstract| bib| preprint]
  

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  Scoring Imprecise Credences: A Mildly Immodest Proposal (w/ Conor Mayo-Wilson)
  Philosophy and Phenomenological Research 93(1): 55–78, 2016.
  

  Jim Joyce argues for two amendments to probabilism. The first is the doctrine that credences are rational, or not, in virtue of their accuracy or "closeness to the truth" (Joyce 1998). The second is a shift from a numerically precise model of belief to an imprecise model represented by a set of probability functions (Joyce 2010). We argue that both amendments cannot be satisfied simultaneously. To do so, we employ a (slightly-generalized) impossibility theorem of Seidenfeld, Schervish, and Kadane (2012), who show that there is no strictly proper scoring rule for imprecise probabilities.
        The question then is what should give way. Joyce, who is well aware of this no-go result, thinks that a quantifiability constraint on epistemic accuracy should be relaxed to accommodate imprecision. We argue instead that another Joycean assumption—called strict immodesty—should be rejected, and we prove a representation theorem that characterizes all "mildly" immodest measures of inaccuracy.

  @article{IP-accuracy:2016,
  title = {Scoring Imprecise Credences: A Mildly Immodest Proposal},
  author = {Conor Mayo-Wilson and Gregory Wheeler},
  journal = {Philosophy and Phenomenological Research},
  year = {2016},
  volume = {93},
  number = {1},
  pages = {55–78}
  }

  [abstract| bib| preprint| journal]
  

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  Dilation, Disintegrations, and Delayed Decisions (w/ Arthur Paul Pedersen)
  Proceedings of the 9th International Symposium on Imprecise Probability: Theories and Applications (ISIPTA 2015), Pescara, Italy: 227–236, 2015.
  

  Both dilation and non-conglomerability have been alleged to conflict with a fundamental principle of Bayesian methodology that we call Good's Principle: one should always delay making a terminal decision between alternative courses of action if given the opportunity to first learn, at zero cost, the outcome of an experiment relevant to the decision. In particular, both dilation and non-conglomerability have been alleged to permit or even mandate choosing to make a terminal decision in deliberate ignorance of relevant, cost-free information. Although dilation and non-conglomerability share some simularities, some authors, including Walley and Seidenfeld, Schervish and Kadane, maintain that there are important differences between the two that warrant endorsing different normative positions regarding dilation (which is given a pass) and non-conglomerability (which is not). This article reassesses the grounds for treating dilation and non-conglomerability different. Our analysis exploits a new and general characterization result for dilation to draw a closer connection between dilation and non-conglomerability.

  @inproceedings{isipta15_delayed-decisions:2015,
  title = {Dilation, Disintegrations, and Delayed Decisions},
  author = {Arthur Paul Pedersen and Gregory Wheeler},
  booktitle = {Proceedings of the 9th International Symposium on Imprecise Probability: Theories and Applications},
  address = {Pescara, Italy},
  year = {2015},
  pages = {227--236}
  }

  [abstract| bib| preprint]
  

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  Is there a Logic of Information?
  Journal of Experimental and Theoretical Artificial Intelligence 27(1), 95–98, 2015.
  

  Information-based epistemology maintains that 'being informed' is an independent cognitive state that cannot be reduced to knowledge or to belief, and the modal logic KTB has been proposed as a model. But what distinguishes the KTMB analysis of 'being informed', the Brouwersche schema, is precisely its downfall, for no logic of information should include (B) and, more generally, no epistemic modal should include (B), either.

  @article{Wheeler.B:2015,
  title = {Is there a Logic of Information?},
  author = {Gregory Wheeler},
  journal = {Journal of Experimental and Theoretical Artificial Intelligence},
  year = {2015},
  volume = {27},
  number = {1},
  pages = {95–98}
  }

  [abstract| bib| preprint| journal]
  
  —— See also "Logic for Lunatics," Choice and Inference, August 20, 2013, [url]

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  Demystifying Dilation (w/ Arthur Paul Pedersen)
  Erkenntnis 79(6), 1305–42, 2014.
  

  Dilation occurs when an interval probability estimate of some event E is properly included in the interval probability estimate of E conditional on every event F of some partition, which means that one’s initial estimate of E becomes less precise no matter how an experiment turns out. Critics maintain that dilation is a pathological feature of imprecise probability models, while others have thought the problem is with Bayesian updating. However, two points are often overlooked: (1) knowing that E is stochastically independent of F (for all F in a partition of the underlying state space) is sufficient to avoid dilation, but (2) stochastic indepen- dence is not the only independence concept at play within imprecise probability models. In this paper we give a simple characterization of dilation formulated in terms of deviation from stochastic independence, propose a measure of dilation, and distinguish between proper and improper dilation. Through this we revisit the most sensational examples of dilation, which play up independence between dilator and dilatee, and find the sensationalism undermined by either fallacious reasoning with imprecise probabilities or improperly constructed imprecise probability models.

  @article{PedWhe:2014,
  title = {Coherence and Confirmation Through Causations},
  author = {Arthur Paul Pedersen and Gregory Wheeler},
  journal = {Erkenntnis},
  year = {2014},
  volume = {79},
  number = {6},
  pages = {1305–42}
  }

  [abstract| bib| preprint| journal]
  

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  Coherence and Confirmation Through Causation (w/ Richard Scheines)
  Mind 122(435), 135–70, 2013.
  

  Coherentism maintains that coherent beliefs are more likely to be true than incoherent beliefs, and that coherent evidence provides more confirmation of a hypothesis when the evidence is made coherent by the explanation provided by that hypothesis. Although probabilistic models of credence ought to be well-suited to justifying such claims, negative results from Bayesian epistemology have suggested otherwise. In this essay we argue that the connection between coherence and confirmation should be understood as a relation mediated by the causal relationships among the evidence and a hypothesis, and we offer a framework for doing so by fitting together probabilistic models of coherence, confirmation, and causation. We show that the causal structure among the evidence and hypothesis is sometimes enough to determine whether the coherence of the evidence boosts confirmation of the hypothesis, makes no difference to it, or even reduces it. We also show that, ceteris paribus, it is not the coherence of the evidence that boosts confirmation, but rather the ratio of the coherence of the evidence to the coherence of the evidence conditional on a hypothesis.

  @article{CCC:2013,
  title = {Coherence and Confirmation Through Causation},
  author = {Gregory Wheeler and Richard Scheines},
  journal = {Mind},
  year = {2013},
  volume = {122},
  number = {435},
  pages = {135–70}
  }

  [abstract| bib| preprint| journal]
  

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  Objective Bayesian Calibration and the Problem of Non-convex Evidence
  The British Journal for the Philosophy of Science 63(4), 841–850, 2012.
  

  Jon Williamson's Objective Bayesian Epistemology relies upon a calibration norm to constrain credal probability by both quantitative and qualitative evidence. One role of the calibration norm is to ensure that evidence works to constrain a convex set of probability functions. This essay brings into focus a problem for Williamson's theory when qualitative evidence specifies non-convex constraints.

  @article{Wheeler.calibration:2012,
  title = {Objective Bayesian Calibration and the Problem of Non-convex Evidence},
  author = {Gregory Wheeler},
  journal = {The British Journal for the Philosophy of Science},
  year = {2012},
  volume = {63},
  number = {4},
  pages = {841–850}
  }

  [abstract| bib| preprint| journal]
  

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  Why the Hardest Logic Puzzle Ever Cannot be Solved in Less Than Three Questions (w/ Pedro Barahona)
  Journal of Philosophical Logic 41(1), 493–503, 2012.
  

  Rabern and Rabern (2008) and Uzquiano (2010) have each presented increasingly harder versions of 'the hardest logic puzzle ever' (Boolos 1996), and each has provided a two-question solution to his predecessor's puzzle. But Uzquiano's puzzle is different from the original and different from Rabern and Rabern's in at least one important respect: it cannot be solved in less than three questions. In this paper we solve Uzquiano's puzzle in three questions and show why there is no solution in two. Finally, to cement a tradition, we introduce a puzzle of our own.

  @article{WheBar:2012,
  title = {Why the Hardest Logic Puzzle Ever Cannot be Solved in Less Than Three Questions},
  author = {Gregory Wheeler and Pedro Barahona},
  journal = {Journal of Philosophical Logic},
  year = {2012},
  issue = {41},
  number = {1},
  pages = {493–503}
  }

  [bib| preprint| journal]
  —— Featured in New Scientist, December 2012.

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  Focused Correlation and Confirmation
  The British Journal for the Philosophy of Science 60(1), 79–100, 2009.
  

  This essay presents results about a deviation from independence measure called focused correlation. This measure explicates the formal relationship between probabilistic de- pendence of an evidence set and the incremental confirmation of a hypothesis, resolves a basic question underlying Peter Klein and Ted Warfield’s ‘truth-conduciveness’ problem for Bayesian coherentism, and provides a qualified rebuttal to Erik Olsson’s claim that there is no informative link between correlation and confirmation. The generality of the result is compared to recent programs in Bayesian epistemology that attempt to link correlation and confirmation by utilizing a conditional evidential independence condition. Several properties of focused correlation are also highlighted.

  @article{Wheeler:2009,
  title = {Focused Correlation and Confirmation},
  author = {Gregory Wheeler},
  journal = {The British Journal for the Philosophy of Science},
  year = {2009},
  volume = {60},
  number = {1},
  pages = {79--100}
  }

  [abstract| bib| preprint| journal]
  

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• A complete archive of my papers may be found here.