Subjective Bayesianism, probability spaces, and the Sleeping Beauty problem
by Lee Elkin
draft only
My intention in this paper is to provide a two-pronged argument in response to the Sleeping Beauty puzzle. I will... more
My intention in this paper is to provide a two-pronged argument in response to the Sleeping Beauty puzzle. I will first argue against Ruth Weintraub’s (2004) defense of the Thirder position by showing that the new evidence that she claims SB gains is irrelevant for updating her initial credence from 1/2 to 1/3 on the first awakening. To show this, I will use Bayesian analysis and conditionalize on the new piece of evidence that Weintraub claims that SB gains upon being awakened.
The second prong of the argument is to offer a solution to the puzzle without the need of SB acquiring new information. I believe that Thirders vacillate between probability spaces from Sunday night to Monday afternoon, and this is what causes the puzzle to arise. If we establish two distinct mathematical probability spaces independent of one another, then the probabilistic issues will resolve themselves and therefore the puzzle dissipates. Given my proposed solution to the problem, I remain neutral between Thirdism and Halfism since what I take to be relevant are the questions asked and the relevant probability spaces under consideration.
Download (.doc) Belief and certainty
by Dylan Dodd
draft only
I argue that one believes that p only if one's credence in p is 1. I argue that one believes that p only if one's credence in p is 1.
Carnapian modal and epistemic arithmetic
by Jan Heylen
Carrara M., Morato V. (Eds.), Language, Knowledge, and Metaphysics. Selected papers from the First SIFA Graduate Conference (pp. 97-121). Londen:. College Publications.
Carnapian Modal and Epistemic Logic and Arithmetic with Descriptions
by Jan Heylen
PhD thesis defended at the University of Leuven in May 2009. The thesis was supervised by prof. Leon Horsten. The committee consisted of prof. Igor Douven, prof. Roger Vergauwen, prof. Antoon Vandevelde, and dr. Paul Egré.
Is the Conjunction Fallacy tied to Probabilistic Confirmation?
Crupi et al. (2008) offer a confirmation-theoretic, Bayesian account of the conjunction fallacy —- an error in... more
Crupi et al. (2008) offer a confirmation-theoretic, Bayesian account of the conjunction fallacy —- an error in reasoning that occurs when subjects judge that Pr(h1 & h2|e) > Pr(h1|e). They introduce three formal conditions that are satisfied by classical conjunction fallacy cases, and they show that these same conditions imply that h1 & h2 is confirmed by e to a greater extent than is h1 alone. Consequently, they suggest that people are tracking this confirmation relation when they commit conjunction fallacies. I offer three experiments testing the merits of Crupi et al.’s account specifically and confirmation-theoretic accounts of the conjunction fallacy more generally. The results of Experiment 1 show that, although Crupi et al.’s conditions do seem to be causally linked to the conjunction fallacy, they are not necessary for it; there exist cases that do not meet their three conditions in which subjects still tend to commit the fallacy. The results of Experiments 2 and 3 show that Crupi et al.’s conditions, and those offered by other confirmation-theoretic accounts of the fallacy, are not sufficient for the fallacy either; there exist cases that meet all three of CFT’s conditions in which subjects do not tend to commit the fallacy. Additionally, these latter experiments show that such confirmation-theoretic conditions are at best only weakly causally relevant to the presence of the conjunction fallacy. Given these findings, CFT’s account specifically, and any general confirmation-theoretic account more broadly, falls short of offering a satisfying explanation of the presence of the conjunction fallacy. (Forthcoming in a special issue of Synthese on "Probability, Confirmation, and Reasoning Fallacies").
Note: Katya Tentori and Vincenzo Crupi's response to my research on confirmation-theoretic accounts of the conjunction fallacy may be found in the same issue of Synthese.
New Hope for Shogenji's Coherence Measure
I show that the two most devastating objections to Shogenji's formal account of coherence necessarily involve... more I show that the two most devastating objections to Shogenji's formal account of coherence necessarily involve information sets of cardinality n>2. Given this, I surmise that the problem with Shogenji's measure has more to do with his means of generalizing the measure than with the measure itself. I defend this claim by offering an alternative generalization of Shogenji's measure. This alternative retains the intuitive merits of the original measure while avoiding both of the relevant problems that befall it. In the light of all of this, I suggest that there is new hope for Shogenji's analysis: Shogenji's early and influential attempt at measuring coherence, when generalized in a subset-sensitive way, is able to clear its most troubling objections. (British Journal for the Philosophy of Science (2011) 62(1): 125-142).
On the Alleged Impossibility of Bayesian Coherentism
The success of Bovens and Hartmann’s recent "impossibility result" against Bayesian Coherentism relies upon... more The success of Bovens and Hartmann’s recent "impossibility result" against Bayesian Coherentism relies upon the adoption of a specific set of ceteris paribus conditions. In this paper, I argue that these conditions are not clearly appropriate; certain proposed coherence measures motivate different such conditions and also call for the rejection of at least one of Bovens and Hartmann's conditions. I show that there exist sets of intuitively plausible ceteris paribus conditions that allow one to sidestep the impossibility result. This shifts the debate from the merits of the impossibility result itself to the underlying choice of ceteris paribus conditions. (Philosophical Studies (2008) 141(3): 323-331).
On a Bayesian Analysis of the Virtue of Unification
In three recent papers, Wayne Myrvold (1996, 2003) and Timothy McGrew (2003) have developed Bayesian accounts of the... more In three recent papers, Wayne Myrvold (1996, 2003) and Timothy McGrew (2003) have developed Bayesian accounts of the virtue of unification. In his account, McGrew demonstrates that, ceteris paribus, a hypothesis that unifies its evidence will have a higher posterior probability than a hypothesis that does not. Myrvold, on the other hand, offers a specific measure of unification that can be applied to individual hypotheses. He argues that one must account for this measure in order to calculate correctly the degree of confirmation that a hypothesis receives from its evidence. Using the probability calculus, I prove that the two accounts of unification require the same underlying inequality; thus, McGrew and Myrvold have accounted for unification in fundamentally identical probabilistic terms. I then evaluate five putative counterexamples to this account and show that these examples, far from disqualifying it, serve to clarify our notion of unification by disentangling it from a host of other concepts. (Philosophy of Science (2005) 72(4): 594-607).
The Logic of Explanatory Power
Co-authored with Jan Sprenger
This article introduces and defends a probabilistic measure of the explanatory power that a particular explanans has... more This article introduces and defends a probabilistic measure of the explanatory power that a particular explanans has over its explanandum. To this end, we propose several intuitive, formal conditions of adequacy for an account of explanatory power. Then, we show that these conditions are uniquely satisfied by one particular probabilistic function. We proceed to strengthen the case for this measure of explanatory power by proving several theorems, all of which show that this measure neatly corresponds to our explanatory intuitions. Finally, we briefly describe some promising future projects inspired by our account. (Philosophy of Science (2011) 78(1): 105-127).
Comparing Probabilistic Measures of Explanatory Power
Recently, in attempting to account for explanatory reasoning in probabilistic terms, Bayesians have proposed several... more Recently, in attempting to account for explanatory reasoning in probabilistic terms, Bayesians have proposed several measures of the degree to which a hypothesis explains a given set of facts. These candidate measures of "explanatory power" are shown to have interesting normative interpretations and consequences. What has not yet been investigated, however, is whether any of these measures are also descriptive of people’s actual explanatory judgments. Here, I present my own experimental work investigating this question. I argue that one measure in particular is an accurate descriptor of explanatory judgments. Then, I discuss some interesting implications of this result for both the epistemology and the psychology of explanatory reasoning. (Philosophy of Science, Forthcoming).
Studies in the Logic of Explanatory Power
Human reasoning often involves explanation. In everyday affairs, people reason to hypotheses based on the explanatory... more
Human reasoning often involves explanation. In everyday affairs, people reason to hypotheses based on the explanatory power these hypotheses afford; I might, for example, surmise that my toddler has been playing in my office because I judge that this hypothesis delivers a good explanation of the disarranged state of the books on my shelves. But such explanatory reasoning also has relevance far beyond the commonplace. Indeed, explanatory reasoning plays an important role in such varied fields as the sciences, philosophy, theology, medicine, forensics, and law.
This dissertation provides an extended study into the logic of explanatory reasoning via two general questions. First, I approach the question of what exactly we have in mind when we make judgments pertaining to the explanatory power that a hypothesis has over some evidence. This question is important to this study because these are the sorts of judgments that we constantly rely on when we use explanations to reason about the world. Ultimately, I introduce and defend an explication of the concept of explanatory power in the form of a probabilistic measure. This formal explication allows us to articulate precisely some of the various ways in which we might reason explanatorily.
The second question this dissertation examines is whether explanatory reasoning constitutes an epistemically respectable means of gaining knowledge. I defend the following ideas: The probability theory can be used to describe the logic of explanatory reasoning, the normative standard to which such reasoning attains. Explanatory judgments, on the other hand, constitute heuristics that allow us to approximate reasoning in accordance with this logical standard while staying within our human bounds. The most well known model of explanatory reasoning, Inference to the Best Explanation, describes a cogent, nondeductive inference form. And reasoning by Inference to the Best Explanation approximates reasoning directly via the probability theory in the real world. Finally, I respond to some possible objections to my work, and then to some more general, classic criticisms of Inference to the Best Explanation. In the end, this dissertation puts forward a clearer articulation and novel defense of explanatory reasoning. (Successfully defended on June 14, 2011).
Review essay on Huber, F. and C. Schmidt-Petri (eds.) Degrees of Belief
published in Grazer Philosophische Studien 80
A review of Huber and Schmidt-Petri's excellent new collection of survey articles on a wide variety of topics in the... more A review of Huber and Schmidt-Petri's excellent new collection of survey articles on a wide variety of topics in the theory of degrees of belief.
How serious is the paradox of serious of possibility?
by Simone Duca
Co-authored with Hannes Leitgeb, forthcoming in 'Mind'
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An Objective Justification of Bayesianism I: Measuring Inaccuracy (with Hannes Leitgeb)
(2010) Philosophy of Science 77:201-235
One of the fundamental problems of epistemology is to say when the evidence in an agent's possession justifies the... more
One of the fundamental problems of epistemology is to say when the evidence in an agent's possession justifies the beliefs she holds. In this paper and its sequel, we defend the Bayesian solution to this problem by appealing to the following fundamental norm:
ACCURACY An epistemic agent ought to minimize the inaccuracy of her partial beliefs.
In this paper, we make this norm mathematically precise in various ways. We describe three epistemic dilemmas that an agent might face if she attempts to follow ACCURACY, and we show that the only inaccuracy measures that do not give rise to such dilemmas are the quadratic inaccuracy measures. In the sequel, we derive the main tenets of Bayesianism from the relevant mathematical versions of ACCURACY to which this characterization of the legitimate inaccuracy measures gives rise, but we also show that unless the requirement of Rigidity is imposed from the start, Jeffrey conditionalization has to be replaced by a different method of update in order for ACCURACY to be satisfied.
An Objective Justification of Bayesianism II: The Consequences of Minimizing Inaccuracy (With Hannes Leitgeb)
(2010) Philosophy of Science 77:236-272. Chosen for Philosophers' Annual 2010.
One of the fundamental problems of epistemology is to say when the evidence in an agent’s possession justifies the... more
One of the fundamental problems of epistemology is to say when the evidence in an agent’s possession justifies the beliefs she holds. In this paper and its prequel, we defend the Bayesian solution to this problem by appealing to the following fundamental norm:
ACCURACY An epistemic agent ought to minimize the inaccuracy of her partial beliefs.
In the prequel, we made this norm mathematically precise; in this paper, we derive its consequences. We show that the two core tenets of Bayesianism follow from the norm, while the characteristic claim of the Objectivist Bayesian follows from the norm along with an extra assumption. Finally, we consider Richard Jeffrey’s proposed generalization of conditionalization. We show not only that his rule cannot be derived from the norm, unless the requirement of Rigidity is imposed from the start, but further that the norm reveals it to be illegitimate. We end by deriving an alternative updating rule for those cases in which Jeffrey's is usually supposed to apply.
An improper introduction to epistemic utility theory
(2011) EPSA Philosophy of Science: Amsterdam 2009 (edited by de Regt, H., Hartmann, S. and S. Okasha)
Beliefs come in different strengths. What are the norms that govern these strengths of belief? Let an agent's belief... more Beliefs come in different strengths. What are the norms that govern these strengths of belief? Let an agent's belief function at a particular time be the function that assigns, to each of the propositions about which she has an opinion, the strength of her belief in that proposition at that time. Traditionally, philosophers have claimed that an agent's belief function at any time ought to be a probability function (Probabilism), and that she ought to update her belief function upon obtaining new evidence by conditionalizing on that evidence (Conditionalization). Until recently, the central arguments for these claims have been pragmatic. But these putative justifications fail to identify what is epistemically irrational about violating Probabilism or Conditionalization. A new approach, which I will call epistemic utility theory, attempts to remedy this. It treats beliefs as epistemic acts; and it appeals to the notion of an epistemic utility function, which measures of how epistemically valuable a particular belief function is for a particular way the world might be. It then formulates fundamental epistemic norms that are analogous to the fundamental practical norms that underlie decision theory. I survey the results obtained so far in this young research project, and present a sustained critique of certain assumptions that have been made by a number of philosophers working in this area.