Abstract. I argue for an epistemic conception of voting, a conception on which the purpose of the... more Abstract. I argue for an epistemic conception of voting, a conception on which the purpose of the ballot is at least in some cases to identify which of several policy proposals will best promote the public good. To support this view I first briefly investigate several notions of the kind of public good that public policy should promote. Then I examine the probability logic of voting as embodied in two very robust versions of the Condorcet Jury Theorem and some related results. These theorems show that if the number of voters or legislators is sufficiently large and the average of their individual propensities to select the better of two policy proposals is a little above random chance, and if each person votes his or her own best judgment (rather than in alliance with a block or faction), then the majority is extremely likely to select the better alternative. Here ‘better alternative ’ means that policy or law that will best promote the public good. I also explicate a Convincing Maj...
Eliminative induction is a method for finding the truth by using evidence to eliminate false comp... more Eliminative induction is a method for finding the truth by using evidence to eliminate false competitors. It is often characterized as" induction by means of deduction"; the accumulating evidence eliminates false hypotheses by logically contradicting them, while the true ...
Revising classical logic—to deal with the paradoxes of self-reference, or vague propositions, for... more Revising classical logic—to deal with the paradoxes of self-reference, or vague propositions, for the purposes of scientific theory or of metaphysical anti-realism—requires the revision of probability theory. This chapter reviews the connection between classical logic and classical probability, clarifies nonclassical logic, giving simple examples, explores modifications of probability theory, using formal analogies to the classical setting, and provides two foundational justifications for these ‘nonclassical probabilities’. There follows an examination of extensions of the nonclassical framework: to conditionalization and decision theory in particular, before a final review of open questions and alternative approaches, and an evaluation of current progress.
Rereading Russell: Minnesota Studies in the …, 1989
Human Knowledge: Its Scope and Limits was first published in 1948. 1 The view on inductive infere... more Human Knowledge: Its Scope and Limits was first published in 1948. 1 The view on inductive inference that Russell develops there has received relatively little careful study and, I believe, has been largely misunderstood. Grover Maxwell was one of the few ...
Confirmation theory is the study of the logic by which scientific hypotheses may be confirmed or ... more Confirmation theory is the study of the logic by which scientific hypotheses may be confirmed or disconfirmed (or supported or refuted) by evidence. A specific theory of confirmation is a proposal for such a logic. Presumably the epistemic evaluation of scientific hypotheses should largely depend on their empirical content — on what they say the evidentially accessible parts of the world are like, and on the extent to which they turn out to be right about that. Thus, all theories of confirmation rely on measures of how well various alternative hypotheses account for the evidence. Most contemporary confirmation theories employ probability functions to provide such a measure. They measure how well the evidence fits what the hypothesis says about the world in terms of how likely it is that the evidence would occur if the hypothesis were true. Such hypothesis-based probabilities of evidence claims are called likelihoods. Clearly, when the evidence is more likely according to one hypothe...
Confirmation theory is the study of the logic by which scientific hypotheses may be confirmed or ... more Confirmation theory is the study of the logic by which scientific hypotheses may be confirmed or disconfirmed (or supported or refuted) by evidence. A specific theory of confirmation is a proposal for such a logic. Presumably the epistemic evaluation of scientific hypotheses ...
I argue for an epistemic conception of voting, a conception on which the purpose of the ballot is... more I argue for an epistemic conception of voting, a conception on which the purpose of the ballot is at least in some cases to identify which of several policy proposals will best promote the public good. To support this view I first briefly investigate several notions of the kind of public good that public policy should promote. Then I examine the probability logic of voting as embodied in two very robust versions of the Condorcet Jury Theorem and some related results. These theorems show that if the number of voters or legislators is sufficiently large and the average of their individual propensities to select the better of two policy proposals is a little above random chance, and if each person votes his or her own best judgment (rather than in alliance with a block or faction), then the majority is extremely likely to select the better alternative. Here ‘better alternative’ means that policy or law that will best promote the public good. I also explicate a Convincing Majorities The...
Idea: E [∼Ra &∼Ba] confirms H [(∀x)(Rx ⊃ Bx)] relative to >, but E doesn’t confirm H relative ... more Idea: E [∼Ra &∼Ba] confirms H [(∀x)(Rx ⊃ Bx)] relative to >, but E doesn’t confirm H relative to some background K ≠ >. Question: Which K ≠ >? Answer: K = ∼Ra. Idea: If you already know that ∼Ra, then observing a’s color won’t tell you anything about the color of ravens. Distinguish the following two claims: (PC) ∼Ra &∼Ba confirms (∀x)(Rx ⊃ Bx), relative to >. (PC*) ∼Ra &∼Ba confirms (∀x)(Rx ⊃ Bx), relative to ∼Ra. Intuition (I). (PC) is true, but (PC*) is false. [Why? ∼Ra reduces the size of the set of possible counterexamples to (∀x)(Rx ⊃ Bx) [12].] Nice idea! Sadly, (I) is inconsistent with their confirmation theory!
Direct inferences identify certain probabilistic credences or confirmation-function-likelihoods w... more Direct inferences identify certain probabilistic credences or confirmation-function-likelihoods with values of objective chances or relative frequencies. The best known version of a direct inference principle is David Lewis's Principal Principle. Certain kinds of statements undermine direct inferences. Lewis calls such statements inadmissible. We show that on any Bayesian account of direct inference several kinds of intuitively innocent statements turn out to be inadmissible. This may pose a significant challenge to Bayesian accounts of direct inference. We suggest some ways in which these challenges may be addressed.
Abstract. I argue for an epistemic conception of voting, a conception on which the purpose of the... more Abstract. I argue for an epistemic conception of voting, a conception on which the purpose of the ballot is at least in some cases to identify which of several policy proposals will best promote the public good. To support this view I first briefly investigate several notions of the kind of public good that public policy should promote. Then I examine the probability logic of voting as embodied in two very robust versions of the Condorcet Jury Theorem and some related results. These theorems show that if the number of voters or legislators is sufficiently large and the average of their individual propensities to select the better of two policy proposals is a little above random chance, and if each person votes his or her own best judgment (rather than in alliance with a block or faction), then the majority is extremely likely to select the better alternative. Here ‘better alternative ’ means that policy or law that will best promote the public good. I also explicate a Convincing Maj...
Eliminative induction is a method for finding the truth by using evidence to eliminate false comp... more Eliminative induction is a method for finding the truth by using evidence to eliminate false competitors. It is often characterized as" induction by means of deduction"; the accumulating evidence eliminates false hypotheses by logically contradicting them, while the true ...
Revising classical logic—to deal with the paradoxes of self-reference, or vague propositions, for... more Revising classical logic—to deal with the paradoxes of self-reference, or vague propositions, for the purposes of scientific theory or of metaphysical anti-realism—requires the revision of probability theory. This chapter reviews the connection between classical logic and classical probability, clarifies nonclassical logic, giving simple examples, explores modifications of probability theory, using formal analogies to the classical setting, and provides two foundational justifications for these ‘nonclassical probabilities’. There follows an examination of extensions of the nonclassical framework: to conditionalization and decision theory in particular, before a final review of open questions and alternative approaches, and an evaluation of current progress.
Rereading Russell: Minnesota Studies in the …, 1989
Human Knowledge: Its Scope and Limits was first published in 1948. 1 The view on inductive infere... more Human Knowledge: Its Scope and Limits was first published in 1948. 1 The view on inductive inference that Russell develops there has received relatively little careful study and, I believe, has been largely misunderstood. Grover Maxwell was one of the few ...
Confirmation theory is the study of the logic by which scientific hypotheses may be confirmed or ... more Confirmation theory is the study of the logic by which scientific hypotheses may be confirmed or disconfirmed (or supported or refuted) by evidence. A specific theory of confirmation is a proposal for such a logic. Presumably the epistemic evaluation of scientific hypotheses should largely depend on their empirical content — on what they say the evidentially accessible parts of the world are like, and on the extent to which they turn out to be right about that. Thus, all theories of confirmation rely on measures of how well various alternative hypotheses account for the evidence. Most contemporary confirmation theories employ probability functions to provide such a measure. They measure how well the evidence fits what the hypothesis says about the world in terms of how likely it is that the evidence would occur if the hypothesis were true. Such hypothesis-based probabilities of evidence claims are called likelihoods. Clearly, when the evidence is more likely according to one hypothe...
Confirmation theory is the study of the logic by which scientific hypotheses may be confirmed or ... more Confirmation theory is the study of the logic by which scientific hypotheses may be confirmed or disconfirmed (or supported or refuted) by evidence. A specific theory of confirmation is a proposal for such a logic. Presumably the epistemic evaluation of scientific hypotheses ...
I argue for an epistemic conception of voting, a conception on which the purpose of the ballot is... more I argue for an epistemic conception of voting, a conception on which the purpose of the ballot is at least in some cases to identify which of several policy proposals will best promote the public good. To support this view I first briefly investigate several notions of the kind of public good that public policy should promote. Then I examine the probability logic of voting as embodied in two very robust versions of the Condorcet Jury Theorem and some related results. These theorems show that if the number of voters or legislators is sufficiently large and the average of their individual propensities to select the better of two policy proposals is a little above random chance, and if each person votes his or her own best judgment (rather than in alliance with a block or faction), then the majority is extremely likely to select the better alternative. Here ‘better alternative’ means that policy or law that will best promote the public good. I also explicate a Convincing Majorities The...
Idea: E [∼Ra &∼Ba] confirms H [(∀x)(Rx ⊃ Bx)] relative to >, but E doesn’t confirm H relative ... more Idea: E [∼Ra &∼Ba] confirms H [(∀x)(Rx ⊃ Bx)] relative to >, but E doesn’t confirm H relative to some background K ≠ >. Question: Which K ≠ >? Answer: K = ∼Ra. Idea: If you already know that ∼Ra, then observing a’s color won’t tell you anything about the color of ravens. Distinguish the following two claims: (PC) ∼Ra &∼Ba confirms (∀x)(Rx ⊃ Bx), relative to >. (PC*) ∼Ra &∼Ba confirms (∀x)(Rx ⊃ Bx), relative to ∼Ra. Intuition (I). (PC) is true, but (PC*) is false. [Why? ∼Ra reduces the size of the set of possible counterexamples to (∀x)(Rx ⊃ Bx) [12].] Nice idea! Sadly, (I) is inconsistent with their confirmation theory!
Direct inferences identify certain probabilistic credences or confirmation-function-likelihoods w... more Direct inferences identify certain probabilistic credences or confirmation-function-likelihoods with values of objective chances or relative frequencies. The best known version of a direct inference principle is David Lewis's Principal Principle. Certain kinds of statements undermine direct inferences. Lewis calls such statements inadmissible. We show that on any Bayesian account of direct inference several kinds of intuitively innocent statements turn out to be inadmissible. This may pose a significant challenge to Bayesian accounts of direct inference. We suggest some ways in which these challenges may be addressed.
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