Dizadji-Bahmani, Foad, Frigg, Roman and Hartmann, Stephan. Confirmation and reduction: A bayesian account

2011, Synthese,79(2): 321-338.

Abstract: Various scientific theories stand in a reductive relation to each other. In a recent article, the authors argue that a generalized version of the Nagel-Schaffner model (GNS) is the right account of this relation. In this article, they present a Bayesian analysis of how GNS impacts on confirmation. They formalize the relation between the reducing and the reduced theory before and after the reduction using Bayesian networks, and thereby show that, post-reduction, the two theories are confirmatory of each other. They ask when a purported reduction should be accepted on epistemic grounds. To do so, they compare the prior and posterior probabilities of the conjunction of both theories before and after the reduction and ask how well each is confirmed by the available evidence

Comment: This article is an interesting reading for advanced courses in philosophy of science or logic. It could serve as further reading for modules focused on Bayesian networks, reduction or confirmation. Previous knowledge of bayesianism is required for understanding the article. No previous knowledge of thermodynamics is needed.

Emery, Nina, and . The Metaphysical Consequences of Counterfactual Skepticism

2015, Philosophy and Phenomenological Research 92 (3).

Abstract: A series of recent arguments purport to show that most counterfactuals of the form if A had happened then C would have happened are not true. These arguments pose a challenge to those of us who think that counterfactual discourse is a useful part of ordinary conversation, of philosophical reasoning, and of scientific inquiry. Either we find a way to revise the semantics for counterfactuals in order to avoid these arguments, or we find a way to ensure that the relevant counterfactuals, while not true, are still assertible. In this paper, the author argues that regardless of which of these two strategies we choose, the natural ways of implementing these strategies all share a surprising consequence: they commit us to a particular metaphysical view about chance.

Comment: Really detailed article about counterfactual skepticism and chance pluralism. Could be useful in metaphysics classes, although the paper has consequences for many other fields (eg. philosophy of science). In principle it is recomendable for postgraduate students or senior undergraduate students who are confident enough with the topic

Emery, Nina, and . Chance, Possibility and explanation

2015, The British Journal for the Philosophy of Science 0(2015): 1–64

Summary: In this paper the author argues against the common and influential view that non-trivial chances arise only when the fundamental laws are indeterministic. The problem with this view, she claims, is not that it conflicts with some antecedently plausible metaphysics of chance or that it fails to capture our everyday use of ‘chance’ and related terms, but rather that it is unstable. Any reason for adopting the position that non-trivial chances arise only when the fundamental laws are indeterministic is also a reason for adopting a much stronger, and far less attractive, position. Emery suggests an alternative account, according to which chances are probabilities that play a certain explanatory role: they are probabilities that explain associated frequencies.

Comment: This could serve as a secondary reading for those studying metaphysic theories of chance. Previous background in metaphysics is needed. The paper is recommended for postgraduate students.

Eriksson, Lina, and Alan Hájek. What are Degrees of Belief?

2007, Studia Logica 86(2): 185-215.

Probabilism is committed to two theses:
1) Opinion comes in degrees – call them degrees of belief, or credences.
2) The degrees of belief of a rational agent obey the probability calculus.

Correspondingly, a natural way to argue for probabilism is:
i) to give an account of what degrees of belief are, and then
ii) to show that those things should be probabilities, on pain of irrationality.

Most of the action in the literature concerns stage ii). Assuming that stage i) has been adequately discharged, various authors move on to stage ii) with varied and ingenious arguments. But an unsatisfactory response at stage i) clearly undermines any gains that might be accrued at stage ii) as far as probabilism is concerned: if those things are not degrees of belief, then it is irrelevant to probabilism whether they should be probabilities or not.

In this paper, the authors scrutinize the state of play regarding stage i). We critically examine several of the leading accounts of degrees of belief: reducing them to corresponding betting behavior (de Finetti); measuring them by that behavior (Jeffrey); and analyzing them in terms of preferences and their role in decision-making more generally (Ramsey, Lewis, Maher). We argue that the accounts fail, and so they are unfit to subserve arguments for probabilism. We conclude more positively: “degree of belief” should be taken as a primitive concept that forms the basis of our best theory of rational belief and decision: probabilism.

Comment: This paper is accessible to an advanced undergraduate audience in a formal philosophy course, since it provides an overview of the different accounts of the notion of degrees of belief. However, it's most adequate for graduate level, where it could be used in a formal epistemology course or in a course on the philosophy of probability.

Hesse, Mary, and . The Hunt for Scientific Reason

1980, PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980: 3-22.

Abstract: The thesis of underdetermination of theory by evidence has led to an opposition between realism and relationism in philosophy of science. Various forms of the thesis are examined, and it is concluded that it is true in at least a weak form that brings realism into doubt. Realists therefore need, among other things, a theory of degrees of confirmation to support rational theory choice. Recent such theories due to Glymour and Friedman are examined, and it is argued that their criterion of “unification” for good theories is better formulated in Bayesian terms. Bayesian confirmation does, however, have consequences that tell against realism. It is concluded that the prospects are dim for scientific realism as usually understood.

Comment: Good article to study in depth the concepts of realism, underdetermination, confirmation and Bayesian theory. It will be most useful for postgraduate students in philosophy of science.

Nelkin, Dana, and . The lottery paradox, knowledge and rationality

2000, Philosophical Review: 109 (3): 373-409.

Summary: The knowledge version of the paradox arises because it appears that we know our lottery ticket (which is not relevantly different from any other) will lose, but we know that one of the tickets sold will win. The rationality version of the paradox arises because it appears that it is rational to believe of each single ticket in, say, a million-ticket lottery that it will not win, and that it is simultaneously rational to believe that one such ticket will win. It seems, then, that we are committed to attributing two rational beliefs to a single agent at a single time, beliefs that, together with a few background assumptions, are inconsistent and can be seen by the agent to be so. This has seemed to many to be a paradoxical result: an agent in possession of two rational beliefs that she sees to be inconsistent. In my paper, I offer a novel solution to the paradox in both its rationality and knowledge versions that emphasizes a special feature of the lottery case, namely, the statistical nature of the evidence available to the agent. On my view, it is neither true that one knows nor that it is rational to believe that a particular ticket will lose. While this might seem surprising at first, it has a natural explanation and lacks the serious disadvantages of competing solutions.

Comment: The lottery paradox is one of the most central paradox in epistemology and philosophy of probability. Nelkin's paper is a milestone in the literature on this topic after which discussions on the lottery paradox flourish. It is thus a must-have introductory paper on the lottery paradox for teachings on paradoxes of belief, justification theory, rationality, etc.

Shogenji, Tomoji, and . The Degree of Epistemic Justification and the Conjunction Fallacy

2012, Synthese 184 (1): 29-48.

Abstract: This paper describes a formal measure of epistemic justification motivated by the dual goal of cognition, which is to increase true beliefs and reduce false beliefs. From this perspective the degree of epistemic justification should not be the conditional probability of the proposition given the evidence, as it is commonly thought. It should be determined instead by the combination of the conditional probability and the prior probability. This is also true of the degree of incremental confirmation, and I argue that any measure of epistemic justification is also a measure of incremental confirmation. However, the degree of epistemic justification must meet an additional condition, and all known measures of incremental confirmation fail to meet it. I describe this additional condition as well as a measure that meets it. The paper then applies the measure to the conjunction fallacy and proposes an explanation of the fallacy.

Comment: This interesting paper on epistemic justification requires prerequisite knowledge on formal epistemology. It is hence suitable for an advanced undergraduate course or graduate course on epistemology or formal epistemology.