An Essay on Induction and the Aims of Science. Australasian Journal of Philosophy 74, S. Lin, Hanti, Kevin T.
In this paper, we compare and contrast two methods for revising qualitative viz.
The second method is the AGM approach to belief revision. Our aim here is to provide the most straightforward explanation of the ways in which these two methods agree and disagree with each other. Setup We will be talking about a very simple and highly idealized epistemic agent who has both numerical degrees of confidence viz.
When it comes to the qualitative attitudes of our idealized agent, we will attend only to the beliefs of the agent i. We adopt the notation B p to indicate that our agent believes that p, and the notation B to denote the set of propositions in A that our agent believes.
Again, because we Hannes leitgeb lockean thesis interested in belief revision, we will make use of two belief sets: Do not cite or quote without permission.
We would like to thank audiences at Tilburg, Boulder, Maryland, and Kent for stimulating discussions. In this respect, we follow the pluralistic approach of Leitgeb .
Ultimately, we will be comparing and contrasting two belief revision operators: While traditional approaches to credence and belief have been developed largely in isolation of each other, more recently various authors have been investigating joint constraints on quantitative and qualitative epistemic attitudes.
The Lockean thesis requires that an agent believe p iff her credence in p is at least t, for some Lockean threshold t.
Intuitively, this constraint requires that an agent believe all and only the propositions that she takes to be sufficiently probable.
This normative Lockean thesis provides an intuitively plausible rational constraint since it would seem irrational for an agent to believe a proposition that she deems improbable; similarly, it would seem rational i.
As we will see shortly, the expected utility theory EUT approach to belief revision requires that both the prior and the posterior belief sets and credences satisfy joint Lockean constraints.
It is well known that Lockean approaches sometimes permit belief sets that are neither closed under logical consequence nor deductively consistent. On the other hand, approaches to belief revision that rely solely on logical considerations like AGM tend to require that agents always have deductively closed and consistent belief sets.
In comparing AGM with EUT revision, we will not belabor this well-known source of disagreement between the two paradigms. Rather, we will focus most of our attention on some of the less widely known divergences and similarities between the two approaches.
In the next section, we sketch EUT theory and provide its veritistic motivation along with an illuminating application. See  for a survey of such arguments. And, the worlds in W will correspond to the state-descriptions of the propositional language which generates A.
But, this convergence is only a result of the fact that probabilistic certainties must behave logically. For those less familiar with the belief revision literature and more familiar with non-monotonic inference, Vacuity corresponds to the inference rule called Rational Monotony.
The remainder of the paper examines and demonstrates the similarities and differences between the two approaches to belief revision. As such, we will not extensively discuss the background motivations for either theory.
Thus, EUT must presuppose some way of measuring the epistemic utility of a belief set B. In other words, B maximizes EEU just in case our agent believes exactly those propositions in A to which they assign a sufficiently high credence, where the w. And, this synchronic coherence requirement immediately lifts to a diachronic coherence requirement, given the assumption that our agent updates her credences via conditionalization.
We will compare and contrast these two operators in detail shortly. This principle is always satisfied by the AGM revision operator .
Additionally, we will assume that the values of r and w are on the unit interval [0, 1], although this choice of scale is purely conventional, as any linear transformation of hr, wi would yield the same requirements.
Pruss  argues that w should be at least 2. Because our present analyses only depend on our weak assumptions about r and w, we will not place any further restrictions on their values.
Historically, these kinds of EUT-derived Lockean-style constraints trace back to the work of Hempel .The Stability of Belief How Rational Belief Coheres with Probability Hannes Leitgeb. Develops a new theory of rational belief; Mathematical aspects of the argument clearly explained.
Hannes Leitgeb (LMU Munich) Belief as Qualitative Probability March 3 / 14 Absolute Belief and “ ” of the Lockean Thesis In many cases a . beliefs, degress of belief and the lockean thesis this paper is a chapter from f.
huber, c. schmidt-petri (eds.), degrees of belief, synthese library reducing belief simpliciter to degrees of belief hannes leitgeb march abstract we prove that given reasonable assumptions, it is possible to give an explicit de?ni-. Hannes Leitgeb.
Ludwig-Maximilians-University of Munich Although the logical closure of belief and the Lockean thesis are attractive postulates in themselves, initially this may seem like a.
The book explains what this stability thesis amounts to, how the thesis relates to other joint principles of belief and degrees of belief, such as the so-called Lockean thesis, and how the approach avoids notorious paradoxes, such as the famous Lottery Paradox.
Chapter 3 Logical Closure and the Lockean Thesis The last chapter determined a bridge principle for rational (all-or-nothing) belief and de-grees of belief which I called the Humean thesis on belief.