Accuracy, probabilism, and the insufficiency of the alethic

The best and most popular argument for probabilism is the accuracy-dominance argument, which purports to show that alethic considerations alone support the view that an agent’s degrees of belief should always obey the axioms of probability. I argue that extant versions of the accuracy-dominance argument face a problem. In order for the mathematics of the argument to function as advertised, we must assume that every omniscient credence function is classically consistent; there can be no worlds in the set of dominance-relevant worlds that obey some other logic. This restriction cannot be motivated on alethic grounds unless we’re also willing to accept that rationality requires belief in every metaphysical necessity, as the distinction between a priori logical necessities and a posteriori metaphysical ones is not an alethic distinction. To justify the restriction to classically consistent worlds, non-alethic motivation is required. And thus, if there is a version of the accuracy-dominance argument in support of probabilism, it isn’t one that is grounded in alethic considerations alone.

Quantum-Like Sampling

Probability theory is built around Kolmogorov’s axioms. To each event, a numerical degree of belief between 0 and 1 is assigned, which provides a way of summarizing the uncertainty. Kolmogorov’s probabilities of events are added, the sum of all possible events is one. The numerical degrees of belief can be estimated from a sample by its true fraction. The frequency of an event in a sample is counted and normalized resulting in a linear relation. We introduce quantum-like sampling. The resulting Kolmogorov’s probabilities are in a sigmoid relation. The sigmoid relation offers a better importability since it induces the bell-shaped distribution, it leads also to less uncertainty when computing the Shannon’s entropy. Additionally, we conducted 100 empirical experiments by quantum-like sampling 100 times a random training sets and validation sets out of the Titanic data set using the Naïve Bayes classifier. In the mean the accuracy increased from 78.84% to 79.46%.

Reasoning about Beliefs and Meta-Beliefs by Regression in an Expressive Probabilistic Action Logic

In a recent paper Belle and Lakemeyer proposed the logic DS, a probabilistic extension of a modal variant of the situation calculus with a model of belief based on weighted possible worlds. Among other things, they were able to precisely capture the beliefs of a probabilistic knowledge base in terms of the concept of only-believing. While intuitively appealing, the logic has a number of shortcomings. Perhaps the most severe is the limited expressiveness in that degrees of belief are restricted to constant rational numbers, which makes it impossible to express arbitrary belief distributions. In this paper we will address this and other shortcomings by extending the language and modifying the semantics of belief and only-believing. Among other things, we will show that belief retains many but not all of the properties of DS. Moreover, it turns out that only-believing arbitrary sentences, including those mentioning belief, is uniquely satisfiable in our logic. For an interesting class of knowledge bases we also show how reasoning about beliefs and meta-beliefs after performing noisy actions and sensing can be reduced to reasoning about the initial beliefs of an agent using a form of regression.

The strategic and epistemic properties of `know'

In communicating about certainty, speakers make choices among available formulations and hearers will aim to recover speaker intentions. In two studies, we assess speakers' production choices and hearers' interpretations to test (a) how maximal certainty is formulated, (b) whether those formulations adjust depending on context, and (c) whether speakers' context-driven adjustments are apparent to hearers. We compare the lower-certainty formulation `I believe that the deadline is tomorrow' [`believe'] with two high-certainty formulations, `I know that the deadline is tomorrow' [`know'] and `The deadline is tomorrow' [bare assertion]. Following Williamson (2000) and De Rose (2002), it is unclear which one of the latter two conveys higher epistemic standards. Given the unclear picture, we investigate when (if ever) `know' should be felicitous to utter over the bare assertion. One reason could be that `know' may be uttered felicitously for a wider range of contexts than the bare assertion (De Rose, 1992).Furthermore, `know' might be a useful linguistic tool for speakers to structure the subsequent dialogue to their liking. By presupposing content speakers assume or act as if the conveyed information was already shared knowledge and not up for debate. Thus, hearers might be more inclined to accept and accommodate e.g. Lewis (1979) presupposed content than asserted content.We investigated whether interlocutors align in the way they convey and recover meaning from statements about degrees of belief, comparing their behaviour across cooperative and uncooperative scenarios. Our results suggest (a) that speakers use know>bare assertion>believe for content with successively lower evidentiality scores and that hearers likewise infer know>bare assertion>believe in the same relative ordering. Regarding (b), speakers used `know' strategically in the uncooperative scenario to overstate their knowledge indicating that the usage of `know' is context-dependent. Regarding (c), hearers seemingly fail to recover these production strategies. This may be due to our experimental design where we investigated comprehension from a bystander point of view, or might similarly suggest that speakers succeed with their strategic approach.

QBism and the limits of scientific realism

QBism is an agent-centered interpretation of quantum theory. It rejects the notion that quantum theory provides a God’s eye description of reality and claims instead that it imposes constraints on agents’ subjective degrees of belief. QBism’s emphasis on subjective belief has led critics to dismiss it as antirealism or instrumentalism, or even, idealism or solipsism. The aim of this paper is to consider the relation of QBism to scientific realism. I argue that while QBism is an unhappy fit with a standard way of thinking about scientific realism, an alternative conception I call “perspectival normative realism” may allow for a reconciliation.

Decisions on Probabilistic Selling for Consumers with Different Risk Attitudes

Consumer attitudes toward probabilistic goods are affected not only by their personal preferences, but also by their risk propensity. However, because the probability of obtaining their preferred items is determined by the retailer, consumers must search for related information and rely on their own subjective judgments to reduce the risk of not obtaining them. This study investigates the effects that consumer risk attitudes and word of mouth have on consumers’ purchase decisions regarding probabilistic goods and develops a pricing model for probabilistic selling in which a retailer offers probabilistic goods to heterogeneous consumers with different risk attitudes and possible social interactions. The analytical results show that a retailer’s profit decreases as the degree of risk aversion increases under the probabilistic selling strategy. In addition, word of mouth affects consumers’ purchasing decisions regarding different degrees of belief that they will obtain their preferred items. When the word-of-mouth effect decreases, the consumers’ perceived probability of obtaining their preferred items also decreases, which, consequently, reduces the retailer’s profits.

Practical reasoning and degrees of outright belief

According to a suggestion by Williamson (Knowledge and its limits, Oxford University Press, 2000, p. 99), outright belief comes in degrees: one has a high/low degree of belief iff one is willing to rely on the content of one’s belief in high/low-stakes practical reasoning. This paper develops an epistemic norm for degrees of outright belief so construed. Starting from the assumption that outright belief aims at knowledge, it is argued that degrees of belief aim at various levels of strong knowledge, that is, knowledge which satisfies particularly high epistemic standards. This account is contrasted with and shown to be superior to an alternative proposal according to which higher degrees of outright belief aim at higher-order knowledge. In an “Appendix”, it is indicated that the logic of degrees of outright belief is closely linked to ranking theory.

Beyond Chance and Credence

Probability concepts permeate physics. This is obvious in statistical mechanics, in which probabilities appear explicitly. But even in cases when predictions are made with near-certainty, there is are implicit probabilistic assumptions in play, as it is assumed that molecular fluctuations can be neglected. How are we to understand these probabilistic concepts? This book offers a fresh look at these familiar topics, urging readers to see them in a new light. It argues that the traditional choices between probabilities as objective chances or degrees of belief is too limiting, and introduces a new concept, called epistemic chances, that combines physical and epistemic considerations. Thinking of probabilities in this way solves some of the puzzles associated with the use of probability and statistical mechanics. The book includes some history of discussions of probability, from the eighteenth to the twentieth century, and introductions to conceptual issues in thermodynamics and statistical mechanics. It should be of interest to philosophers interested in probability, and to physicists and philosophers of physics interested in understanding how probabilistic concepts apply to the physical world.

Probabilities in Quantum Mechanics

This chapter examines the role played by probabilities on each of the major approaches to understanding quantum mechanics. It is argued that the sorts of considerations brought up in previous chapters, having to do with limitations on precise knowledge of physical states, and the result of applying dynamical evolution to agents’ degrees of belief about those states, have a part to play on each of those approaches. The chapter includes an introduction to the basic formalism of quantum mechanics.