Conditional Belief

This chapter first presents the static and dynamic rules of ranking theory. Then it shows how ranking theory solves the problem of iterated belief revisions.

Applications in Epistemology

This chapter applies ranking theory to two problems in epistemology and the philosophy of science: conceptual belief change, including logical learning, as well as learning indicative conditionals. The chapter concludes with a defense of rigidity.

Why Should I?

This chapter first answers the question of why conditional beliefs should obey the axioms and update rule of ranking theory. This includes a defense of the conditional theory of conditional belief that characterizes conditional belief in terms of belief and counterfactuals. Then the instrumentalist view of rationality, or normativity, underlying this answer is discussed. The chapter concludes with a discussion of conditional obligation and conditional belief.

Belief and Counterfactuals

This book is the first of two volumes on belief and counterfactuals. It consists of six of a total of eleven chapters. The first volume is concerned primarily with questions in epistemology and is expository in parts. Among other theories, it provides an accessible introduction to belief revision and ranking theory. Ranking theory specifies how conditional beliefs should behave. It does not tell us why they should do so nor what they are. This book fills these two gaps. The consistency argument tells us why conditional beliefs should obey the laws of ranking theory by showing them to be the means to attaining the end of holding true and informative beliefs. The conditional theory of conditional belief tells us what conditional beliefs are by specifying their nature in terms of non-conditional belief and counterfactuals. In addition, the book contains several novel arguments, accounts, and applications. These include an argument for the thesis that there are only hypothetical imperatives and no categorical imperatives; an account of the instrumentalist understanding of normativity, or rationality, according to which one ought to take the means to one’s ends; as well as solutions to the problems of conceptual belief change, logical learning, and learning conditionals. A distinctive feature of the book is its unifying methodological approach: means-end philosophy. Means-end philosophy takes serious that philosophy is a normative discipline, and that philosophical problems are entangled with each other. It also explains the importance of logic to philosophy, without being a technical theory itself.

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.

A directed link prediction method using graph convolutional network based on social ranking theory

Graph convolutional networks (GCN) have recently emerged as powerful node embedding methods in network analysis tasks. Particularly, GCNs have been successfully leveraged to tackle the challenging link prediction problem, aiming at predicting missing links that exist yet were not found. However, most of these models are oriented to undirected graphs, which are limited to certain real-life applications. Therefore, based on the social ranking theory, we extend the GCN to address the directed link prediction problem. Firstly, motivated by the reciprocated and unreciprocated nature of social ties, we separate nodes in the neighbor subgraph of the missing link into the same, a higher-ranked and a lower-ranked set. Then, based on the three kinds of node sets, we propose a method to correctly aggregate and propagate the directional information across layers of a GCN model. Empirical study on 8 real-world datasets shows that our proposed method is capable of reserving rich information related to directed link direction and consistently performs well on graphs from numerous domains.

Degrees of Doxastic Justification

This paper studies degrees of doxastic justification. Dependency relations among different beliefs are represented in terms of causal models. Doxastic justification, on this picture, is taken to run causally downstream along appropriate causal chains. A theory is offered which accounts for the strength of a derivative belief in terms of (i) the strength of the beliefs on which it is based, and (ii) the epistemic quality of the belief-forming mechanisms involved. It is shown that the structure of degrees of justification converges to ranking theory under ideal conditions.

Ranked Programming

While probabilistic programming is a powerful tool, uncertainty is not always of a probabilistic kind. Some types of uncertainty are better captured using ranking theory, which is an alternative to probability theory where uncertainty is measured using degrees of surprise on the integer scale from 0 to ∞. In this paper we combine probabilistic programming methodology with ranking theory and develop a ranked programming language. We use the Scheme programming language a basis and extend it with the ability to express both normal and exceptional behaviour of a model, and perform inference on such models. Like probabilistic programming, our approach provides a simple and flexible way to represent and reason with models involving uncertainty, but using a coarser grained and computationally simpler kind of uncertainty.

Evidence from Lightness and Color

What, then, is the evidence that sensory systems link stimulus inputs to useful responses empirically as a means of generating successful behavior in a physical world that the senses cannot measure? This chapter focuses on evidence derived from studies of lightness and color in vision, the brain system that has been most extensively studied in this regard. The argument here, and in the following chapters that consider other perceptual qualities and systems, is that evolved circuitry based on accumulated experience with frequency of occurrence of biologically useful stimuli accomplishes this feat. This strategy, called empirical ranking theory, explains why the qualities we perceive are always at odds with physical measurements.