Doxastic decisions and controlling belief

I critique Matthias Steup’s account of exercising direct voluntary control over coming to have doxastic attitudes via doxastic decisions. I show that the sort of agency Steup argues is exercised in doxastic decision-making is not sufficient for agents to exercise direct voluntary control over their doxastic attitudes. This counts against such putative decisions being the locus of direct control in doxastic agency. Finally, I briefly consider what, if any, consequences the failure of Steup’s theory of doxastic agency may have for epistemic deontologism.     

Core and Ancillary Epistemic Virtues

We argue, primarily by appeal to phenomenological considerations related to the experiential aspects of agency, that belief fixation is broadly agentive; although it is rarely (if ever) voluntary, nonetheless, it is phenomenologically agentive because of its significant phenomenological similarities to voluntary-agency experience. An important consequence is that epistemic rationality, as a central feature of belief fixation, is an agentive notion. This enables us to introduce and develop a distinction between core and ancillary epistemic virtues. Core epistemic virtues involve several inter-related kinds of epistemic rationality in belief fixation. Other “habits of mind” pertinent to belief fixation constitute ancillary epistemic virtues. Finally, we discuss the relationship between both kinds of virtues, offering a unified account of epistemic virtuousness.     

Belief revision conditionals: basic iterated systems

It is now well known that, on pain of triviality, the probability of a conditional cannot be identified with the corresponding conditional probability [25]. This surprising impossibility result has a qualitative counterpart. In fact, Peter Gärdenfors showed in [13] that believing ‘If A then B’ cannot be equated with the act of believing B on the supposition that A — as long as supposing obeys minimal Bayesian constraints.Recent work has shown that in spite of these negative results, the question ‘how to accept a conditional?’ has a clear answer. Even if conditionals are not truth-carriers, they do have precise acceptability conditions. Nevertheless most epistemic models of conditionals do not provide acceptance conditions for iterated conditionals. One of the main goals of this essay is to provide a comprehensive account of the notion of epistemic conditionality covering all forms of iteration.First we propose an account of the basic idea of epistemic conditionality, by studying the conditionals validated by epistemic models where iteration is permitted but not constrained by special axioms. Our modeling does not presuppose that epistemic states should be represented by belief sets (we only assume that to each epistemic state corresponds an associated belief state). A full encoding of the basic epistemic conditionals (encompassing all forms of iteration) is presented and a representation result is proved.In the second part of the essay we argue that the notion of change involved in the evaluation of conditionals is suppositional, and that such notion should be distinguished from the notion of updating (modelled by AGM and other methods). We conclude by considering how some of the recent modellings of iterated change fare as methods for iterated supposing.     

齐次、可加及线性g-估价

彭实戈通过倒向随机微分方程介绍了g-估价的概念.一般来说,给定一个生成元g,对应的条件g-估价系统通常不是齐次,可加或线性的,那么我们自然要问:满足什么样条件的生成元g才能使得这些性质成立,本文回答了这一问题.     

Linguistic Understanding and Knowledge of Truth-Conditions

What do you know when you know what a sentence means? According to some theories, understanding a sentence is, in part, knowing its truth-conditions. Dorit Bar-On, Claire Horisk, and William Lycan have defended such theories on the grounds of an “epistemic determination argument” (“EDA”). That argument turns on the ideas (a) that understanding a sentence, along with knowledge of the non-linguistic facts, suffices to know its truth-value, and (b) that being able to determine a sentence’s truth-value given knowledge of the non-linguistic facts is knowing its truth-conditions. I argue that the EDA withstands the objections recently raised by Daniel Cohnitz and Jaan Kangilaski, but fails for other reasons. It equivocates between a fine-grained and a coarse grained conception of “facts.”     

Epistemic irrelevance in credal nets: The case of imprecise Markov trees

We focus on credal nets, which are graphical models that generalise Bayesian nets to imprecise probability. We replace the notion of strong independence commonly used in credal nets with the weaker notion of epistemic irrelevance, which is arguably more suited for a behavioural theory of probability. Focusing on directed trees, we show how to combine the given local uncertainty models in the nodes of the graph into a global model, and we use this to construct and justify an exact message-passing algorithm that computes updated beliefs for a variable in the tree. The algorithm, which is linear in the number of nodes, is formulated entirely in terms of coherent lower previsions, and is shown to satisfy a number of rationality requirements. We supply examples of the algorithm’s operation, and report an application to on-line character recognition that illustrates the advantages of our approach for prediction. We comment on the perspectives, opened by the availability, for the first time, of a truly efficient algorithm based on epistemic irrelevance.     

What Is Entitlement?

In his seminal paper, “Content Preservation,” Tyler Burge defends an original account of testimonial knowledge. The originality of the account is due, in part, to the fact that it is cast within a novel epistemic framework. The central feature of that framework is the introduction of the concept of entitlement, which is alleged to be a distinctive type of positive epistemic support or warrant. Entitlement and justification, according to Burge, are sub-species of warrant. Justification is the internalist form of warrant, but entitlement is epistemically externalist. My focus in this paper is Burge’s conception of entitlement, and there are three primary issues that I wish to address. What is the relationship between entitlement and the more traditional concept of justification? In what sense is entitlement epistemically externalist? Has Burge introduced a new epistemic concept or merely coined a new term for a familiar epistemic concept?     

Frege’s Ancestral and Its Circularities

After presenting the ordinary and the Fregean formulations of the ancestral, I raise the question of what is their relationship, the natural candidate being that the Fregean version is an analysans intended to improve upon, and replace, the common notion of ancestral (the analysandum). Next, two types of circles that arise in connection with the Fregean ancestral are presented, and it is claimed that one of the circles makes it impossible to maintain the just described (??replacement??) interpretation. A reference is made to Kerry, who was the first to point out a circularity in Frege??s ancestral. Some of Frege??s remarks are examined in order to tentatively sketch, an answer to the issue of the relationship between ordinary and Fregean ancestral; the latter, if not as an analysans replacing the common notion, can still be seen as a profound enrichment of the former.     

Bergmann’s Dilemma and Internalism’s Escape

Michael Bergmann has argued that internalist accounts of justification face an insoluble dilemma. This paper begins with an explanation of Bergmann??s dilemma. Next, I review some recent attempts to answer the dilemma, which I argue are insufficient to overcome it. The solution I propose presents an internalist account of justification through direct acquaintance. My thesis is that direct acquaintance can provide subjective epistemic assurance without falling prey to the quagmire of difficulties that Bergmann alleges all internalist accounts of justification cannot surmount.     

Looking back to the roots of partially correct constructs: The case of the area model in probability

We use the notion Partially Correct Constructs (PaCCs) for students’ constructs that partially match the mathematical principles underlying the learning context. A frequent expression of partial construction of mathematical principles is that a student’s words or actions provide an inaccurate or misleading picture of the student’s knowledge. In this study, we analyze the learning process of a grade 8 student, who learns a topic in elementary probability. The student successfully accomplishes a sequence of several tasks without apparent difficulty. When working on a further task, which seems to require nothing beyond his proven competencies, he encounters difficulties. Using the epistemic actions of the RBC model for abstraction in context as tracers, we analyze his knowledge constructing processes while working on the previous tasks, and identify some of his constructs as PaCCs that are concealed in these processes and explain his later difficulties. In addition, our research points to the complexity of the knowledge structures students are expected to deal with in their attempts to learn an elementary mathematical topic with understanding.     

Finite metacyclic groups as active sums of cyclic subgroups

The notion of active sum provides an analogue for groups of what the direct sum is for abelian groups. One natural question then is which groups are the active sum of a family of cyclic subgroups. Many groups have been found to give a positive answer to this question, while the case of finite metacyclic groups remained unknown. In this note we show that every finite metacyclic group can be recovered as the active sum of a discrete family of cyclic subgroups.     

Combinatorics and Algorithms for Augmenting Graphs

The notion of augmenting graphs generalizes Berge’s idea of augmenting chains, which was used by Edmonds in his celebrated solution of the maximum matching problem. This problem is a special case of the more general maximum independent set (MIS) problem. Recently, the augmenting graph approach has been successfully applied to solve MIS in various other special cases. However, our knowledge of augmenting graphs is still very limited and we do not even know what the minimal infinite classes of augmenting graphs are. In the present paper, we find an answer to this question and apply it to extend the area of polynomial-time solvability of the maximum independent set problem.     

Epistemological Disjunctivism and the New Evil Demon

In common with traditional forms of epistemic internalism, epistemological disjunctivism attempts to incorporate an awareness condition on justification. Unlike traditional forms of internalism, however, epistemological disjunctivism rejects the so-called New Evil Genius thesis. In so far as epistemological disjunctivism rejects the New Evil Genius thesis, it is revisionary. After explaining what epistemological disjunctivism is, and how it relates to traditional forms of epistemic internalism / externalism, I shall argue that the epistemological disjunctivist’s account of the intuitions underlying the New Evil Genius thought experiment is incomplete at best. Therefore, as presented, epistemological disjunctivism is unable to accommodate the core guiding intuitions of epistemic internalism. Given the stated aim of not being revisionary on this score, the view is at a dialectical disadvantage over the traditional forms of epistemic internalism the position is meant to replace. Unfortunately, therefore, at present, the impasse between internalism and externalism remains.     

Understanding, Integration, and Epistemic Value

Understanding enjoys a special kind of value, one not held by lesser epistemic states such as knowledge and true belief. I explain the value of understanding via a seemingly unrelated topic, the implausibility of veritism. Veritism holds that true belief is the sole ultimate epistemic good and all other epistemic goods derive their value from the epistemic value of true belief. Veritism entails that if you have a true belief that p, you have all the epistemic good qua p. Veritism is a plausible and widely held view; I argue that it is untenable. I argue that integration among beliefs possesses epistemic value independent from the good of true belief, and so has value veritism cannot account for. I argue further that this integration among beliefs comprises the distinctive epistemic value of understanding.     

AGM-consistency and perfect Bayesian equilibrium. Part I: definition and properties

We provide a general notion of perfect Bayesian equilibrium which can be applied to arbitrary extensive-form games and is intermediate between subgame-perfect equilibrium and sequential equilibrium. The essential ingredient of the proposed definition is the qualitative notion of AGM-consistency, which has an epistemic justification based on the theory of belief revision introduced by Alchourrón, Gärdenfors and Makinson. AGM-consistency is a generalization of the notion of consistency introduced by Kreps and Wilson as part of the definition of sequential equilibrium.     

Role of Interaction in Enhancing the Epistemic Utility of 3D Mathematical Visualizations

Many epistemic activities, such as spatial reasoning, sense-making, problem solving, and learning, are information-based. In the context of epistemic activities involving mathematical information, learners often use interactive 3D mathematical visualizations (MVs). However, performing such activities is not always easy. Although it is generally accepted that making these visualizations interactive can improve their utility, it is still not clear what role interaction plays in such activities. Interacting with MVs can be viewed as performing low-level epistemic actions on them. In this paper, an epistemic action signifies an external action that modifies a given MV in a way that renders learners’ mental processing of the visualization easier, faster, and more reliable. Several, combined epistemic actions then, when performed together, support broader, higher-level epistemic activities. The purpose of this paper is to examine the role that interaction plays in supporting learners to perform epistemic activities, specifically spatial reasoning involving 3D MVs. In particular, this research investigates how the provision of multiple interactions affects the utility of 3D MVs and what the usage patterns of these interactions are. To this end, an empirical study requiring learners to perform spatial reasoning tasks with 3D lattice structures was conducted. The study compared one experimental group with two control groups. The experimental group worked with a visualization tool which provided participants with multiple ways of interacting with the 3D lattices. One control group worked with a second version of the visualization tool which only provided one interaction. Another control group worked with 3D physical models of the visualized lattices. The results of the study indicate that providing learners with multiple interactions can significantly affect and improve performance of spatial reasoning with 3D MVs. Among other findings and conclusions, this research suggests that one of the central roles of interaction is allowing learners to perform low-level epistemic actions on MVs in order to carry out higher-level cognitive and epistemic activities. The results of this study have implications for how other 3D mathematical visualization tools should be designed.     

The Value of Lesser Goods: The Epistemic Value of Entitlement

The notion of entitlement plays an important role in some influential epistemologies. Often the epistemological motive for introducing the concept is to accommodate certain externalist intuitions within an internalist framework or, conversely, to incorporate internalist traits into an otherwise externalist position. In this paper two prominent philosophers will be used as examples: Tyler Burge as a representative of the first option and Fred Dretske as one of the second. However, even on the assumption that the concept of entitlement is sufficiently clarified, accomplishing these results is easier said than done – especially if we also want to ascribe positive epistemic value to entitlement. It will be shown that the epistemic value of entitlement is either granted at the expense of the epistemic value of justification or the value ends up below the level of value at which the epistemologists employing the concept of entitlement are aiming.     

Knowledge versus Understanding: The Cost of Avoiding Gettier

In the current discussion on epistemic value, several philosophers argue that understanding enjoys higher epistemological significance and epistemic value than knowledge??the epistemic state the epistemological tradition has been preoccupied with. By noting a tension between the necessary conditions for understanding in the perhaps most prominent of these philosophers, Jonathan Kvanvig, this paper disputes the higher epistemological relevance of understanding. At the end, on the basis of the results of the previous sections, some alternative comparative contrasts between knowledge and understanding are briefly explored, including one in which an analogue to the KK-principle for knowledge, the ??UU-principle??, does not hold for a different reason than that for which the former principle fails.     

On the Compatibility of Epistemic Internalism and Content Externalism

In this paper I consider a recent argument of Timothy Williamson’s that epistemic internalism and content externalism are indeed incompatible, and since he takes content externalism to be above reproach, so much the worse for epistemic internalism. However, I argue that epistemic internalism, properly understood, remains substantially unaffected no matter which view of content turns out to be correct. What is key to the New Evil Genius thought experiment is that, given everything of which the inhabitants are consciously aware, the two worlds are subjectively indistinguishable for them, which is what matters on internalist accounts of epistemic justification. I argue that even if a standard moral of the New Evil Genius intuition is untenable due to considerations arising from content externalism, the case can be understood as supporting epistemic internalism in a way that is wholly compatible with content externalism. In short, epistemic internalism is committed to sameness of justificatory status between subjectively indistinguishable counterparts, not sameness of content of their justifiers.