Showing by Avowing

Dorit Bar-On aims to account for the distinctive security of avowals by appealing to expression. She officially commits herself only to a negative characterization of expression, contending that expressive behavior is not epistemically based in self-judgments. I argue that her account of avowals, if it relies exclusively on this negative account of expression, can't achieve the explanatory depth she claims for it. Bar-On does explore the possibility that expression is a kind of perception-enabling showing. If she endorsed this positive account, her argument would re-gain an explanatory advantage over its rivals. But extending this account to linguistic expressive behavior would bring Bar-On very close to constitutive accounts of first-person authority.     

Ownership, Agency, and Defeat

In this article, I respond to Jennifer Duke-Yonge’s (2012) discussion of my article ‘Reflective Luck and Belief Ownership’ (Breyer, Acta Analytica, 25:133–154, 2010) and defend my Taking Responsibility account of belief ownership against her insightful criticisms.     

The vile,dopey, evil and odious game players

Many of my friends celebrate anniversaries these days, be it 50th birthday, or 60th, 70th, 80th, even 90th. It is to be deplored that they all accumulate together, rather than distribute themselves uniformly over my lifetime! It is now Gert Sabidussi’s turn, who just joined the octogenarians club, and it is a pleasure to dedicate a paper to him, since he did, and continues to do, excellent algebraic graph theory, including insights into the automorphism group of graphs, studies of stable graphs, Sabidussi representation theorems for symmetric graphs, Sabidussi’s compatibility conjecture, Sabidussi graphs, etc. Many leading mathematicians throughout the world are working on problems and insights initiated by Gert. He does all this in a relaxed playful way, as I witnessed when I acquired my own Sabidussi number 1. Hence it is only natural to relate here the fun that Gert and his friend Wil had while playing games in Dubrovnik, where a grand conference took place in 2009 honoring Gert. Unfortunately, I had to skip that conference, but, unknown to them, I planted a listening device.     

Bar-On on Self-Knowledge and Expression

I critically discuss the account of self-knowledge presented in Dorit Bar-On’s Speaking My Mind (OUP 2004), focusing on Bar-On’s understanding of what makes our capacity for self-knowledge puzzling and on her ‘neo-expressivist’ solution to the puzzle. I argue that there is an important aspect of the problem of self-knowledge that Bar-On’s account does not sufficiently address. A satisfying account of self-knowledge must explain not merely how we are able to make accurate avowals about our own present mental states, but how we can reasonably regard ourselves as entitled to claim self-knowledge. Addressing this aspect of the problem of self-knowledge requires confronting questions about the metaphysical nature of mental states, questions that Bar-On’s approach seeks to avoid.     

Reasoning about relationships between quantities to reorganize inverse function meanings: The case of Arya

Researchers have argued high school students, college students, pre-service teachers, and in-service teachers do not construct productive inverse function meanings. In this report, I first summarize the literature examining students’ and teachers’ inverse function meanings. I then provide my theoretical perspective, including my use of the terms understanding and meaning and my operationalization of productive inverse function meanings. I describe a conceptual analysis of ways students may reorganize their limited inverse function meanings into productive meanings via reasoning about relationships between covarying quantities. I then present one pre-service teacher’s activity in a semester long teaching experiment to characterize how her quantitative, covariational, and bidirectional reasoning supported her in reorganizing her limited inverse function meanings into more productive meanings. I describe how this reorganization required her to reconstruct her meanings for various related mathematical ideas. I conclude with research and pedagogical implications stemming from this work and directions for future research.     

Virtual encounters: the murky and furtive world of mathematical inventiveness

Based on Châtelet’s insights into the nature of mathematical inventiveness, drawn from historical analyses, we propose a new way of framing creativity in the mathematics classroom. The approach we develop emphasizes the social and material nature of creative acts. Our analysis of creative acts in two case studies involving primary school classrooms also reveals the characteristic ways in which digital technologies can occasion such acts.     

Individual and Collective Mathematical Development: The Case of Statistical Data Analysis

In the first part of this article, I clarify how we analyze students' mathematical reasoning as acts of participation in the mathematical practices established by the classroom community. In doing so, I present episodes from a recently completed classroom teaching experiment that focused on statistics. Against the background of this analysis, I then broaden my focus in the final part of the article by developing the themes of change, diversity, and equity.     

Against the Minimalistic Reading of Epistemic Contextualism: A Reply to Wolfgang Freitag

Several philosophers have argued that the factivity of knowledge poses a problem for epistemic contextualism (EC), which they have construed as a knowability problem. On a proposed minimalistic reading of EC’s commitments, Wolfgang Freitag argues that factivity yields no knowability problem for EC. I begin by explaining how factivity is thought to generate a contradiction out of paradigmatic contextualist cases on a certain reading of EC’s commitments. This reductio results in some kind of reflexivity problem for the contextualist when it comes to knowing her theory: either a knowability problem or a statability problem. Next, I set forth Freitag’s minimalistic reading of EC and explain how it avoids the reductio, the knowability problem and the statability problem. I argue that despite successfully evading these problems, Freitag’s minimalistic reading saddles EC with several other serious problems and should be rejected. I conclude by offering my own resolution to the problems.     

Rethinking common belief,revision, and backward induction

Whether rationality and common belief in rationality jointly entail the backward inductive outcome in centipede games has long been debated. Stalnaker’s compelling negative argument appeals to the AGM belief revision postulates to argue that off-path moves may be rational, given the revisions they may prompt. I counter that the structure of common belief and the principles of AGM justify an additional assumption about revision. I then prove that, given my proposed constraint, for all finite, n-player, extensive form, perfect information games with a unique backward inductive solution, if there is initial common belief in rationality, then backward induction is guaranteed.     

Propositional interval neighborhood logics: Expressiveness, decidability, and undecidable extensions

In this paper, we investigate the expressiveness of the variety of propositional interval neighborhood logics (PNL), we establish their decidability on linearly ordered domains and some important subclasses, and we prove the undecidability of a number of extensions of PNL with additional modalities over interval relations. All together, we show that PNL form a quite expressive and nearly maximal decidable fragment of Halpern–Shoham’s interval logic HS.     

In Defence of a Minimal Conception of Epistemic Contextualism: A Reply to M. D. Ashfield’s Response

The article responds to the objections M.D. Ashfield has raised to my recent attempt at saving epistemic contextualism from the knowability problem. First, it shows that Ashfield’s criticisms of my minimal conception of epistemic contextualism, even if correct, cannot reinstate the knowability problem. Second, it argues that these criticisms are based on a misunderstanding of the commitments of my minimal conception. I conclude that there is still no reason to maintain that epistemic contextualism has the knowability problem.     

A (Different) Virtue Responsibilism: Epistemic Virtues Without Motivations

Debate rages in virtue epistemology between virtue reliabilists and responsibilists. Here, I develop and argue for a new kind of responsibilism that is more conciliar to reliabilism. First, I argue that competence-based virtue reliabilism(s) cannot adequately ground epistemic credit. Then, with this problem in hand, I show how Aristotle’s virtue theory is motivated by analogous worries. Yet, incorporating too many details of Aristotelian moral theory leads to problems, notably the problem of unmotivated belief. As a result, I suggest a re-turn to Aristotle to develop a distinctively epistemological virtue theory that does not require any motive or affect for epistemic virtue. Nevertheless, my theory affirms that virtues are acquired, agent-expressive traits. The result is a conciliar responsibilism that leans closer to reliabilism. I end by arguing that my virtue responsibilism can solve worries facing both reliabilism and (extant) responsibilism.     

A probabilistic logic based on the acceptability of gambles

This article presents a probabilistic logic whose sentences can be interpreted as asserting the acceptability of gambles described in terms of an underlying logic. This probabilistic logic has a concrete syntax and a complete inference procedure, and it handles conditional as well as unconditional probabilities. It synthesizes Nilsson’s probabilistic logic and Frisch and Haddawy’s anytime inference procedure with Wilson and Moral’s logic of gambles.Two distinct semantics can be used for our probabilistic logic: (1) the measure–theoretic semantics used by the prior logics already mentioned and also by the more expressive logic of Fagin, Halpern, and Meggido and (2) a behavioral semantics. Under the measure–theoretic semantics, sentences of our probabilistic logic are interpreted as assertions about a probability distribution over interpretations of the underlying logic. Under the behavioral semantics, these sentences are interpreted only as asserting the acceptability of gambles, and this suggests different directions for generalization.     

A New Series: Blacks and Colleges: 1: The Dot and The Elephant

As recently as last year, I thought that “education”—the discipline—was too tiresome a subject to sustain my interest for more than a moment or two. I hastily abandoned this conviction after five minutes in front of a classroom. As a teacher, or as someone trying to teach, education became for me a living thing.

By happy, unplanned circumstance, my teaching and the research for this project began at the same time. The two assignments have dovetailed in a way that no amount of planning could have forecast.

This article is written from a black perspective—something which does not necessarily reside within a black skin. Retaining this perspective, particularly as a writer, requires among other things an agonizing bending of the mind. One is constantly obliged to see and weigh things including black education—from several points of view and finally to ask: “What does this or that event mean for black people at large—for ‘the movement’?“

The necessity for all of this is not readily understood by white people. The fact is that to be black in this country is to be part of “the movement.” Whether one is conscious of this fact or not, whether one rushes out to “join” something or not, matters little. One belongs whether one is male or female, unemployed, skilled in carpentry, or deep in clinical psychology. One “withdraws” from the movement only at great psychic cost. To be in it is painfully expensive as well, but this pain is offset by that particular joy that comes from embracing one's own people.     

The catwalk task: Reflections and synthesis: Part 1

In this article I recount my experiences with a series of encounters with the catwalk task and reflect on the professional growth that these opportunities afforded. First, I reflect on my own mathematical work on the catwalk task, including my efforts to fit various algebraic models to the data. Second, I reflect on my experiences working with a group of high school students on the catwalk task and my interpretations of their mathematical thinking. Finally, I reflect on the entire experience with the catwalk problem, as a mathematics learner, as a teacher, and as a professional.     

A Novel Interpretation of Plato’s Theory of Forms

In several recent issues of this journal, I argued for an account of property possession as strict, numerical identity. While this account has stuck some as being highly idiosyncratic in nature, it is not entirely something new under the sun, since as I will argue in this paper, it turns out to have a historic precedent in Plato’s theory of forms. Indeed, the purpose of this paper is twofold. The first is to show that my account of property possession can be utilized to provide a novel interpretation of Plato’s theory of forms. And the second is to show that once it has been divorced from a variety of implausible doctrines with which it has historically been wedded, Plato’s central insight that all properties possess themselves, far from being of mere historical interest, is independently plausible, ironically enough, even from an empirical point of view.     

Triangles, Schemes and Worlds: Reply to Nulty

Nulty proposes a “Davidsonian” argument for metaphysical pluralism, the thesis that there are (or could be) many actual worlds, which appeals to the possibility of alien forms of triangulation. I dispute Nulty’s reading of Davidson on two important points: Davidson’s attack on the notion of a conceptual scheme is not, as Nulty thinks, directed at pluralism, and his understanding of the notions of objective truth and reality is at odds with the conception needed for Nulty’s argument. I also show that the pluralist argument fails on its own terms as it requires an assimilation of worlds to worldviews. But there is much of value in Nulty’s paper despite these important flaws. When the confusions are cleared up, we are left with an intriguing and novel line of argument for conceptual relativism.     

Unrestricted Quantification and Reality: Reply to Kim

In my book, Worlds and Individuals, Possible and Otherwise, I use the novel idea of modal tense to respond to a number of arguments against modal realism. Peter van Inwagen’s million-carat-diamond objection is one of them. It targets the version of modal realism by David Lewis and exploits the fact that Lewis accepts absolutely unrestricted quantification. The crux of my response is to use modal tense to neutralize absolutely unrestricted quantification. Seahwa Kim says that even when equipped with modal tense, I am unsuccessful, given my view of reality and the proper use of modal tense in speaking of reality. I counter her attempt at resurrecting van Inwagen’s objection and clarify how we should use modal tense and how we should talk about reality.