We analyze two problems in mathematics – the first (stated in our title) is extracted from Wittgenstein’s “Philosophy for Mathematicians”; the second (“What set of numbers is non-denumerable?”) is taken from Cantor. We then consider, by way of comparison, a problem in musical aesthetics concerning a Brahms variation on a theme by Haydn. Our aim is to bring out and elucidate the essentially riddle-like character of these problems.

The creative process has the potential to increase wellbeing and foster human flourishing (Dolan and Metcalfe, 2012 ; Forgeard and Eichner, 2014 ; O’Brien and Murray, 2015 ; Conner et al., 2018 ; Kaufman, 2018 ), yet has received little attention in the humanistic management literature. In this paper, we present three experiments showing that idea originators experience greater relationship conflict with counterparts who have committed perceived “idea theft”, i.e., proposed identical or related ideas. We test a model that identifies (...) a mechanism—self-threat—that mediates the relationship between idea theft and relationship conflict and identifies an intervention to ameliorate that self-threat via self-affirmation. Study 1 demonstrates the idea originator’s attribution of malign attributions to, and negative moral emotions toward, the counterpart. Study 2 demonstrates that idea originators ostracize both those who propose identical ideas and those who propose merely related ideas. In Study 3, evidence for self-threat as the mechanism underlying the negative relational consequences is provided via both a direct test of mediation as well as via moderation by self-affirmation. Our research contributes to the nascent idea theft literature and suggests a way to reduce its negative consequences. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in (...) the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

This report reviews what quantum physics and information theory have to tell us about the age-old question, How come existence? No escape is evident from four conclusions: (1) The world cannot be a giant machine, ruled by any preestablished continuum physical law. (2) There is no such thing at the microscopic level as space or time or spacetime continuum. (3) The familiar probability function or functional, and wave equation or functional wave equation, of standard quantum theory provide mere continuum idealizations (...) and by reason of this circumstance conceal the information-theoretic source from which they derive. (4) No element in the description of physics shows itself as closer to primordial than the elementary quantum phenomenon, that is, the elementary device-intermediated act of posing a yes-no physical question and eliciting an answer or, in brief, the elementary act of observer-participancy. Otherwise stated, every physical quantity, every it, derives its ultimate significance from bits, binary yes-or-no indications, a conclusion which we epitomize in the phrase, it from bit. (shrink)

Ed. Daniel Greenberger, 750pp May 1995 164.95.

I consider two threats to the idea that on-line intelligent behaviour (the production of fluid and adaptable responses to ongoing sensory input) must or should be explained by appeal to neurally located representations. The first of these threats occurs when extra-neural factors account for the kind of behavioural richness and flexibility normally associated with representation-based control. I show how this anti-representational challenge can be met, if we apply the thought that, to be a representational system, an action-oriented neural system must (...) not only be the source of at least some of the observed behavioural richness and flexibility, it must also feature two architectural traits, namely arbitrariness and homuncularity. Unfortunately, however, this solution opens the door to our second threat to representation. The homuncularity condition will not be met by any system in which the causal contribution of each component is massively context-sensitive and variable over time. I end by discussing the empirical bet that biological nervous systems will not exhibit this style of causation. (shrink)

Information-based epistemology maintains that ‘being informed’ is an independent cognitive state that cannot be reduced to knowledge or to belief, and the modal logic KTB has been proposed as a model. But what distinguishes the KTB analysis of ‘being informed’, the Brouwersche schema (B), is precisely its downfall, for no logic of information should include (B) and, more generally, no epistemic logic should include (B), either.

In _Reconstructing the Cognitive World_, Michael Wheeler argues that we should turn away from the generically Cartesian philosophical foundations of much contemporary cognitive science research and proposes instead a Heideggerian approach. Wheeler begins with an interpretation of Descartes. He defines Cartesian psychology as a conceptual framework of explanatory principles and shows how each of these principles is part of the deep assumptions of orthodox cognitive science. Wheeler then turns to Heidegger's radically non-Cartesian account of everyday cognition, which, (...) he argues, can be used to articulate the philosophical foundations of a genuinely non-Cartesian cognitive science. Finding that Heidegger's critique of Cartesian thinking falls short, even when supported by Hubert Dreyfus's influential critique of orthodox artificial intelligence, Wheeler suggests a new Heideggerian approach. He points to recent research in "embodied-embedded" cognitive science and proposes a Heideggerian framework to identify, amplify, and clarify the underlying philosophical foundations of this new work. He focuses much of his investigation on recent work in artificial intelligence-oriented robotics, discussing, among other topics, the nature and status of representational explanation, and whether cognition is computation rather than a noncomputational phenomenon best described in the language of dynamical systems theory. Wheeler's argument draws on analytic philosophy, continental philosophy, and empirical work to "reconstruct" the philosophical foundations of cognitive science in a time of a fundamental shift away from a generically Cartesian approach. His analysis demonstrates that Heideggerian continental philosophy and naturalistic cognitive science need not be mutually exclusive and shows further that a Heideggerian framework can act as the "conceptual glue" for new work in cognitive science. (shrink)

This essay presents results about a deviation from independence measure called focused correlation . This measure explicates the formal relationship between probabilistic dependence of an evidence set and the incremental confirmation of a hypothesis, resolves a basic question underlying Peter Klein and Ted Warfield's ‘truth-conduciveness’ problem for Bayesian coherentism, and provides a qualified rebuttal to Erik Olsson's claim that there is no informative link between correlation and confirmation. The generality of the result is compared to recent programs in Bayesian epistemology (...) that attempt to link correlation and confirmation by utilizing a conditional evidential independence condition. Several properties of focused correlation are also highlighted. Introduction Correlation Measures 2.1 Standard covariance and correlation measures 2.2 The Wayne–Shogenji measure 2.3 Interpreting correlation measures 2.4 Correlation and evidential independence Focused Correlation Conclusion Appendix CiteULike Connotea Del.icio.us What's this? (shrink)

Michael Tonry, Sentencing Matters (New York: Oxford University Press, 1996, 240pp.

One approach to hypnosis suggests that for hypnotic experience to occur frontal lobe activity must be attenuated. For example, cold control theory posits that a lack of awareness of intentions is responsible for the experience of involuntariness and/or the subjective reality of hypnotic suggestions. The mid-dorso-lateral prefrontal cortex and the ACC are candidate regions for such awareness. Alcohol impairs frontal lobe executive function. This study examined whether alcohol affects hypnotisability. We administered 0.8 mg/kg of alcohol or a placebo to 32 (...) medium susceptible participants. They were subsequently hypnotised and given hypnotic suggestions. All participants believed they had received some alcohol. Participants in the alcohol condition were more susceptible to hypnotic suggestions than participants in the placebo condition. Impaired frontal lobe activity facilitates hypnotic responding, which supports theories postulating that attenuation of executive function facilitates hypnotic response, and contradicts theories postulating that hypnotic response involves enhanced inhibitory, attentional or other executive function. (shrink)

In a rich and thought-provoking paper, Lambros Malafouris argues that taking material culture seriously means to be ‘systematically concerned with figuring out the causal efficacy of materiality in the enactment and constitution of a cognitive system or operation’ (Malafouris 2004, 55). As I understand this view, there are really two intertwined claims to be established. The first is that the things beyond the skin that make up material culture (in other words, the physical objects and artefacts in which cultural networks (...) and systems of human social relations are realized) may be essential to the enactment of, and be partly constitutive of, certain cognitive systems or operations. The consequence of establishing this claim is supposed to be that we have a mandate to recast the boundaries of the mind so as to include, as proper parts of the mind, things located beyond the skin. Thus, in talking about the contribution of the world to cognition, Malafouris (2004, 58) concludes that ‘what we have traditionally construed as an active or passive but always clearly separated external stimulus for setting a cognitive mechanism into motion, may be after all a continuous part of the machinery itself; at least ex hypothesi’. This is the position that, in philosophical circles, is known increasingly as the extended mind hypothesis (Clark & Chalmers 1998; Menary forthcoming). Henceforth I shall refer to this hypothesis as EM. A stock example will help bring the idea into view. Rumelhart et al. (1986) note that most of us solve difficult multiplication problems by using ‘pen and paper’ as an external resource. This environmental prop enables us to transform a difficult cognitive problem into a set of simpler ones, and to temporarily store the results of certain intermediate calculations. For the fan of EM, the distributed combination of this external resource and certain inner psychological processes constitutes a cognitive system in its own right. (shrink)

Coherentism maintains that coherent beliefs are more likely to be true than incoherent beliefs, and that coherent evidence provides more confirmation of a hypothesis when the evidence is made coherent by the explanation provided by that hypothesis. Although probabilistic models of credence ought to be well-suited to justifying such claims, negative results from Bayesian epistemology have suggested otherwise. In this essay we argue that the connection between coherence and confirmation should be understood as a relation mediated by the causal relationships (...) among the evidence and a hypothesis, and we offer a framework for doing so by fitting together probabilistic models of coherence, confirmation, and causation. We show that the causal structure among the evidence and hypothesis is sometimes enough to determine whether the coherence of the evidence boosts confirmation of the hypothesis, makes no difference to it, or even reduces it. We also show that, ceteris paribus, it is not the coherence of the evidence that boosts confirmation, but rather the ratio of the coherence of the evidence to the coherence of the evidence conditional on a hypothesis. (shrink)

Examines the philosophical, scientific, and theological aspects of the character of the human mind.

Michael Dummett famously maintained that analytic philosophy was simply philosophy that followed Frege in treating the philosophy of language as the basis for all other philosophy (1978, 441). But one important insight to emerge from computer science is how difficult it is to animate the linguistic artifacts that the analysis of thought produces. Yet, modeling the effects of thought requires a new skill that goes beyond analysis: procedural literacy. Some of the most promising research in philosophy makes use of a (...) variety of modeling techniques that go beyond basic logic and elementary probability theory. What unifies this approach is a focus on what Alan Perlis called procedural literacy. This essay argues that the future spoils in philosophical research will disproportionally go to those who are procedurally literate. (shrink)

In this chapter we draw connections between two seemingly opposing approaches to probability and statistics: evidential probability on the one hand and objective Bayesian epistemology on the other.

Some recent cognitive-scientific research suggests that a considerable amount of intelligent action is generated not by the systematic activity of internal representations, but by complex interactions involving neural, bodily, and environmental factors. Following an analysis of this threat to representational explanation, we pursue an analogy between the role of genes in the production of biological form and the role of neural states in the production of behaviour, in order to develop a notion of genic representation. In both cases an appeal (...) to normal ecological context is used to balance multi-factoral, interactive causal determination against the intuition that certain aspects of the causal nexus play a special role in promoting adaptive success. Certain worries abut this vision help us to get a better grip on the concept of genic representation itself. We end with a puzzle concerning the relation between cognition and representation. (shrink)

The frame problem is the difficulty of explaining how non-magical systems think and act in ways that are adaptively sensitive to context-dependent relevance. Influenced centrally by Heideggerian phenomenology, Hubert Dreyfus has argued that the frame problem is, in part, a consequence of the assumption (made by mainstream cognitive science and artificial intelligence) that intelligent behaviour is representation-guided behaviour. Dreyfus' Heideggerian analysis suggests that the frame problem dissolves if we reject representationalism about intelligence and recognize that human agents realize the property (...) of thrownness (the property of being always already embedded in a context). I argue that this positive proposal is incomplete until we understand exactly how the properties in question may be instantiated in machines like us. So, working within a broadly Heideggerian conceptual framework, I pursue the character of a representation-shunning thrown machine. As part of this analysis, I suggest that the frame problem is, in truth, a two-headed beast. The intra-context frame problem challenges us to say how a purely mechanistic system may achieve appropriate, flexible and fluid action within a context. The inter-context frame problem challenges us to say how a purely mechanistic system may achieve appropriate, flexible and fluid action in worlds in which adaptation to new contexts is open-ended and in which the number of potential contexts is indeterminate. Drawing on the field of situated robotics, I suggest that the intra-context frame problem may be neutralized by systems of special-purpose adaptive couplings, while the inter-context frame problem may be neutralized by systems that exhibit the phenomenon of continuous reciprocal causation. I also defend the view that while continuous reciprocal causation is in conflict with representational explanation, special-purpose adaptive coupling, as well as its associated agential phenomenology, may feature representations. My proposal has been criticized recently by Dreyfus, who accuses me of propagating a cognitivist misreading of Heidegger, one that, because it maintains a role for representation, leads me seriously astray in my handling of the frame problem. I close by responding to Dreyfus' concerns. (shrink)

Andy Clark has argued that language is “in many ways the ultimate artifact” (Clark 1997, p.218). Fuelling this conclusion is a view according to which the human brain is essentially no more than a patterncompleting device, while language is an external resource which is adaptively fitted to the human brain in such a way that it enables that brain to exceed its unaided (pattern-completing) cognitive capacities, in much the same way as a pair of scissors enables us to “exploit our (...) basic manipulative capacities to fulfill new ends” (Clark 1997, pp.193-4). How should we respond to this bold reconceptualization of our linguistic abilities? First we need to understand it properly. So I begin by identifying and unpacking (and making a small “Heideggerian” amendment to) Clark’s main language-specific claims. That done I take a step back. Clark’s approach to language is generated from a theoretical perspective which sees cognition as distributed over brain, body, and world. So I continue my investigation of Clark’s incursion into linguistic territory by uncovering and illustrating those key ideas from the overall distributed cognition research programme which are particularly relevant in the present context. I then use this analysis as a spring-board from which to examine a crucial issue that arises for Clark’s account of language, namely linguistic inner rehearsal. I argue that while there is much to recommend in Clark’s treatment of this issue, some significant difficulties remain to be overcome. Via this critique of Clark’s position, alongside some proposals for how the revealed problems might be addressed, I hope to edge us that bit closer to a full understanding of our linguistic abilities. (shrink)

This impressive volume of essays that includes contributions from Herbert Dreyfus, Sean Kelly, Mike Wheeler, Dan Zahavi, and Shaun Gallagher reflects an emerging trend in cognitive science, and explores this new approach to cognitive science informed by Heidegger's thoughts on human existence.

In his groundbreaking book, Against Coherence (2005), Erik Olsson presents an ingenious impossibility theorem that appears to show that there is no informative relationship between probabilistic measures of coherence and higher likelihood of truth. Although Olsson's result provides an important insight into probabilistic models of epistemological coherence, the scope of his negative result is more limited than generally appreciated. The key issue is the role conditional independence conditions play within the witness testimony model Olsson uses to establish his result. Olsson (...) maintains that his witness model yields charitable ceteris paribus conditions for any theory of probabilistic coherence. Not so. In fact, Olsson's model, like Bayesian witness models in general, selects a peculiar class of models that are in no way representative of the range of options available to coherence theorists. Recent positive results suggest that there is a way to develop a formal theory of coherence after all. Further, although Bayesian witness models are not conducive to the truth, they are conducive to reliability. (shrink)

This paper presents statistical default logic, an expansion of classical (i.e., Reiter) default logic that allows us to model common inference patterns found in standard inferential statistics, including hypothesis testing and the estimation of a populations mean, variance and proportions. The logic replaces classical defaults with ordered pairs consisting of a Reiter default in the first coordinate and a real number within the unit interval in the second coordinate. This real number represents an upper-bound limit on the probability of accepting (...) the consequent of an applied default and that consequent being false. A method for constructing extensions is then defined that preserves this upper bound on the probability of error under a (skeptical) non-monotonic consequence relation. (shrink)

Dilation occurs when an interval probability estimate of some event E is properly included in the interval probability estimate of E conditional on every event F of some partition, which means that one’s initial estimate of E becomes less precise no matter how an experiment turns out. Critics maintain that dilation is a pathological feature of imprecise probability models, while others have thought the problem is with Bayesian updating. However, two points are often overlooked: (1) knowing that E is stochastically (...) independent of F (for all F in a partition of the underlying state space) is sufficient to avoid dilation, but (2) stochastic independence is not the only independence concept at play within imprecise probability models. In this paper we give a simple characterization of dilation formulated in terms of deviation from stochastic independence, propose a measure of dilation, and distinguish between proper and improper dilation. Through this we revisit the most sensational examples of dilation, which play up independence between dilator and dilatee, and find the sensationalism undermined by either fallacious reasoning with imprecise probabilities or improperly constructed imprecise probability models. (shrink)

According to the extended cognition hypothesis (henceforth ExC), there are conditions under which thinking and thoughts (or more precisely, the material vehicles that realize thinking and thoughts) are spatially distributed over brain, body and world, in such a way that the external (beyond-the-skin) factors concerned are rightly accorded fully-paid-up cognitive status.1 According to functionalism in the philosophy of mind, “what makes something a mental state of a particular type does not depend on its internal constitution, but rather on the way (...) it functions, or the role it plays, in the system of which it is a part” (Levin 2008). The respective fates of these two positions may not be independent of each other. The claim that ExC is in some way a form of, dependent on, entailed by, or at least commonly played out in terms of, functionalism is now pretty much part of the received view of things (see, e.g., Adams and Aizawa 2008; Clark and Chalmers 1998; Clark 2005, 2008, this volume a, b, forthcoming; Menary 2007; Rupert 2004; Sprevak manuscript; Wheeler forthcoming). Thus ExC might be mandated by the existence of functionally specified cognitive systems whose boundaries are located partly outside the skin. This is the position that Andy Clark has recently dubbed extended functionalism (Clark 2008, forthcoming; see also Wheeler forthcoming). (shrink)

Samuel C. Wheeler, III; The Extension of Deconstruction, The Monist, Volume 69, Issue 1, 1 January 1986, Pages 3–21, https://doi.org/10.5840/monist19866913.

We examine the notion of conditionals and the role of conditionals in inductive logics and arguments. We identify three mistakes commonly made in the study of, or motivation for, non-classical logics. A nonmonotonic consequence relation based on evidential probability is formulated. With respect to this acceptance relation some rules of inference of System P are unsound, and we propose refinements that hold in our framework.

Two compelling principles, the Reasonable Range Principle and the Preservation of Irrelevant Evidence Principle, are necessary conditions that any response to peer disagreements ought to abide by. The Reasonable Range Principle maintains that a resolution to a peer disagreement should not fall outside the range of views expressed by the peers in their dispute, whereas the Preservation of Irrelevant Evidence Principle maintains that a resolution strategy should be able to preserve unanimous judgments of evidential irrelevance among the peers. No standard (...) Bayesian resolution strategy satisfies the PIE Principle, however, and we give a loss aversion argument in support of PIE and against Bayes. The theory of imprecise probability allows one to satisfy both principles, and we introduce the notion of a set-based credal judgment to frame and address a range of subtle issues that arise in peer disagreements. (shrink)

One goal of normative multi-agent system theory is to formulate principles for normative system change that maintain the rule-like structure of norms and preserve links between norms and individual agent obligations. A central question raised by this problem is whether there is a framework for norm change that is at once specific enough to capture this rule-like behavior of norms, yet general enough to support a full battery of norm and obligation change operators. In this paper we propose an answer (...) to this question by developing a bimodal logic for norms and obligations called NO. A key to our approach is that norms are treated as propositional formulas, and we provide some independent reasons for adopting this stance. Then we define norm change operations for a wide class of modal systems, including the class of NO systems, by constructing a class of modal revision operators that satisfy all the AGM postulates for revision, and constructing a class of modal contraction operators that satisfy all the AGM postulates for contraction. More generally, our approach yields an easily extendable framework within which to work out principles for a theory of normative system change. (shrink)

Mark Richard Wheeler - Aristotle on Truth - Journal of the History of Philosophy 44:3 Journal of the History of Philosophy 44.3 469-470 Paolo Crivelli. Aristotle on Truth. Cambridge-New York: Cambridge University Press, 2004. Pp. xi + 340. Cloth, $85.00. A thorough contemporary study of Aristotle's theory of truth is welcome. Adopting a frankly analytic approach, Professor Crivelli addresses all of the most important Aristotelian texts on truth. He provides close and careful exegesis, attending to philological and interpretive difficulties (...) related to the manuscripts and alternative translations. In the spirit of Hintikka, Łukasiewicz, and Mignucci, the tools of contemporary logical analysis are applied effectively and yield rigorous restatements of Aristotle's.. (shrink)

Henry Kyburg’s lottery paradox (1961, p. 197) arises from considering a fair 1000 ticket lottery that has exactly one winning ticket. If this much is known about the execution of the lottery it is therefore rational to accept that one ticket will win. Suppose that an event is very likely if the probability of its occurring is greater than 0.99. On these grounds it is presumed rational to accept the proposition that ticket 1 of the lottery will not win. Since (...) the lottery is fair, it is rational to accept that ticket 2 won’t win either—indeed, it is rational to accept for any individual ticket i of the lottery that ticket i will not win. However, accepting that ticket 1 won’t win, accepting that ticket 2 won’t win, . . . , and accepting that ticket 1000 won’t win entails that it is rational to accept that no ticket will win, which entails that it is rational to accept the contradictory proposition that one ticket wins and no ticket wins. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Response to Masafumi Ogawa, “Music Teacher Education in Japan: Structure, Problems, and Perspectives”Peggy WheelerMasafumi Ogawa's paper presents challenge after challenge facing the teacher and the teacher educator in Japan. One has the sense that a lifetime of frustrations with the national curriculum, the set-up of student teaching, and the definition of music as a school subject each made its way into the paper. Even choosing to focus on teacher (...) training still leaves a very broad topic for a relatively short paper. The central challenge seems to be the curriculum. How does the curriculum impact the teacher and the teacher training process? How does the underlying definition of music as well as the purpose that definition implies affect the curriculum? His paper also identifies a series of dualities or tensions that exist between two important components: the curriculum or teacher education. The fact that Japanese and American music education systems seem to be at opposite ends of some of these dualities is a compelling reason for exploring and discussing them.In the arena of teacher preparation, the dualities as they appear in their relative proportion of the teacher education curriculum are (1) performance versus academic music courses, such as history, theory, and composition, and (2) education versus music courses—a familiar lament among music education students. In student teaching, modeling in the classroom by the cooperating teacher is contrasted with providing opportunities for the student teacher to experiment with the teaching process. Evaluation of student teaching is a three-way tension involving the student teacher, the cooperating teacher, and the university professor.In his discussion of the school curriculum, Ogawa deplores the triumph of attitude over skill, and pleads for discernment in the application of national standards to meet the needs of the community and students. He returns to the nature of music and music education at several points in his paper, expanding the meaning and function of music beyond music as art. His dissatisfaction with the seemingly teacher-proof curriculum peaks when he advocates for the autonomy of the teacher in the classroom. Giving teachers the opportunity to devise their own curriculum seems to go to the other extreme. Having taught with colleagues who had virtually no training in music, a standard curriculum at the district or national level provides some essential boundaries.Ogawa's discussion of the impact of the national Course of Study on Japanese music education was particularly intriguing. As teacher certification in the United [End Page 205] States has begun to promote and reward National Board Certification, it is striking to consider the restrictions and disempowerment that Ogawa describes and credits to the omnipresent Course of Study. For someone unfamiliar with the Japanese system of education, some of the descriptions were enticing but brief. Other descriptions were a bit confusing, but after visiting the MEXT website, I think most of this confusion is due to translation. It is difficult to take any phrase that is packed with meaning in one culture and find a suitable phrase in another culture that will convey the associations that are connected with it. I would recommend quoting complete descriptions or including an appendix. A reference to the history of Japanese music education on Kensho Takeshi's website would also provide more context, particularly for the connection between emotion, music, and ethics.I want to thank Ogawa for stimulating me to consider issues of curriculum including how I have changed my views of curriculum since I returned to school teaching. First, I will describe my change of perspective. Then I would like to close by describing an aspect of curriculum and teacher education that has surfaced this past year. I would call this the meta-curriculum, and I wonder how we can prepare new teachers for this part of teaching. It seems to me that the world of philosophy is the quintessential and perhaps the only appropriate arena for this preparation.Beyond Curriculum in the ClassroomLike the first spring rain on newly cut grass, music education has a fresh and vital look to me. I returned to public school teaching this year after a hiatus of seventeen years. After focusing on viola performance and liberal arts... (shrink)

Jon Williamson's Objective Bayesian Epistemology relies upon a calibration norm to constrain credal probability by both quantitative and qualitative evidence. One role of the calibration norm is to ensure that evidence works to constrain a convex set of probability functions. This essay brings into focus a problem for Williamson's theory when qualitative evidence specifies non-convex constraints.

In this paper, we present a new semantic challenge to the moral error theory. Its first component calls upon moral error theorists to deliver a deontic semantics that is consistent with the error-theoretic denial of moral truths by returning the truth-value false to all moral deontic sentences. We call this the ‘consistency challenge’ to the moral error theory. Its second component demands that error theorists explain in which way moral deontic assertions can be seen to differ in meaning despite necessarily (...) sharing the same intension. We call this the ‘triviality challenge’ to the moral error theory. Error theorists can either meet the consistency challenge or the triviality challenge, we argue, but are hard pressed to meet both. (shrink)