The physiological blind spot corresponds to the optic disc where the retina contains no light-detecting photoreceptor cells. Our perception seemingly fills in this gap in input. Here we suggest that rather than an active process, such perceptual filling-in could instead be a consequence of the integration of visual inputs at higher stages of processing discounting the local absence of retinal input. Using functional brain imaging, we resolved the retinotopic representation of the physiological blind spot in early human visual cortex and (...) measured responses while participants perceived filling-in. Responses in early visual areas simply reflected the absence of visual input. In contrast, higher extrastriate regions responded more to stimuli in the eye containing the blind spot than the fellow eye. However, this signature was independent of filling-in. We argue that these findings agree with philosophical accounts that posit that the concept of filling-in of absent retinal input is unnecessary. (shrink)

The challenges raised in this article are not with information theory per se, but the assumptions surrounding it. Neuroscience isn't sufficiently critical about the appropriate ‘receiver’ or ‘channel’, focuses on decoding ‘parts’, and often relies on a flawed ‘veridicality’ assumption. If these problematic assumptions were questioned, information theory could be better directed to help us understand how the brain works.

Human behavior depends on the ability to effectively introspect about our performance. For simple perceptual decisions, this introspective or metacognitive ability varies substantially across individuals and is correlated with the structure of focal areas in prefrontal cortex. This raises the possibility that the ability to introspect about different perceptual decisions might be mediated by a common cognitive process. To test this hypothesis, we examined whether inter-individual differences in metacognitive ability were correlated across two different perceptual tasks where individuals made judgments (...) about different and unrelated visual stimulus properties. We found that inter-individual differences were strongly correlated between the two tasks for metacognitive ability but not objective performance. Such stability of an individual’s metacognitive ability across different perceptual tasks indicates a general mechanism supporting metacognition independent of the specific task. (shrink)

There are two major semantic theories of proper names: Semantic Descriptivism and Direct Reference. According to Semantic Descriptivism, the semantic content of a proper name N for a speaker S is identical to the semantic content of a definite description “the F” that the speaker associates with the name. According to Direct Reference, the semantic content of a proper name is identical to its referent. Semantic Descriptivism suffers from a number of drawbacks first pointed out by Donnellan (1970) and Kripke (...) (1972). Direct Reference faces difficulties of its own, most importantly the problem of empty names. The most promising Directly Referential solution to this problem is the Unfilled Proposition view, according to which utterances of sentences containing empty names semantically express unfilled propositions. But this view faces the problem of accounting for the intuition that negative existentials involving empty names are true. The most promising way of dealing with this problem within Unfilled Proposition theory is to suppose (i) that utterances of sentences may be used to pragmatically convey propositions they do not semantically express, and (ii) that the proposition pragmatically conveyed by a speaker S's utterance of a sentence containing an empty name N (where “the F” is a definite description S associates with N) is identical to the proposition semantically expressed by an utterance of the sentence obtained by replacing N with “the F”. Call this view “Pragmatic Descriptivism”. With respect to the problem of negative existentials, Pragmatic Descriptivists can insist that, although an utterance of “Santa does not exist” is literally neither true nor false, our taking it to be true may be explained as the result of our having confused the unfilled proposition it semantically expresses with the clearly true descriptive proposition it pragmatically conveys. Despite its theoretical virtues, Pragmatic Descriptivism has recently come under fire. Everett (2003), in particular, has advanced four different lines of criticism, to which Adams and Dietrich (2004) have responded in some detail. In this article, I have two main aims. The first is to argue that Adams and Dietrich's replies to Everett's criticisms (with one exception) are ineffective. I conclude that there is no acceptable strategy for solving the problem of empty names within Direct Reference theory. The second is to argue that there is a promising alternative to Semantic Descriptivism and Direct Reference that requires us to fill unfilled propositions with names, thereby solving the problem of empty names. (shrink)

This article explores the process of teaching Christian theological ethics beyond the common focus on European and North American sources. In conversation with moves to decolonise university curricula, the article proposes a theology of listening, an example of a research seminar for master’s and doctoral students at the University of Aberdeen on Christian ethics beyond Europe and North America, and an exploration of broader challenges for the formation of the theologian. The article asks, what can we learn when we give (...) up power and control when teaching and learning theology? How can we shift our methods of knowing and practising theology? We write as theologians from India, Mexico, and the United States living in the United Kingdom. We reflect on forms of exclusion in theological method and formation that arise from colonising, systemic violence, and inequalities. The article considers intercultural challenges when encountering different methods of reflection on the Christian experience. In a search for a more profoundly theological approach, we propose listening to the other as integral to doing theology. In an intercultural move, we draw on Dietrich Bonhoeffer's theology of listening, proposing that theology must be an advent of voices from beyond our usual places and methods. (shrink)

Descartes is widely portrayed as the arch proponent of “the epistemological transparency of thought” (or simply, “Transparency”). The most promising version of this view—Transparency-through-Introspection—says that introspecting (i.e., inwardly attending to) a thought guarantees certain knowledge of that thought. But Descartes rejects this view and provides numerous counterexamples to it. I argue that, instead, Descartes’s theory of self-knowledge is just an application of his general theory of knowledge. According to his general theory, certain knowledge is acquired only through clear and distinct (...) intellection. Thus, in his view, certain knowledge of one’s thoughts is acquired only through clear and distinct intellection of one’s thoughts. Introspection is a form of intellection and it can be clear and distinct. Ordinarily, however, introspection isn’t clear and distinct but is instead confused with dubitable perceptions of bodies. To make introspection clear and distinct, we need to “sharply separate” it from all perceptions of bodies by doubting all perceptions of bodies. Without such radical doubt, introspection remains confused and we lack certain knowledge not just of the specific features of our thoughts, but even of the minimal claim that a thought exists. Far from being the high priest of Transparency, Descartes is radically opposed to it. (shrink)

Computer-simulated scenarios have been part of psychological research on problem solving for more than 40 years. The shift in emphasis from simple toy problems to complex, more real-life oriented problems has been accompanied by discussions about the best ways to assess the process of solving complex problems. Psychometric issues such as reliable assessments and addressing correlations with other instruments have been in the foreground of these discussions and have left the content validity of complex problem solving in the background. In (...) this paper, we return the focus to content issues and address the important features that define complex problems. (shrink)

We present a new “reason-based” approach to the formal representation of moral theories, drawing on recent decision-theoretic work. We show that any moral theory within a very large class can be represented in terms of two parameters: a specification of which properties of the objects of moral choice matter in any given context, and a specification of how these properties matter. Reason-based representations provide a very general taxonomy of moral theories, as differences among theories can be attributed to differences in (...) their two key parameters. We can thus formalize several distinctions, such as between consequentialist and non-consequentialist theories, between universalist and relativist theories, between agent-neutral and agent-relative theories, between monistic and pluralistic theories, between atomistic and holistic theories, and between theories with a teleological structure and those without. Reason-based representations also shed light on an important but under-appreciated phenomenon: the “underdetermination of moral theory by deontic content”. (shrink)

While ordinary decision theory focuses on empirical uncertainty, real decision-makers also face normative uncertainty: uncertainty about value itself. From a purely formal perspective, normative uncertainty is comparable to (Harsanyian or Rawlsian) identity uncertainty in the 'original position', where one's future values are unknown. A comprehensive decision theory must address twofold uncertainty -- normative and empirical. We present a simple model of twofold uncertainty, and show that the most popular decision principle -- maximising expected value (`Expectationalism') -- has different formulations, namely (...) Ex-Ante Expectationalism, Ex-Post Expectationalism, and hybrid theories. These alternative theories recommend different decisions, reasoning modes, and attitudes to risk. But they converge under an interesting (necessary and sufficient) condition. (shrink)

The Gamer’s Dilemma consists of three intuitively plausible but conflicting assertions: (i) Virtual murder is morally permissible. (ii) Virtual child molestation is morally forbidden. (iii) There is no relevant moral difference between virtual murder and virtual child molestation in computer games. Numerous attempts to resolve (or dissolve) the Gamer’s Dilemma line the field of computer game ethics. Mostly, the phenomenon is approached using expressivist argumentation: Reprehensible virtual actions express something immoral in their performance but are not immoral by themselves. Consequentialists, (...) on the other hand, claim that the immorality of virtual actions arises from their harmful consequences. I argue that both approaches have serious difficulties meeting the moral challenge posed by the Gamer’s Dilemma. They tend to confuse the morality of in-game actions either with the morality of their real-world counterparts or with the morality of games as objects. Following this critical analysis, I will develop a Kantian argument and defend it against two objections. So far, deontological responses to the Gamer’s Dilemma have been sought in vain. Yet, with Kant, its moral challenge can be met by looking at the gamer’s reasons. From this perspective, the Gamer’s Dilemma is based on a false assumption: the moral status of gaming acts does not derive from a normative equation with their real-world counterparts but only from their justifications. (shrink)

Can an AGI create a more intelligent AGI? Under idealized assumptions, for a certain theoretical type of intelligence, our answer is: “Not without outside help”. This is a paper on the mathematical structure of AGI populations when parent AGIs create child AGIs. We argue that such populations satisfy a certain biological law. Motivated by observations of sexual reproduction in seemingly-asexual species, the Knight-Darwin Law states that it is impossible for one organism to asexually produce another, which asexually produces another, and (...) so on forever: that any sequence of organisms (each one a child of the previous) must contain occasional multi-parent organisms, or must terminate. By proving that a certain measure (arguably an intelligence measure) decreases when an idealized parent AGI single-handedly creates a child AGI, we argue that a similar Law holds for AGIs. (shrink)

The contemporary theory of epistemic democracy often draws on the Condorcet Jury Theorem to formally justify the ‘wisdom of crowds’. But this theorem is inapplicable in its current form, since one of its premises – voter independence – is notoriously violated. This premise carries responsibility for the theorem's misleading conclusion that ‘large crowds are infallible’. We prove a more useful jury theorem: under defensible premises, ‘large crowds are fallible but better than small groups’. This theorem rehabilitates the importance of deliberation (...) and education, which appear inessential in the classical jury framework. Our theorem is related to Ladha's (1993) seminal jury theorem for interchangeable (‘indistinguishable’) voters based on de Finetti's Theorem. We also prove a more general and simpler such jury theorem. (shrink)

Legg and Hutter, as well as subsequent authors, considered intelligent agents through the lens of interaction with reward-giving environments, attempting to assign numeric intelligence measures to such agents, with the guiding principle that a more intelligent agent should gain higher rewards from environments in some aggregate sense. In this paper, we consider a related question: rather than measure numeric intelligence of one Legg- Hutter agent, how can we compare the relative intelligence of two Legg-Hutter agents? We propose an elegant answer (...) based on the following insight: we can view Legg-Hutter agents as candidates in an election, whose voters are environments, letting each environment vote (via its rewards) which agent (if either) is more intelligent. This leads to an abstract family of comparators simple enough that we can prove some structural theorems about them. It is an open question whether these structural theorems apply to more practical intelligence measures. (shrink)

We define a notion of the intelligence level of an idealized mechanical knowing agent. This is motivated by efforts within artificial intelligence research to define real-number intelligence levels of compli- cated intelligent systems. Our agents are more idealized, which allows us to define a much simpler measure of intelligence level for them. In short, we define the intelligence level of a mechanical knowing agent to be the supremum of the computable ordinals that have codes the agent knows to be codes (...) of computable ordinals. We prove that if one agent knows certain things about another agent, then the former necessarily has a higher intelligence level than the latter. This allows our intelligence no- tion to serve as a stepping stone to obtain results which, by themselves, are not stated in terms of our intelligence notion (results of potential in- terest even to readers totally skeptical that our notion correctly captures intelligence). As an application, we argue that these results comprise evidence against the possibility of intelligence explosion (that is, the no- tion that sufficiently intelligent machines will eventually be capable of designing even more intelligent machines, which can then design even more intelligent machines, and so on). (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)

Can an agent's intelligence level be negative? We extend the Legg-Hutter agent-environment framework to include punishments and argue for an affirmative answer to that question. We show that if the background encodings and Universal Turing Machine (UTM) admit certain Kolmogorov complexity symmetries, then the resulting Legg-Hutter intelligence measure is symmetric about the origin. In particular, this implies reward-ignoring agents have Legg-Hutter intelligence 0 according to such UTMs.

John Broome has developed an account of rationality and reasoning which gives philosophical foundations for choice theory and the psychology of rational agents. We formalize his account into a model that differs from ordinary choice-theoretic models through focusing on psychology and the reasoning process. Within that model, we ask Broome’s central question of whether reasoning can make us more rational: whether it allows us to acquire transitive preferences, consistent beliefs, non-akratic intentions, and so on. We identify three structural types of (...) rationality requirements: consistency requirements, completeness requirements, and closedness requirements. Many standard rationality requirements fall under this typology. Based on three theorems, we argue that reasoning is successful in achieving closedness requirements, but not in achieving consistency or completeness requirements. We assess how far our negative results reveal gaps in Broome's theory, or deficiencies in choice theory and behavioral economics. (shrink)

We present a game mechanic called pseudo-visibility for games inhabited by non-player characters (NPCs) driven by reinforcement learning (RL). NPCs are incentivized to pretend they cannot see pseudo-visible players: the training environment simulates an NPC to determine how the NPC would act if the pseudo-visible player were invisible, and penalizes the NPC for acting differently. NPCs are thereby trained to selectively ignore pseudo-visible players, except when they judge that the reaction penalty is an acceptable tradeoff (e.g., a guard might accept (...) the penalty in order to protect a treasure because losing the treasure would hurt even more). We describe an RL agent transformation which allows RL agents that would not otherwise do so to perform some limited self-reflection to learn the training environments in question. (shrink)

Recent years have witnessed growing controversy over the “wisdom of the multitude.” As epistemic critics drawing on vast empirical evidence have cast doubt on the political competence of ordinary citizens, epistemic democrats have offered a defense of democracy grounded largely in analogies and formal results. So far, I argue, the critics have been more convincing. Nevertheless, democracy can be defended on instrumental grounds, and this article demonstrates an alternative approach. Instead of implausibly upholding the epistemic reliability of average voters, I (...) observe that competitive elections, universal suffrage, and discretionary state power disable certain potent mechanisms of elite entrenchment. By reserving particular forms of power for the multitude of ordinary citizens, they make democratic states more resistant to dangerous forms of capture than non-democratic alternatives. My approach thus offers a robust defense of electoral democracy, yet cautions against expecting too much from it—motivating a thicker conception of democracy, writ large. (shrink)

After generalizing the Archimedean property of real numbers in such a way as to make it adaptable to non-numeric structures, we demonstrate that the real numbers cannot be used to accurately measure non-Archimedean structures. We argue that, since an agent with Artificial General Intelligence (AGI) should have no problem engaging in tasks that inherently involve non-Archimedean rewards, and since traditional reinforcement learning rewards are real numbers, therefore traditional reinforcement learning probably will not lead to AGI. We indicate two possible ways (...) traditional reinforcement learning could be altered to remove this roadblock. (shrink)

“There is no world of thought that is not a world of language,” Walter Benjamin remarked, “and one only sees in the world what is preconditioned by ...

Discussions of Aristotle’s Metaphysics Z tend to treat it either as an independent treatise on substance and essence or as preliminary to the main conclusions of the Metaphysics. I argue instead that Z is central to Aristotle’s project of first philosophy in the Metaphysics: the first philosopher seeks the first causes of being qua being, especially substances, and in Z, Aristotle establishes that essences or forms are the first causes of being of perceptible substances. I also argue that the centrality (...) of Z to first philosophy is compatible with its status as theology. (shrink)

Through modern driver assistant systems, algorithmic decisions already have a significant impact on the behavior of vehicles in everyday traffic. This will become even more prominent in the near future considering the development of autonomous driving functionality. The need to consider ethical principles in the design of such systems is generally acknowledged. However, scope, principles and strategies for their implementations are not yet clear. Most of the current discussions concentrate on situations of unavoidable crashes in which the life of human (...) beings is existentially affected. In this paper, we argue that ethical considerations should be mandatory for any algorithmic decision of autonomous vehicles, instead of a limitation to hazard situations. Such an ethically aligned behavior is relevant because autonomous vehicles, like any other traffic participants, operate in a shared public space, where every behavioral decision impacts the operational possibilities of others. These possibilities concern the fulfillment of a road-user’s safety, utility and comfort needs. We propose that, to operate ethically in such space, an autonomous vehicle will have to take its behavior decisions according to a just distribution of operational possibilities among all traffic participants. Using an application on a partially-autonomous prototype vehicle, we describe how to apply and implement concepts of distributive justice to the driving environment and demonstrate the impact on its behavior in comparison to an advanced but egoistic decision maker. (shrink)

We present a general framework for representing belief-revision rules and use it to characterize Bayes's rule as a classical example and Jeffrey's rule as a non-classical one. In Jeffrey's rule, the input to a belief revision is not simply the information that some event has occurred, as in Bayes's rule, but a new assignment of probabilities to some events. Despite their differences, Bayes's and Jeffrey's rules can be characterized in terms of the same axioms: "responsiveness", which requires that revised beliefs (...) incorporate what has been learnt, and "conservativeness", which requires that beliefs on which the learnt input is "silent" do not change. To illustrate the use of non-Bayesian belief revision in economic theory, we sketch a simple decision-theoretic application. (shrink)

Under the independence and competence assumptions of Condorcet’s classical jury model, the probability of a correct majority decision converges to certainty as the jury size increases, a seemingly unrealistic result. Using Bayesian networks, we argue that the model’s independence assumption requires that the state of the world (guilty or not guilty) is the latest common cause of all jurors’ votes. But often – arguably in all courtroom cases and in many expert panels – the latest such common cause is a (...) shared ‘body of evidence’ observed by the jurors. In the corresponding Bayesian network, the votes are direct descendants not of the state of the world, but of the body of evidence, which in turn is a direct descendant of the state of the world. We develop a model of jury decisions based on this Bayesian network. Our model permits the possibility of misleading evidence, even for a maximally competent observer, which cannot easily be accommodated in the classical model. We prove that (i) the probability of a correct majority verdict converges to the probability that the body of evidence is not misleading, a value typically below 1; (ii) depending on the required threshold of ‘no reasonable doubt’, it may be impossible, even in an arbitrarily large jury, to establish guilt of a defendant ‘beyond any reasonable doubt’. (shrink)

Democratic decision-making is often defended on grounds of the ‘wisdom of crowds’: decisions are more likely to be correct if they are based on many independent opinions, so a typical argument in social epistemology. But what does it mean to have independent opinions? Opinions can be probabilistically dependent even if individuals form their opinion in causal isolation from each other. We distinguish four probabilistic notions of opinion independence. Which of them holds depends on how individuals are causally affected by environmental (...) factors such as commonly perceived evidence. In a general theorem, we identify causal conditions guaranteeing each kind of opinion independence. These results have implications for whether and how ‘wisdom of crowds’ arguments are possible, and how truth-conducive institutions can be designed. (shrink)

In light of Jewish tradition and the metaphysics of time, we argue that God can and will change the past. The argument makes for a new answer to the problem of evil and a new theory of atonement.

Advocates of dynamic systems have suggested that higher mental processes are based on continuous representations. In order to evaluate this claim, we first define the concept of representation, and rigorously distinguish between discrete representations and continuous representations. We also explore two important bases of representational content. Then, we present seven arguments that discrete representations are necessary for any system that must discriminate between two or more states. It follows that higher mental processes require discrete representations. We also argue that discrete (...) representations are more influenced by conceptual role than continuous representations. We end by arguing that the presence of discrete representations in cognitive systems entails that computationalism (i.e., the view that the mind is a computational device) is true, and that cognitive science should embrace representational pluralism. (shrink)

Bertrand Russell and the Nature of Propositions offers the first book-length defence of the Multiple Relation Theory of Judgement (MRTJ). Although the theory was much maligned by Wittgenstein and ultimately rejected by Russell himself, Lebens shows that it provides a rich and insightful way to understand the nature of propositional content. In Part I, Lebens charts the trajectory of Russell’s thought before he adopted the MRTJ. Part II reviews the historical story of the theory: What led Russell to deny the (...) existence of propositions altogether? Why did the theory keep evolving throughout its short life? What role did G. F. Stout play in the evolution of the theory? What was Wittgenstein’s concern with the theory, and, if we can’t know what his concern was exactly, then what are the best contending hypotheses? And why did Russell give the theory up? In Part III, Lebens makes the case that Russell’s concerns with the theory weren’t worth its rejection. Moreover, he argues that the MRTJ does most of what we could want from an account of propositions at little philosophical cost. This book bridges the history of early analytic philosophy with work in contemporary philosophy of language. It advances a bold reading of the theory of descriptions and offers a new understanding of the role of Stout and the representation concern in the evolution of the MRTJ. It also makes a decisive contribution to philosophy of language by demonstrating the viability of a no-proposition theory of propositions. (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, 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 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)

What is the relationship between degrees of belief and binary beliefs? Can the latter be expressed as a function of the former—a so-called “belief-binarization rule”—without running into difficulties such as the lottery paradox? We show that this problem can be usefully analyzed from the perspective of judgment-aggregation theory. Although some formal similarities between belief binarization and judgment aggregation have been noted before, the connection between the two problems has not yet been studied in full generality. In this paper, we seek (...) to fill this gap. The paper is organized around a baseline impossibility theorem, which we use to map out the space of possible solutions to the belief-binarization problem. Our theorem shows that, except in limiting cases, there exists no belief-binarization rule satisfying four initially plausible desiderata. Surprisingly, this result is a direct corollary of the judgment-aggregation variant of Arrow’s classic impossibility theorem in social choice theory. (shrink)

In 2011, Hibbard suggested an intelligence measure for agents who compete in an adversarial sequence prediction game. We argue that Hibbard’s idea should actually be considered as two separate ideas: first, that the intelligence of such agents can be measured based on the growth rates of the runtimes of the competitors that they defeat; and second, one specific (somewhat arbitrary) method for measuring said growth rates. Whereas Hibbard’s intelligence measure is based on the latter growth-rate-measuring method, we survey other methods (...) for measuring function growth rates, and exhibit the resulting Hibbard-like intelligence measures and taxonomies. Of particular interest, we obtain intelligence taxonomies based on Big-O and Big-Theta notation systems, which taxonomies are novel in that they challenge conventional notions of what an intelligence measure should look like. We discuss how intelligence measurement of sequence predictors can indirectly serve as intelligence measurement for agents with Artificial General Intelligence (AGIs). (shrink)

A fundamental question asked in modal logic is whether a given theory is consistent. But consistent with what? A typical way to address this question identifies a choice of background knowledge axioms (say, S4, D, etc.) and then shows the assumptions codified by the theory in question to be consistent with those background axioms. But determining the specific choice and division of background axioms is, at least sometimes, little more than tradition. This paper introduces generic theories for propositional modal logic (...) to address consistency results in a more robust way. As building blocks for background knowledge, generic theories provide a standard for categorical determinations of consistency. We argue that the results and methods of this paper help to elucidate problems in epistemology and enjoy sufficient scope and power to have purchase on problems bearing on modalities in judgement, inference, and decision making. (shrink)

A group is often construed as one agent with its own probabilistic beliefs (credences), which are obtained by aggregating those of the individuals, for instance through averaging. In their celebrated “Groupthink”, Russell et al. (2015) require group credences to undergo Bayesian revision whenever new information is learnt, i.e., whenever individual credences undergo Bayesian revision based on this information. To obtain a fully Bayesian group, one should often extend this requirement to non-public or even private information (learnt by not all or (...) just one individual), or to non-representable information (not representable by any event in the domain where credences are held). I pro- pose a taxonomy of six types of ‘group Bayesianism’. They differ in the information for which Bayesian revision of group credences is required: public representable information, private representable information, public non-representable information, etc. Six corre- sponding theorems establish how individual credences must (not) be aggregated to ensure group Bayesianism of any type, respectively. Aggregating through standard averaging is never permitted; instead, different forms of geometric averaging must be used. One theorem—that for public representable information—is essentially Russell et al.’s central result (with minor corrections). Another theorem—that for public non-representable information—fills a gap in the theory of externally Bayesian opinion pooling. (shrink)

One shortcoming of the chain rule is that it does not iterate: it gives the derivative of f(g(x)), but not (directly) the second or higher-order derivatives. We present iterated differentials and a version of the multivariable chain rule which iterates to any desired level of derivative. We first present this material informally, and later discuss how to make it rigorous (a discussion which touches on formal foundations of calculus). We also suggest a finite calculus chain rule (contrary to Graham, Knuth (...) and Patashnik's claim that "there's no corresponding chain rule of finite calculus"). (shrink)

Guided by the APA Ethics Code and social justice, this book helps psychologists solve ethical dilemmas while empowering those impacted by their work.

Aristotle analyses a large range of objects as composites of matter and form. But how exactly should we understand the relation between the matter and form of a composite? Some commentators have argued that forms themselves are somehow material, that is, forms are impure. Others have denied that claim and argued for the purity of forms. In this paper, I develop a new purist interpretation of Metaphysics Z.10-11, a text central to the debate, which I call 'hierarchical purism'. I argue (...) that hierarchical purism can overcome the difficulties faced by previous versions of purism as well as by impurism. Roughly, on hierarchical purism, each composite can be considered and defined in two different ways: From the perspective of metaphysics, composites are considered only insofar as they have forms and defined purely formally. From the perspective of physics, composites are considered insofar as they have forms and matter and defined with reference to both. Moreover, while the metaphysical definition is a definition in the strict sense of 'definition', the physical definition is a definition in a loose sense. Analogous points hold for intelligible composites and geometry. Finally, neither sort of definitional practice implies that, for Aristotle, forms are impure. (shrink)

This morning I intended to get out of bed when my alarm went off. Hearing my alarm, I formed the intention to get up now. Yet, for a time, I remained in bed, irrationally lazy. It seems I irrationally failed to execute my intention. Such cases of execution failure pose a challenge for Mentalists about rationality, who believe that facts about rationality supervene on facts about the mind. For, this morning, my mind was in order; it was my action that (...) apparently made me irrational. What, then, should Mentalists say about the phenomenon of execution failure? The phenomenon of execution failure, and the puzzle it raises for Mentalists, have rarely been discussed. This paper addresses the puzzle in two parts. First, it argues that execution failure is a real phenomenon. It is possible for agents to irrationally fail to act on their present-directed intentions. It follows that Mentalists in the philosophy of action must solve the puzzle of explaining what is irrational about cases of execution failure. Second, this paper begins the search for such a solution. It considers six possible resolutions to the puzzle, arguing that none is obviously the most attractive. These resolutions include a requirement of overall conative consistency, an appeal to the norm of intention consistency, a form of Volitionalism, an appeal to factive mental states, and a proposal due to Garrett Cullity, and a novel requirement of proper functioning. (shrink)

Condorcet's famous jury theorem reaches an optimistic conclusion on the correctness of majority decisions, based on two controversial premises about voters: they are competent and vote independently, in a technical sense. I carefully analyse these premises and show that: whether a premise is justi…ed depends on the notion of probability considered; none of the notions renders both premises simultaneously justi…ed. Under the perhaps most interesting notions, the independence assumption should be weakened.