There is a theorem that shows that it is impossible for an algorithm to jointly satisfy the statistical fairness criteria of Calibration and Equalised Odds non-trivially. But what about the recently advocated alternative to Calibration, Base Rate Tracking? Here, we show that Base Rate Tracking is strictly weaker than Calibration, and then take up the question of whether it is possible to jointly satisfy Base Rate Tracking and Equalised Odds in non-trivial scenarios. We show that it is not, thereby establishing (...) an even more general impossibility theorem. (shrink)

In many assessment problems—aptitude testing, hiring decisions, appraisals of the risk of recidivism, evaluation of the credibility of testimonial sources, and so on—the fair treatment of different groups of individuals is an important goal. But individuals can be legitimately grouped in many different ways. Using a framework and fairness constraints explored in research on algorithmic fairness, I show that eliminating certain forms of bias across groups for one way of classifying individuals can make it impossible to eliminate such bias across (...) groups for another way of dividing people up. And this point generalizes if we require merely that assessments be approximately bias-free. Moreover, even if the fairness constraints are satisfied for some given partitions of the population, the constraints can fail for the coarsest common refinement, that is, the partition generated by taking intersections of the elements of these coarser partitions. This shows that these prominent fairness constraints admit the possibility of forms of intersectional bias. (shrink)

I provide a characterization of weakly pseudo-rationalizable choice functions---that is, choice functions rationalizable by a set of acyclic relations---in terms of hyper-relations satisfying certain properties. For those hyper-relations Nehring calls extended preference relations, the central characterizing condition is weaker than (hyper-relation) transitivity but stronger than (hyper-relation) acyclicity. Furthermore, the relevant type of hyper-relation can be represented as the intersection of a certain class of its extensions. These results generalize known, analogous results for path independent choice functions.

Recent impossibility theorems for fair risk assessment extend to the domain of epistemic justice. We translate the relevant model, demonstrating that the problems of fair risk assessment and just credibility assessment are structurally the same. We motivate the fairness criteria involved in the theorems as also being appropriate in the setting of testimonial justice. Any account of testimonial justice that implies the fairness/justice criteria must be abandoned, on pain of triviality.

Our aim here is to present a result that connects some approaches to justifying countable additivity. This result allows us to better understand the force of a recent argument for countable additivity due to Easwaran. We have two main points. First, Easwaran’s argument in favour of countable additivity should have little persuasive force on those permissive probabilists who have already made their peace with violations of conglomerability. As our result shows, Easwaran’s main premiss – the comparative principle – is strictly (...) stronger than conglomerability. Second, with the connections between the comparative principle and other probabilistic concepts clearly in view, we point out that opponents of countable additivity can still make a case that countable additivity is an arbitrary stopping point between finite and full additivity. (shrink)

There has been recent discussion of a puzzle posed by emotions that are backward looking. Though our emotions commonly diminish over time, how can they diminish fittingly if they are an accurate appraisal of an event that is situated in the past? Agnes Callard (2017) has offered a solution by providing an account of anger in which anger is both backwards looking and resolvable, yet her account depends upon contrition to explain anger’s fitting diminishment. My aim is to explain how (...) anger can fittingly diminish even when there is lack of contrition. I propose a permissivism about fittingness by showing that both anger and compassion are fitting responses to blameworthy behaviour. I argue that anger is rendered fitting because it accurately appraises the behaviour, whereas compassion becomes fitting as a valuational response to what the behaviour reveals about the lived experience of the offender. I then respond to some worries my account raises, and I clarify details of my account to show that it is not unrealistic to the way some of our anger actually does diminish. I end with a proposal that our anger can fittingly diminish through the act of forgiveness when compassion is not a forthcoming affective response. (shrink)

This paper generalizes rationalizability of a choice function by a single acyclic binary relation to rationalizability by a set of such relations. Rather than selecting those options in a menu that are maximal with respect to a single binary relation, a weakly pseudo-rationalizable choice function selects those options that are maximal with respect to at least one binary relation in a given set. I characterize the class of weakly pseudo-rationalizable choice functions in terms of simple functional properties. This result also (...) generalizes Aizerman and Malishevski's characterization of pseudo-rationalizable choice functions, that is, choice functions rationalizable by a set of total orders. (shrink)

There has been much interest in conspiracy theories (CTs) amongst philosophers in recent years. The aim of this paper will be to apply some of the philosophical research to issues in political theory. I will first provide an overview of some of the philosophical discussions about CTs. While acknowledging that particularism is currently the dominant position in the literature, I will contend that the ‘undue scepticism problem’, a modified version of an argument put forward by Brian Keeley, is an important (...) general objection to many CTs. This in turn leads to some substantial conclusions for liberal political philosophy, as the undue scepticism problem sets up a strong argument against non-liberal alternatives to liberal thought. I shall argue that we are justified in having far more doubt about the reliability of official sources in non-liberal societies, and it is legitimate to be more sceptical about claims designed to bolster non-liberal politics. Moreover, because scepticism is often more warranted in non-liberal societies, this may provide the possibility for the state to be stable, even if it is highly tyrannical or ineffective. These considerations are not intended to be decisive, but raise unresolved questions about the viability of non-liberal politics. (shrink)

Merging of opinions results underwrite Bayesian rejoinders to complaints about the subjective nature of personal probability. Such results establish that sufficiently similar priors achieve consensus in the long run when fed the same increasing stream of evidence. Initial subjectivity, the line goes, is of mere transient significance, giving way to intersubjective agreement eventually. Here, we establish a merging result for sets of probability measures that are updated by Jeffrey conditioning. This generalizes a number of different merging results in the literature. (...) We also show that such sets converge to a shared, maximally informed opinion. Convergence to a maximally informed opinion is a (weak) Jeffrey conditioning analogue of Bayesian “convergence to the truth” for conditional probabilities. Finally, we demonstrate the philosophical significance of our study by detailing applications to the topics of dynamic coherence, imprecise probabilities, and probabilistic opinion pooling. (shrink)

Bayesians often appeal to “merging of opinions” to rebut charges of excessive subjectivity. But what happens in the short run is often of greater interest than what happens in the limit. Seidenfeld and coauthors use this observation as motivation for investigating the counterintuitive short run phenomenon of dilation, since, they allege, dilation is “the opposite” of asymptotic merging of opinions. The measure of uncertainty relevant for dilation, however, is not the one relevant for merging of opinions. We explicitly investigate the (...) short run behavior of the metric relevant for merging, and show that dilation is independent of the opposite of merging. (shrink)

An aspect of Peirce’s thought that may still be underappreciated is his resistance to what Levi calls _pedigree epistemology_, to the idea that a central focus in epistemology should be the justification of current beliefs. Somewhat more widely appreciated is his rejection of the subjective view of probability. We argue that Peirce’s criticisms of subjectivism, to the extent they grant such a conception of probability is viable at all, revert back to pedigree epistemology. A thoroughgoing rejection of pedigree in the (...) context of probabilistic epistemology, however, _does_ challenge prominent subjectivist responses to the problem of the priors. (shrink)

In the face of an impossibility result, some assumption must be relaxed. The Mere Addition Paradox is an impossibility result in population ethics. Here, I explore substantially weakening the decision-theoretic assumptions involved. The central finding is that the Mere Addition Paradox persists even in the general framework of choice functions when we assume Path Independence as a minimal decision-theoretic constraint. Choice functions can be thought of either as generalizing the standard axiological assumption of a binary “betterness” relation, or as providing (...) a general framework for a normative (rather than axiological) theory of population ethics. Path Independence, a weaker assumption than typically (implicitly) made in population ethics, expresses the idea that, in making a choice from a set of alternatives, the order in which options are assessed or considered is ethically arbitrary and should not affect the final choice. Since the result establishes a conflict between the relevant ethical principles and even very weak decision-theoretic principles, we have more reason to doubt the ethical principles. (shrink)

This article reviews an epochal change in international thinking about physical punishment of children from being a reasonable method of chastisement to one that is harmful to children and troubling to families. In addition, the article suggests shifts in thinking about physical punishment were originally pioneered as part and parcel of the dismantling of national laws granting fathers’ specific rights to admonish children under conventions of patria potestas. A comparative historical framework of analysis involving two case studies of Ireland and (...) Ghana illustrates non-unilinear pathways of international convergence towards the prohibition of physical punishment. The comparative historical analysis highlights the 1930s and 1940s as an era when Ireland began to reject patria potestas and religious or judicial rulings which allowed for children to be given ‘a good beating’ in family and school settings. However, from the same period, Ghana is seen to experience Christian remonstrations not to ‘spare the rod’ leading to the ‘conventional’ tradition of ‘this is how we do it here’. Two case studies serve to illustrate that banning physical punishment was less controversial in Ireland where allied traditions of patria potestas and disciplinarian Christian beliefs had lost their moral hegemony than in Ghana where such beliefs still held influence. The article concludes overall that normative campaigns against physical punishment of children emanate from a coherent paradigm of family policy where childcare, education, and well-being of children are embedded as everyday societal responsibilities rather than privatised or patriarchal familial obligations. The coherent model offers an alternative moral hegemony to neo-liberal and Janus-faced conceptualisations of good or ‘intact’ families versus ‘broken’ or ‘troubled’ families. (shrink)

Epistemic states of uncertainty play important roles in ethical and political theorizing. Theories that appeal to a “veil of ignorance,” for example, analyze fairness or impartiality in terms of certain states of ignorance. It is important, then, to scrutinize proposed conceptions of ignorance and explore promising alternatives in such contexts. Here, I study Lerner’s probabilistic egalitarian theorem in the setting of imprecise probabilities. Lerner’s theorem assumes that a social planner tasked with distributing income to individuals in a population is “completely (...) ignorant” about which utility functions belong to which individuals. Lerner models this ignorance with a certain uniform probability distribution, and shows that, under certain further assumptions, income should be equally distributed. Much of the criticism of the relevance of Lerner’s result centers on the representation of ignorance involved. Imprecise probabilities provide a general framework for reasoning about various forms of uncertainty including, in particular, ignorance. To what extent can Lerner’s conclusion be maintained in this setting? (shrink)

Supra-Bayesianism is the Bayesian response to learning the opinions of others. Probability pooling constitutes an alternative response. One natural question is whether there are cases where probability pooling gives the supra-Bayesian result. This has been called the problem of Bayes-compatibility for pooling functions. It is known that in a common prior setting, under standard assumptions, linear pooling cannot be nontrivially Bayes-compatible. We show by contrast that geometric pooling can be nontrivially Bayes-compatible. Indeed, we show that, under certain assumptions, geometric and (...) Bayes-compatible pooling are equivalent. Granting supra-Bayesianism its usual normative status, one upshot of our study is thus that, in a certain class of epistemic contexts, geometric pooling enjoys a normative advantage over linear pooling as a social learning mechanism. We discuss the philosophical ramifications of this advantage, which we show to be robust to variations in our statement of the Bayes-compatibility problem. (shrink)

ABSTRACT Drawing inspiration from Fred Dretske, L. S. Carrier, John A. Barker, and Robert Nozick, we develop a tracking analysis of knowing according to which a true belief constitutes knowledge if and only if it is based on reasons that are sensitive to the fact that makes it true, that is, reasons that wouldn’t obtain if the belief weren’t true. We show that our sensitivity analysis handles numerous Gettier-type cases and lottery problems, blocks pathways leading to skepticism, and validates (...) the epistemic closure thesis that correct inferences from known premises yield knowledge of the conclusions. We discuss the plausible views of Ted Warfield and Branden Fitelson regarding cases of knowledge acquired via inference from false premises, and we show how our sensitivity analysis can account for such cases. We present arguments designed to discredit putative counterexamples to sensitivity analyses recently proffered by Tristan Haze, John Williams and Neil Sinhababu, which involve true statements made by untrustworthy informants and strange clocks that sometimes display the correct time while running backwards. Finally, we show that in virtue of employing the paradox-free subjunctive conditionals codified by Relevance Logic theorists instead of the paradox-laden subjunctive conditionals codified by Robert Stalnaker and David Lewis. (shrink)

Philosophical interest in situated cognition has been focused most intensely on the claim that human cognitive processes extend from the brain into the tools humans use. As we see it, this radical hypothesis is sustained by two kinds of mistakes, the confusion of coupling relations with constitutive relations and an inattention to the mark of the cognitive. Here we wish to draw attention to these mistakes and show just how pervasive they are. That is, for all that the radical philosophers (...) have said, the mind is still in the head. (shrink)

For two ideally rational agents, does learning a finite amount of shared evidence necessitate agreement? No. But does it at least guard against belief polarization, the case in which their opinions get further apart? No. OK, but are rational agents guaranteed to avoid polarization if they have access to an infinite, increasing stream of shared evidence? No.

This paper explores the question of what logic is not. It argues against the wide spread assumptions that logic is: a model of reason; a model of correct reason; the laws of thought, or indeed is related to reason at all such that the essential nature of the two are crucially or essentially co-illustrative. I note that due to such assumptions, our current understanding of the nature of logic itself is thoroughly entangled with the nature of reason. I show that (...) most arguments for the presence of any sort of essential re- lationship between logic and reason face intractable problems and demands, and fall well short of addressing them. These arguments include those for the notion that logic is normative for reason (or that logic and correct reason are in some way the same thing), that logic is some sort of description of correct reason and that logic is an abstracted or idealised version of correct reason. A strong version of logical realism is put forward as an alternative view, and is briefly explored. (shrink)

In this paper, I present my solutions to two closely related questions about pleasure. One of these questions is fairly well known. The second question seems to me to be at least as interesting as the first, but it apparently hasn't interested quite so many philosophers.

Embodied cognition is sweeping the planet. On a non-embodied approach, the sensory system informs the cognitive system and the motor system does the cognitive system’s bidding. There are causal relations between the systems but the sensory and motor systems are not constitutive of cognition. For embodied views, the relation to the sensori-motor system to cognition is constitutive, not just causal. This paper examines some recent empirical evidence used to support the view that cognition is embodied and raises questions about some (...) of the claims being made by supporters. (shrink)

In a recent very interesting and important challenge to tracking theories of knowledge, Williams & Sinhababu claim to have devised a counter-example to tracking theories of knowledge of a sort that escapes the defense of those theories by Adams & Clarke. In this paper we will explain why this is not true. Tracking theories are not undermined by the example of the backward clock, as interesting as the case is.

I argue that one in particular of CrispinWright’s attempts to capture our common or intuitive concepts of objectivity, warrant, and other associated notions, relies on an ambiguity between a given constructivist reading of the concepts and at least one other, arguablymore ‘ordinary’, version of the notions he tries to accommodate. I do this by focusing on one case in point, and concluding with a brief argument showing how this case generalises. I demonstrate why this ambiguity is unacceptable and also that (...) its resolution undermines the aim it serves: to account for and accommodate our ordinary conception of (at least) objectivity, warrant (or justication) and truth. (shrink)

In a recent paper, Tristan Haze offers two examples that, he claims, are counterexamples to Nozick's Theory of Knowledge. Haze claims his examples work against Nozick's theory understood as relativized to belief forming methods M. We believe that they fail to be counterexamples to Nozick's theory. Since he aims the examples at tracking theories generally, we will also explain why they are not counterexamples to Dretske's Conclusive Reasons Theory of Knowledge.

A semantics is presented for Storrs McCall's separate axiomatizations of Aristotle's accepted and rejected polysyllogisms. The polysyllogisms under discussion are made up of either assertoric or apodeictic propositions. The semantics is given by associating a property with a pair of sets: one set consists of things having the property essentially and the other of things having it accidentally. A completeness proof and a semantic decision procedure are given.

In this article, we will describe higher order thought theories of consciousness. Then we will describe some examples from synesthesia. Finally, we will explain why the latter may be relevant to the former.

This book consists of an edited collection of original essays of the highest academic quality by seasoned experts in their fields of cognitive science. The essays are interdisciplinary, drawing from many of the fields known collectively as “the cognitive sciences.” Topics discussed represent a significant cross-section of the most current and interesting issues in cognitive science. Specific topics include matters regarding machine learning and cognitive architecture, the nature of cognitive content, the relationship of information to cognition, the role of language (...) and communication in cognition, the nature of embodied cognition, selective topics in visual cognition, brain connectivity, computation and simulation, social and technological issues within the cognitive sciences, and significant issues in the history of neuroscience. This book will be of interest to both professional researchers and newer students and graduate students in the fields of cognitive science—including computer science, linguistics, philosophy, psychology and neuroscience. The essays are in English and are designed to be as free as possible of technical jargon and therefore accessible to young scholars and to scholars who are new to the cognitive neurosciences. In addition to several entries by single authors, the book contains several interesting roundtables where researchers contribute answers to a central question presented to those in the focus group on one of the core areas listed above. This exciting approach provides a variety of perspectives from across disciplines on topics of current concern in the cognitive sciences. (shrink)

In this article, I shall contend that Rawlsian public reason liberalism (PRL) is in tension with non-anthropocentric environmentalism. I will argue that many reasonable citizens reject non-anthropocentric values, and PRL cannot allow them to be used as the justification for ecological policies. I will analyse attempts to argue that PRL can incorporate non-anthropocentric ideas. I shall consider the view, deployed by theorists such as Derek Bell and Mark A. Michael, that PRL can make a distinction between constitutional essentials and non-essentials, (...) and therefore ecocentric values can be employed when only non-essentials are at stake. I will also consider Simon Hailwood’s argument that PRL can incorporate concern for nature based on its ‘otherness’. I shall conclude that both positions fail to rebut the claim that PRL excludes non-anthropocentric viewpoints. I will consider the question of whether PRL’s exclusion of non-anthropocentric ethics is a problem, and I shall show that appealing to purely anthropocentric arguments leads to a variety of unpalatable conclusions. I will suggest that comprehensive liberalism can include non-anthropocentric concerns, and hence is superior from an environmental perspective. (shrink)

Fred's semantics for McCall's syntactic presentation of Aristotle's assertoric and apodeictic syllogistic is altered to free it from Thom's objections that it is unAristotelian. The altered semantics rejects Baroco-XLL and Bocardo-LXL, which Thom says Aristotle should have accepted. Aristotle's proofs that use ecthesis are formalized by using singular sentences. With one exception the (acceptance) axioms for McCall's system L-X-M are derivable. Formal proofs are shown to be sound.

Tristan Haze claims we have made two mistakes in replying to his two attempted counter-examples to Tracking Theories of Knowledge. Here we respond to his two recent claims that we have made mistakes in our reply. We deny both of his claims.

Fred shows how problems with Slater's restriction of the classical propositional logic can be solved.

This essay has two aims. The first is to correct an increasingly popular way of misunderstanding Belot's Orgulity Argument. The Orgulity Argument charges Bayesianism with defect as a normative epistemology. For concreteness, our argument focuses on Cisewski et al.'s recent rejoinder to Belot. The conditions that underwrite their version of the argument are too strong and Belot does not endorse them on our reading. A more compelling version of the Orgulity Argument than Cisewski et al. present is available, however---a point (...) that we make by drawing an analogy with de Finetti's argument against mandating countable additivity. Having presented the best version of the Orgulity Argument, our second aim is to develop a reply to it. We extend Elga's idea of appealing to finitely additive probability to show that the challenge posed by the Orgulity Argument can be met. (shrink)

We provide counterexamples to some purported characterizations of dilation due to Pedersen and Wheeler :1305–1342, 2014, ISIPTA ’15: Proceedings of the 9th international symposium on imprecise probability: theories and applications, 2015).

John Rawls’ A Theory of Justice allows social facts behind his veil-of-ignorance, thereby lessening the veil’s capacity for neutrality and defense of liberal principles. Rawls assumes social facts are discoverable without presupposed political values. But even if value-neutral social science is possible, real-world opinions, defined by political/social world-views, open the veil to bias since social facts from a non-liberal view may bolster non-liberal programmes. Alternatively, depriving those behind the veil of knowledge of social facts strips them of vital information necessary (...) for creating a just, well-organized society. These reservations do not constitute decisive criticisms but point out unresolved tension in Rawls’ original position, and the veil’s status of neutrality is undermined. (shrink)

McCall's system for contingent syllogisms is modified. A semantics for the resulting system is provided.

The paper shows that for any invalid polysyllogism there is a procedure for constructing a model with a domain with exactly three members and an interpretation that assigns non-empty, non-universal subsets of the domain to terms such that the model invalidates the polysyllogism.

One semantic and two syntactic decision procedures are given for determining the validity of Aristotelian assertoric and apodeictic syllogisms. Results are obtained by using the Aristotelian deductions that necessarily have an even number of premises.

A theorem due to Shoesmith and Smiley that axiomatizes two-valued multiple-conclusion logics is extended to partial logics.

In the 17th century, Hobbes stated that we reason by addition and subtraction. Historians of logic note that Hobbes thought of reasoning as “a ‘species of computation’” but point out that “his writing contains in fact no attempt to work out such a project.” Though Leibniz mentions the plus/minus character of the positive and negative copulas, neither he nor Hobbes say anything about a plus/minus character of other common logical words that drive our deductive judgments, words like ‘some’, ‘all’, ‘if’, (...) and ‘and’, each of which actually turns out to have an oppositive, character that allows us, “in our silent reasoning,” to ignore its literal meaning and to reckon with it as one reckons with a plus or a minus operator in elementary algebra or arithmetic. These ‘logical constants’ of natural language figure crucially in our everyday reasoning. Because Hobbes and Leibniz did not identify them as the plus and minus words we reason with, their insight into what goes on in ‘ratiocination’ did not provide a guide for a research program that could develop a +/- logic that actually describes how we reason deductively. I will argue that such a +/- logic provides a way back from modern predicate logic—the logic of quantifiers and bound variables that is now ‘standard logic’—to an Aristotelian term logic of natural language that had been the millennial standard logic. (shrink)