The reference class problem arises when we want to assign a probability to a proposition (or sentence, or event) X, which may be classified in various ways, yet its probability can change depending on how it is classified. The problem is usually regarded as one specifically for the frequentist interpretation of probability and is often considered fatal to it. I argue that versions of the classical, logical, propensity and subjectivist interpretations also fall prey to their own (...) variants of the reference class problem. Other versions of these interpretations apparently evade the problem. But I contend that they are all “no-theory” theories of probability - accounts that leave quite obscure why probability should function as a guide to life, a suitable basis for rational inference and action. The reference class problem besets those theories that are genuinely informative and that plausibly constrain our inductive reasonings and decisions. I distinguish a “metaphysical” and an “epistemological” reference class problem. I submit that we can dissolve the former problem by recognizing that probability is fundamentally a two-place notion: conditional probability is the proper primitive of probability theory. However, I concede that the epistemological problem remains. (shrink)

Scholars belong to multiple communities of credit simultaneously. When these communities disagree about a scholarly achievement’s credit assignment, this raises a puzzle for decision and game theor...

Elselijn Kingma argues that Christopher Boorse’s biostatistical theory (the BST) does not show how the reference classes it uses are objective and naturalistic. Recently, philosophers of medicine have attempted to rebut Kingma’s concerns. I argue that these rebuttals are theoretically unconvincing, and that there are clear examples of physicians adjusting their reference classes according to their prior knowledge of health and disease. I focus on the use of age-adjusted reference classes to diagnose low bone mineral density in (...) children. In addition to using the BST’s age, sex, and species, physicians also choose to use other factors to define reference classes, such as pubertal status, bone age, body size, and muscle mass. I show that physicians calibrate the reference classes they use according to their prior knowledge of health and disease. Reference classes are also chosen for pragmatic reasons, such as to predict fragility fractures. (shrink)

Evolutionary biology distinguishes differences in survival and reproduction rates due to selection from those due to drift. The distinction is usually thought to be founded in probabilistic facts: a difference in (say) two variants' average lifespans over some period of time that is due to selection is explained by differences in the probabilities relevant to survival; in the purest cases of drift, by contrast, the survival probabilities are equal and the difference in lifespans is a matter of chance. When there (...) is a difference in actual average lifespans there is always a difference in causal histories, but in drift, the causal differences make no contribution to the relevant probabilities. Some writers have claimed that the framework that determines which causes contribute to the probabilities, and so the framework that determines when the relevant probabilities differ and when they are equal, is imposed by modelers rather than being an objective fact of nature, and so that the distinction between selection and drift, however practically useful, is unreal. This paper uses my work on biological probabilities (Bigger than Chaos) and probabilistic explanation (Depth) to argue for the objectivity of, and the importance of the objectivity of, the distinction between selection and drift. (shrink)

There has been a long history of discussion on the usefulness of formal methods in legal settings.1 Some of the recent debate has focussed on foundational issues in statistics, in particular, how the reference-class problem affects legal decisions based on certain types of statistical evidence.2 Here we examine aspects of this debate, stressing why the reference-class problem presents serious difficulties for the kinds of statistical inferences under consideration and the relevance of this for the (...) use of statistics in the courtroom. We also consider the relevance of foundational statistical issues in the broader context of.. (shrink)

The assumption that we are typical observers plays a core role in attempts to make multiverse theories empirically testable. A widely shared worry about this assumption is that it suffers from systematic ambiguity concerning the reference class of observers with respect to which typicality is assumed. As a way out, Srednicki and Hartle recommend that we empirically test typicality with respect to different candidate reference classes in analogy to how we test physical theories. Unfortunately, as this paper (...) argues, this idea fails because typicality is not the kind of assumption that can be subjected to empirical tests. As an alternative, a background information constraint on observer reference class choice is suggested according to which the observer reference class should be chosen such that it includes precisely those observers who one could possibly be, given one’s assumed background information. (shrink)

The objective Bayesian view of proof (or logical probability, or evidential support) is explained and defended: that the relation of evidence to hypothesis (in legal trials, science etc) is a strictly logical one, comparable to deductive logic. This view is distinguished from the thesis, which had some popularity in law in the 1980s, that legal evidence ought to be evaluated using numerical probabilities and formulas. While numbers are not always useful, a central role is played in uncertain reasoning by the (...) ‘proportional syllogism’, or argument from frequencies, such as ‘nearly all aeroplane flights arrive safely, so my flight is very likely to arrive safely’. Such arguments raise the ‘problem of the reference class’, arising from the fact that an individual case may be a member of many different classes in which frequencies differ. For example, if 15 per cent of swans are black and 60 per cent of fauna in the zoo is black, what should I think about the likelihood of a swan in the zoo being black? The nature of the problem is explained, and legal cases where it arises are given. It is explained how recent work in data mining on the relevance of features for prediction provides a solution to the reference class problem. (shrink)

Big data increasingly enables prediction of the behaviour and characteristics of individuals. This is ethically concerning on privacy grounds. However, this article discusses other reasons for concern. These predictions usually rely on generalisations about what certain sorts of people tend to do. Generalisations of this sort are often under scrutiny in legal cases, where, for example, lawyers argue that people with prior convictions are more likely to be guilty of the crime they are currently on trial for. This article applies (...) criteria for distinguishing acceptable from unacceptable generalisations in legal cases to a number of big data examples. It argues that these criteria are helpful, and highlights three issues that should be taken into account when deciding whether predictions about individuals are ethical. (shrink)

Probabilistic inference from frequencies, such as "Most Quakers are pacifists; Nixon is a Quaker, so probably Nixon is a pacifist" suffer from the problem that an individual is typically a member of many "reference classes" (such as Quakers, Republicans, Californians, etc) in which the frequency of the target attribute varies. How to choose the best class or combine the information? The article argues that the problem can be solved by the feature selection methods used in contemporary (...) Big Data science: the correct reference class is that determined by the features relevant to the target, and relevance is measured by correlation (that is, a feature is relevant if it makes a difference to the frequency of the target). (shrink)

Methods of machine learning (ML) are gradually complementing and sometimes even replacing methods of classical statistics in science. This raises the question whether ML faces the same methodological problems as classical statistics. This paper sheds light on this question by investigating a long-standing challenge to classical statistics: the reference class problem (RCP). It arises whenever statistical evidence is applied to an individual object, since the individual belongs to several reference classes and evidence might vary across them. (...) Thus, the problem consists in choosing a suitable reference class for the individual. I argue that deep neural networks (DNNs) are able to overcome specific instantiations of the RCP. Whereas the criteria of narrowness, reliability, and homogeneity, that have been proposed to determine a suitable reference class, pose an inextricable tradeoff to classical statistics, DNNs are able to satisfy them in some situations. On the one hand, they can exploit the high dimensionality in big-data settings. I argue that this corresponds to the criteria of narrowness and reliability. On the other hand, ML research indicates that DNNs are generally not susceptible to overfitting. I argue that this property is related to a particular form of homogeneity. Taking both aspects together reveals that there are specific settings in which DNNs can overcome the RCP. (shrink)

I present in this paper an analysis of the Simulation argument from a dialectical contextualist's standpoint. This analysis is grounded on the reference class problem. I begin with describing Bostrom’s Simulation Argument step-by-step. I identify then the reference class within the Simulation argument. I also point out a reference class problem, by applying the argument successively to several references classes: aware-simulations, rough-simulations and cyborg-type simulations. Finally, I point out that there are three (...) levels of conclusion within the Simulation Argument, depending on the chosen reference class, that yield each final conclusions of a fundamentally different nature. (shrink)

Elselijn Kingma argues that Christopher Boorse’s biostatistical theory does not show how the reference classes it uses—namely, age groups of a sex of a species—are objective and naturalistic. Boorse has replied that this objection is of no concern, because there are no examples of clinicians’ choosing to use reference classes other than the ones he suggests. Boorse argues that clinicians use the reference classes they do because these reflect the natural classes of organisms to which their patients (...) belong. Drawing on a thorough exploration of how the disease osteoporosis is defined in adults, I argue that clinicians do indeed make choices about which reference classes to use in diagnosis. Clinicians use young adult reference classes to diagnose osteoporosis in elderly patients. They also use young female reference classes to diagnose osteoporosis in elderly males. Clinicians adjust their reference classes so that the diagnosis of osteoporosis reflects a person’s risk of sustaining a fragility fracture. The ethical intuition that people with the same risk of fracture should receive the same diagnosis overwhelms the naturalistic intuition that reference classes should reflect natural classes of organisms of uniform functional design. Clinicians construct a variety of reference class types, including pathological reference classes and epidemiological population-specific reference classes, to serve this ethical intuition. I show how clinicians use several reference classes at once so that they can more accurately predict risk of fracture. Ultimately, the reference classes chosen and used in medical practice are quite different from those proposed in naturalistic philosophy of medicine. (shrink)

In attempting to form rational personal probabilities by direct inference, it is usually assumed that one should prefer frequency information concerning more specific reference classes. While the preceding assumption is intuitively plausible, little energy has been expended in explaining why it should be accepted. In the present article, I address this omission by showing that, among the principled policies that may be used in setting one’s personal probabilities, the policy of making direct inferences with a preference for frequency information (...) for more specific reference classes yields personal probabilities whose accuracy is optimal, according to all proper scoring rules, in situations where all of the relevant frequency information is point-valued. Assuming that frequency information for narrower reference classes is preferred, when the relevant frequency statements are point-valued, a dilemma arises when choosing whether to make a direct inference based upon relatively precise-valued frequency information for a broad reference class, R, or upon relatively imprecise-valued frequency information for a more specific reference class, R*. I address such cases, by showing that it is often possible to make a precise-valued frequency judgment regarding R* based on precise-valued frequency information for R, using standard principles of direct inference. Having made such a frequency judgment, the dilemma of choosing between and is removed, and one may proceed by using the precise-valued frequency estimate for the more specific reference class as a premise for direct inference. (shrink)

Experimenters sometimes insist that it is unwise to examine data before determining how to analyze them, as it creates the potential for biased results. I explore the rationale behind this methodological guideline from the standpoint of an error statistical theory of evidence, and I discuss a method of evaluating evidence in some contexts when this predesignation rule has been violated. I illustrate the problem of potential bias, and the method by which it may be addressed, with an example from (...) the search for the top quark. A point in favor of the error statistical theory is its ability, demonstrated here, to explicate such methodological problems and suggest solutions, within the framework of an objective theory of evidence. (shrink)

ABSTRACT There is a popular way of appealing to consistency of judgment or principle whose result is to rule out relevant information. To avoid the danger of judging similar cases differently, relevantly different cases are treated alike. So the information distinguishing them is lost. I try to formulate, defend and apply a requirement upon determining whether situations are similar with respect to a principle. Adherence to the requirement is a way to prevent the loss of information through illicit appeals to (...) consistency. Part II examines a difficulty for the requirement proposed. The difficulty concerns determinateness: given the requirement's broad scope, it cannot yield judgments on specific cases without prejudging substantive issues. Without reaching any solution to the difficulty, I point out that parallel difficulties arise for similar requirements in diverse areas, and that the problem can be mitigated to varying degrees in actual applications of these requirements. (shrink)

Paul Franceschi | : Je présente dans cet article une analyse de l’argument de la Simulation selon le point de vue du contextualisme dialectique, fondée sur le problème de la classe de référence. Je décris tout d’abord l’argument de la Simulation de manière détaillée. J’identifie ensuite la classe de référence et j’applique successivement l’argument à trois classes de référence distinctes : les simulations conscientes de leur propre nature de simulation, les simulations imparfaites et les simulations à immersion. Finalement, je montre (...) qu’il existe trois niveaux de conclusion dans l’argument de la Simulation, selon la classe de référence choisie, qui engendrent des conclusions finales d’une nature très différente. | : I present in this paper an analysis of the Simulation argument from a dialectical contextualist standpoint. This analysis is grounded on the reference class problem. I begin with describing in detail Bostrom’s Simulation Argument. I identify then the reference class within the Simulation argument. I also point out a reference class problem, by applying the argument successively to three different reference classes : aware-simulations, imperfect simulations and immersion-simulations. Finally, I point out that there are three levels of conclusion within the Simulation Argument, depending on the chosen reference class, that yield each final conclusions of a fundamentally different nature. (shrink)

The question of the relationship between ontology and theology, the main problem of the interpretation in volume 3, is also the guiding question of our last volume. The history of metaphysics is a history of the efforts towards an outlook on the world and life, which are about the meaning and connection of fundamental concepts: being, life, intellect, unity, truth, goodness. From these, the concept of divinity is derived. As in the previous volumes, a rich material of original texts (...) and interpretations is spread out. (shrink)

Objective Apeiron was founded in 1966 and has developed into one of the oldest and most distinguished journals dedicated to the study of ancient philosophy, ancient science, and, in particular, of problems that concern both fields. Apeiron is committed to publishing high-quality research papers in these areas of ancient Greco-Roman intellectual history; it also welcomes submission of articles dealing with the reception of ancient philosophical and scientific ideas in the later western tradition. The journal appears quarterly. Articles are peer-reviewed on (...) a double-blind basis. Topics ancient philosophy ancient science reception of ancient philosophical and scientific ideas in the later western tradition Article formats Original Articles. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Kennedy Institute of Ethics Journal 10.2 (2000) 175-188 [Access article in PDF] Scope Note 38 Bioethics Resources on the Web * Once described as an "enormous used book store with volumes stacked on shelves and tables and overflowing onto the floor" (Pool, Robert. 1994. Turning an Info-Glut into a Library. Science 266 (7 October): 20-22, p. 20), Internet resources now receive numerous levels of organization, from basic directory listings (...) to elaborate "links" (cross-references to other Internet documents) that flash and glow in the dark. In many ways, the Internet functions as a direct extension of the traditional library. Following linked references across various sites is an electronic version of browsing library stacks, and the serendipitous discoveries made while "surfing the Net" recall the wonders of physically going "book-to-book." Although many of the Internet's best aspects augment library strengths by eliminating physical distance from sources, Net resources pose unique problems for researchers. It is not always clear who is responsible for the content of Web documents, when the document was produced, or how often (if ever) it is updated. Internet resource tools, then, must enable researchers to identify appropriate resources and to evaluate what they find when they get there. Web Research as Taking "Snapshots" Given the Internet's visual nature and fluid content, the process of conducting research on the Web has been likened to taking an informal picture of information on a specific date at a particular time. This metaphor also conveys the "zoom-in" aspect of searching through Web pages by going from general to specific categories. In the first section of this Scope Note, National Reference Center for Bioethics Literature (NRCBL) staff present a snapshot of bioethics resources taken during the spring months of 2000. Entries are divided into the categories of directories, electronic journals, full-text documents, news/current awareness, and teaching resources. In the two subsequent sections, this series of categories is repeated for entries on a specific topic within bioethics-genetics-and again for general search and evaluation tools. Where a Web site may contain pages applicable [End Page 175] to more than one category, multiple entries are made for that site with appropriate information for each category.Much as telecommunication advances have strengthened the relationship of patients and providers as partners, the dynamic nature of the Internet acknowledges that the researcher functions as a librarian whenever accessing the Web. It is our hope that BIOETHICSLINE and the other NRCBL databases not only will enable researchers to search the Web more efficiently, but also will help them to evaluate what they find when they get there. Bioethicsline on the Web: An International Plan in Progress Once only available through libraries, the U.S. National Library of Medicine (NLM), the funding agency for the ongoing development of the BIOETHICS LINE® database from the Kennedy Institute, has provided free Web access to that database of 63,000 citations since September 1998 through Internet Grateful Med. Plans are now underway to eliminate such specialty databases and incorporate all citations into PubMed (for journal articles) or LOCATORplus (for book-like materials and chapters in books). Both of these databases are likewise available at no cost on the Web. In the transition to PubMed and LOCATORplus some features of BIOETHICSLINE that presently are available may be lost. Researchers are encouraged to contact the National Reference Center for Bioethics Literature with search requests or for search strategy assistance with either the current or the future system ([email protected]).The inclusion of bioethics citations in PubMed and LOCATORplus will have several advantages. First, unique keywords from the Bioethics Thesaurus will be considered for inclusion in Medical Subject Headings (MeSH), the indexing vocabulary for PubMed and LOCATORplus, thereby enhancing retrieval of relevant clinical literature by offering more precise terminology covering ethical issues. Second, it will be easier to identify foreign-language materials, which are not currently included in the scope of BIOETHICSLINE. Third, the updating schedule will become more frequent. On the other hand, there may be some loss of searching precision because certain specialized features... (shrink)

I here aim to show that a particular approach to the problem of induction, which I will call “induction by direct inference”, comfortably handles Goodman’s problem of induction. I begin the article by describing induction by direct inference. After introducing induction by direct inference, I briefly introduce the Goodman problem, and explain why it is, prima facie, an obstacle to the proposed approach. I then show how one may address the Goodman problem, assuming one adopts induction (...) by direct inference as an approach to the problem of induction. In particular, I show that a relatively standard treatment of what some have called the “Reference Class problem” addresses the Goodman Problem. Indeed, plausible and relatively standard principles of direct inference yield the conclusion that the Goodman inference (involving the grue predicate) is defeated, so it is unnecessary to invoke considerations of ‘projectibility’ in order to address the Goodman problem. I conclude the article by discussing the generality of the proposed approach, in dealing with variants of Goodman’s example. (shrink)

To think about how to anchor abstract symbols to objects in the world is to become part of a tradition in philosophy with a long history, and an especially rich recent past. It is to ask, with Wittgenstein, “What makes my thought about him, a thought about him?” and thus it is to wonder not just about the nature of referring expressions or singular terms, but about the nature of referring beings. With this in mind I hereby endeavor—briefly, incompletely, but (...) hopefully still usefully—to introduce what in my judgment is the single best philosophical starting-point for those interested in understanding the referential connections between symbols and the world, and the cognitive, epistemic, and linguistic capacities which support them: The Varieties of Reference by Gareth Evans.1 It is worthwhile first of all to note, as the title indicates, that it is the varieties of reference that are of interest. It is Evans’ contention that no single theory can account for our various use of singular terms; although the different kinds of reference share certain features, and rely on related cognitive, linguistic and epistemic capacities, it appears that, rather than being a class defined by necessary and sufficient criteria for membership, they form a family of abilities, united, like a thread, by its overlapping fibers. Evans does not defend this claim so much as display it in his account. Much of the underlying variety in reference can be brought out by considering the guiding principle of the work as a whole, which Evans.. (shrink)

The article begins by describing two longstanding problems associated with direct inference. One problem concerns the role of uninformative frequency statements in inferring probabilities by direct inference. A second problem concerns the role of frequency statements with gerrymandered reference classes. I show that past approaches to the problem associated with uninformative frequency statements yield the wrong conclusions in some cases. I propose a modification of Kyburg’s approach to the problem that yields the right conclusions. Past (...) theories of direct inference have postponed treatment of the problem associated with gerrymandered reference classes by appealing to an unexplicated notion of projectability . I address the lacuna in past theories by introducing criteria for being a relevant statistic . The prescription that only relevant statistics play a role in direct inference corresponds to the sort of projectability constraints envisioned by past theories. (shrink)

In this thesis, I give a metascientific account of causality in medicine. I begin with two historical cases of causal discovery. These are the discovery of the causation of Burkitt’s lymphoma by the Epstein-Barr virus, and of the various viral causes suggested for cervical cancer. These historical cases then support a philosophical discussion of causality in medicine. This begins with an introduction to the Russo- Williamson thesis (RWT), and discussion of a range of counter-arguments against it. Despite these, I argue (...) that the RWT is historically workable, given a small number of modifications. I then expand Russo and Williamson’s account. I first develop their suggestion that causal relationships in medicine require some kind of evidence of mechanism. I begin with a number of accounts of mechanisms and produce a range of consensus features of them. I then develop this consensus position by reference to the two historical case studies with an eye to their operational competence. In particular, I suggest that it is mechanistic models and their representations which we are concerned with in medicine, rather than the mechanism as it exists in the world. -/- I then employ these mechanistic models to give an account of the sorts of evidence used in formulating and evaluating causal claims. Again, I use the two human viral oncogenesis cases to give this account. I characterise and distinguish evidence of mechanism from evidence of difference-making, and relate this to mechanistic models. I then suggest the relationship between types of evidence presents us with a means of tackling the reference-class problem. This sets the scene for the final chapter. Here, I suggest the manner in which these two different classes of evidence become integrated is also reflected in the way that developing research programmes change as their associated causal claims develop. (shrink)

This work examines the influence of reference dependence, including value selection bias and congruence effects, on diagnostic reasoning. Across two studies, we explored how dependence on the initial problem structure influences the ability to solve simplified precursors to the more traditional Bayesian reasoning problems. Analyses evaluated accuracy and types of response errors as a function of congruence between the problem presentation and question of interest, amount of information, need for computation, and individual differences in numerical abilities. Across (...) all problem variations, there was consistent and strong evidence of a value selection bias in that incorrect responses almost always conformed to values that were provided in the problem rather than other errors including those related to computation. The most consistent and unexpected error across all conditions in the first experiment was that people were often more likely to utilize the superordinate value as part of their solution rather than the anticipated reference class values. This resulted in a weakened effect of congruence, with relatively low accuracy even in congruent conditions, and a dominant response error of the superordinate value. Experiment 2 confirmed that the introduction of a new sample drew attention away from the provided reference class, increasing reliance on the overall sample size. This superordinate preference error, along with the benefit of repeating the PPV reference class within the question, demonstrated the importance of reference dependence based on the salience of information within the response prompt. Throughout, higher numerical skills were generally associated with higher accuracy, whether calculations were required or not. (shrink)

In his recent book Moral Skepticisms Walter Sinnott-Armstrong argues in great detail for contrastivism with respect to justified moral belief and moral knowledge. I raise three questions concerning this view. First, how would Sinnott-Armstrong account for constraints on admissible contrast classes? Secondly, how would he deal with notorious problems concerning relevant reference classes? Finally, how can he account for basic features of moral agency? It turns out that the last problem is the most serious one for his account.

The generality problem is usually taken to arise only for externalist theories of knowledge or justification. In this paper, first, I argue that even internalist theories run afoul of a variant of the generality problem. This is because S may have multiple pieces of evidence concerning the reliability of the token process by which S forms the belief in question, and they determine the degree of Sʼs internalist justification differently. Second, I offer a solution to the generality (...) class='Hi'>problem for internalist theories: Sʼs practical reason rather than epistemic reason picks out a piece of evidence concerning reliability as relevant. (shrink)

Les expériences de «classe inversée» apparaissent aujourd'hui prometteuses. Alors que, dans les «classes traditionnelles», on «fait cours» à l'Ecole avant d'envoyer les élèves «travailler» chez eux, dans les «classes inversées», le professeur propose aux élèves de prendre connaissance d'un exposé enregistré ou d'une séquence illustrée puis les accueille en classe pour répondre à leurs questions et les accompagner dans la réalisation d'exercices ou de projets... On comprend que ce modèle pédagogique soit particulièrement attractif : à l'ère du numérique, au moment (...) où tant de ressources documentaires sont disponibles, le professeur voit ainsi son rôle renouvelé et peut se consacrer pleinement à l'appropriation des connaissances. Mais il ne faut pas, pour autant, basculer dans la naïveté spontanéiste. Prendre connaissance d'une information ou regarder une vidéo pour en tirer quelques enseignements ne vont pas de soi et le risque existe que beaucoup d'élèves n'en profitent guère. De même, interroger le professeur pour mieux comprendre un phénomène, faire un exercice de manière autonome ou travailler en petits groupes pour résoudre un problème ne sont pas des comportements faciles à mettre en oeuvre. Etre intellectuellement actif, s'engager dans un travail et le mener à bien ne se décrète pas, cela se forme. Et, précisément, l'ouvrage d'Alain Taurisson et de Claire Herviou nous montre comment faire. Prenant appui sur des travaux scientifiques éprouvés et des expérimentations solides, présentant les références théoriques nécessaires et donnant de très nombreux exemples d'outils utilisables, les auteurs fondent une véritable «pédagogie de l'activité», garantissant pleinement l'engagement de chaque élève tant dans la prise d'information que dans l'assimilation et le réinvestissement des connaissances. Ils font ainsi de la «classe inversée» une véritable «pédagogie alternative». Au service de la réussite de toutes et tous. Et pour retrouver le bonheur d'enseigner... (shrink)

It is an ongoing controversy whether natural selection is a cause of population change, or a mere statistical description of how individual births and deaths accumulate. In this paper I restate the problem in terms of the reference class problem, and propose how the structure of stable equilibrium can provide a solution in continuity with biological practice. Insofar natural selection can be understood as a tendency towards equilibrium, key statisticalist criticisms are avoided. Further, in a modification (...) of the Newtonian-force analogy, it can be suggested that a better metaphor for natural selection is that of an emergent force, similar in nature to entropic forces: with magnitude and direction, but lacking a spatiotemporal origin or point of application. (shrink)

The Probably Approximately Correct (PAC) learning is a machine learning model introduced by Leslie Valiant in 1984. The PACi reducibility refers to the PAC reducibility independent of size and computation time. This reducibility in PAC learning resembles the reducibility in Turing computability. The ordering of concept classes under PAC reducibility is nonlinear, even when restricted to particular concrete examples.Due to the resemblance to Turing Reducibility, we suspected that there could be incomparable PACi and PAC degrees for the PACi and PAC (...) reducibilities as in Turing incomparable degrees. In 1957 Friedberg and in 1956 Muchnik independently solved the Post problem by constructing computably enumerable sets A and B of incomparable degrees using the priority construction method. We adapt this idea to PACi and PAC reducibilities and construct two effective concept classes C and D such that C is not reducible to D and vice versa. When considering PAC reducibility it was necessary to work on the size of an effective concept class, thus we use Kolmogorov complexity to obtain the size. The non-learnability of concept classes in the PAC learning model is explained by the existence of PAC incomparable degrees.Analogous to the Turing jump, we give a jump operation on effective concept classes for the zero jump. To define the zero jump operator for PACi degrees the join of all the effective concept classes is constructed and proved that it is a greatest element. There are many properties proven for existing degrees. Thus we can explore proving those properties to PACi and PAC degrees. But if we prove an embedding from those degrees to PACi and PAC degrees then those properties will be true for PACi and PAC degrees without explicitly proving them.Abstract prepared by Dodamgodage Gihnee M. Senadheera and taken directly from the thesisE-mail: [email protected]: https://www.proquest.com/docview/2717762461/abstract/ACD19F29A8774AF6PQ/1?accountid=13864. (shrink)

This book aims to develop certain aspects of Gottlob Frege’s theory of meaning, especially those relevant to intensional logic. It offers a new interpretation of the nature of senses, and attempts to devise a logical calculus for the theory of sense and reference that captures as closely as possible the views of the historical Frege. (The approach is contrasted with the less historically-minded Logic of Sense and Denotation of Alonzo Church.) Comparisons of Frege’s theory with those of Russell and (...) others are given. It is in the end shown that developing Frege’s theory in these ways reveals serious problems hitherto largely unnoticed, including those possibly rendering a Fregean intensional logic inconsistent even if his naïve class theory is excluded. (shrink)

The article is devoted to a comparative analysis of the political views of the philosophers of Montaigne circle. The ideas put forward by Charron and La Boétie were important not only for the period of religious wars of the 16th century, but also for various aspects of the genesis of modern philosophy. If autocracy is unacceptable in principle for La Boétie, then Charron is a supporter of a monarchical state structure, although he condemns tyrannical rule. La Boétie justifies his position (...) with references to the need to protect political free­dom. Autocracy, he believes, is inseparable from arbitrariness, illegal and gross violation of the interests of the country’s residents. People can refuse freedom only voluntarily, from force of habit of obeying tyrannical power, once established by deception or violence. He considers it possible to end religious strife by a revival of the Church and a moral re­newal. La Boétie’s political ideal is a republic. Charron, by contrast, considers the king a true sovereign. But rulers often have both shortcomings and vices, sometimes giving rise to tyranny, expressed in disregard for the laws and traditions of the country. Charron, like La Boétie, sees the reason for the religious wars in the damage of morals. He also sees a compromise as the best solution; to withdraw compatriots from the state of civil con­frontation is possible peacefully. For Charron, as for La Boétie, social inequality, class hi­erarchy seems to be an invariable condition of social existence. For both, violence is an unacceptable form of implementing social improvements. Both see religion as an im­portant pillar of social life. In the coordinate system of the two thinkers of the Montaigne circle, religious considerations are not taken beyond the general contours of their political reflections. It is noteworthy that for the philosophical landscape of the late Renaissance, the problem of religious confrontation turns out to be closely associated with the question of the best form of social structure. Discussions about it continue in our time. (shrink)

The Direct Reference account of the semantics of singular terms is widely assumed to be inconsistent with the traditional Individualist account of psychological states. Because of this assumption, and because of the weight of the evidence for Direct Reference, Anti-Individualism has found supporters despite its counterintuitiveness. In this dissertation, it is argued that Direct Reference and Individualism are not genuinely inconsistent, but that the inconsistency emerges only with the additional assumption of Propositionalism--the orthodox, proposition-based framework for understanding (...) thought and language. Consequently, it is not necessary to endorse Anti-Individualism in order to accept Direct Reference, so long as Propositionalism is accepted only in an attenuated form, if at all. ;It is argued that the best strategy for resolving the inconsistency is to retain all of Propositionalism apart from the Relational Analysis of belief ascriptions. An alternative analysis--the Quantified Relational Analysis --is developed and motivated. According to QRA, an ascription of the form X believes that S attributes the property of believing some member of the class of propositions containing the proposition that S and finer-grained versions of it. QRA is extended also to de re belief locutions. The conjunction of Direct Reference, Individualism, and the remnants of Propositionalism plus QRA is termed Russellian Non-Parallelism. ;Like all Direct Reference theories, Russellian Non-Parallelism has the consequence that co-referring names and other genuine terms are freely substitutable for each other, despite the datum that ordinary speakers intuitively regard such substitutions in belief contexts as suspect. These intuitions are accounted for both pragmatically and semantically. The pragmatic explanation specifies a mechanism whereby the audience sometimes infers from the choice of genuine terms the subject's way of thinking of the objects involved. The semantic explanation motivates an idiomatic reading of ascriptions, on which, under certain circumstances, the choice of co-referring terms in ascriptions literally indicates different belief contents. Russellian Non-Parallelism is then applied to enhanced substitution puzzles and to some other traditional problems, such as the contingent a priori. Finally there is a discussion of pertinent contemporary literature. (shrink)

Both philosophy and theology are given a raison d'etre by their problems. Some of their problems they share, and some they do not. They share a concern with the nature of morality and they share the problem of human freedom. But the filioque issue and the controversy between Arius and Athanasius regarding the consubstaniality of the persons of the Trinity belong to theology, if contemporary theology will have them. The problems of reference and denotation, and of classes, in (...) the cast given them by Frege, Russell and others, are exclusively in the domain of philosophy. Sometimes the problems shared by philosophy and theology are also human problems: they intimately touch human lives and have palpable ramifications for the way men live. Camus, who said with a flourish that the only philosophical problem is whether or not to commit suicide, was saying in part that the only philosophical problems worth considering are human problems. And William James would perhaps concur; he would insist that only philosophical problems that are “living, forced and momentous” present a genuine option to men. (shrink)

Students’ cheating is a serious problem: It undermines the chance to adequately promote, support, and evaluate them. To explain cheating behavior, research seldom focuses on perceived teachers’ characteristics. Thus, we investigate the relationship between students’ cheating behavior and an important teacher characteristic, individual reference norm orientation. We examined cheating on written exams, on homework, and in oral exams among N = 601 students in N = 31 language classes. Results from doubly manifest multi-level analyses showed that, on the (...) classroom level, cheating on written exams and on homework occurred less frequently the more the classroom of students perceived their teachers as having an IRNO. We found no further evidence for other cheating factors or student characteristics. This supports the idea that teacher characteristics are associated with some forms of students’ cheating behavior. (shrink)

Although the term taxon is one of the most common concepts in biology, a range of its meanings cannot be comprehended by an universal definition. Usually, biologists construe their knowledge of “the same” taxon by substantially different interpretations, so they find themselves in need either to justify this “multiplication of taxon essences”, or to surmount their plurality unifying its interpretations into a single explanation of what a taxon is. In both cases, an ontological status (“reality”) of that taxon is questioned. (...) Therefore, discrepancy between universality of the taxon concept in biology and unavoidable plurality of its interpretations can be regarded as a source of problem of the taxon ontology. The present work aims to clarify the premises of this discrepancy using phenomenological approach. Three ways of the taxon positing (as a class, as a place in the world, and as a individualized body) have been distinguished. Taxon as a class is established by common essence that is shared by a set of living beings. These living beings are regarded as speculative objects beyond an idea of the world, i.e. as objects of the experimental science. A question about ontology of taxon as a class refers to the scholastic problem of universalia; its status can be defined within the scope of the nominalism/realism opposition. Taxon as a place of common appearance of the specimens is regarded in the context of the etiological relations unifying various entities into the entire world. Taxon as a place refers to a certain position in the Natural System that is construed as an etiological map of the world. In this case a specimen of a living being is known as a curiosity, i.e. representant of its relationships as well as of the place of its origin. Ontological status of a taxon as a place is to be clarified within the framework of the natural/artificial opposition. The positing of a taxon as a collective body marked off by limits of joint survival of living beings is characteristic for biology in the strict sense which arose in the very beginning of the 19 century. A taxon as a body established by the techniques of disciplinary power sensu M. Foucault extended from the human bodies to bodies of other living beings. The ontological status of a taxon as a collective body can be defined within the scope of the wild/domesticated opposition. Therefore, the discrepancy between the universality of the taxon concept and the plurality of its interpretations is underlayed by interpenetration of three distinct modi of taxon establishing. Distinguishing between these three modi can clarify sources of ontological problems concerned with the term taxon in each case when they arise. (shrink)

Herein I investigate how four dogmas underpinning the traditional concepts of universality, the genus, class, and abstract universal, generate four paradoxes of self-reference. The four dogmas are the following: (1) that contradiction entails the total absence of determinacy, (2) the necessary finitude of the concept, (3) the separation of principles of universality and particularity, and (4) the necessity of appealing to foundations. In section III I show how these dogmas underpin the paradoxes of self-reference and how one (...) cannot make progress on these paradoxes as long as these four dogmas are in place. Corresponding to the abovementioned dogmas are the four paradoxes of self-reference: (1a) the problem of the .. (shrink)

“Collective impact problems” refer to situations where there is a collective harm or benefit, but where no single action seems to make a difference one way or the other. Collective impact problems arise when considering several pressing ethical issues in business, such as shareholder and consumer activism, business and climate change, factory farming and animal welfare, fair-trade and sweatshop labor, and corporate philanthropy. Unfortunately, business ethics textbooks do not explicitly deal with collective impact problems and, as such, students may be (...) lacking the theoretical and practical skills necessary to deal with issues of significant moral concern. This paper helps to address this gap by introducing the reader to some collective impact cases in business ethics, detailing the challenges that collective impact problems pose for consequentialist and non-consequentialists alike, and highlighting some of the promising pedagogical benefits of using collective impact cases in a business ethics class. (shrink)

The paradoxes of self-reference are genuinely paradoxical. The liar paradox, Russell’s paradox and their cousins pose enormous difficulties to anyone who seeks to give a comprehensive theory of semantics, or of sets, or of any other domain which allows a modicum of self-reference and a modest number of logical principles. One approach to the paradoxes of self-reference takes these paradoxes as motivating a non-classical theory of logical consequence. Similar logical principles are used in each of the paradoxical (...) inferences. If one or other of these problematic inferences are rejected, we may arrive at a consistent (or at least, a coherent) theory. In this paper I will show that such approaches come at a serious cost. The general approach of using the paradoxes to restrict the class of allowable inferences places severe constraints on the domain of possible propositional logics, and on the kind of metatheory that is appropriate in the study of logic itself. Proof-theoretic and model-theoretic analyses of logical consequence make provide different ways for non-classical responses to the paradoxes to be defeated by revenge problems: the redefinition of logical connectives thought to be ruled out on logical grounds. Non-classical solutions are not the “easy way out” of the paradoxes. (shrink)

We report two studies on the effect of implicitly versus explicitly conveying affirmation and denial problems about conditionals. Recently Evans and Handley (1999) and Schroyens et al. (1999b, 2000b) showed that implicit referencing elicits matching bias: Fewer determinate inferences are made, when the categorical premise (e.g., B) mismatches the conditional's referred clause (e.g., A). Also, the effect of implicit affirmation (B affirms not-A) is larger than the effect of implicit denial (B denies A). Schroyens et al. hypothesised that this interaction (...) is due to uncertainty in the case-wise affirmation of the contrast class of negated elements involved in implicit affirmations. In Experiment 1 we tested this hypothesis by manipulating the set size of the conditional clauses. The results confirm that binary sets, where the contrast class is a singleton, eliminate the differential effect of implicit affirmation and denial. With non-binary sets the interaction is not modulated by the scope of the contrast class (3, 5, 9 elements). Experiment 2 further investigated the role of contrast classes by using class inclusion to construct implicit affirmations (Mammal vs Mammal or Monkey) and implicit denial (No-Mammal vs Mammal or Monkey), in addition to the standard implicit problems mediated by contrast-class inclusion [(No-)Mammal/No-Mammal; Reptile; Snake). Findings indicate that class inclusion (Mammal/Monkey; Reptile/ Snake) only marginally affects performance, and is independent of the type of problem. This would suggest that the implicitness problem-type interaction is dependent on constructing contrast classes. However, the experiment failed to replicate the interaction, even on the subset of problems repeating the abstract letter/number format of Experiment 1. Moreover, with the natural binary set-sizes (vowels/consonants) the implicitness effect was eliminated entirely. (shrink)

The system presented by the author in The Logical Foundations of Statistical Inference suffered from certain technical difficulties, and from a major practical difficulty; it was hard to be sure, in discussing examples and applications, when you had got hold of the right reference class. The present paper, concerned mainly with the characterization of randomness, resolves the technical difficulties and provides a well structured framework for the choice of a reference class. The definition of randomness that (...) leads to this framework is simplified and clarified in a number of respects. It resolves certain puzzles raised by S. Spielman and W. Harper in their contributions to Profiles: Henry E. Kyburg, Jr. and Isaac Levi 1982). (shrink)

This chapter analyzes the control problem, the unique principal‐agent problem that arises with the creation of an artificial superintelligent agent. It distinguishes two broad classes of potential methods for addressing this problem, capability control and motivation selection, and examines several specific techniques within each class. It also alludes to the esoteric possibility of “anthropic capture”. Capability control methods seek to prevent undesirable outcomes by limiting what the superintelligence can do. This might involve boxing methods or incentive (...) methods, stunting method. In addition, capability control methods might involve tripwires method. Motivation selection can involve explicitly formulating a goal or set of rules to be followed (direct specification) or setting up the system so that it can discover an appropriate set of values for itself by reference to some implicitly or indirectly formulated criterion (indirect normativity). (shrink)

It is often taken for granted that notions of health and disease are generally applicable across the biological world, in that they are not restricted to contemporary human beings, and can be unproblematically applied to a variety of organisms both past and present (taking relevant differences between species into account). In the historical sciences it is also common to normatively contrast health states of individuals and populations from different times and places: e.g., to say that due to nutrition or pathogen (...) load, some lived healthier lives than others. However, health concepts in contemporary philosophy of medicine have not been developed with such cross-lineage, non-human, or diachronic uses in mind, and this generates what I call the ‘new normal’ problem. I argue that the new normal problem shows that current naturalistic approaches to health (when based on biological reference classes) are worryingly incomplete. Using examples drawn from evolutionary archaeology and the human fossil record, I outline an alternative, function-based strategy for naturalizing health that might help address the new normal problem. Interestingly, this might also reconstruct a certain uniqueness for humans in the philosophy and science of health, due to the deep history of obligate enculturation and cultural adaptation that archaeology demonstrates. (shrink)

This paper presents a puzzle about moral responsibility. The problem is based upon the indeterminacy of relevant reference classes as applied to action. After discussing and rejecting a very tempting response I propose moral contextualism instead, that is, the idea that the truth value of judgments of the form S is morally responsible for x depends on and varies with the context of the attributor who makes that judgment. Even if this reply should not do all the expected (...) work it is a first step. (shrink)

"A valuable collection both for original source material as well as historical formulations of current problems."-- The Review of Metaphysics "Much more than a mere collection of papers . . . a valuable addition to the literature."-- Mathematics of Computation An anthology of fundamental papers on undecidability and unsolvability by major figures in the field, this classic reference opens with Godel's landmark 1931 paper demonstrating that systems of logic cannot admit proofs of all true assertions of arithmetic. Subsequent papers (...) by Godel, Church, Turing, and Post single out the class of recursive functions as computable by finite algorithms. Additional papers by Church, Turing, and Post cover unsolvable problems from the theory of abstract computing machines, mathematical logic, and algebra, and material by Kleene and Post includes initiation of the classification theory of unsolvable problems. Suitable for graduate and undergraduate courses. 1965 ed. (shrink)

The language we use over the course of conversation changes as we establish common ground and learn what our partner finds meaningful. Here we draw upon recent advances in natural language processing to provide a finer‐grained characterization of the dynamics of this learning process. We release an open corpus (>15,000 utterances) of extended dyadic interactions in a classic repeated reference game task where pairs of participants had to coordinate on how to refer to initially difficult‐to‐describe tangram stimuli. We find (...) that different pairs discover a wide variety of idiosyncratic but efficient and stable solutions to the problem of reference. Furthermore, these conventions are shaped by the communicative context: words that are more discriminative in the initial context (i.e., that are used for one target more than others) are more likely to persist through the final repetition. Finally, we find systematic structure in how a speaker's referring expressions become more efficient over time: Syntactic units drop out in clusters following positive feedback from the listener, eventually leaving short labels containing open‐class parts of speech. These findings provide a higher resolution look at the quantitative dynamics of ad hoc convention formation and support further development of computational models of learning in communication. (shrink)

With automation of routine decisions coupled with more intricate and complex information architecture operating this automation, concerns are increasing about the trustworthiness of these systems. These concerns are exacerbated by a class of artificial intelligence that uses deep learning, an algorithmic system of deep neural networks, which on the whole remain opaque or hidden from human comprehension. This situation is commonly referred to as the black box problem in AI. Without understanding how AI reaches its conclusions, it is (...) an open question to what extent we can trust these systems. The question of trust becomes more urgent as we delegate more and more decision-making to and increasingly rely on AI to safeguard significant human goods, such as security, healthcare, and safety. Models that “open the black box” by making the non-linear and complex decision process understandable by human observers are promising solutions to the black box problem in AI but are limited, at least in their current state, in their ability to make these processes less opaque to most observers. A philosophical analysis of trust will show why transparency is a necessary condition for trust and eventually for judging AI to be trustworthy. A more fruitful route for establishing trust in AI is to acknowledge that AI is situated within a socio-technical system that mediates trust, and by increasing the trustworthiness of these systems, we thereby increase trust in AI. (shrink)

The obstacle to more objective knowledge of early Pythagoreanism is the ideological conflict over the proper mission of historiography. Not only the confusing evidence, but also the different investigative procedures and theories of history employed, make solving the Pythagorean problem difficult. I analyze the historiographic methodologies of some modern historians of Pythagoreanism in respect to the kinds of historical explanation they provide. Immediately ideological controversy arises between idealist and materialist historians. ;My critical evaluation proceeds from two theses. The content (...) of ideas reflects their social referents. Consequently, one must identify the class interests of early Pythagoreans. Writing history is a contemporary undertaking by which historians reflect their own social interests. Therefore, historiographic methodology continually must be objectified to overcome the subjectivism of historical relativism. ;I review the reconstructions of six historians. John Burnet, an empiricist, held that the Greeks entirely broke from their religious past to develop philosophy. F. M. Cornford, a Durkheimian, used anthropology to reveal philosophy's totemic content. J. E. Raven is a philologist; he maintaned that ancient philosophy was the Eleatic-Pythagorean debate. W. K. C. Guthrie, an eclectic, held that science served Pythagorean religious interests. These idealist historians attributed the Greek achievement to absolutized temperaments or racial factors; the development of ideas is not mediated by practical necessity. George Thomson and Alban Winspear are historical materialists. They explained ancient philosophy by showing the class interests of philosophers in a mercantile economy based on slave labor. ;After introducing the Pythagorean problem, I present, by chapter, first an exposition of each historian's account of the causes of Greek philosophy and then his exposition of early Pythagoreanism. My analyses follow each section. In the first part of the final chapter I discuss each historian in the context of the ideological controversy. In the second part I present a general outline of procedure for scientific historiography. (shrink)