Platonism, considered as a philosophy of mathematics, can be formulated in two interestingly different ways. Strong platonism holds that numerals, for example, refer to certain non-physical, non-mental entities. Weak platonism holds only that numerals uniquely apply to certain non-physical, non-mental entities. (Of course, there may even be weaker views that deserve to be called ‘platonistic.’The distinction between referring to an object and uniquely applying to an object may be illustrated as follows. If there is a tallest person and I say, (...) ‘the tallest person is over seven feet tall,’ without knowing who that person is, then my use of ‘the tallest person’ uniquely applies to someone, but it does not refer to anyone. The distinction is at least as old as Russell, for we might put his views in our terms by saying that for Russell only logically proper names refer to things, while ordinary proper names and definite descriptions at best uniquely apply to things. (shrink)

The Nature of God explores a perennial problem in the philosophy of religion.

This is a book grounded in the real ethical challenges of modern business practice, with a world-religious perspective so necessary in an era of globalization.

The Stanford Encyclopedia of Philosophy is an open access, dynamic reference work designed to organize professional philosophers so that they can write, edit, and maintain a reference work in philosophy that is responsive to new research. From its inception, the SEP was designed so that each entry is maintained and kept up to date by an expert or group of experts in the field. All entries and substantive updates are refereed by the members of a distinguished Editorial Board before they (...) are made public. (shrink)

It was proposed that the data from Monte Carlo statistical investigations be subjected to analysis of variance methods rather than the conventional techniques of tabling, graphing, and inspecting the data. Two examples in which analysis of variance methods were applied to published Monte Carlo studies were presented. It was suggested that balanced factorial designs should be used whenever possible in Monte Carlo studies so that analysis of variance methods would be directly applicable. Finally, three advantages of analysis of variance methods (...) over conventional techniques were described and analysis of variance methods were contrasted with a possible alternative analytical method, multiple regression analysis. (shrink)

National Book Award Finalist. How did humanity originate and why does a species like ours exist on this planet? Do we have a special place, even a destiny in the universe? Where are we going, and perhaps, the most difficult question of all, "Why?" In The Meaning of Human Existence, his most philosophical work to date, Pulitzer Prize–winning biologist Edward O. Wilson grapples with these and other existential questions, examining what makes human beings supremely different from all other species. (...) Searching for meaning in what Nietzsche once called "the rainbow colors" around the outer edges of knowledge and imagination, Wilson takes his readers on a journey, in the process bridging science and philosophy to create a twenty-first-century treatise on human existence—from our earliest inception to a provocative look at what the future of mankind portends. Continuing his groundbreaking examination of our "Anthropocene Epoch," which he began with The Social Conquest of Earth, described by the New York Times as "a sweeping account of the human rise to domination of the biosphere," here Wilson posits that we, as a species, now know enough about the universe and ourselves that we can begin to approach questions about our place in the cosmos and the meaning of intelligent life in a systematic, indeed, in a testable way. Once criticized for a purely mechanistic view of human life and an overreliance on genetic predetermination, Wilson presents in The Meaning of Human Existence his most expansive and advanced theories on the sovereignty of human life, recognizing that, even though the human and the spider evolved similarly, the poet's sonnet is wholly different from the spider's web. Whether attempting to explicate "The Riddle of the Human Species," "Free Will," or "Religion"; warning of "The Collapse of Biodiversity"; or even creating a plausible "Portrait of E.T.," Wilson does indeed believe that humanity holds a special position in the known universe. The human epoch that began in biological evolution and passed into pre-, then recorded, history is now more than ever before in our hands. Yet alarmed that we are about to abandon natural selection by redesigning biology and human nature as we wish them, Wilson soberly concludes that advances in science and technology bring us our greatest moral dilemma since God stayed the hand of Abraham. (shrink)

Mathematical pluralism can take one of three forms: (1) every consistent mathematical theory consists of truths about its own domain of individuals and relations; (2) every mathematical theory, consistent or inconsistent, consists of truths about its own (possibly uninteresting) domain of individuals and relations; and (3) the principal philosophies of mathematics are each based upon an insight or truth about the nature of mathematics that can be validated. (1) includes the multiverse approach to set theory. (2) helps us to understand (...) the significance of the distinguished non‐logical individual and relation terms of even inconsistent theories. (3) is a metaphilosophical form of mathematical pluralism and hasn't been discussed in the literature. In what follows, I show how the analysis of theoretical mathematics in object theory exhibits all three forms of mathematical pluralism. (shrink)

Science provides us with representations of atoms, elementary particles, polymers, populations, genetic trees, economies, rational decisions, aeroplanes, earthquakes, forest fires, irrigation systems, and the world’s climate. It's through these representations that we learn about the world. This entry explores various different accounts of scientific representation, with a particular focus on how scientific models represent their target systems. As philosophers of science are increasingly acknowledging the importance, if not the primacy, of scientific models as representational units of science, it's important to (...) stress that how they represent plays a fundamental role in how we are to answer other questions in the philosophy of science (e.g. the scientific realism debate). This entry begins by disentangling ‘the’ problem of scientific representation, before critically evaluating the current options available in the literature. (shrink)

The so-called ergodic hierarchy (EH) is a central part of ergodic theory. It is a hierarchy of properties that dynamical systems can possess. Its five levels are egrodicity, weak mixing, strong mixing, Kolomogorov, and Bernoulli. Although EH is a mathematical theory, its concepts have been widely used in the foundations of statistical physics, accounts of randomness, and discussions about the nature of chaos. We introduce EH and discuss its applications in these fields.

In this entry, Frege’s logic is introduced and described in some detail. It is shown how the Dedekind-Peano axioms for number theory can be derived from a consistent fragment of Frege’s logic, with Hume’s Principle replacing Basic Law V.

This book tackles the issues that arise in connection with intensional logic -- a formal system for representing and explaining the apparent failures of certain important principles of inference such as the substitution of identicals and existential generalization -- and intentional states --mental states such as beliefs, hopes, and desires that are directed towards the world. The theory offers a unified explanation of the various kinds of inferential failures associated with intensional logic but also unifies the study of intensional contexts (...) and intentional states by grounding the explanation of both phenomena in a single theory. When an axiomatized realm of abstract entities is added to the metaphysical structure of the world, we can use them to identify and individuate the contents of directed mental states. The special abstract entities can be viewed as the objectified contents of mental files, and they play a crucial role in the analysis of truth conditions of the sentences involved in inferential failures. (shrink)

Protein–protein interactions are thought to be mediated by domains, which are autonomous folding units of proteins. Recently, a second type of interaction has been suggested, mediated by short segments termed linear motifs, which are related to recognition elements of intrinsically disordered regions. Here, we propose a third kind of protein–protein recognition mechanism, mediated by disordered regions longer than 20–30 residues. Bioinformatics predictions and well‐characterized examples, such as the kinase‐inhibitory domain of Cdk inhibitors and the Wiskott–Aldrich syndrome protein (WASP)‐homology domain 2 (...) of actin‐binding proteins, show that these disordered regions conform to the definition of domains rather than motifs, i.e., they represent functional, evolutionary, and structural units. Their functions are distinct from those of short motifs and ordered domains, and establish a third kind of interaction principle. With these points, we argue that these long disordered regions should be recognized as a distinct class of biologically functional protein domains. (shrink)

Protein–protein interactions are thought to be mediated by domains, which are autonomous folding units of proteins. Recently, a second type of interaction has been suggested, mediated by short segments termed linear motifs, which are related to recognition elements of intrinsically disordered regions. Here, we propose a third kind of protein–protein recognition mechanism, mediated by disordered regions longer than 20–30 residues. Bioinformatics predictions and well‐characterized examples, such as the kinase‐inhibitory domain of Cdk inhibitors and the Wiskott–Aldrich syndrome protein (WASP)‐homology domain 2 (...) of actin‐binding proteins, show that these disordered regions conform to the definition of domains rather than motifs, i.e., they represent functional, evolutionary, and structural units. Their functions are distinct from those of short motifs and ordered domains, and establish a third kind of interaction principle. With these points, we argue that these long disordered regions should be recognized as a distinct class of biologically functional protein domains. (shrink)

In this book, Zalta attempts to lay the axiomatic foundations of metaphysics by developing and applying a (formal) theory of abstract objects. The cornerstones include a principle which presents precise conditions under which there are abstract objects and a principle which says when apparently distinct such objects are in fact identical. The principles are constructed out of a basic set of primitive notions, which are identified at the end of the Introduction, just before the theorizing begins. The main reason for (...) producing a theory which defines a logical space of abstract objects is that it may have a great deal of explanatory power. It is hoped that the data explained by means of the theory will be of interest to pure and applied metaphysicians, logicians and linguists, and pure and applied epistemologists. (shrink)

AI systems that demonstrate significant bias or lower than claimed accuracy, and resulting in individual and societal harms, continue to be reported. Such reports beg the question as to why such systems continue to be funded, developed and deployed despite the many published ethical AI principles. This paper focusses on the funding processes for AI research grants which we have identified as a gap in the current range of ethical AI solutions such as AI procurement guidelines, AI impact assessments and (...) AI audit frameworks. We highlight the responsibilities of funding bodies to ensure investment is channelled towards trustworthy and safe AI systems and provides case studies as to how other ethical funding principles are managed. We offer a first sight of two proposals for funding bodies to consider regarding procedures they can employ. The first proposal is for the inclusion of a Trustworthy AI Statement’ section in the grant application form and offers an example of the associated guidance. The second proposal outlines the wider management requirements of a funding body for the ethical review and monitoring of funded projects to ensure adherence to the proposed ethical strategies in the applicants Trustworthy AI Statement. The anticipated outcome for such proposals being employed would be to create a ‘stop and think’ section during the project planning and application procedure requiring applicants to implement the methods for the ethically aligned design of AI. In essence it asks funders to send the message “if you want the money, then build trustworthy AI!”. (shrink)

In the last decade, the UK Government has attempted to implement improved processes and procedures in modelling and analysis in response to the Laidlaw report of 2012 and the Macpherson review of 2013. The Laidlaw report was commissioned after failings during the Intercity West Coast Rail (ICWC) Franchise procurement exercise by the Department for Transport (DfT) that led to a legal challenge of the analytical models used within the exercise. The Macpherson review looked into the quality assurance of Government analytical (...) models in the context of the experience with the Intercity West Coast franchise competition. This paper examines what progress has been made in the 8 years since the Laidlaw report in model building and best practise in government and proposes several recommendations for ways forward. This paper also discusses the Lords Science and Technology Committees of June 2020 that analysed the failings in the modelling of COVID. Despite going on to influence policy, many of the same issues raised within the Laidlaw and Macpherson Reports were also present in the Lords Science and Technology Committee enquiry. We examine the technical and organisational challenges to progress in this area and make recommendations for a way forward. (shrink)

Call for Written evidence - Risk Assessment and Risk Planning.

In The Ultimate Betrayal: Is There Happy Meat?, Bohanec (2013) proposed that farmed animals raised humanely may experience betrayal when slaughtered. I argue based on personal experience that humans often betray trust relationships with farmed animals. Using published scientific literature, I find that typical farmed animals (mammals) and farmed fishes are both cognitively capable of a rudimentary experience of betrayal. However, the manner in which fishes are typically maintained does not present opportunities for human-fish trust relationships to develop. Eating farmed (...) fishes presents fewer ethical implications than eating cows, at least in some cases. (shrink)

To date researchers planning experiments have always lived by the mantra that 'using equal sample sizes gives the best results' and although unequal groups are also used in experimentation, it is not the preferred method of many and indeed actively discouraged in literature. However, during live study planning there are other considerations that we must take into account such as availability of study participants, statistical power and, indeed, the cost of the study. These can all make allocating equal sample sizes (...) difficult, and sometimes near impossible. This, some might say, means that the study would not adhere to rigorous statistical standard (Rosenbaum and Rubin, 1985). However, here we present evidence that, not only is this a false assumption, but that we may actually gain more power in the study by actually using unequal groups. Here, data from a Sepsis Biomarker study is used, in which the aim is to predict, by biomarker level and presence, whether the patient would go on to develop sepsis. It was found that larger control groups may give more power to studies looking for an effect in the mid range but not for large or small effects. This study shows merit in the hypothesis that more power can be achieved when a larger control group is used. Published by the Ministry of Defence at dstl - Reference DSTLTR92592 P2PP2R-2016-02-23T13:39:45. (shrink)

In many learning or inference tasks human behavior approximates that of a Bayesian ideal observer, suggesting that, at some level, cognition can be described as Bayesian inference. However, a number of findings have highlighted an intriguing mismatch between human behavior and standard assumptions about optimality: People often appear to make decisions based on just one or a few samples from the appropriate posterior probability distribution, rather than using the full distribution. Although sampling-based approximations are a common way to implement Bayesian (...) inference, the very limited numbers of samples often used by humans seem insufficient to approximate the required probability distributions very accurately. Here, we consider this discrepancy in the broader framework of statistical decision theory, and ask: If people are making decisions based on samples—but as samples are costly—how many samples should people use to optimize their total expected or worst-case reward over a large number of decisions? We find that under reasonable assumptions about the time costs of sampling, making many quick but locally suboptimal decisions based on very few samples may be the globally optimal strategy over long periods. These results help to reconcile a large body of work showing sampling-based or probability matching behavior with the hypothesis that human cognition can be understood in Bayesian terms, and they suggest promising future directions for studies of resource-constrained cognition. (shrink)

Marie Oldfield, Pro Bono Economics & Refugee Council. Over half the total applications for asylum the UK receives each year are initially rejected, yet nearly a third of these initial rejections are subsequently overturned on appeal. This process that fails to get decisions right first time imposes significant costs, not just on the applicants themselves, but also more widely on UK taxpayers. Asylum seekers are not entitled to welfare benefits nor employment except in some limited cases, and are often (...) placed in unsuitable conditions with lack of appropriate support to prepare their case for asylum. These unfortunate circumstances mean that they are unable to gather and present all the required evidence first time, even when the case for asylum is legitimate. As a result, the application is rejected and thus begins a cycle of appeals that might eventually lead to a successful outcome for the asylum seeker but will, in the process, burden the taxpayer with unnecessary administrative cost and cause the asylum seeker needless distress and prevent them from accessing suitable economic opportunities. • Our study estimates that there are approximately 4,000 initial rejections that are successfully appealed each year and, with each appeal incurring direct administrative costs of around £1,000, the price tag of incorrect initial decisions adds up to a hefty £4 million per year in unnecessary administrative costs alone. • There are other costs, too, that negatively impact asylum seekers and taxpayers, albeit in a more indirect manner. The longer the appeals process is dragged out, the more delay there is to successful asylum seekers entering the labour market which means lost economic activity and forgone tax revenue for the Exchequer. Long periods of unemployment also result in skills attrition and lower the probability of the asylum seeker successfully entering the labour market in the future. • A lengthy appeals process heightens stress and worsens mental health in asylum seekers, a group arguably already more vulnerable on this front. Unnecessary human suffering aside, there is also a monetary cost borne by the taxpayer should NHS mental health services become involved. Thus, there is a pressing and viable case for providing asylum seekers a stable environment in which to complete their applications for asylum. This would increase the likelihood of reaching correct decisions in the first instance, avoid unnecessary administrative costs of an arduous appeals process, enable successful asylum seekers to access the labour market and contribute to the Exchequer, and avoid placing extra demands on already strained NHS mental health services. (shrink)

Some recently-proposed counterexamples to the traditional definition of essential property do not require a separate logic of essence. Instead, the examples can be analysed in terms of the logic and theory of abstract objects. This theory distinguishes between abstract and ordinary objects, and provides a general analysis of the essential properties of both kinds of object. The claim ‘x has F necessarily’ becomes ambiguous in the case of abstract objects, and in the case of ordinary objects there are various ways (...) to make the definition of ‘F is essential to x’ more fine-grained. Consequently, the traditional definition of essential property for abstract objects in terms of modal notions is not correct, and for ordinary objects the relationship between essential properties and modality, once properly understood, addresses the counterexample. (shrink)

Papers addressing the role which human motivation plays in a wide range of specialties including clinical psychology, internal medicine, sports psychology, ...

In this brilliant analysis of mind-body problems Edward Pols adds new dimen­sions to the discussion of basic issues. The prisoner is Socrates, who, in a se­ries of actions involving moral decisions, finds himself under sentence of death, and who has now decided to undergo the sentence rather than accept the opportuni­ty to escape provided by powerful friends. Pols takes as his point of departure Socrates’ nai;ve statement of the contrast be­tween a scientific analysis of a moral action and the (...) point of view taken by the agent himself, and his rejection of the adequacy of the scientific analysis. (shrink)