We give a unified account of some results in the development of Polyadic Inductive Logic in the last decade with particular reference to the Principle of Spectrum Exchangeability, its consequences for Instantial Relevance, Language Invariance and Johnson's Sufficientness Principle, and the corresponding de Finetti style representation theorems.

We consider the desirability, or otherwise, of various forms of induction in the light of certain principles and inductive methods within predicate uncertain reasoning. Our general conclusion is that there remain conflicts within the area whose resolution will require a deeper understanding of the fundamental relationship between individuals and properties.

In this paper we consider a natural generalization of the Principle of Instantial Relevance and give a complete characterization of the probabilistic belief functions satisfying this principle as a family of discrete probability functions parameterized by a single real δ ∊ [0, 1).

We consider the problem of induction over languages containing binary relations and outline a way of interpreting and constructing a class of probability functions on the sentences of such a language. Some principles of inductive reasoning satisfied by these probability functions are discussed, leading in turn to a representation theorem for a more general class of probability functions satisfying these principles.

It took nearly two thousand years for society to recognize the Hippocratic insistence that “the doctor knows best”1 was an inadequate approach to medical decisionmaking. Today, patient-centered medicine has come to understand that the individual patient has a significant role in the decisionmaking process.2.

Death in the Clinic fills a gap in contemporary medical education by explicitly addressing the concrete clinical realities about death with which practitioners, patients, and their families continue to wrestle. Visit our website for sample chapters!

Reasoning under uncertainty, that is, making judgements with only partial knowledge, is a major theme in artificial intelligence. Professor Paris provides here an introduction to the mathematical foundations of the subject. It is suited for readers with some knowledge of undergraduate mathematics but is otherwise self-contained, collecting together the key results on the subject, and formalising within a unified framework the main contemporary approaches and assumptions. The author has concentrated on giving clear mathematical formulations, analyses, justifications and consequences of (...) the main theories about uncertain reasoning, so the book can serve as a textbook for beginners or as a starting point for further basic research into the subject. It will be welcomed by graduate students and research workers in logic, philosophy, and computer science as a textbook for beginners, a starting point for further basic research into the subject, and not least, an account of how mathematics and artificial intelligence can complement and enrich each other. (shrink)

We give an account of some relationships between the principles of Constant and Atom Exchangeability and various generalizations of the Principle of Instantial Relevance within the framework of Inductive Logic. In particular we demonstrate some surprising and somewhat counterintuitive dependencies of these relationships on ostensibly unimportant parameters, such as the number of predicates in the overlying language.

The opinion of Mr. Justice Francis of the English High Court which denied the parents of Charlie Gard, who had been born with an extremely rare mutation of a genetic disease, the right to take their child to the United States for a proposed experimental treatment occasioned world wide attention including that of the Pope, President Trump, and the US Congress. The case raise anew a debate as old as the foundation of Western medicine on who should decide and on (...) what standard when there is a conflict between a family and the treating physicians over a possible treatment. This paper will explore the different approaches of the British and American courts on the issue and the various proposals from that of John Rawls in his A Theory of Justice to a processed-based approach for resolving such disputes. As carefully crafted as the opinion of Mr Justice Nicholas Francis in the Gard case proved to be, it left commentators unsatisfied. A widespread criticism, captured in an article by Michael Dougherty in The National Review was for the state to ‘get out of the way of the parents trying to act in the best interests of the child’.1 Although he conceded the parents could be adding to the suffering of the child by taking Charlie to America for an experimental therapy and agreed that such a choice ‘may be the wrong decision,’ in Dougherty’s view, it should still be ‘their decision’. Dougherty’s stand was the popular response to the question of ‘Who should decide?’ It fails, however, to propose any rationale for the decision. It provided no norms, no standards and no guidelines for the parents. Their motive could equally well be indifference to the suffering of the child as concern for his well-being. Furthermore, even good, loving parents may make …. (shrink)

We give a complete characterization of Priest's Finite Inconsistent Arithmetics observing that his original putative characterization included arithmetics which cannot in fact be realized.

This paper is a sequel to an earlier result of the authors that in making inferences from certain probabilistic knowledge bases the maximum entropy inference process, ME, is the only inference process respecting “common sense.” This result was criticized on the grounds that the probabilistic knowledge bases considered are unnatural and that ignorance of dependence should not be identified with statistical independence. We argue against these criticisms and also against the more general criticism that ME is representation dependent. In a (...) final section, however, we provide a criticism of our own of ME, and of inference processes in general, namely that they fail to satisfy compactness. (shrink)

We examine the closure conditions of the probabilistic consequence relation of Hawthorne and Makinson, specifically the outstanding question of completeness in terms of Horn rules, of their proposed (finite) set of rules O. We show that on the contrary no such finite set of Horn rules exists, though we are able to specify an infinite set which is complete.

We answer some problems set by Priest in [11] and [12], in particular refuting Priest's Conjecture that all LP-models of Th(N) essentially arise via congruence relations on classical models of Th(N). We also show that the analogue of Priest's Conjecture for I δ₀ + Exp implies the existence of truth definitions for intervals [0,a] ⊂ₑ M ⊨ I δ₀ + Exp in any cut [0,a] ⊂e K ⊆ M closed under successor and multiplication.

Several recent articles raise an issue long unaddressed in the medical literature: physician compliance with patient or family requests for futile or ineffectice therapy. Although they agree philosophically that such treatment ought not be given, most physicians have followed the course described by Stanley Fiel, in which a young patient dying of cystic fibrosis was accepted “for evaluation” by a transplant center even though he has already passed the threshold of viability as a candidate for a heart-lung transplant. Dr. Fiel (...) reported this action was taken not in the hope of doing the transplant but so that the family could assure themselves they had done “everything possible.” The patient, after a long and stressful cross-country flight, arrived at the hospital in respiratory failure. He died soon thereafter far from home and familiar surroundings. (shrink)

B.K.Matilal, and earlier J.F.Staal, have suggested a reading of the `Nyaya five limb schema' (also sometimes referred to as the Indian Schema or Hindu Syllogism) from Gotama's Nyaya-Sutra in terms of a binary occurrence relation. In this paper we provide a rational justification of a version of this reading as Analogical Reasoning within the framework of Polyadic Pure Inductive Logic.

We characterize those identities and independencies which hold for all probability functions on a unary language satisfying the Principle of Atom Exchangeability. We then show that if this is strengthen to the requirement that Johnson's Sufficientness Principle holds, thus giving Carnap's Continuum of inductive methods for languages with at least two predicates, then new and somewhat inexplicable identities and independencies emerge, the latter even in the case of Carnap's Continuum for the language with just a single predicate.

As the only nation in the western world without a national health insurance program, the United States faces ongoing issues of access and fairness in health care coverage. The Clinton administration tried and failed to address the problem of universal coverage. Since then we have focused on the narrower, but nonetheless real, issues of fairness and equity in the benefits package provided in insurance plans. The LORAN Commission spent two years trying to devise agreed-upon principles to govern such issues. The (...) lesson learned was the same as that of the Ethics Force study: there was no possibility of getting agreement, let alone consensus, among the participants on how to decide what should be a covered benefit. There were, however, two generally agreed upon principles that emerged regarding health care: “Every individual should be treated alike,” and “When it comes to health, cost cannot be a consideration.” That formula translated into providing everyone with everything. The only certain outcome from such a policy would be fiscal insolvency and ultimately bankruptcy. (shrink)

The paper describes and proves completeness theorems for a series of proof systems formalizing common sense reasoning about uncertain knowledge in the case where this consists of sets of linear constraints on a probability function.

In a recent essay, George Annas, the legal columnist for The New England Journal of Medicine, observed that the resuscitation of extremely premature infants, even over parental objection, is not problematic because “once the child's medical status has been determined, the parents have the legal authority to make all subsequent decisions.” Annas himself is quick to concede that treatment in a high-technology neonatal intensive care unit frequently takes on a life of its own. He also acknowledges that although bioethicists and (...) courts agree that there is no ethical or legal difference between withholding or withdrawing a respirator from a patient, parents and physicians find the withdrawal much more emotionally troubling. (shrink)

We examine the closure conditions of the probabilistic consequence relation of Hawthorne and Makinson, specifically the outstanding question of completeness in terms of Horn rules, of their proposed (finite) set of rules O. We show that on the contrary no such finite set of Horn rules exists, though we are able to specify an infinite set which is complete.

We investigate the relative probabilistic support afforded by the combination of two analogies based on possibly different, structural similarity (as opposed to e.g. shared predicates) within the context of Pure Inductive Logic and under the assumption of Language Invariance. We show that whilst repeated analogies grounded on the same structural similarity only strengthen the probabilistic support this need not be the case when combining analogies based on different structural similarities. That is, two analogies may provide less support than each would (...) individually. (shrink)

(2011). Standards, Norms, and Guidelines for Permissible Withdrawal of Life Support From Seriously Compromised Newborns. The American Journal of Bioethics: Vol. 11, No. 2, pp. 33-34.

We present six significant open problems in Pure Inductive Logic, together with their background and current status, with the intention of raising awareness and leading ultimately to their resolution.

The children were nestled all snug in their beds.While visions of sugar-plums danced in their heads.Clement Moore's cherished ‘Twas the Night Before Christmas captures the hopes, dreams and visions...

We examine the idea that similar problems should have similar solutions (to paraphrase van Fraassen’s slogan ‘Problems which are essentially the same must receive essentially the same solution’, see van Fraassen in Laws and symmetry, Oxford Univesity Press, Oxford, 1989, p. 236) in the context of symmetries of sentence algebras within Inductive Logic and conclude that by itself this is too generous a notion upon which to found the rational assignment of probabilities. We also argue that within our formulation of (...) symmetry the paradoxes associated with the so called ‘Principle of Indifference’ collapse, but only to be replaced by genuinely irremediable examples of the same phenomenon. (shrink)

The American Journal of Bioethics, Volume 11, Issue 11, Page 13-14, November 2011.

How does a self-described “simple teacher of religion” at the College of the Holy Cross get involved in bioethics? Nothing in my training or experience had prepared me for involvement in medicine. Much like that of my moral theology professor and then mentor, Richard McCormick, my training was in moral theology and social ethics. I also had an abiding interest in the courts and constitutional law. That interest led to a doctoral dissertation at the University of Southern California's Program in (...) Social Ethics on “The Supreme Court's Understanding of Religion in Conscientious Objector Cases.” Interestingly, doctoral work in the late 1960s on the ethical dimension of war was the starting point for other ethicists such as Leroy Walters and James Childress who subsequently became early voices in bioethics. (shrink)

The Clinton administration's revised rules regulating but not prohibiting the common practice in managed care of linking physician compensation with cost cutting and control of services demonstrates the complexity of ethical issues in managed care. As originally proposed, the federal guidelines on payment for Medicare and Medicaid services would have precluded any interrelationship between payment to physicians and delivery of services. Such a restriction would have gutted the primary mechanism in managed care plans to curb the unacceptably high cost of (...) healthcare delivery: making physicians directly responsible for cost control by placing them at direct financial risk. At first blush such a linkage seems to involve an obvious and irreconcilable conflict of interest. How can a physician be responsible for the well-being of a patient while at the same time aware that a proportion of his or her income is linked to the provision of cost-conscious care? (shrink)

The issue of physician refusal of requested treatment has fueled a two-pronged debate in our society-one on the meaning of futility and the other on the limits of patient autonomy. The latter is a genuinely philosophic dispute; the former, it seems, is a modern relapse into nominalism.It is not the meaning of a word, but the moral basis for the actions of the par-ticipants that should be the focus of our attention, Yet the medical literature distracts us with articles titled (...) “Medical Futility: Its Meaning and Ethical Implica-tions” “The Problem with Futility” “Who Defines Futility?,” “The Illusion of Futility,” and even “Beyond Futility.”The history of the futility debate, which was launched by a 1983 study of Bedell and Delbanco that demonstrated the ineffectiveness of CPR for certain catego-ries of patients, has been documented elsewhere. Here we will inquire if the term, and its rapid intrusion into the medical lexicon, serves a useful purpose or if, as Truog suggested, we would all be better off if this new buzzword were jettisoned. (shrink)