The sum, difference, product and quotient of two functions with different domains are usually defined only on their common domain. This paper extends these definitions so that the sum and other operations are essentially defined anywhere that at least one of the components is defined. This idea is applied to propositions and events, expressed as indicator functions, to define conditional propositions and conditional events as three-valued indicator functions that are undefined when their condition is false. Extended operations of "and", "or", (...) "not" and "conditioning" are then defined on these conditional events with variable conditions. The probabilities of the disjunction and of the conjunction of two conditionals are expressed in terms of the conditional probabilities of the component conditionals. In a special case, these are shown to be weighted averages of the component conditional probabilities where the weights are the relative probabilities of the various conditions. Next, conditional random variables are defined to be random variables X whose domain has been restricted by a condition on a second random variable Y. The extended sum, difference, product and conditioning operations on functions are then applied to these conditional random variables. The expectation of a random variable and the conditional expectation of a conditional random variable are recounted. Theorem 1 generalizes the standard result that the conditional expectation of the sum of two conditional random variables with disjoint and exhaustive conditions is a weighted sum of the conditional expectations of the component conditional random variables. Because of the extended operations, the theorem is true for arbitrary conditions. Theorem 2 gives a formula for the expectation of the product of two conditional random variables. After the definition of independence of two random variables is extended to accommodate the extended operations, it is applied to the formula of Theorem 2 to simplify the expectation of a product of conditional random variables. Two examples end the paper. The first concerns a work force of n workers of different output levels and work shifts. The second example involves two radars with overlapping surveillance regions and different detection error rates. One radar's error rate is assumed to be sensitive to fog and the other radar's error rate is assumed to be sensitive to air traffic density. The combined error rate over the combined surveillance region given heavy fog and moderate air traffic is computed. (shrink)

This paper uses a non-distributive system of Boolean fractions (a|b), where a and b are 2-valued propositions or events, to express uncertain conditional propositions and conditional events. These Boolean fractions, 'a if b' or 'a given b', ordered pairs of events, which did not exist for the founders of quantum logic, can better represent uncertain conditional information just as integer fractions can better represent partial distances on a number line. Since the indeterminacy of some pairs of quantum events is due (...) to the mutual inconsistency of their experimental conditions, this algebra of conditionals can express indeterminacy. In fact, this system is able to express the crucial quantum concepts of orthogonality, simultaneous verifiability, compatibility, and the superposition of quantum events, all without resorting to Hilbert space. A conditional (a|b) is said to be "inapplicable" (or "undefined") in those instances or models for which b is false. Otherwise the conditional takes the truth-value of proposition a. Thus the system is technically 3-valued, but the 3rd value has nothing to do with a state of ignorance, nor to some half-truth. People already routinely put statements into three categories: true, false, or inapplicable. As such, this system applies to macroscopic as well as microscopic events. Two conditional propositions turn out to be simultaneously verifiable just in case the truth of one implies the applicability of the other. Furthermore, two conditional propositions (a|b) and (c|d) reside in a common Boolean sub-algebra of the non-distributive system of conditional propositions just in case b = d, their conditions are equivalent. Since all aspects of quantum mechanics can be represented with this near classical logic, there is no need to adopt Hilbert space logic as ordinary logic, just a need perhaps to adopt propositional fractions to do logic, just as we long ago adopted integer fractions to do arithmetic. The algebra of Boolean fractions is a natural, near-Boolean extension of Boolean algebra adequate to express quantum logic. While this paper explains one group of quantum anomalies, it nevertheless leaves no less mysterious the 'influence-at-a-distance', quantum entanglement phenomena. A quantum realist must still embrace non-local influences to hold that "hidden variables" are the measured properties of particles. But that seems easier than imaging wave-particle duality and instant collapse, as offered by proponents of the standard interpretation of quantum mechanics. (shrink)

This paper shows that the non-Boolean logic of quantum measurements is more naturally represented by a relatively new 4-operation system of Boolean fractions—conditional events—than by the standard representation using Hilbert Space. After the requirements of quantum mechanics and the properties of conditional event algebra are introduced, the quantum concepts of orthogonality, completeness, simultaneous verifiability, logical operations, and deductions are expressed in terms of conditional events thereby demonstrating the adequacy and efficacy of this formulation. Since conditional event algebra is nearly Boolean (...) and consists merely of ordered pairs of standard events or propositions, quantum events and the so-called “superpositions” of states need not be mysterious, and are here fully explicated. Conditional event algebra nicely explains these non-standard “superpositions” of quantum states as conjunctions or disjunctions of conditional events, Boolean fractions, but does not address the so-called “entanglement phenomena” of quantum mechanics, which remain physically mysterious. Nevertheless, separating the latter phenomena from superposition issues adds clarity to the interpretation of quantum entanglement, the phenomenon of influence propagated at faster than light speeds. With such treacherous possibilities present in all quantum situations, an observer has every reason to be completely explicit about the environmental–instrumental configuration, the conditions present when attempting quantum measurements. Conditional event algebra allows such explication without the physical and algebraic remoteness of Hilbert space. (shrink)

This brief opening for a special issue of Tradition and Discovery: The Polanyi Society Periodical on Philip Clayton’s thought and its connection with that of Michael Polany introduces Clayton’s essay and the responses by Martinez Hewlett, Gregory R. Peterson, Andy F. Sanders and Waler B. Gulick.

Philosophy is often conceived in the Anglophone world today as a subject that focuses on questions in particular ‘‘core areas,’’ pre-eminently epistemology and metaphysics. This article argues that the contemporary conception is a new version of the scholastic ‘‘self-indulgence for the few’’ of which Dewey complained nearly a century ago. Philosophical questions evolve, and a first task for philosophers is to address issues that arise for their own times. The article suggests that a renewal of philosophy today should turn the (...) contemporary conception inside out, attending to and developing further the valuable work being done on the supposed ‘‘periphery’’ and attending to the ‘‘core areas’’ only insofar as is necessary to address genuinely significant questions. (shrink)

Mountaineering is a dangerous activity. For many mountaineers, part of its very attraction is the risk, the thrill of danger. Yet mountaineers are often regarded as reckless or even irresponsible for risking their lives. In this paper, we offer a defence of risk-taking in mountaineering. Our discussion is organised around the fact that mountaineers and non-mountaineers often disagree about how risky mountaineering really is. We hope to cast some light on the nature of this disagreement – and to argue that (...) mountaineering may actually be worthwhile because of the risks it involves. Section 1 introduces the disagreement and, in doing so, separates out several different notions of risk. Sections 2–4 then consider some explanations of the disagreement, showing how a variety of phenomena can skew people's risk judgements. Section 5 then surveys some recent statistics, to see whether these illuminate how risky mountaineering is. In light of these considerations, however, we suggest that the disagreement is best framed not simply in terms of how risky mountaineering is but whether the risks it does involve are justified. The remainder of the paper, sections 6–9, argues that risk-taking in mountaineering often is justified – and, moreover, that mountaineering can itself be justified by and because of the risks it involves. (shrink)

The advance of science and human knowledge is impeded by misunderstandings of various statistics, insufficient reporting of findings, and the use of numerous standardized and non-standardized presentations of essentially identical information. Communication with journalists and the public is hindered by the failure to present statistics that are easy for non-scientists to interpret as well as by use of the word significant, which in scientific English does not carry the meaning of "important" or "large." This article promotes a new standard method (...) for reporting two-group and two-variable statistics that can enhance the presentation of relevant information, increase understanding of findings, and replace the current presentations of two-group ANOVA, t-tests, correlations, chi-squares, and z-tests of proportions. A brief call to highly restrict the publication of risk ratios, odds ratios, and relative increase in risk percentages is also made, since these statistics appear to provide no useful scientific information regarding the magnitude of findings. (shrink)

Despite the bad reputation of the legal profession, law remains king in America. A highly diverse society relies on the laws to maintain a working sense of the dignity and inviability of each individual. And a persistent element in contemporary debates is the fear that naturalistic theories of the human person will erode our belief that we have a dignity greater than that of other natural objects. Thus the endurance of the creation vs. evolution debate is due less to the (...) arguments of creationists, or to the continued influence of the book of Genesis, than to the reading of the evidence provided by Phillip E. Johnson of the University of California, Berkeley, Law School. (shrink)

Suppose that a person P 1 dies some time during 1978. Many years later, the resurrection world, a perennial object of Christian concern, begins on the morning of the day of judgment. On its first morning there are in that world distinct persons, P 2 and P 3 , each of whom is related in remarkably intimate ways to P 1 . You are to imagine that each of them satisfies each of the criteria or conditions necessary for identity with (...) P 1 to some extent, that both of them satisfy these conditions to exactly the same extent, and that every other denizen of the resurrection world satisfies each of these conditions to a lesser extent than P 2 and P 3 do. Thus, for example, philosophers often claim that bodily continuity is a necessary condition for personal identity. If it is, you might assume that the body P 2 has on the morning of the day of judgment contains some of the same atoms the body of P1 1 contained when P 1 died, and that P 2 's body on that day contains exactly n atoms from P 1 's body at the time of death just in case P 3 's body on that day contains exactly n atoms from P 1 's body at the time of death. Or, again, some philosophers hold that connectedness of memory is necessary for personal identity. If so, you are to suppose that on the morning of the day of judgment P 3 seems to remember some of the events in the life of P 1 having happened to him, and that P 3 seems to remember a certain event in the life of P 1 having happened to him just in case P 2 seems to remember that very event in the life of P 1 having happened to him. You are to fill in the details by adding complete parity between P 2 and P 3 with respect to similarity of DNA molecules, character traits and whatever else you deem relevant to personal identity. And, finally, you are to complete the story by imagining that P 2 and P 3 live very different sorts of lives in the resurrection world. To heighten the poignancy of the story, you might imagine that P 2 enjoys forever after the beatitude promised to the blessed while P 3 suffers the everlasting torments reserved for the damned. (shrink)

I aim to illuminate foundational epistemological issues by reflecting on 'epistemic consequentialism'—the epistemic analogue of ethical consequentialism. Epistemic consequentialism employs a concept of cognitive value playing a role in epistemic norms governing belief-like states that is analogous to the role goodness plays in act-governing moral norms. A distinction between 'direct' and 'indirect' versions of epistemic consequentialism is held to be as important as the familiar ethical distinction on which it is based. These versions are illustrated, respectively, by cognitive decision-theory and (...) reliabilism. Cognitive decision-theory is defended, and various conceptual issues concerning it explored. A simple dilemma suggests that epistemic consequentialism has radical consequences. (shrink)

Roger Crisp has inspired two important criticisms of Scanlon's buck-passing account of value. I defend buck-passing from the wrong kind of reasons criticism, and the reasons and the good objection. I support Rabinowicz and Rønnow-Rasmussen's dual role of reasons in refuting the wrong kind of reasons criticism, even where its authors claim it fails. Crisp's reasons and the good objection contends that the property of goodness is buck-passing in virtue of its formality. I argue that Crisp conflates general and formal (...) properties, and that Scanlon is ambiguous about whether the formal property of a reason can stop the buck. Drawing from Wallace, I respond to Crisp's reasons and the good objection by developing an augmented buck-passing account of reasons and value, where the buck is passed consistently from the formal properties of both to the substantive properties of considerations and evaluative attitudes. I end by describing two unresolved problems for buck-passers. (shrink)

Philip Quinn, John A. O’Brien Professor at the University of Notre Dame from 1985 until his death in 2004, was well known for his work in the philosophy of religion, political philosophy, and core areas of analytic philosophy. Although the breadth of his interests was so great that it would be virtually impossible to identify any subset of them as representative, the contributors to this volume provide an excellent introduction to, and advance the discussion of, some of the questions (...) of central importance to Quinn in the last years of his working life. Paul J. Weithman argues in his introduction that Quinn’s interest and analyses in many areas grew out of a distinctive and underlying sensibility that we might call “liberal faith.” It included belief in the value of a liberal education and in rigorous intellectual inquiry, the acceptance of enduring religious, cultural, and political pluralism, along with a keen awareness of problems posed by pluralism, and a deeply held but non-utopian faith in liberal democratic politics. These provocative essays, at the cutting edge of epistemology, the philosophy of religion, philosophical theology, and political philosophy, explore the tenets of liberal faith and invite continuing engagement with the philosophical issues. “Philip Quinn was admired enormously throughout the world of professional philosophy.... His reputation for rigor, his tireless service to the profession, and his essentially ‘non-dogmatic,’ but philosophically sophisticated faith is widely admired... The essays in this volume are first-rate contemporary philosophy along with an excellent introduction to Quinn’s work.” —_Charles Taliaferro, St. Olaf College_ "The papers that form _Liberal Faith_ give insightful treatments of three types of questions: first, how can we conscientiously believe something when there are many people we admire who do not believe it, and what is the underlying relation here between justification and rationality; second, what does it mean to desire union with God, and can Christians properly believe in the possibility of eternal self-annihilation; third, how should liberal democracy accommodate the religious convictions of its members, whether some comprehensive doctrine such as a religion is required to justify a commitment to human equality, and whether there is an absolute moral prohibition on the state use of torture. The volume has an unusually good introduction putting the papers into dialog with each other and with the work of Philip Quinn. The papers are cohesive because the central themes of Philip Quinn's work hold together into a picture of how Christianity and Liberal Democracy fit together." —_John Hare, Noah Porter Professor of Philosophical Theology, Yale Divinity School _ “This is a collection of high quality essays dealing with various topics related to Philip Quinn’s work. The book makes an original contribution by virtue of its individual papers, each of which is new. These essays will be of interest to scholars and students who followed Quinn’s work, especially in philosophy of religion and political philosophy.“ —_John Greco, The Leonard and Elizabeth Eslick Chair in Philosophy, Saint Louis University _. (shrink)

It has become fashionable to try to prove the impossibility of there being a God. Findlay's celebrated ontological disproof has in the past quarter century given rise to vigorous controversy. More recently James Rachels has offered a moral argument intended to show that there could not be a being worthy of worship. In this paper I shall examine the position Rachels is arguing for in some detail. I shall endeavor to show that his argument is unsound and, more interestingly, that (...) the genuine philosophical perplexity which motivates it can be dispelled without too much difficulty. (shrink)

In a recent paper, Robert A. Oakes argues that a doctrine central to, and partially constitutive of, classical theism implies a certain sort of pantheism. The doctrine in question is a modal form of the claim that God conserves in existence the world of contingent things; alternatively, it is the view that all contingently existing things are necessarily continuously dependent upon God for their existence. And the variety of pantheism at stake is a modal form of the thesis that all (...) contingent things are, in some sense, included within the being of God. (shrink)

It seems clear that the ontological argument can no longer be dismissed as a silly fallacy. The dogma of the impossibility of necessary existence is seriously threatened by the case of necessary existential truths in mathematics, and as for the claim that the ontological argument must beg the question, since by mentioning God in the premise his existence is presupposed, it is undermined by the fact that we often refer to things—Hamlet for instance— we do not for a moment think (...) exist. The doctrine that existence is not a property , insofar as it does not reduce to one of the foregoing points, is very murky, for the sense in which ‘red’ is a predicate and ‘exists’ is not has never been clearly defined. Moreover, the way many believers hold that ‘God exists’ is immune to empirical refutation strongly suggests that we are dealing here with an analytic statement, which is just what the ontological argument should be expected to produce. It seems in order, then, to conduct theological discussion under the supposition that the argument is in fact sound. (shrink)

To study the interaction of forces that produce chest wall motion, we propose a model based on the lever system of Hillman and Finucane :951–961, 1987) and introduce some dynamic properties of the respiratory system. The passive elements are considered as elastic compartments linked to the open air via a resistive tube, an image of airways. The respiratory muscles force is applied to both compartments. Parameters of the model are identified in using experimental data of airflow signal measured by pneumotachography (...) and rib cage and abdomen signals measured by respiratory inductive plethysmography on eleven healthy volunteers in five conditions: at rest and with four level of added loads. A breath by breath analysis showed, whatever the individual and the condition are, that there are several breaths on which the airflow simulated by our model is well fitted to the airflow measured by pneumotachography as estimated by a determination coefficient R2 ≥ 0.70. This very simple model may well represent the behaviour of the chest wall and thus may be useful to interpret the relative motion of rib cage and abdomen during quiet breathing. (shrink)

The work of Sophocles shows the human suffering which might be caused by evil without the presence of guilt. Within the historic confrontation of the Athenian political stage, the presentation of the tragic conflict opposes the illustrated omnipotence: to present that what is divine as incomprehensible is one of the traditional features of Sophocles’ work and his announcement of anti-modernity. “Not-understanding” is the banner of silence when faced with the limit of natural reason. As a response to sophist thought, which (...) replaced the divine paradigm, the preponderance of the gods in the work of Sophocles might be seen as an affirmation. What is characteristic of the traditional restoration proposed by Sophocles is not only the appearance of the Gods in his works, but the particular way in which they reveal themselves. Knowing that what is divine is not characteristic of men because it is not a feature of the former to be understood to a lesser degree than that of its own nature. That is exactly the stage where the struggle between the reality of knowing and the relative appearance of knowing occurs. Bearing this interpretative intention in mind, the aim of the paper is to highlight the way in which evil reveals itself in Oedipus the King, as a device chosen by the gods to trigger the unfolding of the nature of the hero. (shrink)

In recent decades, psychological research on the effects of mindfulness-based interventions has greatly developed and demonstrated a range of beneficial outcomes in a variety of populations and contexts. Yet, the question of how to foster subjective well-being and happiness remains open. Here, we assessed the effectiveness of an integrated mental training program The Art of Happiness on psychological well-being in a general population. The mental training program was designed to help practitioners develop new ways to nurture their own happiness. This (...) was achieved by seven modules aimed at cultivating positive cognition strategies and behaviors using both formal and informal practices. The program was conducted over a period of 9 months, also comprising two retreats, one in the middle and one at the end of the course. By using a set of established psychometric tools, we assessed the effects of such a mental training program on several psychological well-being dimensions, taking into account both the longitudinal effects of the course and the short-term effects arising from the intensive retreat experiences. The results showed that several psychological well-being measures gradually increased within participants from the beginning to the end of the course. This was especially true for life satisfaction, self-awareness, and emotional regulation, highlighting both short-term and longitudinal effects of the program. In conclusion, these findings suggest the potential of the mental training program, such as The Art of Happiness, for psychological well-being. (shrink)

Since the turn of the century there has been a strong trend to break through the wall which has separated philosophy from the “special sciences” and to investigate the problems which require a good judgment in both philosophy and science. The evolution of science itself and the increasing relevance of science in human life have given immense momentum to this trend. But this momentum could not be appreciated in its actual strength because scientists who wanted to raise their voices had (...) trouble in finding a Journal where they could communicate with the people who were interested, for almost all the scientific journals were devoted exclusively to technical papers. In founding Philosophy of Science Dr. Malisoff started the construction of a channel by which this important flow of scientific investigation could reach its public. This line of thought found in the journal a possibility of self-expression and it became a real force in the life of the community of scientists and scholars, and even of educated men in general. From the first volume, papers were published which have later been quoted in every discussion about the philosophy of science. I mention, as an example only, R. Carnap's paper on Testability and Meaning. Nobody who has wanted information and stimulation in this modern field of investigation could get it without looking into Malisoff's Philosophy of Science. (shrink)

Let $\mathcal{L}$ be a propositional language with standard Boolean connectives plus two modalities: an S4-ish topological modality $\square$ and a temporal modality $\bigcirc$ , understood as ‘next’. We extend the topological semantic for S4 to a semantics for the language $\mathcal{L}$ by interpreting $\mathcal{L}$ in dynamic topological systems, i.e. ordered pairs $\langle X, f\rangle$ , where X is a topological space and f is a continuous function on X. Artemov, Davoren and Nerode have axiomatized a logic S4C, and have shown (...) that S4C is sound and complete for this semantics. Zhang and Mints have shown that S4C is complete relative to a particular topological space, Cantor space. The current paper produces an alternate proof of the Zhang-Mints result. (shrink)

One way to do socially relevant investigations of science is through conceptual analysis of scientific terms used in special-interest science (SIS). SIS is science having welfare-related consequences and funded by special interests, e.g., tobacco companies, in order to establish predetermined conclusions. For instance, because the chemical industry seeks deregulation of toxic emissions and avoiding costly cleanups, it funds SIS that supports the concept of "hormesis" (according to which low doses of toxins/carcinogens have beneficial effects). Analyzing the hormesis concept of its (...) main defender, chemical-industry-funded Edward Calabrese, the paper shows Calabrese and others fail to distinguish three different hormesis concepts, H, HG, and HD. H requires toxin-induced, short-term beneficial effects for only one biological endpoint, while HG requires toxin-induced, net-beneficial effects for all endpoints/responses/subjects/ages/conditions. HD requires using the risk-assessment/regulatory default rule that all low-dose toxic exposures are net-beneficial, thus allowable. Clarifying these concepts, the paper argues for five main claims. (1) Claims positing H are trivially true but irrelevant to regulations. (2) Claims positing HG are relevant to regulation but scientifically false. (3) Claims positing HD are relevant to regulation but ethically/scientifically questionable. (4) Although no hormesis concept (H, HG, or HD) has both scientific validity and regulatory relevance, Calabrese and others obscure this fact through repeated equivocation, begging the question, and data-tri mm ing. Consequently (5) their errors provide some undeserved rhetorical plausibility for deregulating low-dose toxins. (shrink)