Lüders and Pauli proved the $\mathcal{CPT}$ theorem based on Lagrangian quantum field theory almost half a century ago. Jost gave a more general proof based on “axiomatic” field theory nearly as long ago. The axiomatic point of view has two advantages over the Lagrangian one. First, the axiomatic point of view makes clear why $\mathcal{CPT}$ is fundamental—because it is intimately related to Lorentz invariance. Secondly, the axiomatic proof gives a simple way to calculate the $\mathcal{CPT}$ transform of any relativistic field (...) without calculating $\mathcal{C}$ , $\mathcal{P}$ and $\mathcal{T}$ separately and then multiplying them. The purpose of this pedagogical paper is to “deaxiomatize” the $\mathcal{CPT}$ theorem by explaining it in a few simple steps. We use theorems of distribution theory and of several complex variables without proof to make the exposition elementary. (shrink)

This paper studies the model of the quantum electrodynamics (QED) of a single nonrelativistic electron due to W. Pauli and M. Fierz and studied further by P. Blanchard. This model exhibits infrared divergence in a very simple context. The infrared divergence is associated with the inequivalence of the Hilbert spaces associated with the free Hamiltonian and with the complete Hamiltonian. Infrared divergences that are visible in the perturbative description disappear in the space of the clothed electrons. In this model when (...) the Hamiltonian is expressed in terms of the “physical” fields that create the electron together with its cloud of soft photons, the variational principle suggested earlier can be applied. At finite time the Heisenberg field of the model acts in the space of the perturbative electron together with a finite number of perturbative photons, while the “physical” field can be chosen to act in the space of the exact (“physical”) electron eigenstates together with a finite number of physical photons. The space of the physical (or clothed) electron states can be chosen to be a Fock space. (shrink)

Quons are particles characterized by the parameter q, which permits smooth interpolation between Bose and Fermi statistics; q = 1 gives bosons, q = -1 gives fermions. In this paper we give a heuristic argument for an extension of conservation of statistics to quons with trilinear couplings of the form ffb, where f is fermion-like and b is boson-like. We show that q f 2 = qb. In particular, we relate the bound on qγ for photons to the bound on (...) qe for electrons, allowing the very precise bound for electrons to be carried over to photons. An extension of this argument suggests that all particles are fermions or bosons to a high precision. (shrink)

It has sometimes been said that it is useless to try to prevent wars since man has an ineradicable combative instinct. The term instinct is very ambiguous in its application to humans, and it may be interesting to see what occurs amongst the insects, many of whose species show the highest development of instinctive behaviour.Many insect species are predatory, but if they depend on other distinct species, the relation is analogous to hunting or to a crude form of agriculture. Aggressive (...) behaviour to be comparable with war must concern the different members of one species. There are many laboratory experiments which illustrate the effects of competition when a population begins to exceed the capacity of its food supply. In Flour beetles, for instance, the adult beetles and the larvae eat any egg or pupae which they happen to meet in their ceaseless burrowing through the flour. There is thus a fixed population density at which eggs are eaten as fast as they are laid. In Grain weevils, the effect of crowding is to reduce the rate at which eggs are laid by the females who appear to suffer from overstimulation when crowded. Other effects, usually harmful, may be produced by the accumulation of the products of respiration or of digestion. Finally, if the food supply is too small, there will be death from starvation. If, for instance, too many blowfly eggs are added to a piece of meat, the flies produced will either be small, weak, and infertile or, if the excess has been too great, the larvae may all starve when half grown. Thus, a piece of meat which could have produced 100 normal flies may produce none at all if a tenfold excess of eggs is laid on it. (shrink)

A Christian approach to the issues that constitute bioethics is inevitable for us who cherish the truth of historic, creedal, trinitarian Christianity. Scripture teaches and the Greek and Latin Church Fathers as well as the Reformers aver that man, created in the image of God, has an inherent, if vestigial, sense of right and wrong and a conscience however marred by the fall and by rebellion. We must believe that we share this most basic ecumenism with all humanity, not because (...) of rational observation and analysis of nature, but because Scripture reveals it. We who are convinced of the truth of historic, creedal, trinitarian Christianity have a high view of Scripture and hold it to be infallible and utterly trustworthy irrespective of the importance we assign to our specific post-biblical traditional distinctives. This is a narrower but much more vital ecumenism than the first. Faithful adherence to Scripture inevitably manifests itself in remarkably similar priorities and values, often, lamentably, not because of, but in spite of, ourselves. (shrink)

The present study tested the hypothesis that centrality of religiosity as defined as the position of an individual’s religious construct system in personality moderates the relationship between the experience of forgiveness by God and forgivingness for others. Participants completed measures of forgiveness by God, forgivingness, and centrality of religiosity. The moderating hypothesis was tested by treating centrality of religiosity both as a continuous variable and as a categorical variable with reference to a typological distinction. Results indicate that centrality of religiosity (...) moderates the positive relationship between forgiveness by God and forgivingness for others, implying that this relation only occurs if the religious construct system is in a central position in personality, but not if it is in a subordinate position. These results underline the importance of considering centrality of religiosity as an individual difference variable. (shrink)

We introduce a logic BI in which a multiplicative (or linear) and an additive (or intuitionistic) implication live side-by-side. The propositional version of BI arises from an analysis of the proof-theoretic relationship between conjunction and implication; it can be viewed as a merging of intuitionistic logic and multiplicative intuitionistic linear logic. The naturality of BI can be seen categorically: models of propositional BI's proofs are given by bicartesian doubly closed categories, i.e., categories which freely combine the semantics of propositional intuitionistic (...) logic and propositional multiplicative intuitionistic linear logic. The predicate version of BI includes, in addition to standard additive quantifiers, multiplicative (or intensional) quantifiers ∀ new and ∃ new which arise from observing restrictions on structural rules on the level of terms as well as propositions. We discuss computational interpretations, based on sharing, at both the propositional and predicate levels. (shrink)

Things and Their Place in Theories Our talk of external things, our very notion of things, is just a conceptual apparatus that helps us to foresee and ...

In recent years, the biological inheritance of what has been traditionally known as original sin has come more clearly to the fore. Examining the genetic forebears of Homo sapiens has allowed for a richer understanding of what exactly the "propagation" of original sin might really mean. The wounded imperfection of the human biological inheritance has clarified matters concerning the question of where exactly original sin comes from. Since the human experience of sentience and agency is built biologically upon the shoulders (...) of its ancestors, the human experience of being always-already bound by sin—an essential component of the meaning of original sin—comes into clearer relief. At the same time, a much richer... (shrink)

In partial fulfilment of the requirements for the degree of Master of Education in Philosophy of Education, Department of Educational Foundations.

The following is the transcript of a lecture taken in shorthand by Hans-Georg Backhaus. The transcript was originally published as an appendix in Hans-Georg Backhaus, Dialektik der Wertform. Untersuchungen zur marxschen Ökonomiekritik, a complete translation of which is forthcoming in the Historical Materialism book series.

The essays in this volume explore current work in central areas of philosophy, work unified by attention to salient questions of human action and human agency. They ask what it is for humans to act knowledgeably, to use language, to be friends, to act heroically, to be mortally fortunate, and to produce as well as to appreciate art. The volume is dedicated to J. O. Urmson, in recognition of his inspirational contributions to these areas. All the essays but one have (...) been specially written for this volume. (shrink)