It is demonstrated on the basis of the Dirac equation that quarks cannot be confined by a vector gluon potential of the form(r/r 0)a or[ln(r/r 0]a, a>0, if the quark-gluon interaction conserves parity. In order to confine quarks with the parity-conserving interaction, the effective gluon potential must be a pseudovector or a scalar. These are shown in a simple Yang-Mills field with theSU(2) group.

The majority of our linguistic exchanges, such as everyday conversations, are divided into turns; one party usually talks at a time, with only relatively rare occurrences of brief overlaps in which there are two simultaneous speakers. Moreover, conversational turn-taking tends to be very fast. We typically start producing our responses before the previous turn has finished, i.e., before we are confronted with the full content of our interlocutor’s utterance. This raises interesting questions about the nature of linguistic understanding. Philosophical theories (...) typically focus on linguistic understanding characterized either as an ability to grasp the contents of utterances in a given language or as outputs of this ability—mental states of one type or another. In this paper, I supplement these theories by developing an account of the process of understanding. I argue that it enables us to capture the dynamic and temporal aspect of understanding and reconcile philosophical investigations with empirical research on language comprehension. (shrink)

In the framework of population dynamics, we start from the logistic equation describing the evolution of one species with limited food supply. A split device allows us to consider the population as two sub-populations x and y evolving analogously. The dynamical system has a one-parameter family of equilibria which is structurally unstable. Then small perturbations of the system (describing functional or ethological differentiations between the sub-species) lead in general to a new system involving a fast and a slow dynamics with (...) a finite number of equilibria. In simple situations where the differentiation is clearly either an advantage or an inconvenience for one of the subspecies, the stable equilibrium amounts to extinction of the disadvantaged subspecies (elementary Darwinism). Oppositely more complex differentiations (involving both advantages and inconveniences) often lead to stable equilibria with well-defined non zero proportions of the sub-populations (preservation of the biodiversity). Other examples are concerned with symbiosis-like differentiations, leading to preservation, whereas the opposite case (mutual nuisances) has an unstable equilibrium and lead to extinction of one or the other subspecies according to the initial conditions. The case of a scission into three subspecies is more rich in consequences. In certain cases, predator-prey relations lead to auto-organization phenomena with stable diversity-preserving diversity. Cases of instability are also possible, leading to orbits tending towards a poly-cycle.This implies some kind of pseudo-extinction: this amounts to “pseudo-periodic-like” orbits with “pseudo-periods” larger and larger, tending to infinity; each pseudo-period contains parts where one of the sub-populations practically vanish. Other non-linear perturbations lead to stable orbits. (shrink)

Context: Strict finitism is usually not taken seriously as a possible view on what mathematics is and how it functions. This is due mainly to unfamiliarity with the topic. Problem: First, it is necessary to present a “decent” history of strict finitism and, secondly, to show that common counterarguments against strict finitism can be properly addressed and refuted. Method: For the historical part, the historical material is situated in a broader context, and for the argumentative part, an evaluation of arguments (...) and counterarguments is presented. Results: The main result is that strict finitism is indeed a viable option, next to other constructive approaches, in mathematics. Implications: Arguing for strict finitism is more complex than is usually thought. For future research, strict finitist mathematics itself needs to be written out in more detail to increase its credibility. In as far as strict finitism is a viable option, it will change our views on such “classics” as the platonist-constructivist discussion, the discovery-construction debate and the mysterious applicability problem . Constructivist content: Strict finitism starts from the idea that counting is an act of labeling, hence the mathematician is an active subject right from the start. It differs from other constructivist views in that the finite limitations of the human subject are taken into account. (shrink)

During the 1970s, prenatal screening technologies were in their infancy, but were being swiftly harnessed to uncover and prevent spina bifida. The historical rise of this screening process and prevention programme is analysed in this paper, and the role of ethical debates in key studies, editorials and letters reported in the Lancet, and other related texts and governmental documents between 1972 and 1983, is considered. The silence that surrounded rigorous ethical debate served to highlight where discussion lay—namely, within the justifications (...) offered for the prevention of spina bifida, and the efficacy and benefits of screening. In other words, the ethical justification for screening and prevention of spina bifida, when the authors are not explicitly interested in ethics, is considered. These justifications held certain notions of disability as costly to society, with an imperative to screen and prevent spina bifida for the good of the society. (shrink)

According to the causal interpretation of quantum mechanics, one can precisely define the state of an individual particle in a many-body system by its position, momentum, and spin. It is shown in the EPR spin experiment that the quantum torque brings about an instantaneous change in the state of one of the particles when the other undergoes a local interaction, but that such a transfer of “information” cannot be extracted by any experiment subject to the laws of quantum mechanics.

There are quantum solutions for computational problems that make use of interference at some stage in the algorithm. These stages can be mapped into the physical setting of a single particle travelling through a many-armed interferometer. There has been recent foundational interest in theories beyond quantum theory. Here, we present a generalized formulation of computation in the context of a many-armed interferometer, and explore how theories can differ from quantum theory and still perform distributed calculations in this set-up. We shall (...) see that quaternionic quantum theory proves a suitable candidate, whereas box-world does not. We also find that a classical hidden variable model first presented by Spekkens : 32100, 2007) can also be used for this type of computation due to the epistemic restriction placed on the hidden variable. (shrink)

The aim of this paper is to investigate the variety of symmetric closure algebras, that is, closure algebras endowed with a De Morgan operator. Some general properties are derived. Particularly, the lattice of subvarieties of the subvariety of monadic symmetric algebras is described and an equational basis for each subvariety is given.

In August of 1971, President Nixon announced that the United States was “closing the gold window,” bringing an end to the postwar system of international exchange rate stability and precipitating a period of significant uncertainty and transformation in global institutions. Although this critical historical episode is important for an understanding of historical “neoliberalism” and institutional change, modern sociological perspectives have scarcely been applied to it. The present analysis uses archival data to show that closing the gold window was never the (...) goal or preferred strategy of the Nixon administration, which had spent years preparing much more modest reforms. Nevertheless, US policymakers took this unilateral action as a contingency plan to achieve a short-term goal, knowing that it would dramatically change the functioning of the international economy. Surprisingly, the autonomous structure of the IMF did not channel US initiatives toward gradual evolution but rather helped determine a radical change in strategy. (shrink)

Open peer commentary on the article “Second-Order Science: Logic, Strategies, Methods” by Stuart A. Umpleby. Upshot: The author makes a strong plea for second-order science but somehow mathematics remains out of focus. The major claim of this commentary is that second-order science requires second-order mathematics.