Explanatory boundaries

We seldom ask questions about the boundaries on explanation, yet arguably, these boundaries mark an essential feature of the modern scientific worldview the boundaries were quite different in ancient science. There are other boundaries that seem accidental or arbitrary, but perhaps are not. Chemists think it their business to explain why oxygen gas is diatomic, phosphorus gas polyatomic, and helium gas monatomic. The stabilities of these molecules are derivative, not fundamental, facts of chemistry. But the stability of the oxygen, or phosphorus, or helium atoms are not the subjects of chemical explanation at all. What determines our explanatory boundaries by discipline Is it pure historical accident, or a disparity of experimental techniques, or faith in a kind of logical "screening off," faith that, for example, the behavior of molecules would be the same no matter what the explanation of atomic stability ... 

Any scientific endeavor makes decisions about what sorts of theories to pursue and develop. Inevitably, some fundamental constraints are placed on what is judged to be legitimate or interesting content, as the preceding discussion of explanatory boundaries illustrates. Moreover, once the subject matter of a discipline has been settled, additional issues arise regarding how theories are, or should be, manifested in practice. All decisions of these sorts are ones of representation, and chemistry offers bountiful opportunity to explore not only the significance of representational choices for scientific inquiry but the very nature of representation itself. 

This contribution as a chapter in the special volume of ADVANCES IN QUANTUM CHEMISTRY on Confined Quantum Systems is focussed on (i) the hydrogen atom, (ii) confinement by conoidal boundaries, and (iii) semi-infinite spaces however, some of its discussions may extend their validity to other physical systems and to confinement in closed volumes. The limitations in the title are given as a point of reference, and also take into account that several of the other chapters deal with confinement in finite volumes. A semantic parenthesis is also appropriate and self-explanatory Compare conical curves (circles, ellipses, parabolas, hyperbolas and their radial asymptotes) with conoidal surfaces (spheres, spheroids, paraboloids, hyperboloids and their radial asymptotic cones). 

Unlike a fish out of water, a table of guideline values separated from its explanatory text does not die. Instead it takes on a new, unintentional and often undesirable life of its own. The numbers therein take on a significance far in excess of that for which they were intended contexts are lost, boundaries are forgotten and interpretations of exceedance become irrelevant. In the attempt to speed up, simplify or reduce the cost of risk assessment the magic number reigns. 

We present here some aspects of the surface chemistry and some explanatory models for vrater-polymer and related Interfaces. The term "poljrmer" will be taken to mean an essentially organic material, of sufficiently high molecular weight and (or) sufficiently cross-linked that a stiff (as opposed to fluid) phase is Involved. The material Is Insoluble In water, so that the term "water-polymer" Interface refers to what Is macroscopIcally an ordinary phase boundary. Typical polymers In the present context will be polytetrafluorethylene (PTFE), and polyethylene (PE). Solutions of macromolecules are thus not considered, nor is the related topic of so-called hydrophobic bonding, although some of what Is discussed here is relevant to that subject. 

At various points in the research cycle, as researchers inevitably encounter results that are somewhat different than expected, they will alter the ceteris paribus conditions, the explanatory model, the selection of relevant theories, the boundary conditions of the phenomena under scrutiny, even the standard operating procedures of their laboratory equipment. Essentially anything, whether theoretical or instrumental, that can be bent to its near-breaking point will be bent theory and model will be made to accommodate instruments and experiment design and vice versa, until expectations of acceptable experimental outcomes closely match actual experimental outcomes. 

N-DEs are the standard form of explanation in science and take the following form. Given a set of facts (e.g., initial and boundary conditions) and a set of laws (be they causes, processes, or outcomes see Bock 1993), both of which form the explanatory sentence, or explanans, a particular conclusion, or explanandum, follows (Hempel and Oppenheim 1948 Hempel 1965 335-338). N-DEs answer the question, how has a particular phenomenon [explanandum] occurred N-DEs apply to universal (nonlimited sets of phenomena) and... 

Full Mark (100%) General spreadsheet ahle to solve all problems with ability to cope with a range of boundary conditions and load histories as specified in self-explanatory input data. The spreadsheet will make good use of macros and some Visual Basic programming... 

Reduction reconciles diversity and directionality with strong unity. Diversity is descriptive, or conceptual in nature. Directionality is the directionality of explanatory dependence. Unity is cashed out in terms of identity. The direction of reduction depends upon features of the descriptions under which an object is presented by the expressions flanking the reduction predicate. These features of the descriptions under which an object is presented by the expressions flanking the reduction predicate can be captured by the notion of a property structure. This final chapter contains an outlook on the connection between reduction as conceived of here and the notion of a scientific level, physicalism, various forms of unification, grounding, and intervention. All these topics have been studied extensively the present chapter thus merely suggests that the so explicated notion can be used to illuminate some aspects of these topics that clearly transcend the boundaries of the various reduction-debates in the philosophy of mind and the philosophy of science. 

The proposed algorithm can be extended to n-revolute manipulator chains with no great additional efforts by using an extension of the formulation of Eqs.(8)-(10). As an explanatory example the case of four-revolute manipulators can be illustrated by using the workspace evaluation formulation proposed in [13]. In this case, a generalization of the workspace formulation can be deduced by considering that each boundary point of a three-revolute manipulator workspace will trace a torus when the first two joints in the chains are... 

NXgeli (1858 and later ) introduces the concept "micelle" for a polymolecular aggregate which has internal crystal structure the solid colloids are "Micellvcrbande", the sols "Micellarlosungen". In contrast to crystals which also have external crystal structure, they form non-stoichiometric compounds with the medium (water). Van Bemmelen (1877 and later ) has confirmed this latter point for many gels by the introduction of adsorption as the explanatory principle (he still speaks of absorption) in this case we therefore find the introduction of boundary surface phenomena. 

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