Reduction in Physical Science

The potential reducibility of chemical entities to their physical bases is a matter of dispute between ontological reductionists on one hand, and emergentists on the other. However, relevant debates typically revolve around the reducibility of so-called ‘higher-level’ chemical entities, such as molecules. Perhaps surprisingly, even committed proponents of emergence for these higher-level chemical entities appear to accept that the ‘lowest-level’ chemical entities – atomic species – are reducible to their physical bases. In particular, the microstructural view of chemical elements, actively (...) developed and defended by emergentists, appears to hold that the explanatory power of nuclear charge justifies being reductionist about atomic species. My first task in this paper is to establish that nuclear charge cannot ultimately provide explanations sufficient to justify a reductionist approach to atomic species, unless we abandon the persuasive intuition that the presence of an element in a substance ought to explain the properties of that substance. The ‘missing piece’ for explaining the properties of substances by way of their elemental constituents is the electronegativity values of participant atoms. But electronegativity is a strikingly disunified concept that appears distinctly unamenable to analysis by way of fundamental physical principles. Through evaluating the uncertain physical identity of electronegativity, as well as its widespread and indispensable epistemic utility in chemical practice, I argue that electronegativity provides compelling grounds to seriously consider emergence for atomic species. (shrink)

Gravitation is interpreted to be an “ontomathematical” force or interaction rather than an only physical one. That approach restores Newton’s original design of universal gravitation in the framework of “The Mathematical Principles of Natural Philosophy”, which allows for Einstein’s special and general relativity to be also reinterpreted ontomathematically. The entanglement theory of quantum gravitation is inherently involved also ontomathematically by virtue of the consideration of the qubit Hilbert space after entanglement as the Fourier counterpart of pseudo-Riemannian space. Gravitation can be (...) also interpreted as purely mathematical or logical “force” or “interaction” as a corollary from its ontomathematical (rather than physical) realization. The ontomathematical approach to gravitation is implicit in general relativity equating it to operators in pseudo-Riemannian space obeying the Einstein field equation and also well-known by the “geometrization of physics”. Quantum mechanics shares the same by the separable complex Hilbert space and defining “physical quantity” by the Hermitian operators on it. One can interpret special Minkowski space involved by special relativity and the qubit Hilbert space of quantum information as Fourier counterparts immediately noticing that general relativity means gravitation as the Fourier counterpart of non-Hermitian operators implying non-unitarity and the violation of energy conservation and thus destroying Pauli’s particle paradigm. Since the Standard model obeys it, this explains the impossibility of “quantum gravitation” in any framework conservatively generalizing the Standard model so that it would include gravitation along with electromagnetic, weak, and strong interactions. Einstein’s geometrization of gravitation can be continued into a purely mathematical theory of it following Euclid’s realization for geometry to be exhaustively built in a deductive and axiomatic way as well as Riemann’s parametrization of all the class of Euclidean and non-Euclidean geometries by “space curvature”, then being generalized to Minkowski space as the operators on pseudo-Riemannian space as the Einstein field equation means gravitation. The transition from mathematical gravitation to logical one can rely on the historical lesson of the pair of Lobachevski’s and Riemann’s approaches now “reversely”, i.e., from the latter to the former. Logical gravitation is linkable to Hegel’s dialectical logic and ontological dialectics abandoning their interpretations as a new zero logic substituting classical propionyl logic. The approach of ontomathematics generalizing that of ontology, traceable even to Aristotle’s reformation of Plato’s doctrine, needs Hegel’s doctrine to be formalized as a first-order logic naturally containing Boolean algebra, isomorphic to both classical propositional logic and set theory being the class of all first-order logics, as a sub-logic along with Peano arithmetic as another sub-logic. The first-order logic at issue is called Hilbert arithmetic and elaborated in detail in other papers. It allows for both self-foundation of mathematics to be internally proved as complete and furthermore, quantum mechanics reinterpreted as quantum information to be included by the qubit Hilbert space interpretable in turn as a dual and physical counterpart of Hilbert arithmetic in a narrow sense, that is, both counterparts constitute Hilbert arithmetic in a wide sense, being mathematical and physical simultaneously and thus overcoming the Cartesian dualism of “body” gapped from “mind” by an abyss. Then, the proper philosophical interpretation of gravitation to be the fundamental ontomathematical force or interaction overcomes the ridiculous belief of the Big Bang wrongly alleged to be a scientific theory. Ontomathematical gravitation suggests an omnipresent and omnitemporal medium of “God’s” creation “ex nihilo” following only the natural necessity of quantum-information conservation particularly and locally manifested as energy conservation. (shrink)

Conventional wisdom holds that the von Neumann entropy corresponds to thermodynamic entropy, but Hemmo and Shenker (2006) have recently argued against this view by attacking von Neumann's (1955) argument. I argue that Hemmo and Shenker's arguments fail due to several misunderstandings: about statistical-mechanical and thermodynamic domains of applicability, about the nature of mixed states, and about the role of approximations in physics. As a result, their arguments fail in all cases: in the single-particle case, the finite particles case, and the (...) infinite particles case. (shrink)

The numerous and diverse roles of theory reduction in science have been insufficiently explored in the philosophy literature on reduction. Part of the reason for this has been a lack of attention paid to reduction2 (successional reduction)—although I here argue that this sense of reduction is closer to reduction1 (explanatory reduction) than is commonly recognised, and I use an account of reduction that is neutral between the two. This paper draws attention to the utility—and incredible versatility—of theory reduction. A non-exhaustive (...) list of various applications of reduction in science is presented, some of which are drawn from a particular case-study, being the current search for a new theory of fundamental physics. This case-study is especially interesting because it employs both senses of reduction at once, and because of the huge weight being put on reduction by the different research groups involved; additionally, it presents some unique uses for reduction—revealing, I argue, the fact that reduction can be of specialised and unexpected service in particular scientific cases. The paper makes two other general findings: that the functions of reduction that are typically assumed to characterise the different forms of the relation may instead be understood as secondary consequences of some other roles; and that most of the roles that reduction plays in science can actually also be fulfilled by a weaker relation than (the typical understanding of) reduction. (shrink)

The Emergic Cognitive Model (ECM) is a unified computational model of visual filling-in based on the Emergic Network architecture. The Emergic Network was designed to help realize systems undergoing continuous change. In this thesis, eight different filling-in phenomena are demonstrated under a regime of continuous eye movement (and under static eye conditions as well). -/- ECM indirectly demonstrates the power of unification inherent with Emergic Networks when cognition is decomposed according to finer-grained functions supporting change. These can interact to raise (...) additional emergent behaviours via cognitive re-use, hence the Emergic prefix throughout. Nevertheless, the model is robust and parameter free. Differential re-use occurs in the nature of model interaction with a particular testing paradigm. -/- ECM has a novel decomposition due to the requirements of handling motion and of supporting unified modelling via finer functional grains. The breadth of phenomenal behaviour covered is largely to lend credence to our novel decomposition. -/- The Emergic Network architecture is a hybrid between classical connectionism and classical computationalism that facilitates the construction of unified cognitive models. It helps cutting up of functionalism into finer-grains distributed over space (by harnessing massive recurrence) and over time (by harnessing continuous change), yet simplifies by using standard computer code to focus on the interaction of information flows. Thus while the structure of the network looks neurocentric, the dynamics are best understood in flowcentric terms. Surprisingly, dynamic system analysis (as usually understood) is not involved. An Emergic Network is engineered much like straightforward software or hardware systems that deal with continuously varying inputs. Ultimately, this thesis addresses the problem of reduction and induction over complex systems, and the Emergic Network architecture is merely a tool to assist in this epistemic endeavour. -/- ECM is strictly a sensory model and apart from perception, yet it is informed by phenomenology. It addresses the attribution problem of how much of a phenomenon is best explained at a sensory level of analysis, rather than at a perceptual one. As the causal information flows are stable under eye movement, we hypothesize that they are the locus of consciousness, howsoever it is ultimately realized. (shrink)

The second half of the twentieth century offers distinct perspectives for the historian of science. The role of the State, the expansion of certain industries and the cultural engagement with science were all transformed. The foregrounding of certain strands of physical science in the public and administrative consciousness – nuclear physics and planetary science, for example – had a complement: the ‘backgrounding’ or institutional neglect of a number of other fields. My work in the history of the physical sciences has (...) focused on this little-noticed intellectual terrain, and could be categorised into several types of case study that share distinct research questions, conceptual understandings and historiographical ramifications. -/- My focus is physical sciences that have been identified as peripheral, if categorised at all, by a previous generation of historians of physics. By this I do not mean peripheral in the geographic sense, but marginal, interstitial or boundary-crossing in the context of occupations, disciplines and professions. The types of case study investigated include (i) scientific instruments; (ii) emergent professions or would-be professions; and, (iii) subject areas falling between academic science, industrial application and State interests. (shrink)