Interlevel Relations in Physical Science

Functional reductionism characterises inter-theoretic reduction as the recovery of the upper-level behaviour described by the reduced theory in terms of the lower-level reducing theory. For instance, finding a statistical mechanical realiser that plays the functional role of thermodynamic entropy allows for establishing a reductive link between thermodynamics and statistical mechanics. This view constitutes a unique approach to reduction that enjoys a number of positive features, but has received limited attention in the philosophy of science. -/- This paper aims to clarify (...) the meaning of functional reductionism in science, with a focus on physics, to define both its place with respect to other approaches to reduction and its connection to ontology. To do so, we develop and explore two alternative frameworks for functional reduction, called Syntactic Functional Reductionism and Semantic Functional Reductionism. They represent two different possible stances on the view that expand and improve the basic functional reductionist approach along different lines, and make clear how the approach works in practice. The former elaborates on David Lewis’ account, is connected with the syntactic view of theories, is committed to a logical characterisation of functional roles, and is embedded within Nagelian reductionism. The latter adopts a semantic view of theories, spells out functional roles mainly in terms of mathematical roles within the models of theories, and is expressed in terms of the related structuralist approach to reduction. The development of these frameworks has the final goal of advancing functional reductionism, to make it a fully-fledged alternative account for reduction in science. (shrink)

Several approaches to developing a theory of quantum gravity suggest that spacetime—as described by general relativity—is not fundamental. Instead, spacetime is supposed to be explained by reference to the relations between more fundamental entities, analogous to `atoms' of spacetime, which themselves are not (fully) spatiotemporal. Such a case may be understood as emergence of \textit{content}: a `hierarchical' case of emergence, where spacetime emerges at a `higher', or less-fundamental, level than its `lower-level' non-spatiotempral basis. But quantum gravity cosmology also presents us (...) with the possibility of emergence of \textit{context}: where spacetime emerges from some `prior' non-spatiotemporal state (replacing the Big Bang), due to particular conditions in the early universe. I present a general conception of emergence which is plausibly able to accommodate both pictures. This is a positive conception that does not rely on a failure of reduction or explanation in any sense (indeed, reduction is a necessary feature of quantum gravity, and is useful in understanding emergence in this case). I also consider the possibility that the distinction between content- and context- based explanations is blurred, or usefully `collapsed', in the case of spacetime emergence. (shrink)

While the predominant focus of the philosophical literature on scientific modeling has been on single-scale models, most systems in nature exhibit complex multiscale behavior, requiring new modeling methods. This challenge of modeling phenomena across a vast range of spatial and temporal scales has been called the tyranny of scales problem. Drawing on research in the geosciences, I synthesize and analyze a number of strategies for taming this tyranny in the context of conceptual, physical, and mathematical modeling. This includes several strategies (...) that can be deployed in physical modeling, even when strict dynamical scaling fails. In all cases, I argue that having an adequate conceptual model—given both the nature of the system and the particular purpose of the model—is essential. I draw a distinction between depiction and representation, and use this research in the geosciences to advance a number of debates in the philosophy of modeling. (shrink)

How superposition explains the human mind. And, also, the Universe.

Conservation of a circle is the basis for unification (and, also, then, 'unitization'). Explaining and unifying physics, philosophy, and psychology. All disciplines.

This conclusion indicates exactly my EDWs!!! So, the framework is UNBELIEVABLE similar to my EDWs! The authors avoid any contradiction introducing the “theory of causal witnesses” that represent the correspondences between EDWs, no more or less!!!

I develop an account of naturalness in physics which demonstrates that naturalness assumptions are not restricted to narrow cases in high-energy physics but are a ubiquitous part of how interlevel relations are derived in physics. After exploring how and to what extent we might justify such assumptions on methodological grounds or through appeal to speculative future physics, I consider the apparent failure of naturalness in cosmology and in the Standard Model. I argue that any such naturalness failure threatens to undermine (...) the entire structure of our understanding of intertheoretic reduction, and so risks a much larger crisis in physics than is sometimes suggested; I briefly review some currently-popular strategies that might avoid that crisis. (shrink)

In seeking an answer to the question of what it means for a theory to be fundamental, it is enlightening to ask why the current best theories of physics are not generally believed to be fundamental. This reveals a set of conditions that a theory of physics must satisfy in order to be considered fundamental. Physics aspires to describe ever deeper levels of reality, which may be without end. Ultimately, at any stage we may not be able to tell whether (...) we've reached rock bottom, or even if there is a base level – nevertheless, I draft a checklist to help us identify when to stop digging, in the case where we may have reached a candidate for a final theory. Given that the list is – according to (current) mainstream belief in high-energy physics – complete, and each criterion well-motivated, I argue that a physical theory that satisfies all the criteria can be assumed to be fundamental in the absence of evidence to the contrary (i.e., I argue that the necessary conditions are jointly sufficient for a claim of fundamentality in physics). (shrink)

The issue of shifting scales between the microscopic and the macroscopic dimensions is a recurrent one in the history of science, and in particular the history of microscopy. But it took on new dimensions in the context of early twentieth-century microscophysics, with the progressive realisation that the physical laws governing the macroscopic world were not always adequate for describing the sub-microscopic one. The paper focuses on the researches of Jean Perrin in the 1900s, in particular his use of Brownian motion (...) to produce evidence of the existence of atoms and in favour of the kinetic theory. His results were described by many contemporaries, and subsequently by historians, as the first direct proof of atomic and molecular reality. The paper examines the different strategies developed by Perrin for bridging the macro and sub-microphysical realms and making the latter accessible to the senses; even though neither atoms nor molecules were ever actually seen, and in fact very few visual representations were shown and published in connection with these experiments. This case provides a good example of how visualizing, representing and convincing could be interwoven in the production of evidence about the sub-microphysical realm circa 1900.Keywords: Jean Perrin; Brownian motion; Ultramicroscope; Evidence; Atom; Atomism. (shrink)

In recent years, a change in attitude in particle physics has led to our understanding current quantum field theories as effective field theories. The present paper is concerned with the significance of this EFT approach, especially from the viewpoint of the debate on reductionism in science. In particular, it is a purpose of this paper to clarify how EFTs may provide an interesting case-study in current philosophical discussion on reduction, emergence and inter-level relationships in general.

Contrary to the widespread belief, the problem of the emergence of classical mechanics from quantum mechanics is still open. In spite of many results on the ¯h → 0 asymptotics, it is not yet clear how to explain within standard quantum mechanics the classical motion of macroscopic bodies. In this paper we shall analyze special cases of classical behavior in the framework of a precise formulation of quantum mechanics, Bohmian mechanics, which contains in its own structure the possibility of describing (...) real objects in an observer-independent way. (shrink)

We examine some assumptions about the nature of 'levels of reality' in the light of examples drawn from physics. Three central assumptions of the standard view of such levels (for instance, Oppenheim and Putnam 1958) are (i) that levels are populated by entities of varying complexity, (ii) that there is a unique hierarchy of levels, ranging from the very small to the very large, and (iii) that the inhabitants of adjacent levels are related by the parthood relation. Using examples from (...) physics, we argue that it is more natural to view the inhabitants of levels as the behaviors of entities, rather than entities themselves. This suggests an account of reduction between levels, according to which one behavior reduces to another if the two are related by an appropriate limit relation. By considering cases where such inter-level reduction fails, we show that the hierarchy of behaviors differs in several respects from the standard hierarchy of entities. In particular, while on the standard view, lower-level entities are 'micro' parts of higher-level entities, on our view, a system's macro-level behavior can be seen as a ('non-spatial') part of its micro-level behavior. We argue that this second hierarchy is not really in conflict with the standard view and that it better suits examples of explanation in science. (shrink)

It has been a longstanding problem to show how the irreversible behaviour of macroscopic systems can be reconciled with the time-reversal invariance of these same systems when considered from a microscopic point of view. A result by Lanford shows that, under certain conditions, the famous Boltzmann equation, describing the irreversible behaviour of a dilute gas, can be obtained from the time-reversal invariant Hamiltonian equations of motion for the hard spheres model. Here, we examine how and in what sense Lanford’s theorem (...) succeeds in deriving this remarkable result. Many authors have expressed different views on the question which of the ingredients in Lanford’s theorem is responsible for the emergence of irreversibility. We claim that these interpretations miss the target. In fact, we argue that there is no time-asymmetric ingredient at all. (shrink)

It is an experimental fact that \ -decays produce in a cloud chamber at most one track and that this track points in a random direction. This seems to contradict the description of decay in Quantum Mechanics: according to Gamow a spherical wave is produced and moves radially according to Schrödinger’s equation. It is as if the interaction with the supersaturated vapor turned the wave into a particle. The aim of this note is to place this effect in the context (...) of Schrödinger’s Quantum Mechanics. We shall see that the properties of the initial wave function suggest the introduction of a semiclassical formalism in which the \ -wave can be described as a collection of semiclassical wavelets; each of them interacts with an atom and forms an entangled state. The interaction can be regarded as a semiclassical inelastic scattering event. The measurement selects the wave function of one of the ions, with a probability given by Born’s rule. This ion interacts with the atoms nearby leading to the formation of a droplet. One can reasonably assume that also the wavelet entangled with the selected ion has probability one to remain as part of the description of the system. The measurement process is therefore represented by a unitary operator. The wavelet remains sharply localized on a classical path \ It is still a probability wave: it determines the probability that another atom be ionized. This probability is essentially zero unless the atom lies on \ . This gives the visible track. (shrink)

In previous work, I described several examples combining reduction and emergence: where reduction is understood a la Ernest Nagel, and emergence is understood as behaviour that is novel. Here, my aim is again to reconcile reduction and emergence, for a case which is apparently more problematic than those I treated before: renormalization. My main point is that renormalizability being a generic feature at accessible energies gives us a conceptually unified family of Nagelian reductions. That is worth saying since philosophers tend (...) to think of scientific explanation as only explaining an individual event, or perhaps a single law, or at most deducing one theory as a special case of another. Here we see a framework in which there is a space of theories endowed with enough structure that it provides a family of reductions. (shrink)

We propose a group-theoretical interpretation of the fact that the transition from classical to quantum mechanics entails a reduction in the number of observables needed to define a physical state and \ to \ or \ in the simplest case). We argue that, in analogy to gauge theories, such a reduction results from the action of a symmetry group. To do so, we propose a conceptual analysis of formal tools coming from symplectic geometry and group representation theory, notably Souriau’s moment (...) map, the Mardsen–Weinstein symplectic reduction, the symplectic “category” introduced by Weinstein, and the conjecture according to which “quantization commutes with reduction”. By using the generalization of this conjecture to the non-zero coadjoint orbits of an abelian Hamiltonian action, we argue that phase invariance in quantum mechanics and gauge invariance have a common geometric underpinning, namely the symplectic reduction formalism. This stance points towards a gauge-theoretical interpretation of Heisenberg indeterminacy principle. We revisit this principle in the light of the difference between the set-theoretic points of a phase space and its category-theoretic symplectic points. (shrink)

The fundamental concept of structured chemical system has been introduced and analysed in this paper. This concept, as in biology but not in physics, is very important in chemistry. In fact, the main chemical concepts (molecule and compound) have been identified as systemic concepts and their use in chemical explanation can only be justified in this approach. The fundamental concept of “environment” has been considered and then the system concept in mechanics, chemistry and biology. The differences and the analogies between (...) the use of the systemic approach in these disciplines have been analyzed and correlated to the general problem of reductionism and complexity perspectives. The inanimate–animate dichotomy can be reconsidered in this new approach. Since the chemical systemic concepts of molecule and compound can be dated to the nineteenth century, chemistry can be considered the first true systemic science and its historical evolution can be a model for other sciences (such as the humanities) where the systemic concepts are important. (shrink)

In resisting attempts to explain the unity of a whole in terms of a multiplicity of interacting parts, quantum mechanics calls for an explanatory concept that proceeds in the opposite direction: from unity to multiplicity. Being part of the Scientific Image of the world, the theory concerns the process by which (the physical aspect of) what Sellars called the Manifest Image of the world comes into being. This process consists in the progressive differentiation of an intrinsically undifferentiated entity. By entering (...) into reflexive spatial relations, this entity gives rise to (i) what looks like a multiplicity of relata if the reflexive quality of the relations is not taken into account, and (ii) what looks like a substantial expanse if the spatial quality of the relations is reified. If there is a distinctly quantum domain, it is a non-spatial and non-temporal dimension across which the transition from the unity of this entity to the multiplicity of the world takes place. Instead of being constituents of the physical world, subatomic particles, atoms, and molecules are instrumental in its manifestation. These conclusions are based on the following interpretive principle and its more direct consequences: whenever the calculation of probabilities calls for the addition of amplitudes, the distinctions we make between the alternatives lack objective reality. Applied to alternatives involving distinctions between regions of space, this principle implies that, owing to the indefiniteness of positions, the spatiotemporal differentiation of the physical world is incomplete: the existence of a real-valued spatiotemporal background is an unrealistic idealization. This guarantees the existence of observables whose values are real per se, as against “real by virtue of being indicated by the values of observables that are real per se.” Applied to alternatives involving distinctions between things, it implies that, intrinsically, all fundamental particles are numerically identical and thus identifiable with the aforementioned undifferentiated entity. (shrink)

We define a new class of pseudo effect algebras, called kite pseudo effect algebras, which is connected with partially ordered groups not necessarily with strong unit. In such a case, starting even with an Abelian po-group, we can obtain a noncommutative pseudo effect algebra. We show how such kite pseudo effect algebras are tied with different types of the Riesz Decomposition Properties. Kites are so-called perfect pseudo effect algebras, and we define conditions when kite pseudo effect algebras have the least (...) non-trivial normal ideal. (shrink)

Physics and chemistry underlie the nature of all the world around us, including human brains. Consequently some suggest that in causal terms, physics is all there is. However, we live in an environment dominated by objects embodying the outcomes of intentional design (buildings, computers, teaspoons). The present day subject of physics has nothing to say about the intentionality resulting in existence of such objects, even though this intentionality is clearly causally effective. This paper examines the claim that the underlying physics (...) uniquely causally determines what happens, even though we cannot predict the outcome. It suggests that what occurs is the contextual emergence of complexity: the higher levels in the hierarchy of complexity have autonomous causal powers, functionally independent of lower level processes. This is possible because top-down causation takes place as well as bottom-up action, with higher level contexts determining the outcome of lower level functioning and even modifying the nature of lower level constituents. Stored information plays a key role, resulting in non-linear dynamics that is non-local in space and time. Brain functioning is causally affected by abstractions such as the value of money and the theory of the laser. These are realised as brain states in individuals, but are not equivalent to them. Consequently physics per se cannot causally determine the outcome of human creativity, rather it creates the possibility space allowing human intelligence to function autonomously. The challenge to physics is to develop a realistic description of causality in truly complex hierarchical structures, with top-down causation and memory effects allowing autonomous higher levels of order to emerge with genuine causal powers. (shrink)

Laws of mechanics, quantum mechanics, electromagnetism, gravitation and relativity are derived as “related mathematical identities” based solely on the existence of a joint probability distribution for the position and velocity of a particle moving on a Riemannian manifold. This probability formalism is necessary because continuous variables are not precisely observable. These demonstrations explain why these laws must have the forms previously discovered through experiment and empirical deduction. Indeed, the very existence of electric, magnetic and gravitational fields is predicted by these (...) purely mathematical constructions. Furthermore these constructions incorporate gravitation into special relativity theory and provide corrected definitions for coordinate time and proper time. These constructions then provide new insight into the relationship between manifold geometry and gravitation and present an alternative to Einstein’s general relativity theory. (shrink)

As an approach to a Theory of Everything a framework for developing a coherent theory of mathematics and physics together is described. The main characteristic of such a theory is discussed: the theory must be valid and and sufficiently strong, and it must maximally describe its own validity and sufficient strength. The mathematical logical definition of validity is used, and sufficient strength is seen to be a necessary and useful concept. The requirement of maximal description of its own validity and (...) sufficient strength may be useful to reject candidate coherent theories for which the description is less than maximal. Other aspects of a coherent theory discussed include universal applicability, the relation to the anthropic principle, and possible uniqueness. It is suggested that the basic properties of the physical and mathematical universes are entwined with and emerge with a coherent theory. Support for this includes the indirect reality status of properties of very small or very large far away systems compared to moderate sized nearby systems. Discussion of the necessary physical nature of language includes physical models of language and a proof that the meaning content of expressions of any axiomatizable theory seems to be independent of the algorithmic complexity of the theory. Gödel maps seem to be less useful for a coherent theory than for purely mathematical theories because all symbols and words of any language must have representations as states of physical systems already in the domain of a coherent theory. (shrink)

We present a model that allows one to build structures that evolve continuously from classical to quantum, and we study the intermediate situations, giving rise to structures that are neither classical nor quantum. We construct the closure structure corresponding to the collection of eigenstate sets of these intermediate situations, and demonstrate how the superposition principle disappears during the transition from quantum to classical. We investigate the validity of the axioms of quantum mechanics for the intermediate situations.

This article, written in honor of Fritz Rohrlich, briefly surveys the role of topology in physics.

Computers provide tools suprisingly effective in analyzing physical processes. The interaction of analytical and computer methods of physical research has been synergistic. Examples are given of the conceptual advances which have been spurred by the interaction of computer and classical analysis. It is argued that a new age in physical research is beginning and that the power of computer tools has scarcely been tapped.

Having known classical wave optics and wave mechanics, can we reverse Schrödinger's path and extend the concept of families of rays of light to provide a new exact rendering of quantum optics including the Bose nature of photons? This question is answered in the affirmative, and the implications of the Bose symmetry for certain nonlocal correlations of the many-ray distribution functions are worked out. The similarities and the differences between classical and quantum wave optics are brought out. The ray-ray Bose (...) correlation is analyzed. The generating functional for the many-ray distribution functions is formulated; and the notion of paraxial illumination for quantum optics is made precise. (shrink)

This is a further development of the author's paper “A Unified Theory of Biology and Physics.” It is found that male and female in biology, as well as particle and antiparticle in physics, are analogues of symmetrical sideband pairs in communication theory. This gives a new point of view from which to investigate the significance and characteristics of these different paired entities.These findings are intimately related to the fact that there are two transform domains of representation of entities in all (...) the cases involved. They are the somatic and the genetic domains in biology, the configuration domain and the domain of conserved observables in physics, and the time and frequency domains in communication. (shrink)

It is shown by means of general principles and specific examples that, contrary to a long-standing misconception, the modern mathematical physics of compressible fluid dynamics provides a generally consistent and efficient language for describing many seemingly fundamental physical phenomena. It is shown to be appropriate for describing electric and gravitational force fields, the quantized structure of charged elementary particles, the speed of light propagation, relativistic phenomena, the inertia of matter, the expansion of the universe, and the physical nature of time. (...) New avenues and opportunities for fundamental theoretical research are thereby illuminated. (shrink)

The cell theory of Schleiden and Schwann is generalized to the effect that throughout the natural world, in physics, biology, and sociopsychology, there is a widespread phenomenon of the existence of organized cells, whose organization is usually protected by barriers. These barriers exist not only in space, but in time and even in other domains. These barriers typically not only protect the organization within the cell from external disturbance, but they actively participate in reducing the internal disorganization. It appears that (...) the quantum phase cell or its equivalent, the discrete quantum state, may be a physical analog of the organized biological cell. The sampling and ambiguity theorems of communication theory throw new light on phase cells. The quantum phase cell has both configuration and momentum elements, which are analogous respectively to the somatic elements in the cytoplasm of a cell and the genetic elements in the DNA. A biological cell or organism, a physical quantum state, and a human being as a sociopsychological entity each has a natural individuality. A natural individuality is a somewhat mysterious thing, since in addition to specificity, it also involves stochasticity and complementarity. There are some striking and unexplained spin-analog characteristics in biology which have a relation to boson- and fermion-analog characteristics in biology that corresponds with the known relation in physics. The hypothesis suggested in our earlier paper, that quantum mechanical entropy is diminished in interaction, is clarified and sharpened in this paper. (shrink)

The known facts of quantum physics and biology strongly suggest the following hypotheses: atoms and the fundamental particles have a rudimentary degree of consciousness, volition, or self-activity; the basic features of quantum mechanics are a result of this fact; the quantum mechanical wave properties of matter are actually the conscious properties of matter; and living organisms are a direct result of these properties of matter. These hypotheses are tested by using them to make detailed predictions of new facts, and then (...) by showing that the predictions can be verified. The hypotheses are used to predict successfully that the quantum wave properties of matter are strongly predominant in proteins, to explain the presence and relative abundance of carbon, hydrogen, nitrogen, oxygen, phosphorus, and sulfur in proteins, and to explain diffraction phenomena, the behavior of helium II, the exclusion principle, and causality and determinism in modern science, thus closely relating physics and biology. (shrink)

We show how effect algebras arise in physics and how they can be used to tie together the observables, states and symmetries employed in the study of physical systems. We introduce and study the unifying notion of an effect-observable-state-symmetry-system (EOSS-system) and give both classical and quantum-mechanical examples of EOSS-systems.

The problem of how mathematics and physics are related at a foundational level is of interest. The approach taken here is to work towards a coherent theory of physics and mathematics together by examining the theory experiment connection. The role of an implied theory hierarchy and use of computers in comparing theory and experiment is described. The main idea of the paper is to tighten the theory experiment connection by bringing physical theories, as mathematical structures over C, the complex numbers, (...) closer to what is actually done in experimental measurements and computations. The method replaces C by C n which is the set of pairs, R n,I n, of n figure rational numbers in some basis. The properties of these numbers are based on those of numerical measurement outcomes for continuous variables. A model of space and time based on R n is discussed. The model is scale invariant with regions of constant step size interrupted by exponential jumps. A method of taking the limit n→∞ to obtain locally flat continuum-based space and time is outlined. Also R n based space is invariant under scale transformations. These correspond to expansion and contraction of space relative to a flat background. The location of the origin, which is a space and time singularity, does not change under these transformations. Some properties of quantum mechanics, based on C n and on R n space are briefly investigated. (shrink)

Explanations in physics commonly appeal to data drawn from different length or time scales, as when a “top-down” macroscopic constraint such as rigidity is used to evade the complexities one would confront in attempting to model the situation in a purely “bottom-up” fashion. Such techniques commonly embody rather complex shifts in explanatory strategy.

What is the role of bridge laws in inter-theoretic relations? An assumption shared by many views about these relations is that bridge laws enable reductions. In this article, I acknowledge the naturalness of this assumption, but I question it by presenting a context within thermal physics (involving phase transitions) in which the bridge laws, puzzlingly, seem to contribute to blocking the reduction.

The question is how do Scanning Electron Microscopes (SEMs) give us access to the nano world? The images these instruments produce, I argue, do not allow us to see atoms in the same way that we see trees. To the extent that SEMs and STMs allow us to see the occupants of the nano world it is by way of metaphorical extension of the concept of “seeing”. The more general claim is that changes in scientific instrumentation effect changes in the (...) concepts central to our understanding of scientific results. (shrink)

Symplectic reduction is a formal process through which degeneracy within the mathematical representations of physical systems displaying gauge symmetry can be controlled via the construction of a reduced phase space. Typically such reduced spaces provide us with a formalism for representing both instantaneous states and evolution uniquely and for this reason can be justifiably afforded the status of fun- damental dynamical arena - the otiose structure having been eliminated from the original phase space. Essential to the application of symplectic reduction (...) is the precept that the first class constraints are the relevant gauge generators. This prescription becomes highly problematic for reparameterization invariant theories within which the Hamiltonian itself is a constraint; not least because it would seem to render prima facie distinct stages of a history physically identical and observable functions changeless. Here we will consider this problem of time within non-relativistic me- chanical theory with a view to both more fully understanding the temporal struc- ture of these timeless theories and better appreciating the corresponding issues in relativistic mechanics. For the case of nonrelativistic reparameterization invariant theory application of symplectic reduction will be demonstrated to be both unnec- essary; since the degeneracy involved is benign; and inappropriate; since it leads to a trivial theory. With this anti-reductive position established we will then examine two rival methodologies for consistently representing change and observable func- tions within the original phase space before evaluating the relevant philosophical implications. We will conclude with a preview of the case against symplectic re- duction being applied to canonical general relativity. (shrink)

The autonomy of chemistry and the legitimacy of the philosophy of chemistry are usually discussed in the context of the issue of reduction of chemistry to physics, and defended making use of the failure of reductionistic claims. Until quite recent times a rather widespread viewpoint was, however, that the failure of reductionistic claims concerns actually epistemological aspect of reduction only, but the ontological reduction of chemistry to physics cannot be denied. The new problems of the autonomy of chemistry in the (...) context of reductionism seem to be ontological and metaphysical. In the present paper it is argued that there is no need for some kind of metaphysical-ontological underpinning for rejection of the secondary positions of chemistry and philosophy of chemistry with respect to physics and philosophy of physics. The issue can be elucidated in terms of the philosophy of science accepting practical realism (also known by other names). (shrink)

Sir Karl Popper is one of the few authors to have discussed the reduction of chemistry. His approach consists of what I term naturalistic reduction, which I suggest bears close similarities to the way in which scientists regard reduction. The present article aims to build on Popper's insights into the nature of reduction in science and more specifically to suggest an approach to characterizing a specific sense of the notion of approximate reduction in the context of chemistry. In the course (...) of the discussion, one of Popper's better known passages on the reduction of chemistry is analysed in some detail. (shrink)

This document is a synopsis of discussions at the workshop prepared by Nicholaos Jones and Kevin Coffey, with remarks added by by Chuang Liu, John D. Norton, John Earman, Gordon Belot, Mark Wilson, Bob Batterman and Margie Morrison. The program is included in an appendix.

I argue that the distinctions Robert Batterman (2004) presents between ‘epistemically fundamental’ versus ‘ontologically fundamental’ theoretical approaches can be subsumed by methodologically fundamental procedures. I characterize precisely what is meant by a methodologically fundamental procedure, which involves, among other things, the use of multilinear graded algebras in a theory’s formalism. For example, one such class of algebras I discuss are the Clifford (or Geometric) algebras. Aside from their being touted by many as a “unified mathematical language for physics,” (Hestenes (1984, (...) 1986) Lasenby, et. al. (2000)) Finkelstein (2001, 2004) and others have demonstrated that the techniques of multilinear algebraic ‘expansion and contraction’ exhibit a robust regularizablilty. That is to say, such regularization has been demonstrated to remove singularities, which would otherwise appear in standard field-theoretic, mathematical characterizations of a physical theory. I claim that the existence of such methodologically fundamental procedures calls into question one of Batterman’s central points, that “our explanatory physical practice demands that we appeal essentially to (infinite) idealizations” (2003, 7) exhibited, for example, by singularities in the case of modeling critical phenomena, like fluid droplet formation. By way of counterexample, in the field of computational fluid dynamics (CFD), I discuss the work of Mann & Rockwood (2003) and Gerik Scheuermann, (2002). In the concluding section, I sketch a methodologically fundamental procedure potentially applicable to more general classes of critical phenomena appearing in fluid dynamics. (shrink)