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The debate over the explanatory nature of cognitive models has been waged mostly between two factions: the mechanists and the dynamical systems theorists. The former hold that cognitive models are explanatory only if they satisfy a set of mapping criteria, particularly the 3M/3m* requirement. The latter have argued, pace the mechanists, that some cognitive models are both dynamical and constitute covering-law explanations. In this paper, I provide a minimal model interpretation of dynamical cognitive models, arguing that this both provides needed (...) |
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Recently, many have argued that there are certain kinds of abstract mathematical explanations that are noncausal. In particular, the irrelevancy approach suggests that abstracting away irrelevant causal details can leave us with a noncausal explanation. In this paper, I argue that the common example of Renormalization Group explanations of universality used to motivate the irrelevancy approach deserves more critical attention. I argue that the reasons given by those who hold up RG as noncausal do not stand up to critical scrutiny. (...) |
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This paper presents an in-depth analysis of the anatomy of both thermodynamics and statistical mechanics, together with the relationships between their constituent parts. Based on this analysis, using the renormalization group and finite-size scaling, we give a definition of a large but finite system and argue that phase transitions are represented correctly, as incipient singularities in such systems. We describe the role of the thermodynamic limit. And we explore the implications of this picture of critical phenomena for the questions of (...) |
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Analogies between classical statistical mechanics and quantum field theory played a pivotal role in the development of renormalization group methods for application in the two theories. This paper focuses on the analogies that informed the application of RG methods in QFT by Kenneth Wilson and collaborators in the early 1970's. The central task that is accomplished is the identification and analysis of the analogical mappings employed. The conclusion is that the analogies in this case study are formal analogies, and not (...) |
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Further arguments are offered in defence of the position that the variant of quantum field theory (QFT) that should be subject to interpretation and foundational analysis is axiomatic quantum field theory. I argue that the successful application of renormalization group (RG) methods within alternative formulations of QFT illuminates the empirical content of QFT, but not the theoretical content. RG methods corroborate the point of view that QFT is a case of the underdetermination of theory by empirical evidence. I also urge (...) |
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This is a companion to another paper. Together they rebut two widespread philosophical doctrines about emergence. The first, and main, doctrine is that emergence is incompatible with reduction. The second is that emergence is supervenience; or more exactly, supervenience without reduction.In the other paper, I develop these rebuttals in general terms, emphasising the second rebuttal. Here I discuss the situation in physics, emphasising the first rebuttal. I focus on limiting relations between theories and illustrate my claims with four examples, each (...) |
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Phase transitions are an important instance of putatively emergent behavior. Unlike many things claimed emergent by philosophers, the alleged emergence of phase transitions stems from both philosophical and scientific arguments. Here we focus on the case for emergence built from physics, in particular, arguments based upon the infinite idealization invoked in the statistical mechanical treatment of phase transitions. After teasing apart several challenges, we defend the idea that phase transitions are best thought of as conceptually novel, but not ontologically or (...) |
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In another paper, one of us argued that emergence and reduction are compatible, and presented four examples illustrating both. The main purpose of this paper is to develop this position for the example of phase transitions. We take it that emergence involves behaviour that is novel compared with what is expected: often, what is expected from a theory of the system's microscopic constituents. We take reduction as deduction, aided by appropriate definitions. Then the main idea of our reconciliation of emergence (...) |
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