Mark Wilson presents a highly original and broad-ranging investigation of the way we get to grips with the world conceptually, and the way that philosophical problems commonly arise from this. He combines traditional philosophical concerns about human conceptual thinking with illuminating data derived from a large variety of fields including physics and applied mathematics, cognitive psychology, and linguistics. Wandering Significance offers abundant new insights and perspectives for philosophers of language, mind, and science, and will also reward the interest of psychologists, (...) linguists, and anyone curious about the mysterious ways in which useful language obtains its practical applicability. (shrink)
This article surveys the difficulties in establishing determinism for classical physics within the context of several distinct foundational approaches to the discipline. It explains that such problems commonly emerge due to a deeper problem of ‘missing physics'. The Problems of Formalism Norton's Example Three Species of Classical Mechanics 3.1 Mass point physics 3.2 The physics of perfect constraints 3.3 Continuum mechanics Conclusion CiteULike Connotea Del.icio.us What's this?
Let us begin with the simple observation that applied mathematics can be very tough! It is a common occurrence that basic physical principle instructs us to construct some syntactically simple set of differential equations, but it then proves almost impossible to extract salient information from them. As Charles Peirce once remarked, you can’t get a set of such equations to divulge their secrets by simply tilting at them like Don Quixote. As a consequence, applied mathematicians are often forced to pursue (...) roundabout and shakily rationalized expedients if any useful progress is to be made. Often these provisional and quasi-empirical procedures within applied mathematics loom large in motivating the “anti-realist” or “anti-unificationist” conclusions of Nancy Cartwright and allied authors. (shrink)
Motivated by contemporary debates concerning whether directors inappropriately deploy corporate funds for corporate political donations and the limited research into managerial influence on corporate political donations, we examine the impact of director influences from a network perspective. Using a sample of large listed Australian corporations and their political party donation activity during 2000–2007, we find that both the professional and non-professional networks of directors influence corporate political donations. We observe these influences in relation to donations at the federal and state (...) levels, and with respect to the choice of recipient political parties. (shrink)
Paul uses the hapax legomenon ίλαστήριον in Romans 3:25. Pauline scholars have discussed the background for Paul’s use of the word, whether from the LXX, Second Temple practice or pagan inscriptions. Two altars were found in the Asian city of Metropolis in the early 1990s with the dedication Καίσαρος ἱλαστηρίου. This article discusses their discovery, the history of Metropolis and the possible relationship of Paul to the city. It explores the date of the erection of the altars by establishing a (...) viable sitz im leben early in the reign of Augustus. It then traces the semantic history of the ίλαστήριον and attempts to establish its possible meaning within Pauline theology. Finally, the question whether ίλαστήριον should be added to the vocabulary of imperial ideology in Paul’s writings is addressed. (shrink)
There is considerable likelihood that Gottlob Frege began writing his Foundations of Arithmetic with the expectation that he could introduce his numbers, not with sets, but through some algebraic techniques borrowed from earlier writers of the Gottingen school. These rewriting techniques, had they worked, would have required strong philosophical justification provided by Frege's celebrated "context principle," which otherwise serves little evident purpose in the published Foundations.
This survey article describes Frege's celebrated foundational work against the context of other late nineteenth century approaches to introducing mathematically novel "extension elements" within both algebra and geometry.
Physicists often allow the "laws" of a discipline, formulated as partial differential equations, to be disobeyed along various surfaces, arrayed along the boundary and inside the medium under study. What kinds of considerations permit these lapses in the applicability of the equations? This paper surveys a variety of answers found in the physical literature.
This is one of those cases to which Dr. 8 oodhouse's remark applies with all its force, that a method which leads to true results must have its logic Ã¢â¬â H.S Smith (" On Some of the Methods at Present in Use in Pure Geometry," p. 6) A goodly amount of modern metaphysics has concerned itself, in one form or another, with the question: what attitude should we take in regard to a language whose semantic underpinnings seem less than certain? (...) Since much of standard English is surely of this type, many philosophers have felt driven to extreme and unpalatable resolutions Ã¢â¬â wholesale rejection of attractive logical rules, radical "antirealism", "minimalism" about truth, and so forth, Scientists, however, have long dealt with analogous foundational insecurities and, under the duress of practicality, have framed a set of shifting attitudes towards language and reasoning that seem far more commonsensical than the extreme positions to which pure philosophy has often been led. Following this lead, this essay will recommend a more nuanced approach to linguistic insecurity that is neither naively optimistic nor mired in the gloomy sloughs of antirealism. (shrink)
This paper argues that the principle of necessary identity (f)(g)(f=g then necessarily f=g) cannot be maintained, At least in second order form. A paradox based upon scientific definitional practice is introduced to demonstrate this. A non-Fregean reading of standard contingent identity semantics is provided to explain how such 'definition breaking' works.
This essay traces some of Pierre Duhem's motives for his celebrated "Quine- Duhem thesis" to a specific worry about theory underdetermination that arises within classical mechanics, concerned with the rivalry between Duhem's own thermomechanical approach and the more narrowly "mechanical" treatment pursued by Hertz and others. In the context of the treatments of "physical infinitesimals" common at the time, these two approaches seem empirically indistinguishable. After an exposition of the basic issues, this alleged "underdetermination" is then evaluated from a more (...) modern perspective. (shrink)
I'm scarcely the only reader who has found it puzzling that the self-consistent author of the Meditations, with his firm faith that God has supplied us with clear and distinct ideas sufficient to understand the material world, could have been satisfied with the messy jumble of physical doctrine we seem to find in his ~Priuci les. For example, although Descartes seems to be committed to a relationalism of some sort, his notorious laws of impact look as if they blatantly rely (...) upon an absolute compass of inertia, leading Julian Barbour to complain that Descartes' relationalism is but "froth on the surface of a deep underlying absolutism" (Barbour 1989 p. 600) (by "compass of inertia", I mean "a method of guidance lodged in an absolute background space or spacetime"). (shrink)
Many common approximation methods in physics practice 'causal process avoidance' in their operative procedures and such methodologies weave densely throughout the usual fabric of 'classical mechanics'. It is observed that Hume was unable to find any grounding for a robust conception of 'cause' largely because he unwittingly looked in those regions of mechanics where genuine causal processes had already been tacitly expunged.
A standard illustration' of this situation in this: let M~ be a theory of mechanics employing mass points as basic objects and let Mz be similar yet with only extended objects as its primitive elements. Let M> postulate that mass points come only in dense collections. Granted reasonable assumptions about the further details of Mq and M2, we can define the extended objects of Mz in M~ as dense sets of mass points whereas the latter can be defined in Mz (...) as nested sets of the former. Both theories offer equivalent descriptions of the world in the sense that any claim of Mq can be systematically translated into a theorem of Mz and conversely. (shrink)
We study whether changes in analyst recommendation ratings systems encouraged by the implementation of NASD 2711 in 2002 are associated with improved objectivity and independence in analyst recommendations. Using recommendations issued during windows surrounding major investment banking events, we show that reductions in analyst optimism following the reforms concentrate in the recommendations of analysts whose employer adopted a three-tier rating system at the time of the reforms, and that this effect is generally stronger for analysts whom the underlying incentives to (...) engage in unethical behaviour is greatest. We also find evidence that adoption of the three-tier system improved the market’s perception of the objectivity of analyst recommendations issued after SEOs, and that for hold and sell-type recommendations this effect was stronger for analysts subject to the greatest potential ethical conflicts. While we find some evidence of a general post-reform increase in the profitability of recommendations issued following equity transactions, this improvement was only conditioned by changes to the rating system in our IPO sample. (shrink)
George Boolos, Crispin Wright, and others have demonstrated how most of Frege's treatment of arithmetic can be obtained from a second-order statement that Boolos dubbed ‘Hume's principle’. This note explores the historical evidence that Frege originally planned to develop a philosophical approach to numbers in which Hume's principle is central, but this strategy was abandoned midway through his Grundlagen.
Original explorers often see a puzzling conceptual landscape more vividly than jaded later travelers. This essay surveys several ways in which Descartes and Leibniz recognized descriptive problems within applied mathematics more clearly than later commentators have appreciated.
Early travelers often appreciate the charms of a landscape more vividly than the settlers of later years, who gaze upon the encircling splendors with a dull and acclimated eye. Success in science frequently relies upon subtle forms of explanatory structure that exploit data drawn from different scale levels in surprising ways, yet we moderns overlook the oddities of these procedures through inattentive familiarity. G.W. Leibniz, among his many singular accomplishments, was one of the first scientists to attempt physical modeling in (...) what we shall call a "mixed level" mode and was acutely aware of the methodological challenges that such accounts pose. In particular, he pursued such a course in his 1684 essay on the elastic response of loaded beams (an important scientific subject that Leibniz pioneered') and many of the strangest features of his developed metaphysics directly relate to considerations that arise in such work. The mathematician J.E. (shrink)