Bryan's Research. Comments are welcome; please do not quote without permission.
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Other Cool Stuff
Work in progress
"Structural Realism About Groups
Is Underdetermined"
Philosophy Comp
Draft: 29.Aug.2008
PDF
There is a strong sense in which an ontology of algebraic group is underdetermined, and undermined by theory change in physics. This is a major difficulty for structural realists about groups, since the the ability to avoid these problems has been put forward as the primary motivation for structural realism.
"How Galileo Dropped The Ball and Fermat Picked It Up"
History Comp
Draft: 2.Sep.2008
PDF
How does the velocity of a freely falling body increase? Many 17th-century Jesuits claimed this velocity is
proportional to the distance fallen. But in the Two New Sciences, Galileo mysteriously suggested that
the Jesuit law could only be true if motion were instantaneous. This paper introduces the proof of Galileo's
suggestion given by Pierre Fermat. In particular, I illustrate the context, the physical insight, and the
mathematical techniques central to Fermat's argument, and finally discuss how they might have been received.
"Hypercomputation and Supertasks: Goedel Strikes Back"
Coauthored with Balazs Gyenis
Draft not yet available
If one takes an arbitrary axiomatization of general relativity that also admits Malament-Hogarth spacetimes, then this axiomatization, under certain plausible conditions, can be shown to be inconsistent. We draw conclusions for the Church Turing Thesis and discuss the possible role of Cosmic Censorship.
Recent Papers
by Bryan W. Roberts
Comments welcome. Please do not quote without permission.
2008
"To Biot Not to Be: The Sound of Success"
Draft: Apr 2008
PDF
The central quantitative derivation of the speed of sound equation was first discovered not by Laplace, but by his younger colleague Jean-Baptiste Biot. Biot was able to write carefully operationalized facts about the behavior of heat, plug them into Lagrange's wave equation, and solve for the speed of sound. I provide English translations of Laplace (1816) and Biot (1802) as appendices.
2007
"The Cosmic Time Traveler's Dilemma"
Draft: Dec 2007
PDF
How do recent developments in general relativistic "time machines" bear on the Cosmic Censorship Hypothesis? An adequacy criterion is suggested for the meaningful answering of this question, and applied to various time machine constructions.
"Recurrence Recharged"
Draft: Apr 2007
PDF
Extensions of the notion of eternal recurrence are developed, and used to probe the structure of indeterministic systems.
"Overcoming Metaphysics in Wittgenstein's
Tractatus"
Draft: May 2007
PDF
In what sense does the space of "possible atomic facts" exist? A quasi-modal reading of "possible" is applied in answering this question, inspired by Wittgenstein's analysis of truth-possibility. An application is suggested in reading the so-called Argument for Simples.
"Physics Without Foundations? A Remark on Euler's
Mechanica"
Draft: Mar 2007
PDF
Contrary to recent literature, Euler's Mechanica is not founded on mathematical analysis alone. This analysis of Euler's foundational elements and derivation rules suggests that Euler's foundation for mechanics consists of three parts: a mathematically idealized language, an empirical language, and a rule for bridging between the two.
"Why Newton's Laws are Three"
Draft: Jan 2007
PDF
It is briefly shown that the reason for Newton's decision to enunciate his first law separately from his second may have been the desire to underline causal language in his first law, in contrast with the first law of Descartes.
2006
"The Role of the Euclidean
Reductio"
Draft: Dec 2006
PDF
Foundationalism in the Euclidean tradition provides a systematic, justified basis for reductio inference. A catalogue and classification of these arguments is given, and the necessity of such a justification is addressed.
"The Success of the Caloric Theory: What Cannot Be Inferred"
Draft: Jan 2006
PDF
An analysis of Laplace's derivation of the speed of sound suggests that Laplace's success was heavily motivated by assumptions about the material nature of heat. It is then shown that the claim "caloric exists" can be consistently asserted or denied in the language of modern thermodynamics.