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In his treatment of spacetime singularities, Einstein privileged analytic expressions over geometry. Modern relativists do the reverse and thus find Einstein's discussion baffling. |
"Einstein against Singularities: Analysis versus Geometry," Download. |
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A purely thermodynamic argument precludes dissipationless erasure. Gibbs' "- k p log p" entropy formula, properly applied, does not assign an information entropy to pre-erasure states. Suppressing fluctuations remains the principal source of dissipation in molecular scale processes. |
"The Simply Uninformed Thermodynamics of Erasure," download draft. |
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Adding a conical singularity to a Minkowski spacetime produces a temporally non-orientable spacetime that is everywhere flat excepting in regions enclosing the singularity. Time travel arises in the sense that a traveler, passing the singularity, is returned to the traveler's past where the traveler encounters the traveler's past self. |
"A Simple Minkowskian Time-Travel Spacetime," download draft. |
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Both Wayne Myrvold and I have written pieces, relating to Landauer's principle, in which fluctuations are alluded to in their titles. We explain that the pieces are mutually compatible. |
(With Wayne Myrvold) "On Norton’s '...Shook...' and Myrvold’s 'Shakin’ ...' " Philosophy of Physics, Vol. 1, Issue 1, Article 5. Download. |
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In lotteries and bookmaking, analyzing chance systems globally
provides advantages over local, probabilistic analysis. Global
thinking also explains how ancient thinkers who had no theory of
probability may have found physical randomizers like dice fit for
their purposes in gambling, lot drawing and divination. |
"Lotteries, Bookmaking and Ancient Randomizers: Local and Global
Analyses of Chance," Studies in History and Philosophy of
Science, 95 (2022), pp. 108–117. Download. |
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A precursors to probability theory was a seventeenth century
theory of chance for physical randomizers. It used combinatorics to
count chances and derived a serviceable rule for determining which
are fair wagers. It lacked an epistemic notion of chance and a
precise means to connect chance counts and frequencies; and could
not compare chances across different games. |
"Chance Combinatorics: The Theory that History Forgot," download draft. |
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In the material theory of induction, inductive inferences are
warranted by domain specific facts. Those facts are in turn
supported by further inductive inferences. This volume examines the
large-scale structure of the resulting tangle of inductive
inferences and relations of inductive support. |
The Large-Scale Structure of Inductive Inference.
(Sequel to the earlier volume, The Material Theory of Induction.)
Accepted August, 2023, for publication in BSPSOpen/University of Calgary Press.
Download draft. |
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Mousa Mohammadian, William Peden and Elay Shech have each written
commentaries on The Material Theory of Induction in a
symposium organized by the journal, Metascience. Here is
my responses and my thanks to them. |
"Author’s response to Mousa Mohammadian, William
Peden and Elay Shech," Symposium on The Material Theory of
Induction, in Metascience. 31 (2022) pp.317–323. Download. |
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Which are the good inductive inferences or the proper relations of
inductive support? We have sought for millennia to answer by means
of universally applicable formal rules or schema. These efforts have
failed. Background facts, not rules, ultimately determine which are
the good inductive inferences. No formal rule applies universally.
Each is confined to a restricted domain whose background facts there
authorize them.
The Material Theory of Induction.
Contents:
Preface
Prolog
1. The Material Theory of Induction Stated and Illustrated
2. What Powers Inductive Inference?
3. Replicability of Experiment
4. Analogy
5. Epistemic Virtues and Epistemic Values: A Skeptical Critique
6. Simplicity as a Surrogate
7. Simplicity in Model Selection
8. Inference to the Best Explanation: The General Account.
9. Inference to the Best Explanation: Examples
10. Why Not Bayes
11. Circularity in the Scoring Rule Vindication of Probabilities
12. No Place to Stand: the Incompleteness of All Calculi of
inductive Inference
13. Infinite Lottery Machines
14. Uncountable Problems
15. Indeterministic Physical Systems
16. A Quantum Inductive Logic
Epilog |
The Material Theory
of Induction. BSPSOpen/University of Calgary
Press, 2021.
Open access. FREE download under a CC-BY-NCND 4.0 Creative Commons
license.
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Infinity and chance are dangerous notions that can lead us to deep
puzzlement and baffling paradoxes. Careful examination of them
allows us to see past the paradoxes to a clear and controlled
understanding of what was once perplexing and unapproachable. |
Paradox:
Puzzles of Chance and Infinity
is my new on-line book for an introductory level, undergraduate
course. |
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Contrary to Hume, science has found many ways in which things
connect with other things in the world. Causal metaphysics, however,
has failed to add anything factual to the relations discovered by
science. It is at best an exercise in labeling that may have
practical uses. |
"The Metaphysics of Causation: An Empiricist
Critique." pp. 58-94 in in Yafeng Shen, ed., Alternative Approaches to Causation. Oxford: Oxford University Press, 2024.
Download. |
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In 1824, Sadi Carnot proposed the strange, internally
contradictory notion of a thermodynamically reversible process as
the most efficient in the context of dissipative heat engines. They
are analogous to the reversible geometrical movements that his
father, Lazare, had earlier found to be the most efficient in
ordinary, mechanically dissipative machines. |
"How Analogy Helped Create the New Science of
Thermodynamics" Synthese. 200 (2022), article 269, pp. 1-42.
Download. |
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I develop a deflationary, empiricist account of possibility and
argue that other accounts of possibility, notably metaphysical
possibility, fail, in so far as they seek to go beyond the
empiricist notion.
The figure at left is the realization
of a metaphysically impossible round square ABCD in spherical
geometry. |
"How to Make Possibility Safe for Empiricists." pp.
129-159 in Rethinking the Concept of Laws of Nature: Natural
order in the Light of Contemporary Science. ed. Yemima
Ben-Menahem. Springer, 2022. Download.
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Matt Parker and I disagree on whether a multiple of four is less
likely than an even number in a drawing from an infinite lottery.
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"An Infinite Lottery Paradox" Axiomathes
32, supplement issue 1 (2022), (Special Issue Epistemologia
2022), pp. 1-6. Download.
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A special
issue of Studies in History and Philosophy of Science is
on the material theory of induction and has 14 papers. Here are my
responses to those papers. |
Download draft. |
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In 1972, astronomers John N, Bahcall and Halton Arp debated at the
AAAS whether galactic redshifts resulted from a recession of the
galaxies. The material theory of induction is used to reveal and
assess their competing inductive inferences. |
"Inductive Inferences on Galactic Redshift,
Understood Materially." Ch. 9, pp. 227-246, in C. Soto (ed.), Current Debates in Philosophy of Science, Synthese Library 477. Springer: Cham, Switzerland, 2023. Download |
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Metaphysicians believe that they have uncovered a deep truth about
how things must connect in the world, antecedent to all science: the
principle of causality. They are mistaken. |
"How Not to Think About Causation." Filozofuj!
2019, No.3, pp. 16-18. Read
in Polish or English. |
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Landauer's principle mistakenly associates thermodynamic entropy
creation in a computing device with the logic of the computation
implemented. The mistake derives from a neglect of the dynamical
character of the probability W in Boltzmann's celebrated "S = k ln
W." |
"A Hot Mess," Inference: International Review
of Science. Vol. 4, Issue 3. Download |
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All efforts to design an infinite lottery machine using ordinary
probabilistic randomizers fail. This failure is not a result of a
lack of imagination in design. It is assured by a familiar problem
in set theory: we know no way to construct probabilistically
nonmeasurable sets. |
"How NOT to Build an Infinite Lottery Machine." Studies
in History and Philosophy of Science. 82(2020),
pp. 1-8. Download |
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Ready for a little light entertainment? What happens if one asks
whether an infinite tower of turtles could overcome gravity and
support the world? What happens if we ask if there is some mechanism
in ordinary Newtonian mechanics that would let a castle float in the
air. |
"Turtles all
the way down."
Castles in the air. |
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Einstein insisted that his principle of equivalence was a founding
heuristic for his general theory of relativity. However this
principle was in tension with his theory of 1912 and flatly
contradicted by his theory of 1913. Instead conservation of energy
and momentum provided a pathway to unique gravitational field
equations in both theories. |
"Einstein’s Conflicting Heuristics: The Discovery of
General Relativity," pp. 17-48 in Thinking about Space and Time:
100 Years of Applying and Interpreting General Relativity.
Einstein Studies, Volume 15. C. Beisbart, T. Sauer, C. Wüthrich
(eds). Cham, Switzerland: Birhäuser/Springer Nature, 2020. Download. |
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The measure problem in eternal inflationary cosmology arises
because we try to force a probability distribution where it is not
warranted. The problem is solved by asking which inductive logic is
picked out by the background conditions. That logic is the same
highly non-additive inductive logic as applies to an infinite
lottery. |
"Eternal Inflation: When Probabilities Fail,"Synthese
198 (Suppl 16) (2021), S3853-3875. Download. |
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An infinite lottery machines chooses without favor among a
countable infinity of outcomes. This sort of selection creates
well-known problems for probability theory. But is it really
physically possible to construct such a machine?. |
"How to Build an Infinite Lottery Machine" 8
(2018), pp. 71-95.
(with Alexander R. Pruss) Correction to John D. Norton “How to Build
an Infinite Lottery Machine, ” European Journal for Philosophy
of Science. 8 (2018), pp. 143-44.
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Narrative conventions in a thought experiment allow thought
experimenters great latitude in deciding which processes are typical
and bear generalization and which can be idealized away as
incidental. Misuse of this latitude has allowed one particular
thought experiment to be responsible for many decades of confused
science. |
"The Worst Thought Experiment," The Routledge
Companion to Thought Experiments. Eds. Michael T. Stuart,
James Robert Brown, and Yiftach Fehige. London: Routledge, 2018. pp.
454-68. Download. |
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Our urge to oversimplify has led to many myths about what powered
Einstein's discoveries. Naive thinking? Capricious rule-breaking?
Operational thinking? I correct some myths and try to give a more
accurate picture of how Einstein made two discoveries: special
relativity and the light quantum. |
"How Einstein Did Not Discover," Physics in
Perspective, 18 (2016), pp. 249-282. Download.
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The received view is that a Maxwell's demon must fail to reverse
the second law of thermodynamics for reasons to do with information
and computation. This received view has failed, I argue, and our
continuing preoccupation with it has distracted us from a simpler
and more secure exorcism that merely uses the Liouville theorem of
statistical physics. I extend this exorcism to the quantum case. |
"Maxwell's Demon Does not Compute." In Michael E.
Cuffaro and Samuel C. Fletcher, eds., Physical Perspectives on
Computation, Computational Perspectives on Physics.
Cambridge: Cambridge University Press. 2018. pp. 240-256. Download.
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