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Portrait by
Josephine Norton

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Includes direct links to my papers.

A synopsis of my research in history and philosophy of physics and general philosophy of science, with links to papers.

Some things are just too much fun.

Complete syllabi for my courses and the complete text, videos of "Einstein for Everyone." Also a complete text for my new undergraduate course, Paradox.

Some lecture series I have given.


Editing and Publishing

Distinguished Professor,
Department of History and Philosophy of Science
University of Pittsburgh
Pittsburgh PA USA 15260
412 624 5896

Fragment of Kruskal 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.
erasure 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.
Minkowski time travel 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.
Phase space image 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.
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.
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.
many arches 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.

many arches 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.
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.

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
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.
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.
escapements 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." in Yafeng Shen, ed., Alternative Approaches to Causation. Oxford University Press, forthcoming

Download draft.
Newcomen engine 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.
a round square
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.
Lottery ticket fragment
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.
"An Infinite Lottery Paradox" Axiomathes 32, supplement issue 1 (2022), (Special Issue Epistemologia 2022), pp. 1-6. Download.
Material Theory book
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.
NGC_4319 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
electric experiment 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.
Phase space fragment 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
Dial fragment 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 Science82(2020), pp. 1-8. Download
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.
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.
Stacked Galaxies 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.
jumping flea 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.
Punch 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.
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.
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.


Sydney Harbour Bridge. I was born and grew up in Sydney Australia. I studied chemical engineering at the University of New South Wales (1971-74) and then worked for two years as a technologist at the Shell Oil Refinery at Clyde, Sydney. I then switched fields and began a doctoral program in the School of History and Philosophy of Science at the University of New South Wales (1978-1981). My dissertation was on the history of general relativity.

When it was finished, I visited at the Einstein Papers Project (1982-83) when the Papers were located at Princeton University Press with John Stachel as editor.

In September 1983, I came to Pittsburgh as a visitor in the Center for Philosophy of Science/visiting faculty member in the Department of History and Philosophy of Science at the University of Pittsburgh. I've been in the Department of HPS ever since. I was promoted to full professor in 1997, served as Chair in 2000-2005 and was promoted to Distinguished Professor in 2014. I served as the Director of the Center for Philosophy of Science, from September 2005 to August 2016.




Cathedral of Learning

Updated May 2020 and possibly later too.