John D. Norton 

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CV Research Goodies Teaching Lectures Videos 
Distinguished Professor, Department of History and Philosophy of Science University of Pittsburgh Pittsburgh PA USA 15260 jdnorton@pitt.edu 412 624 5896 
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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.  
A purely thermodynamic argument precludes dissipationless erasure. Gibbs' " k p log p" entropy formula, properly applied, does not assign an information entropy to preerasure states. Suppressing fluctuations remains the principal source of dissipation in molecular scale processes.  "The Simply Uninformed Thermodynamics of Erasure," download draft.  
Adding a conical singularity to a Minkowski spacetime produces a temporally nonorientable 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 TimeTravel Spacetime," download draft.  
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.  
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 largescale structure of the resulting tangle of inductive inferences and relations of inductive support.  The LargeScale Structure of Inductive Inference. Accepted August, 2023, for publication in BSPSOpen/University of Calgary Press. 

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. 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 CCBYNCND 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 online book for an introductory level, undergraduate course. 

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. 

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. 142. Download.  
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.
129159 in Rethinking the Concept of Laws of Nature: Natural
order in the Light of Contemporary Science. ed. Yemima
BenMenahem. Springer, 2022. Download. 

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. 16. Download. 

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.  
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. 227246, in C. Soto (ed.), Current Debates in Philosophy of Science, Synthese Library 477. Springer: Cham, Switzerland, 2023. Download  
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. 1618. Read in Polish or English.  
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  
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. 18. 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. 1748 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.  
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 nonadditive inductive logic as applies to an infinite lottery.  "Eternal Inflation: When Probabilities Fail,"Synthese 198 (Suppl 16) (2021), S38533875. Download.  
An infinite lottery machines chooses without favor among a countable infinity of outcomes. This sort of selection creates wellknown 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. 7195. (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. 14344. Download. 

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. 45468. Download.  
Our urge to oversimplify has led to many myths about what powered Einstein's discoveries. Naive thinking? Capricious rulebreaking? 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. 249282. 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. 240256. Download.  
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Bio 

I was born and grew up in Sydney Australia. I studied chemical
engineering at the University of New South Wales (197174) 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 (19781981). My dissertation was on the history
of general relativity. When it was finished, I visited at the Einstein Papers Project (198283) 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 20002005 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. 

Updated May 2020 and possibly later too. 