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Jan. 8 |
Introduction. Review of topics. Selection of presenters. |
Norton |
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Jan. 8 |
John D. Norton, "Lotteries, Bookmaking and Ancient Randomizers: Local and Global Analyses of Chance,"
Studies in History and Philosophy of Science, 95 (2022), pp. 108–117.
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Norton
 Powerpoint |
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Introduction: the well-entrenched history is that probability theory was discovered by Fermat and Pascal
in a famous correspondence in the mid-seventeenth century over the "problem of points". Or so says
Laplace. It is an obvious mistake in so far as the two did
not introduce any new foundational ideas. That important mathematicians were interested in the problem indicated that chance calculations were mathematically respectable. Their achievement was the solution to a celebrated problem,
whose content remained a fixture in works on probability for a century.
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| 2 |
Jan. 15 |
David, F.N. "The arithmetic triangle and correspondence between Fermat and Pascal" Ch. 9 in
Games, Gods and Gambling New York: Hafner, 1962.
Background if needed: David, F.N. "Letters between Pascal, Fermat ..." Appendix 4 in
Games, Gods and Gambling New York: Hafner, 1962.
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Yiran Chen |
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Jan. 15 |
Christian Huygens, De Rationiciis in Ludo Aleae. Translated as The Value of all Chances in Games of Fortune. London: Se Keimer, 1714. Facsimile. or Reset. |
Kiki Timmermans |
| 3 |
Jan. 22 |
John D. Norton, " Chance Combinatorics: The Theory that History Forgot," Perspectives on
Science 31 (6), (2023), pp. 771–810.
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Norton
Powerpoint |
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Jan. 22 |
"Bernoulli's theorem" para. 123-126 in I. Todhunter, "James Bernoulli," Ch. VII in A History of the Mathematical Theory of Probability. Macmillan, 1865.
Jacob Bernoulli, Part 4 of The Art of Conjecturing.
Parts 1-3 of The Art of Conjecturing continues the study of games of chance using the 17th century method of case counting. Part 4 seeks to extend chance notions beyond case counting in gambling games. Bernoulli introduces what we now know as the weak law of large numbers. It provides an empirical means of discovering probabilities from frequencies. Focus on that law and how Bernoulli seeks to use it.
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Tzvetan Moev |
| 4 |
Jan. 29 |
"Bayes", Ch. XIV in I. Todhunter, A History of the Mathematical Theory of Proability. MacMillan, 1865.
Bayes' original paper is a challenge to read because it is written using the old methods of probabilities as ratios of whole number cases. Present Todhunter's summary, adding details if you can from Bayes' original paper. Note also the greatly limited scope of Bayes' paper compared to modern Bayesian analyses.
Thomas Bayes, “An Essay toward solving a Problem in the Doctrine of Chances.” Philosophical Transactions of the Royal Society of London 53 (1764), pp. 370–418.
Stephen M. Stigler, "Thomas Bayes's Bayesian Inference," Journal of the Royal Statistical Society. Series A (General) , 1982, Vol. 145, No. 2 (1982), pp. 250-258.
| Conny Knieling |
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Jan. 29 | s
The prominent and influential early use of inverse probabilities was Laplace's "rule of succession." It is laid out in detail in a dense and difficulty paper by Laplace of 1774. Its best known version is a very brief application to the probability of sunrises in the concluding pages of Ch.III of Laplace's hugely influential A Philosophical Essay on Probabilities. For my reconstruction of Laplace's calculations, see Appendix, pp. 52-54 in my Large-Scale Structure of Inductive Inference. Today's reading is a wide-ranging review of the history of the rule:
Sandy L. Zabell, "The Rule of Succession" Erkenntnis 31(1989), pp.283-321.
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Tzvetan Moev |
| 5 |
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The use of inverse probabilities in a way more like that of modern Bayesianism in philosophy of science emerges more clearly in the late 19th and early 20th centuries in such writers as W. Stanley Jevons and Harold Jeffries. |
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Feb. 5 |
W. Stanley Jevons, The Principles of Science. New York: MacMillan, 1874. Book II. Ch. XII. "The Inductive or Inverse Application of the Theory of Probabilities" |
Eric Anderson |
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Feb. 5 |
Harold Jeffreys, "Quantitative Laws," Ch. IV in Scientific Inference.Cambridge University Press, 1931. |
Your name here. |
| 6 |
Feb. 12 |
John Maynard Keynes (the Keynes, the famous economist) wrote a significant work in probability. Chapter 1 advances a logical interpretation of probability. Chapter 4 developed the now famous principle of indifference, along with its problems.
John Maynard Keynes, A Treatise on Probability, London: MacMillan, 1921. Ch.1 The Meaning of Probability; Ch. 4 The Principle of Indifference.
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Yian Chen |
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Feb. 12 |
Joseph Bertrand's collection of indifference paradoxes includes his most famous case of a chord in a circle.
Problems for Probability: the Principle of Indifference in John D. Norton Paradox: Puzzles of Chance and Infinity
John D. Norton, " A Demonstration of the Incompleteness of Calculi of Inductive Inference," British Journal for the Philosophy of Science, 70 (2019), pp. 1119–1144.
This paper is included here since it is, at its core, merely a persistent application of the principle of indifference.
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Norton
Powerpoint |
| 7 |
Feb. 19 |
John Venn explored the idea that probabilities are really assertions of frequencies in repeated trials. It was developed by Hans Reichenbach and Wesley Salmon. The most developed version of the frequency interpretation was provided by Richard von Mises.
Richard von Mises, "The Definition of Probability," Chapter 1 in Probability, Statistics and Truth. London: George Allen and Unwin, 1957; Dover reprint, 1981. |
Yiran Chen |
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Feb. 19 |
Alan Hájek's two papers have become the standard response to frequentism.
Alan Hájek, " 'Mises Redux' -- Redux: Fifteen Arguments against Finite Frequentism," Erkenntnis 45,(1997), pp. 209-227.
Alan Hájek, "Arguments Against Hypothetical Frequentism," Erkenntnis, 70(2009), pp. 211–235. |
Amanda Back |
| 8 |
Feb. 26 |
Subjective interpretations emerged in the work of Frank Ramsay, Bruno de Finetti and others in the early 20th century. It was self-styled as a revolutionary, polemical movement and became the standard view in many circles.
Frank Ramsay, "Truth and Probability" (1926) Foundations of Mathematics and other Logical Essays, Ch. VII, p.156-198.
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Your name here. |
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Feb. 26 |
Bruno de Finetti, Chapters 1, 2 and 3 in Philosophical Lectures on Probability. |
Afra Akram |
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Mar. 5 |
Spring Break |
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| 9 |
Mar. 12 |
Richard Jeffrey, Ch. 1 in Subjective Probability: The Real Thing. Ch. 1 Probability Primer.
See Acknowledgements for a sense of the subjectivists' imperialist ambitions.
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Your name here. |
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Mar. 12 |
An enduring puzzle for probabilists is how probabilities could arise in systems that are deterministic in classical physics, such as ordinary coin tosses and roulette wheel spins. The method of arbitrary functions provided an answer of enduring propularity. It was developed by von Kries, Henri Poincaré, Hans Reichenbach and more.
Henri Poincaré, ""Second Example" in his Calcul des Probabilités.; "The Calculus of Probabilities" Ch. XI in Science and Hypothesis. |
Afra Akram |
| 10 |
Mar. 19 |
The enduring problem in the foundation of probability theory has been how to connect the mathematical object of a unit-normed additive measure with things in the world. Cournot's principle provides the link by asserting that high probability events are to be expected. The principle has been much reviled, but also much endorsed and deserves a look.
Glenn Shafer, "'That’s what all the old guys said.' The many faces of Cournot’s principle."
Start with "2.70 Andrei Kolmogorov, 1903–1987" and connect it with as much of the rest of the narrative as seems useful.
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Amanda Back |
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Mar. 19 |
Gal Ben Porath, Chapter 2. "Objective chance just isn’t objective enough" in Conceptual and Ontological Foundations of Stochastic Dynamics. Dissertation, University of Pittsburgh, 2024.
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Mystery celebrity presenter.
Gal Ben-Porath |
| 11 |
Mar. 26 |
E. T. Jaynes, Ch. 1 "Plausible Reasoning"; Ch. 2 "The Quantitative Rules" in Probability Theory: the Logic of Science. Cambridge University Press, 2003.
Jaynes' objective interpretation of probability employed functional representation theorems developed in the 1940s by Cox and others. Jaynes was a physicist whose ideas were heavily informed by his physics. He advocated for the "maximum entropy principle," which is not in the readings. Where the subjective Bayesians saw themselves as a revolutionary movement, Jaynes' condescending arrogance can be read in the margins.
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Kiki Timmermans |
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Mar. 26 |
Ron Giere, "Objective Single-Case probabilities and the Foundations of Statistics," Studies in Logic and the Foundations of Mathematics, 74 (1973) 467–483.
Inesential background in Ron Giere, "A Laplacean Formal Semantics for Single-Case Propensities," Journal of Philosophical Logic, 5, (1976), pp. 321-353.
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Your name here. |
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Apr. 2 |
Term paper proposal submitted in email prior to seminar, by 2pm. |
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| 12 |
Apr. 2 |
Carl Hoefer, Chance in the World: A Humean Guide to Objective Chance. Oxford University Press, 2019. |
Mystery celebrity presenter.
Carl Hoefer |
| 13 |
Apr. 9 |
Wayne Myrvold, Ch.4. What Could a “Natural Measure” Be? and Ch.5. Epistemic Chances, or “Almost-Objective” Probabilities in Beyond Chance and Credence: A Theory of Hybrid Probabilities Oxford University Press, 2021. |
Mystery celebrity presenter.
Wayne Myrvold |
| 14 |
Apr. 16 |
Here is a deceptively simple problem in probability that unexpectedly (at least to me) required an excursion into the esoteric: Non-measurabley sets and the axiom of choice.
John D. Norton, " How NOT to Build an Infinite Lottery Machine" Studies in History and Philosophy of Science. 82(2020), pp. 1-8.
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Norton
Powerpoint
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Apr. 16 |
General Discussion
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All
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April 25 |
Term paper submitted in email by 5pm. |
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