Epistemologia (LM)


Il corso Epistemologia (LM) non verrà erogato nell’anno accademico 2019-2020, e verrà mutuato dal corso Philosophy of computation and Information tenuto dal prof Giuseppe Primiero.

Inductive Logic and Rational Decision

This course aims at developing the basics of probability logic and its application to problems of inductive inference and rational decision. Familiarity with classical propositional logic is a useful pre-requisite for this course.

  1. Logico-mathematical preliminaries (from an elementary algebraic point of view)
  2. Probability logic (a.k.a. inductive logic)
  3. Probability, uncertainty and rationality



The course will be delivered in English if non-Italian speakers are attending. The course-notes however are written in Italian. This guarantees that students who are not proficient in English maximise their understanding of the course material, while giving non-Italian speakers a chance to practice the language.

Lecture notes

Versione aggiornata il 10 maggio 2019


Extra (non examinable)

A tutorial on conditional probability

A tutorial on coherence

Presentation schedule

Please edit this file with your name, id (matricola), presentation topic. I will then schedule all presentations according to their content. Please submit your essay (max 5 pages in standard latex format, or equivalent) by Friday 10th May. Submission means you send the pdf of your essay to all email addresses, including my own. This allows anyone to have a chance to read the essay before your presentation.


Foundations of probability

  • de Finetti, B. (1931). Sul significato soggettivo della probabilità. Fundamenta Mathematicae, 17, 289–329.
  • Ramsey, F. P. (1931). Truth and probability (1926). In R. B. Braithwaite (Ed.), The Foundations of Mathematics and other Logical Essays (pp. 156–198). Kegan, Paul & Co, London.
  • de Finetti, B. (1938). Cambridge Probability Theorists. Rivista Di Matematica per Le Scienze Economiche E Sociali, (2), 79–91.
  • Jeffrey, R. C. (1968). Probable Knowledge. In I. Lakatos (Ed.), The Problem of Inductive Logic (pp. 166–180). North-Holland.
  • de Finetti, B. (1963). La decisione nell’incertezza. Scientia, 98, 61–68.

Topics in probability

  • Syua, E. D. (2013). Jacob Bernoulli and the Mathematics of Tennis, Nuncius, 28, 142–163.
  • Bianchi, L. A. (2018). Bayes e Bias. In Probabilità, Rischio e Previsione”, L’Aquila 3-5 maggio 2017.
  • Isola, S. (2018). Alcune osservazioni su probabilità, illusioni e senso comune. In Probabilità, Rischio e Previsione”, L’Aquila 3-5 maggio 2017.
  • Samet, D., Samet, I., & Schmeidler, D. (2004). One Observation behind Two-Envelope Puzzles. The American Mathematical Monthly, 111(4), 347–351.
  • Grime, J: “Non-transitive Dice

Conditional probability 1 (The Sleeping Beauty Problem)

On Sunday, Beauty is put to sleep. He is awakened once on Monday, and put to sleep again after being administered a memory-erasing drug that causes him to forget his awakening. A fair coin is tossed. If and only if the coin falls tails, Beauty is awakened again on Tuesday. He knows all this. When he awakes on Monday, what should his credence be that the coin will fall heads?

  • Rosenthal, J. S. (2009). A Mathematical Analysis of the Sleeping Beauty Problem. The Mathematical Intelligencer, 31(3), 32-37. doi:10.1007/s00283-009-9060-z
  • Piccione, M., & Rubinstein, A. (1997). On the Interpretation of Decision Problems with Imperfect Recall. Games and Economic Behavior, 20(1), 3-24. doi:10.1006/game.1997.0536
  • Winkler, P. (2017). The Sleeping Beauty. The American Mathematical Monthly, 124(7), 579–587.

Conditional probability 2 (The Monty Hall Problem)

Suppose you’re on a game show, and you’re given the choice of three doors: behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?

  • Rosenthal, J. S. (2008). Monty Hall , Monty Fall , Monty Crawl The Monty Hall Problem and Variants. Math Horizons, 5–7.
  • Gill, R. D. (2011). The Monty Hall problem is not a probability puzzle* (It’s a challenge in mathematical modelling). Statistica Neerlandica, 65(1), 58–71. http://doi.org/10.1111/j.1467-9574.2010.00474.x   

Conditional probability 3 (The Simpson Paradox)

This paradox is the possibility of P(A|B) <P(A|B') even though P(A|B)\ge P(A| B') both under the additional condition C and under the complement C' of that condition.

  •  Blyth, C. R. (1972). On Simpson’ s Paradox and the Sure-Thing Principle. Journal of the American Statistical Association, 67, 363–366.
  • Pearl, J. (1999). Simpson’s Paradox: An Anatomy. http://bayes.cs.ucla.edu/R264.pdf,

Logic and probability

  • de Finetti, B. (1995). The Logic of Probability (1935). Philosophical Studies, 77, 181–190.
  • Hawthorne, J. (2014). A Primer on Rational Consequence Relations, Popper Functions, and Their Ranked Structures. Studia Logica, 102(4), 731–749.
  • Polya, G. (1954) Patterns of plausible inference, vol 2 (Selected chapters)
  • Williamson, J. (2017) Lecture notes on inductive logic (Selected chapters)
  • Williamson, J. (2001) Bayesian Nets and Causality (Selected chapters)
  • Makinson, D. (2012). Logical questions behind the lottery and preface paradoxes  lossy rules for uncertain inference, 511–529. http://doi.org/10.1007/s11229011-9997-2

Probability and forecasting

Probability and society

  • Bacaer, N. (2011). A Short History of Mathematical Population Dynamics. Springer., Chapter 4: “Daniel Bernoulli, d’Alembert and the inoculation of smallpox” (1760)
  • Borel, É. (2014). An Economic Paradox: The Sophism of the Heap of Wheat and Statistical Truths. Erkenntnis, 79 , 1081–1088. http://doi.org/10.1007/s10670-014-9615-z
  • “An argument for divine providence, taken from the constant regularity observ’d in the births of both sexes. By Dr. John Arbuthnott, Physitian in Ordinary to Her Majesty, and Fellow of the College of Physitians and the Royal Society” — read Chapter 17 of Hald, A. (1990). History of Probability and Statistics and Their Applications before 1750. Statistics. Hoboken, NJ, USA: John Wiley & Sons, Inc.