Hilbert’s interpretations of probability

Originally published in The Reasoner Volume 10, Number 5– May 2016


The concept of Probability is interesting, among other reasons, for the variety of ways in which we may be talking about distinct things and yet, in the end, still talking about probability. From the philosophy-of-mathematics point of view, this is vividly illustrated by the fact that, except possibly for one’s views on `finite vs. countable additivity’, one axiomatisation serves a great number of largely incompatible interpretations of the concept being axiomatised. Chapters 1-3 of J. Williamson (2010. In Defence of Objective Bayesianism. Oxford University Press.) offer a wide angle picture which I recommend to those who are unfamiliar with the landscape of probability interpretations.

Viewed at a relative coarse grain, the axiomatisation of probability developed by following a similar path to other mathematical concepts until at the turn of the twentieth century the key motivation became that of securing its applications against the threat of paradoxical consequences Needless to say David Hilbert played an important role in this. The explicit question appears as number “six” in the list of problems Hilbert posed to the audience of the Second International Congress of Mathematicians, in Paris on 8 August 1900:

Six. Mathematical Treatment of the Axioms of Physics. The investigations on the foundations of geometry suggest the problem: To treat in the same manner, by means of axioms, those physical sciences in which already today mathematics plays an important part; in the first rank are the theory of probabilities and mechanics. [] As to the axioms of the theory of probabilities, it seems to me desirable that their logical investigation should be accompanied by a rigorous and satisfactory development of the method of mean values in mathematical physics, and in particular in the kinetic theory of gases.

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Probabilistic mistakes kill (possibly many innocents)

Originally published in The Reasoner Volume 10, Number 4– March 2016


The Oscar winning documentary Citizenfour brought the concept of metadata to the attention of general audiences. As one scene of the film explains, we leave, mostly unwillingly, many digital traces of our daily activities. Most Londoners, for instance, use an Oyster card to travel across the city. When they top-up their Oyster online or opt in for the convenient auto top-up, they effectively allow whoever has access to the data, to track their routine. (And the recent introduction of contactless payment on the London transport system clearly made this even simpler.) This can then be linked to what people buy, what they read on the internet, what they post on social networks, and indeed, to what other people do. That’s metadata.

It goes without saying that metadata is syntax with no semantics. There are many reasons as to why people do what they do, and there are many people travelling independently on the same journey. Quite obviously then, the dots representing their digital traces can be joined in a number of distinct ways, and possibly found to draw specific but wrong pictures. That’s why the Owellian idea that someone possesses a wealth of metadata about us is indeed frightening. But knowing that governments may kill based on that, is rather hard to accept.

The opening of this recent piece by C. Grothoff and J.M. Porup on Arstechnica UK is chilling:

In 2014, the former director of both the CIA and NSA proclaimed that “we kill people based on metadata.” Now, a new examination of previously published Snowden documents suggests that many of those people may have been innocent.

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2(+2) year Postdoctoral Fellowship

matisseThe Department of Philosophy and the Centre for the Study of Social Action (CSSA) at the University of Milan are delighted to announce the opening of a post-doctoral position on Acting Together: Coordination, Collective Goals, and Cooperation. The project, which is jointly led by Professors Hykel Hosni and Corrado Sinigaglia, spans formal and experimental methods and will put particular emphasis on minimalist approaches to coordination, shared agency, and cooperation.

Applicants are expected to have a strong inclination for interdisciplinary work and the potential for excellence in research and publications. There are no restrictions on the applicants’ PhD background, provided it’s relevant to the topic of the project. The appointment will be made initially for two years and it will be renewed for another two years subject to funding. After tax salary will be in the region of 20.000 Euros per year.

The fellow will be a member of the Center for the Study of Social Action and will participate in the wider research community of the Department of Philosophy, the second largest in the country. While the postdoctoral fellow will pursue sound philosophical research, the project is ideally suited to interdisciplinary collaboration with cognitive scientists, economists, mathematical and computational logicians.
The deadline for application is April 26th 2016. We refer potential applicants to the official call for applications. The application form is available here.

Note to non-Italian applicants. Please do not be discouraged by the “Call for application” document applying is a lot easier than it seems! You will need to attach

  • a brief research proposal related to the topic of the project
  • a detailed CV (highlighting your scientific achievements)
  • an abstract of your PhD thesis (draft is OK if you haven’t defended yet)
  • relevant publications

Informal enquiries on the nature of project and the application procedure are welcome.