Are numbers sets? New paper on Philosophia Mathematica

Some time ago, I wrote a post on this blog (here) in which I briefly discussed Steinhart’s proposal according to which numbers are finite von Neumann ordinals. I wasn’t convinced by his argument, and in that post I confusedly tried to articulate an objection.

Finally, after long time, I have found the time to elaborate these thoughts in a more rigorous way. The outcome of this work has been published on the last issue of Philosophia Mathematica.

The paper is available here. A pre-print draft is available here.


CFA: Analogical reasoning in science and mathematics

The Munich Center for Mathematical Philosophy invites abstracts for the following event:

Analogical Reasoning in Science and Mathematics

MCMP, LMU Munich

October 26-28, 2018

Analogy is a powerful, yet controversial, tool of scientific reasoning.  Indeed, many achievements in the history of science and mathematics have been driven by analogical inferences.  Moreover, one can formulate conjectures about domains into which one does not have empirical access just based on analogy with other known domains. Nonetheless, from a logical point of view analogical inferences do not yield conclusions with certainty.  So, what is it that justifies the use of analogy in science and mathematics?  And how reliable is analogical reasoning?  This conference will address such open philosophical problems.

Call for abstracts

We invite the submission of extended abstracts for the conference. Submissions should include a title, a brief abstract (up to 200 words), and a full abstract (up to 1000 words), blinded for peer review. They should be PDF files, submitted by July 31, 2018 to the conference’s EasyChair account.  We will select 4 submissions for presentation at the conference.
We are committed to fostering diversity and equality in our programs.  Submissions from underrepresented groups are particularly welcome. The  conference will be organized and run under the MCMP’s code of conduct.


Please send registration requests by 15 Oct 2018 to the co-chair Giovanni Valente.  The email should have the subject: “register analogical reasoning” and should indicate whether you plan to attend the conference dinner (27 Oct, 2018).  The conference dinner will cost EUR 35 (fixed menu – alcohol not included).

Dates and Deadines

Deadlines for Submission: July 31, 2018
Date of Notification: September 01, 2018
Registration Deadline: October 15th, 2018


Marianna Antonutti Marfori (MCMP/LMU Munich)
Giovanni Valente (Politecnico di Milano)
Erik Curiel (MCMP/LMU Munich)
Michele Ginammi (Department of Philosophy (KGW), University of Salzburg)
Patricia Palacios (MCMP/LMU Munich)


The conference is organized by the Munich Center for Mathematical Philosophy (LMU Munich).  The conference is partly funded by support from the Alexander von Humboldt Foundation and from META at the Politecnico di Milano.

Clickbait in scientific journals: when the citation index fails

In a recent post on the LSE Impact Blog, Portia Roelofs and Max Gallien discuss how standard Academic incentive structure can be hacked to privilege clicks and attention over scientific rigour in research. They present the example of a controversial recent journal publication to illustrate how deliberately provocative articles have the capacity of promoting an interest (and clicks, and citations, and notoriety — and eventually fundings) which is not justified by scientific rigour, but purely by provocative contents. The article in question — they say — “is a travesty, the academic equivalent of a Trump tweet, clickbait with footnotes”.

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The desire to be puzzled

Here is a very interesting post on possible alternatives to Cantor’s Transfinite Numbers Theory! Was Cantor’s notion of infinite really “unavoidable”?
The topic is particularly interesting when considered within the general framework of mathematical development. How does mathematics evolve? What “forces” mathematics to take some roads instead of other roads? And how do these choices influence the way in which we model and understand the natural world?


A prominent professor in the philosophy of mathematics once told me that the key to writing an attractive philosophy paper is to present the reader with a puzzle. “Give me a puzzle, and I’ll be interested”, he said. As I was surrounded by mathematicians and philosophers of mathematics which were steadily exchanging puzzles, I had no doubt that he was right: mathematicians and philosophers of mathematics like puzzles. But then, mightn’t it be the case that this fondness of puzzles influences much more than just our judgment of a philosophy paper (and our conversations over dinner)? Here’s a crazy idea – or maybe not so crazy – does our desire to be puzzled affect our judgement of a certain foundational mathematical theory?

The foundational mathematical theory which I have in mind is, of course, Cantor’s transfinite set theory. Given its general acceptance nowadays, it is easy to forget that in order to generalize arithmetic from the finite to…

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