Wednesday, 27 November 2013

CFP: Deductive and Mathematical Cognition Philosophy Conference -- Bristol

The Deductive and Mathematical Cognition Philosophy Conference will be held at the University of Bristol on 7th and 8th April 2014. The conference aims to investigate the implications of recent empirical developments in the study of deductive and mathematical cognition for established questions in the philosophy of mathematics and logic. We hope to provide an environment for interdisciplinary discourse between philosophers and those working within the relevant empirical disciplines. The conference will spend one day focussing on each field, the first day (April 7th) on Mathematical Cognition and Philosophy of Mathematics and the second (April 8th) on Deductive Cognition and Philosophy of Logic.

Invited Speakers:
Catarina Dutilh Novaes (Groningen)
Helen De Cruz (Oxford)
Bart van Kerkhove (Brussels)

The call for papers is open to any from a diverse range of fields, including but not limited to philosophy, logic, mathematics, psychology, cognitive science, history and anthropology. At least two spaces are reserved for early career academics and graduate student submissions.
For the first day we welcome submissions that focus on the implications of recent findings in the study of mathematical cognition for traditional issues in the philosophy of mathematics. Suggested topics include:
  • Presentations of experimental work that is of interest to philosophers of mathematics.
  • Do recent findings about the nature of mathematical cognition support certain positions in the ontology of mathematics?
    • Do these findings support Structuralism?
    • Do these findings support Fictionalism?
    • To what extent are mathematical entities mind-independent?
  • What can recent findings in the study of mathematical cognition tell us about the nature of mathematical knowledge?
    • Is mathematical knowledge a priori / a posteriori?
    • How do we acquire arithmetical knowledge?
    •  How do we acquire geometrical knowledge?
  • What role does the historical development of mathematical notation play in determining the nature of mathematical knowledge?

For the second day of the conference, we are looking for papers on a wide range of topics introducing empirical sources of information and insight to philosophical questions concerning logic. Such questions may be metaphysical, epistemological or methodological.Topics include but are by no means limited to:
  • Presentations of empirical work into the nature of deductive processes.
  • Implications of empirical work for issues in the epistemology of logic
    • Is logic innate?
    • Can we acquire knowledge of logical principles through introspection?
  • Implications of empirical work for the foundations of logic
    • What is the subject of logic?
    • Are we deductively rational? If not what are the implications for the prescriptive role of logic as a guide to correct reasoning?
  • Should we construct and assess our logics using data from the study of deductive reasoning processes?

Papers should be submitted via Easychair by 15th February 2014 in the following format.
1) A cover letter including the author’s name, university affiliation, contact information, title of paper, topic area, word count, and an abstract of no more than 250 words.
2) A paper prepared for blind review. Submissions should not exceed 4,000 words and should be suitable for a 40-minute presentation.

The registration for delegates that are not presenting a paper is £20, with a reduced fee of £10 for students.

The conference is supported by The British Society for the Philosophy of Science

Saturday, 16 November 2013

Hilbert's Infinite Hotel in 60 seconds

There are 5 other installments in the wonderful series '60-second Adventures in Thought' by the Open University: Zeno's paradox, the grandfather paradox, the Chinese room, the twin paradox, and Schrödinger's cat. Go check them all out!

Friday, 15 November 2013

300,000 pageviews!

Today M-Phi passed the mark of 300,000 pageviews in all-time history. Quite a milestone! I think I speak on behalf of all M-Phi bloggers when thanking readers for their support, and for the many fruitful debates at different posts. Personally, I can say that many discussions led me to revise my views, and that my research and thinking as a whole have greatly benefited from these interactions.

We'll do our best to keep it coming!

Thursday, 14 November 2013

A dialogical analysis of structural rules - Part II

(Cross-posted at NewAPPS)

Two weeks ago, I wrote a post proposing a dialogical perspective on structural rules. In fact, at that point I offered an analysis of only one structural rule, namely left-weakening, and promised that I would come back for more. In this post, I will discuss contraction and exchange (for both, I again restrict myself to the left cases). (I will assume that readers are familiar with the basic principles of my dialogical approach to deductive proofs, as recapped in my previous post on structural rules.)

Contraction, in particular, is very significant, given the recent popularity of restriction on contraction as a way to block the derivation of paradoxes such as the Liar and Curry. What does contraction mean, generally speaking? Contraction is the rule according to which two or more copies of a given formula in a sequent can be collapsed into each other (contracted); in other words, the idea is that the number of copies should not matter for the derivation of the conclusion:

A, A => C
A => C

(If two copies of A give you C, then one copy of A will give you C just the same.) Logics that reject contraction are based on the idea that the number of copies does matter; in the case of linear logic, the most notable non-contractive logic, formulas are seen as resources, which are no longer available once they are used (not that particular copy, in any case), and are sensitive to the number of copies available. (The standard example for resource sensitivity in linear logic is money required to buy a pack of cigarettes, which I think reveals something about the time and place in which the system was developed… Two 5-franc notes do not buy you the same amount of cigarettes as one 5-franc note!) In other words, linear logic has a plausible story to tell on why, given the purpose of the logic (to keep track of resources), the number of copies does matter.

Prima facie, in a dialogical setting, once a proposition is stated and granted, it becomes part of the public domain, as it were, and may be used as many times as necessary – at least by those who explicitly committed to it. So contraction may appear to be unproblematic in this setting. What a proposition stated or granted does is to produce a discursive commitment for the speaker in question, but it also licenses her to refer back to this commitment whenever necessary – in other words, it also creates an entitlement that can be ‘used’ as many time as one wishes. (I’m deliberately using Brandomian terminology here.)

However, one may well conceive of particular kinds of dialogical interaction where, every time a premise is required so as to license a conclusion, a fresh copy of it is required. We would need a story on why, once having granted a particular premise to proponent, opponent might then refuse to grant the same premise when it is asked again by proponent; if opponent will always have to grant premises he has granted before, in practice there is no need to go through the procedure of actually generating the new copies (new commitments).

One reason why discursive commitments may have to be modified during the interaction is if the reasons one had to commit to a statement at a given point no longer hold (say, due to changes in the world, or incoming new information); in that case, the possibility of retracting a commitment may seem plausible after all, in particular if discursive commitment is time-relative. But notice that this is a very different phenomenon from the idea of formulas being used as resources in linear logic; a given statement may no longer be ‘available’ even if it hasn’t been used yet, but simply because there are good reasons to revise one’s prior discursive commitments.

In a similar vein, my friend and former colleague Dora Achourioti has been developing a (thus far unpublished, I think) account of the truth operator where its function is precisely to turn a given statement into something that can be used as many times as one wishes; it becomes a limitless resource (she explicitly adopts a multi-agent perspective, and uses notions from linear logic to formalize this insight). So the presupposition is that this does not hold for other, ‘regular’ occurrences of statements not affected by a truth operator, and thus that contraction does not hold unrestrictedly.

So I conclude that, while contraction is prima facie a very plausible principle in a dialogical setting, there may be purely dialogical reasons to restrict contraction, but which are different from linear logic’s rationale for contraction restriction.

What about exchange? It is not a structural rule that is much discussed in the paradoxes literature, but it is interesting in its own right for different reasons. While contraction entails that the number of copies does not matter, exchange entails that the order in which formulas are presented does not matter.

A, B => C
B, A => C

In a purely model-theoretic conception of (logical) consequence, it is indeed the case that order does not matter, as the sequence (A, B) has the same models as the sequence (B, A). In a dialogical setting, however, it is not at all obvious that order should not matter. This is because every new discursive commitment – every new premise granted by opponent – creates an update in his commitments; naturally, dialogues are intrinsically dynamic processes (and here you see that I am a real Amsterdam child!). Indeed, depending on the specific rules for different kinds of dialogical interaction, a premise A may be granted if it is proposed at a given stage of the debate, but rejected if it is proposed at a different stage (not in the very same interaction, but in an alternative interaction involving the same statements).

For example, the regimented kind of disputations known as obligationes (very popular among Latin medieval logicians) is inherently dynamic. If the starting point of the disputation is the proposition ‘Every human is running’ (which should be accepted if it is possible, even if it is not true, given the rules of the game), and then ‘You are a human’ is proposed, the player (in this case called ‘respondent’) must grant it as irrelevant for the starting point (it is not entailed by it or incompatible with it) and true. Then, if ‘You are running’ is proposed, the player must now accept it, as it follows from her two previous commitments, even though it is false (presumably, she is not running while disputing!). If however, given the same starting point ‘Every human is running’, ‘You are running’ is proposed first, respondent should deny it as irrelevant and false. Then, if ‘You are a human’ is proposed, it should be denied, even though it is true, because this follows from accepting ‘Every human is running’ and denying ‘You are running’. So different responses are required to the same statements depending on their order of presentation.

(However, in other dialogical situations, the order of presentation of premises may not matter; in Aristotle's Topics, for example, the recommendation is that questioner gets answerer to commit to all the premises he will need before he starts drawing conclusions (Book VIII, chapter 1).)

So I conclude that exchange is not a plausible principle from the point of view of the dialogical conception of proofs if we take into account the inherently dynamic nature of dialogues. In dialogues, the order of presentation of premises may well matter. 

(I had intended to talk about cut too, but this post has again reached the reasonable length for the genre. Cut is complicated because it is related to the fundamental property of transitivity, so it cannot be discussed in haste. Maybe in another post?)

Wednesday, 13 November 2013

PhD Position in Logic, Rational Choice or Meta-Ethics at the University of Bayreuth

The Department of Philosophy at the University of Bayreuth invites applications for one PhD position (3 years, E13 TV Z, 0.5 FTE) starting from 01 April 2014 or soon after. The Department is a rapidly growing research and teaching environment at the intersection of Philosophy and Economics and offers excellent career development opportunities. For further details please visit

The successful applicant will conduct his or her doctoral research under the supervision of Prof. Olivier Roy. The applicant will be required to undertake a small amount of teaching in accord with the Bavarian Higher Education Law (BayHSchG). We encourage applications in the following areas:

-    Philosophical Logic (especially epistemic logic or deontic logic)
-    Rational Choice Theory (especially foundations of decision and game theory)
-    Philosophy of Action and Meta-Ethics (especially theories of rationality and normativity)

The list is not exhaustive. Excellent projects in related areas will also be considered.

Applicants should have advanced training in philosophy (typically a Master degree) or in a discipline closely related to philosophy. Projects involving computer science or economics are very welcome.

Applicants should submit a cover letter, a CV, a two-page outline of their proposed PhD research project, BA and MA degree certificates and transcripts, and two academic letters of reference. The complete application package, excluding the letters of reference, should be submitted as a single PDF file. Applications should be submitted electronically to the Secretarial Administrator for the Department of Philosophy, Miss. Sonja Weber ( by 15 January 2014. The letters of references should be sent separately by their author, also to Miss. Sonja Weber.

For further information about the post, the P&E programmes, professional opportunities, and the Department of Philosophy, please contact Prof. Olivier Roy by e-mail:

The University of Bayreuth is an equal opportunity employer and aims to increase the number of female faculty members. Applications from female candidates are, therefore, explicitly encouraged. The University of Bayreuth was accredited as a Family Friendly University by the Hertie Foundation in 2010. Persons with disabilities will be given priority if equally qualified.