How to prove it in Natural Deduction: A Tactical Approach*

Ponente: Selene Linares (UNAM-IIMAS)

Fecha: 11 de mayo, 12 hrs
Lugar: Sala de Investigadores Fernando Salmerón, Instituto de Investigaciones Filosóficas, UNAM.


Resumen: In this talk I will present the content of the paper "How to prove it in Natural Deduction: A Tactical Approach" by Favio E. Miranda-Perea, Atocha Aliseda and me. The motivation for this paper comes out of our experience with teaching natural deduction (ND) and with the way this formal system is implemented by the Coq proof assistant, namely by means of so-called tactics, which are heuristics that transform a goal formula into a sequence of subgoals whose provability implies that of the original formula. We aim at capturing some of these tactics into a system of ND for minimal logic. Our goal is twofold: formal and didactic. The former delivers a formal system with its underlying heuristics to build proofs, which in turn serves our latter purpose, that of making an ideal system for the teaching of ND at an undergraduate level in a computer science program.

Presentación.

* Esta charla será presentada en el 4th International Conference on Tools for Teaching Logic en Rennes, Francia.

Notes on the No Alternatives Argument

Ponente: Philiphe van Basshuysen*

Fecha: 27 de abril, 12 hrs
Lugar: Sala de Investigadores Fernando Salmerón, Instituto de Investigaciones Filosóficas, UNAM.


Resumen: In a recent paper (2015), Dawid, Hartmann and Sprenger give a Bayesian argument in favour of the No Alternatives Argument: the conclusion from a lack of alternatives to a scientific theory to the truth of that theory. If valid, this would constitute a proof for the possibility of non-empirical theory confirmation. In this paper I argue that their "proof" begs the question. 

I challenge the validity of the argument in two steps. I first give a principled line of reasoning concerning one critical assumption of their analysis, namely that the probability of a scientific hypothesis depends on the number of its alternative theories. I claim that arguing for this assumption implies either a regress to non-empirical theory confirmation, or a dubious application of the Principle of Indifference. In either case, the assumption stands on shaky grounds. In the second step, I give a counterexample to the assumption in order to show that it must indeed not be expected to hold. 

I conclude with a more general claim. I claim that Bayesian analyses, and particularly the use of Bayesian nets, are “dangerous” in that they may entice one to be careless about implicit assumptions about probabilistic (in)dependencies, and how they support normative claims. I intend to broaden this investigation by more case studies and, finally, a general line of reasoning as to the boundaries of normative Bayesian analyses. 

Lecturas previas:
Dawid, Hartmann y Sprenger
Basshuysen

Presentación.

*Debido a causas de fuerza mayor, la ponente original que presentaría en esta fecha (Ana Ponce) no podrá asistir al seminario y su charla quedará pendiente para un sesión posterior. Lamentamos los inconvenientes.