I introduce a typical experimental task in psycholinguisticsself—paced reading—and show how to build end-to-end simulations of a human participant in such an experiment; end-to-end means that we model visual and motor processes together with specifically linguistic processes (syntactic and semantic parsing) in a complete model of the experimental task. The model embeds theoretical hypotheses about linguistic representations and parsing processes in an independently motivated cognitive architecture (ACT-R). In turn, the resulting cognitive models can be embedded in Bayesian models to fit them to experimental data, estimate their parameters and perform quantitative model comparison for qualitative theories.
Unveiling the constructive core of classical theories: A contribution to 90 years of Glivenko’s theorem
Glivenko’s well known result of 1929 established that a negated propositional formula provable in classical logic is even provable intuitionistically. Similar later transfers from classical to intuitionistic provability therefore fall under the nomenclature of Glivenko-style results: these are results about classes of formulas for which classical provability yields intuitionistic provability. The interest in isolating such classes lies in the fact that it may be easier to prove theorems by the use of classical rather than intuitionistic logic. Further, since a proof in intuitionistic logic can be associated to a lambda term and thus obtain a computational meaning, such results have more recently been gathered together under the conceptual umbrella “computational content of classical theories.” They also belong to a more general shift of perspective in foundations: rather than developing constructive mathematics separately, as in Brouwer’s program, one studies which parts of classical mathematics can be directly translated into constructive terms.
We shall survey how Glivenko-style results can be easily obtained by the choice of suitable sequent calculi for classical and intuitionistic logic, by the conversion of axioms into inference rules, and by the procedure of geometrization of first order logic.
It is a relatively recent development that research on conditionals is taking a deep and sustained interest in the full range of linguistic markers, their interactions with each other and with other linguistic categories, and the ways in which they drive and constrain the interpretation of the sentences they occur in. Tense and aspect is an area where such attention has already borne fruit; to a lesser extent, we may mention conditional connectives and pro-forms (especially thanks to works like Iatridou 2000 and Iatridou & Embick 1993). More recently, there seems to be a growing interest in two things: on the one hand, more varied aspects of formal marking of conditionals and the ways in which different grammatical categories may be recruited to encode conditional meaning (including aspect, different types of connectives, conjunctions, etc.); on the other hand, the appearance of these markers in other linguistic contexts (like optatives, complement clauses, temporal clauses, interrogatives, etc.).
Saturday, April 6
12:00-2:00: Kai von Fintel & Sabine Iatridou (MIT) “Prolegomena to a Theory of X-Marking”
2:30-3:15: Muyi Yang (UConn) “Explaining negative counterfactuals”
3:15-4:00: Teruyuki Mizuno (UConn) “The structure of might-counterfactuals: a view from Japanese”
4:30-5:30: Paolo Santorio (UC San Diego) “The Double Life of Antecedent Strengthening”
Sunday, April 7
10:00-11:00: Una Stojnić (Columbia): t.b.a.
11:15-12:00: Hiromune Oda (UConn): t.b.a.
1:30-2:30: Will Starr (Cornell) “Indicative Conditionals, Strictly”
After 2:30: coffee & discussion as desired
Recursive counterexamples are classical mathematical theorems that are made false by restricting their quantifiers to computable objects. Historically, they have been important for analysing the mathematical limitations of foundational programs such as constructivism or predicativism. For example, the least upper bound principle is recursively false, and thus unprovable by constructivists. In this talk I will argue that while recursive counterexamples are valuable for analysing foundational positions from an external, set-theoretic point of view, the approach is limited in its applicability because the results themselves are not accessible to the foundational standpoints under consideration. This limitation can be overcome, to some extent, by internalising the recursive counterexamples within a theory acceptable to a proponent of a given foundation; this is, essentially, the method of reverse mathematics. I will examine to what extent the full import of reverse mathematical results can be appreciated from a given foundational standpoint, and propose an analysis based on an analogy with Brouwer’s weak and strong counterexamples. Finally, I will argue that, at least where the reverse mathematical analysis of foundations is concerned, the epistemic considerations above show that reverse mathematics should be carried out within a weak base theory such as RCA0, rather than by studying ω-models from a set-theoretic perspective.
In this talk, I will apply the de re/de dicto distinction to the analysis of mathematical statements and knowledge claims in mathematics. A proof will be said to provide de dicto knowledge of a mathematical statement if it provides knowledge of a purely existential statement, and to provide de re knowledge when it carries additional information concerning the identity criteria for the objects that are proven to exist. I will examine two case studies, one from abstract algebra and one from discrete mathematics, and I will suggest that reverse mathematics can help measuring the ‘de re content’ of two different proofs of the same theorem, and that the de re/de dicto distinction introduced here lines up with certain model theoretic properties of subsystems of second order arithmetic, such as the existence of certain kinds of minimal model. Furthermore, I will argue that there are good reasons not to identify the de re content of a proof with its constructive content nor with its predicative content.