National Research Projects
This is a two-part project funded by CONICET and UBA.
The main goal of this project is to analyse the infinitary paradoxes (Yablo, McGee, Visser, Uzquino) not only in first-order but also in second-order logic. In particular, we will pay attention to Yablo’s paradox, in order to evaluate its finitary and infinitary formulations and their relation to consistency and satisfiability. The inexistence of a standard model in first-order and the unsatisfiability in second-order will concentrate our attention from a conceptual standpoint. At the same time, we will study different notions of circularity and self-reference, in order to establish similarities and differences between infinitary paradoxes and the other semantic paradoxes.
There are several methodological criteria appealed to settle debates and justify positions in contemporary analytic philosophy. The purpose of this project is to evaluate some of these patterns of justification, like the appeal to intuition in the justification of philosophical theses, or the application of reflective equilibrium. The appeal to intuition as a justifying device, plays an important role in epistemology, but also, a more veiled one in logic. The relationships that these criteria have with each other will be examined in the light of contemporary debates on (i) the meaning of knowledge attributions; (ii) the solutions to epistemic and semantic paradoxes.
International Research Projects
The aim of the project is to establish a collaboration between two active research groups (“Reflection and Incompleteness”, which is based in Oxford and funded by the AHRC and “Unrestricted Quantification, Expressiveness and Contextualism”, which is based in Buenos Aires and funded by the Argentinian National Research Council for Science and Technology). There is much overlap between the agendas of our research projects, and we would benefit from an opportunity to exchange our results and facilitate a longstanding cooperation between the groups. Although the senior members of each group have already had some limited opportunity to visit each other, the project would be particularly beneficial for the younger members of each group for whom the opportunities to travel from Oxford to Buenos Aires are much more limited. Three specific areas of overlap in our research projects concern type-free theories of truth, the expressive limitations caused by open endedness of the set-theoretic universe and the means of overcoming them.
The main goal of this project will be to find answers to questions that might lead this topic into some new directions, such us: (i) Does the truth predicate have explanatory power after all, contra the deflationist approach to truth? Could a good theory of truth have no standard models? And if one considers the second-order case with standard semantics, could a good theory of truth have no models while being consistent? (ii) Is there a theory of truth capable of dealing with semantic paradoxes and revenge problems in which every classical principle is valid? Or does the best explanation of these phenomena involve adopting a different notion of logical consequence? (iii) Is there a consistent, systematic, and philosophically illuminating way of expressing intensional notions such as necessity and knowledge in terms of predicates? How can the notorious paradoxes that have been claimed to affect such a treatment of intensional notions be avoided?
In this project, we will explore: i) the precise sense in which operational and substructural approaches weaken classical logic. ii) to what extent these proposals are revenge-free and what are the prospects of achieving such a goal. iii) whether the problem of restricted quantification can be satisfactorily dealth with in paracomplete and paraconsistent theories. iv) if it is possible to provide plausible philosophical interpretations of non-contractive consequence relations and in particular whether the is a plausible reading of the quantifiers. v) in what sense the cut-free approaches are classical and in what sense they are not.