The congress hosted the second edition of the Lullius Lectures, which will be in charge of Prof. Hartry Field (New York U.). Hartry Field is Silver Professor of Philosophy at New York University and a leading contributor to philosophy of mathematics, philosophy of logic, philosophy of language, philosophy of science, metaphysics and epistemology.
He is the author of Science Without Numbers (Blackwell 1980), which won the Lakatos Prize, Realism, Mathematics and Modality(Blackwell 1989), Truth and the Absence of Fact (Oxford 2001) and Saving Truth from Paradox (Oxford, 2008).
His recent work is on semantic paradoxes, especially the Liar paradox and also the paradoxes of vagueness, where he defends a paracomplete approach.
The steering committee of the society organized a symposium on H. Field's work, with talks by David Liggins (University of Manchester) and Elia Zardini (University of Lisbon):
Liggins, David (University of Manchester). The 'hard road' revisited
In this talk, I revisit Field's pivotal contribution to the philosophy of mathematics in the light of Mark Colyvan's distinction between 'easy road' and 'hard road' responses to the indispensability argument. In particular, I focus on the question of which resources are available to a nominalist who follows Field down the 'hard road'.
Zardini, Elia (University of Lisbon). One, and Only One
Standard non-‐classical (i.e. non-‐substructural) solutions to the semantic paradoxes of truth deny either the law of excluded middle or the law of non-‐contradiction; in so doing, they either reject both the truth of a paradoxical sentence and its falsity or accept both the truth of a paradoxical sentence and its falsity. In this sense, both kinds of solutions agree that paradoxical sentences are inconsistent—that such sentences cannot coherently be assigned one and only one truth value. This pattern extends from the semantic paradoxes of truth to the semantic paradoxes of reference: when faced with at least certain particularly recalcitrant paradoxes of naive reference, both kinds of solutions are forced to claim that the paradoxical singular terms in question are inconsistent—that they cannot coherently be assigned one and only one referent. I’ll argue that, contrary to what both kinds of solutions require, under plausible assumptions paradoxical singular terms can be constructed that are forced to refer to a unique object. By considering these and other more traditional paradoxes, I’ll then show how my favoured non-‐contractive solution to the semantic paradoxes, which generally treats paradoxical entities as consistent rather than as inconsistent, can be so deployed as to offer a unified solution to the semantic paradoxes of truth and to those of reference and definability.