Constructional Approaches in the Foundations of Mathematics and Philosophy
KEYNOTES
University of Notre Dame
University of Texas Austin
DISCUSSANTS
C-FORS is glad to announce its first graduate conference.
The topic is constructional appraoches in the foundations of mathematics and in philosophy.
ABOUT THE TOPIC
By “constructional approach” we mean a way to account for a domain of objects by successively constructing its members. The inspiring example for these methods is the famous Iterative Conception of Set, which states that sets are “formed” successively by iterated applications of the operation “set of” (to use Gödel’s terms). The aim of C-FORS is to extend the approach exemplified by the Iterative Conception — which has proven to be quite successful as a natural guard against paradoxes and in justifying the axioms of ZFC — to other formal disciplines. In particular, in the foundations of mathematics the aim of C-FORS is to extend the iterative account of sets to other mathematical entities, such as classes or other intensional objects. On the other hand, in formal philosophy, the aim is to develop constructional approaches that account for hierarchies of higher-order entities and of truth predicates.
ABOUT THE CONFERENCE
The aim of the conference is to bring together graduate students working in the Philosophy of Mathematics and Logic, in Metaphysics and in Ontology and that are interested in (or critical of) constructional (i.e., iterative or hierarchical) accounts in these disciplines. Beside the current members of C-FORS, the discussion shall be guided by the two invited keynotes, Joel David Hamkins (Notre Dame) and Jon Erling Litland (UT Austin), who are both leading experts on topics relevant to the main theme of the conference. In addition, the conference involves the assignment of a commentator to lead the discussion on the contributed talk by each participant. Comments will be provided by scholars that are also experts in their fields.
SCHEDULE
Wednesday 19th (GMH 452)
09.00 – 09.30: Coffee and Welcome
09.30 – 11.00: Keynote
Joel David Hamkins (O’Hara Professor of Logic, University of Notre Dame), The Continuum Hypothesis could have been a fundamental axiom
Abstract
I shall describe a simple historical thought experiment showing how our
attitude toward the continuum hypothesis could easily have been very different than it
is. If our mathematical history had been just a little different, I claim, if certain
mathematical discoveries had been made in a slightly different order, then we would
naturally view the continuum hypothesis as a fundamental axiom of set theory, one
furthermore necessary for mathematics and indeed, indispensable for calculus.
11.00 – 11.30: Break
11.30 – 12.30:
Sofie Vaas (University of Konstanz), Internal Categoricity and Universism
Responds: Tim Button (University College London)
12.30 – 14.00: Lunch
14.00 – 15.00:
Simon Schmitt (University of Turin), Set-Theoretic Bicontextualism
Responds: Deborah Kant (University of Hamburg)
15.00 – 15.30: Break
15.30 – 16.30:
Ismael Ordóñez Miguéns (University of Santiago de Compostela), Liberalising Construction: An argument against countabilism
Responds: Chris Scambler (University of Oxford)
16.30 – 17.00: Break
17.00 – 18.00:
Andrea Lupo (Universiyt of Italian Switzerland), The Generation of Universals
Responds: Sam Roberts (University of Konstanz)
19.30: Dinner at Yokoso
Thursday 20th (GMH 652)
09.00 – 09.30: Coffee and Welcome
09.30 – 11.00: Keynote
Jon Erling Litland (Associate Professor, University of Texas Austin), Generative Relations
Abstract
Many philosophers have been attracted to generative ontologies. There are
some given entities, and all other entities are, ultimately, the result of applying
generative operations – e.g., set formation, cardinal abstraction, structural abstraction… – to the given entities. Most philosophers who have espoused generativism have
treated the generative operations as functions. In this talk I argue that this is wrong and
that generative operations should be understood as relations. Doing this has two
advantages. First, it allows us to make sense of important de re dependence claims.
Second, it gives us a better account of generative operations – like sequence- and
string-formation – that are sensitive to order.
11.00 – 11.30: Break
11.30 – 12.30:
Boaz Darius Laan (University of Oxford), How Platonist can a Modal Potentialist Be?
Responds: Ethan Brauer (University of Oslo)
12.30 – 14.00: Lunch
14.00 – 15.00:
Giorgio Lenta (University of Genova), The Hyperintensional Variant of Kaplan’s Paradox
Responds: Jon Erling Litland (University of Texas Austin)
15.00 – 15.30: Break
15.30 – 16.30:
Yuan Du (University of Gothenburg), A Hybrid Constructional Approach to Higher-order Entities
Responds: Peter Fritz (University of Oslo/University College London)
16.30 – 17.00: Break
17.00 – 18.00:
Pedro Teixeira Yago (Scuola Normale Superiore in Pisa), The Structure of the Hierarchy of Arbitrary Objects
Responds: Neil Barton (National University of Singapore/University of Oslo)
VENUE
The conference takes place at the University of Oslo, Department of Philosophy, Classics, History of Art and Ideas, situated in Blindern Campus, building: Geor Morgenstiernes hus.
The conference room is GMH 452 for Wednesday and GMH 652 for Thursday. They are the conference rooms situated, respectively, at the 4th and 6th floor of the department, at the end of the corridor.
How to get to Blindern (Link 1/Link 2)
- Tram: line 17 and 18 towards Rikshospitalet, Stop at Universitetet Blindern.
- Metro (T Bane): line 4 (Vestli via Storo), 5 (Ringen via Storo) 5 (Sognsvann), Stop at Blindern.
FOR MORE INFORMATIONS, CONTACT