Date: April 12, 2013

Place: University of Notre Dame, McKenna Hall, Rooms 210--214

Time: 9:00 AM--6:00 PM (Eastern Daylight Time)

All interested persons welcome. No admission charge.

Map of Notre Dame campus

McKenna Hall

For further information contact Michael Detlefsen (mdetlef1@nd.edu).

Program
 

Session I: 9:00 AM
 

Professor Joshua Schechter, Philosophy, Brown University

"Small Steps and Giant Leaps in Thought: The Epistemology of Basic Deductive Rules"

Abstract

We are justified in employing the rule of inference Modus Ponens (or
one much like it) as basic in our reasoning. By contrast, we are not
justified in employing any rule that permits inferring some difficult
mathematical theorem from the relevant axioms in a single step. Such
an inferential step is intuitively too large to count as justified.
What accounts for this difference? In this paper, I canvass several
possible explanations. I argue that the most promising approach is to
appeal to features like usefulness or indispensability to important or
required cognitive projects. On the resulting view, whether an
inferential step counts as large or small depends on the importance of
the relevant rule of inference in our thought.

Session II: 10:45 AM

Dr. Claes Strannegård, Linguistics & Theoretical Philosophy, University of Gothenburg

"Proofs and Dreams"

Abstract

I propose a cognitive architecture based on dual process theory. The long-term memory is modeled as a transparent neural network that develops autonomously by interacting with the environment. The working memory is modeled as a buffer containing (links to) nodes from the long-term memory. Computations are defined as processes in which working memory content is being transformed according to rules learned by the long-term memory. In this architecture symbolic and subsymbolic reasoning can be combined and computations ranging from proofs to dreams can be performed.

Lunch: 12:15 PM

Session III: 2:00 PM

Professor Lance Rips, Psychology, Northwestern University

"Counterfactual States and Explanatory Search"

Abstract

Several recent theories have tried to explain the truth of counterfactual conditionals (“If event e1 had been the case, then event e2 would have been the case”) in terms of the causal relations between the events. This talk looks at two such theories that share a common framework—that of Bayes networks (Hiddleston, 2005; Pearl, 2000). The differences between them suggest tests of the theories’ predictions for human reasoning. In these experiments, people answered counterfactual questions about simple machines. Participants learned about devices that have a specific configuration of components, and they answered questions of the form “If component X had not operated, would component Y have operated?” The results suggest that people try to construct an explanation for the counterfactual state—why component X had not operated—while attempting to preserve the device’s operating principles. Participants tended to prefer simpler explanation—explanations that require fewer changes to the device—but they sometimes had trouble tracing the logical implications of these changes.

Session IV: 3:45 PM

Professor Rafael Núñez, Cognitive Science, University of California-San Diego

"Abstraction and the Human Animal: Towards Naturalistic Foundations of
Mathematics"

Abstract

What is mathematics and what are its foundations? The question of the
nature of mathematics has been addressed primarily within the confines
of the philosophy of mathematics (e.g., formal logical) and mathematics
proper (e.g., metamathematics), with little, or no input from other
scientific disciplines. Given current scientific developments —
especially concerning new findings about how human abstraction and
imagination work — this is arguably an unnecessarily narrow approach to
the investigation of such deep and important question. In this
presentation I'll discuss results in cognitive science — the
interdisciplinary scientific investigation of the mind, which gathering
advances in neuroscience, psychology, linguistics, and anthropology,
among others, has empirically investigated mathematics as a human
conceptual system — one that is abstract, precise, objective, effective,
and formalizable, but that is human nonetheless. Discussing cognitive
studies involving the number line and infinitesimal calculus, I'll argue
that the time has come to approach the study of the nature of
Mathematics with empirical observations and testable explanations, and
not just with old philosophical beliefs and dogmas. The portrait of
mathematics has a human face, and it is up to us to get to know it!
 

End of Workshop: 5:30 PM

Sponsors: Department of Philosophy, Notre Dame Journal of Formal Logic, McMahon-Hank II Chair in Philosophy

Director: Michael Detlefsen, Philosophy, University of Notre Dame & University of Paris 7-Diderot

Manager: Mrs. Harriet Baldwin (baldwin.1@nd.edu), Director, Academic Conferences, Institute for Scholarship in the Liberal Arts (ISLA)