November 05, 2014, 6-7:30 PM in 234 Moses Hall

Richard Zach (University of Calgary, Philosophy)

The Decision Problem and Logical Metatheory

The emergence of first-order logic and its metatheory is commonly seen as a switch from a purely axiomatic development of the logical systems in the Hilbert school to a metalogical view that incorporates model-theoretic methods. Although one origin of these model theoretic methods undoubtedly can be found in the work of Skolem and later Gödel and Tarski, to whom they are usually credited, even in the Hilbert school itself work on the decision problem independently gave rise to model-theoretic thinking, occasioned by the needs for proving decidability. The episode shows how mathematical practice can force fundamental changes in methodology.

March 11, 2015, 6-7:30 PM in 234 Moses Hall

Mark Fedyk (Mount Allison University)

Ethics, as an Empirical Discipline

A hallmark of reliable scientific inquiry is the revision of conceptual meaning and associated inferential connections, where the revisions are often induced by empirical evidence, and where the aim of the revisions is usually the accommodation of scientific theories to the natural world as closely as possible. Can ethical inquiry exemplify the same conceptual flexibility, in pursuit of the same aim, and do so without reducing itself to another scientific discipline? I will describe a way of defining ethical norms according to which they are hypotheses that can be subject to empirical evaluation, and I will also describe some of the specific kinds of observations and inferences from empirical data that would be relevant to confirming or disconfirming these ‘empirical’ ethical hypotheses. Of course, I will also present some philosophical arguments in favour of expanding our conception of ethical inquiry so that it can sometimes be pursued using empirical methods. However, my primary focus will simply be to describe what ethics may look like, if it is an empirical discipline.

March 18, 2015, 6-7:30 PM in 470 Stevens Hall

Jeremy Heis (UC Irvine)

Why Did Geometers Stop Using Diagrams?

Joint event with OHST.
The consensus for the last century or so has been that diagrammatic proofs are not genuine proofs. Recent philosophical work, however, has shown that (at least in some circumstances) diagrams can be perfectly rigorous. The implication of this work is that, if diagrammatic reasoning in a particular field is illegitimate, it must be so for local reasons, not because of some in-principle illegitimacy of diagrammatic reasoning in general. In this talk, I try to identify some of the reasons why geometers in particular began to reject diagrammatic proofs. I argue that the reasons often cited nowadays – that diagrams illicitly infer from a particular to all cases, or can’t handle analytic notions like continuity – played little role in this development. I highlight one very significant (but rarely discussed) flaw in diagrammatic reasoning: diagrammatic methods don’t allow for fully general proofs of theorems. I explain this objection (which goes back to Descartes), and how Poncelet and his school developed around 1820 new diagrammatic methods to meet this objection. As I explain, these new methods required a kind of diagrammatic reasoning that is fundamentally different from the now well-known diagrammatic method from Euclid’s Elements. And, as I show (using the case of synthetic treatments of the duals of curves of degrees higher than 2), it eventually became clear that this method does not work. Truly general results in “modern” geometry could not be proven diagrammatically.

April 22, 2015, 6-7:30 PM in 234 Moses Hall

Kerry McKenzie (UCSD)

In No Categorical Terms: Symmetries as a new route to Humeanism about Fundamental Laws

In the metaphysics literature on laws of nature one finds a position called ‘Humeanism’, in which the fundamental properties are taken to have a categorical character and the laws to be contingent as a result. This Humean view is a popular one, perhaps even the default one. But I myself find it borderline unintelligible, largely on account of symmetry.

In this talk, I’ll try to explain why I have such a hard time locating either categorical properties or nomic contingency in contemporary physics, where symmetries have a pivotal role. But I’ll also claim that that doesn’t itself mean that Humeanism is dead in the water; rather, I’ll suggest that we just need to rethink Humeanism, and in particular that we need to think much more seriously about mathematics when doing modal metaphysics.

May 06, 2015, 6-7:30 PM in 234 Moses Hall

Alexei Grinbaum (LARSIM, Gif-sur-Yvette)

The problem of composition from perichoresis to quantum entanglement

Recent work in quantum theory drives home the importance of the composition rule. The amount of entanglement, as for example measured by the Tsirelson bound of Bell inequalities, is a crucial non-classical ingredient describing how two subsystems form a compound system. If modern science performs this analysis through rigorous mathematics, the problem itself is not new. It was known to the Stoics and to Christian theology. Some theoretical questions at the time were remarkably similar to the questions around quantum entanglement. I’ll trace a few repeating motives and will use them to draw a panorama of open problems in quantum theory.