September 27, 2006, 6-7:30 PM in 234 Moses Hall
José Ferreiros (University of Sevilla)
Hilbert, Logicism, and Mathematical Existence
October 11, 2006, 6-7:30 PM in 234 Moses Hall
Franz Huber (Cal Tech, Philosophy)
The Consistency Argument for Ranking Functions
The paper provides an argument for the thesis that an agent’s degrees of disbelief should obey the ranking calculus. This Consistency Argument is based on the Consistency Theorem, which says that an entrenchment function gives rise to consistent and deductively closed beliefs iff it satisfies the ranking axioms. The Consistency Argument is extended to various rank-theoretic update rules.
November 08, 2006, 6-7:30 PM in 234 Moses Hall
Stephen Palmer (UC Berkeley, Psychology)
Rethinking Figure/Ground Organization
Several new results on figure-ground organization from our laboratory will be presented that question the classical view of figure-ground organization as a unitary phenomenon and/or process. What emerges is a different view in which the perceptual interpretation near a depth edge results from a complex interaction among at least four different components: perception of local depth across the edge, shape perception, visual attention, and both modal and amodal completion of the partly occluded surface.
November 29, 2006, 6-7:30 PM in 234 Moses Hall
Dana Scott (Carnegie Mellon University)
The Future of Proof
Gödel showed us many things. Among others he showed us the possibility of proof (via the Completeness Theorem for First-Order Logic); and then quite soon thereafter he showed us the impossibility of proof (via the Incompleteness Theorem for (suitable) Higher-Order Logics). These results are well known and famous, but their impact on the practice of mathematics has perhaps not been very noticeable. To be sure, related recursive unsolvability results have a clear explanatory value in keeping people from searching for algorithms where none can exist. And modern developments in complexity theory show that many easily stated problems have – in general – no quick solutions. But again, many commentators agree that there has not been a big shift in main-stream mathematics as a consequence of Gödel’s fundamental work. However, the insight into formalization sparked by Gödel’s original work is now having major payoffs in mechanized mathematics and proof systems. The lecture will survey some developments, but it will also bring up the questions of what we should now regard as a proof and of how new proof methods develop.
December 06, 2006, 6-7:30 PM in 234 Moses Hall
Roberta Millstein (UC Davis, Philosophy)
Finding the Causes in an Evolving Population: Lessons From an Early Drifter
Biologists and philosophers have been extremely pessimistic about the possibility of demonstrating random drift in nature, particularly when it comes to discriminating random drift from natural selection. However, examination of a historical case – Maxime Lamotte’s study of natural populations of the land snail, Cepaea nemoralis in the 1950s – shows that while some pessimism is warranted, it has been overstated. Indeed, by describing a unique signature for drift, and showing that this signature obtained in the populations under study, Lamotte was able to make a good case for a significant role for drift. It may be difficult to disentangle the causes of drift and selection acting in a population, but it is not (always) impossible. More broadly, this case raises the question of how to disentangle causes when multiple causes are operating. In other words, we need an account that tells us how to figure out which causes are operating, and how to measure their relative effects, if the latter is even possible.
February 28, 2007, 6-7:30 PM in 234 Moses Hall
Terrence Parsons (UCLA, Philosophy)
What is Medieval Supposition Theory?
Medieval writers used the Latin word ‘supposition’ pretty much as we today use ‘reference’ or ‘standing for’. In the sentence ‘Some horse is grey’ the subject term ‘horse’ supposits for, or stands for, each and every currently existing horse. There are (at least) three theories dealing with supposition.
One has to do with whether the term supposits for itself (as in ‘Donkey is a noun’, or for the species or mental concept on which the word is imposed (as in ‘Donkey is a species’), or for the things that its associated form or concept picks out in the world (as in ‘Some donkey is grey’). I’ll describe briefly how this works.
A second has to do with how various items in a sentence restrict or ampliate the range of things that the term supposits for: a past or future tense lets the term ‘donkey’ supposit for past or future donkeys, a modal word lets it supposit for possible donkeys, and a word pertaining to the soul (such as ‘opine’) lets it supposit for any donkey whatever, including non-existent and impossible donkeys (if there are any). I’ll describe this theory and articulate a problem concerning ontological commitment associated with it.
A third – the modes of supposition – has to do with the quantificational status of a term. The term ‘donkey’ has determinate supposition (something like wide-scope-existential) in ‘Some donkey is grey’, it has distributive supposition (something like universal) in ‘Every donkey is grey’, and it has merely confused supposition (something like narrow-scope-existential) in ‘Every grey thing is a donkey’. I’ll describe how the modes of supposition are defined, how one can decide what mode a term has, and some rules of inference that rely on the modes.
March 07, 2007, 6-7:30 PM in 234 Moses Hall
José M. Sagüillo (Department of Logic and Moral Philosophy, University of Santiago de Compostela, Spain)
Two Complementary Concepts of Logical Consequence: Model-theoretic consequence and Information-theoretic consequence
I discuss two concepts of logical consequence and show how they are expressed in the two fundamental logical experiences: that of establishing validity of a given valid argument and that of establishing invalidity of a given invalid argument. The asymmetry between establishing validity and establishing invalidity has long been noted: validity is established through exhibiting a step-by-step deduction of the conclusion from the premise set; invalidity is established by exhibiting a model. Tarski’s transformational conception of logical consequence formulated in his famous 1936 no countermodels definition is implicitly expressed in the process of showing that an argument is invalid – that a model of its premise set is a countermodel of its conclusion. Corcoran’s informational conception of logical consequence formulated in the information-containment postulate of his 1998 article is implicitly expressed in the process of showing that an argument is valid – that the conclusion’s information is contained in that of its premise set. Both found to be indispensable for understanding the rationale of the deductive method. Each complements the other and serves as a check against errors in playing the other. This is not to say that these two conceptions are similar. On the contrary, they exhibit important philosophical differences both ontological and epistemological. Thus, the discussion goes from the ontic question of the nature of logical consequence to the epistemic question of the human capabilities presupposed by practical applications of these two conceptions as they make validity and invalidity accessible properties.
April 11, 2007, 6-7:30 PM in 234 Moses Hall
Tania Lombrozo (UC Berkeley, Psychology)
Empirical Investigations of Explanation and Causation
What constitutes an explanation? This question has received considerable attention in philosophy of science, but relatively little is known about the psychology of explanation. In this talk I’ll present recent empirical work on the psychology of explanation, focusing on teleological explanations–explanations in terms of a function or goal. Drawing on analyses from philosophy, I’ll suggest that people understand teleological explanations as causal explanations: they are only accepted when the function invoked in the explanation played a causal role in bringing about what is being explained. However, I’ll also suggest that casual relationships are evaluated differently in the context of teleological explanations than in the context of mechanistic explanations. These differences map onto different philosophical theories of causation– roughly, a counterfactual account versus a physical connection/transfer of force account. Thus a second, more speculative aim of the talk will be to suggest the psychological reality of multiple concepts of causation.
April 25, 2007, 6-7:30 PM in 234 Moses Hall
Johan van Benthem (Stanford, Philosophy)
I will discuss the ‘social’ aspect of logic as an account of intelligent interaction, witness its role in the study of argumentation, communication, and games in general. This requires the design of dynamic logics for changing information, beliefs, and preferences, which I explain in the setting of strategic behavior in extensive games. I conclude by outlining how this stance throws new light on issues in epistemology and the philosophy of science.