Location: Social and Behavioral Sciences Gateway, room 1321
Attendance is free, but registration with Patty Jones (patty.jones@uci.edu), preferably by Monday, April 1, is appreciated.
Speakers: Agustín Rayo (MIT), Alex Oldemeier (Leeds), Clinton Tolley (UCSD), Michael Kremer (Chicago), Patricia Blanchette (Notre Dame), Peter Hylton (University of Illinois, Chicago)
WORKSHOP SCHEDULE
Friday, 12 April
8:30 Continental Breakfast
9:00 Agustín Rayo (MIT)
Talk Title: "A Guide to the Concept Horse"
Abstract: Frege famously set forth the claim that the concept horse is not a concept. I will articulate a view of concepts and objects according to which Frege’s claim is essentially correct. I will not, however, be concerned with Frege scholarship. I aim to develop a view that is broadly Fregean in spirit, but will not attempt argue that the view is actually Frege’s.
10:30 Alex Oldemeier (Leeds)
Talk Title: “Basic arithmetical knowledge based on implicit definition”
Abstract: How can we justify basic mathematical propositions? Using the Peano axioms as an example, I first briefly present a regress argument that purports to show that they cannot be justified and then discuss whether we can give up the pre-theoretic intuition that they are justified. After that, I show that the regress argument is incomplete by sketching how I think the Peano axioms can be justified after all. My approach is a version of neo-Fregeanism (and a version of Hale’s and Wright’s account of implicit definition in particular). I argue that the Peano axioms can be justified on the basis of apriori knowledge that a certain meaning-fixing stipulation has been made. I close with rebutting objections to the proposal.
12:00 Noon Break
Talk Title: “In what sense is Frege a 'universalist' about logic?”
Abstract: Recently several influential interpreters have argued that Frege embraces what they call a ‘universalist’ conception of logic, according to which logic is the most universal science because it is 'about' everything, in the sense that its basic laws are laws that govern all objects and all concepts, and so, all that there is. Here I explore two important challenges to this interpretation. The first 'particularist' challenge comes from a sense that, far from being universal, Frege actually takes logic's subject-matter to be restricted to a very specific set of individual objects and concepts, such as the truth-values, the numbers, the identity-function, etc, or anything explicitly referred to (rather than indefinitely indicated) by expressions in the Begriffsschrift. The second, perhaps more radical, 'pragmaticist' challenge comes from a sense that, far from being 'about' any objects or concepts directly, Frege takes logic's subject-matter to be instead the activity of inference and so takes its basic laws and rules to directly govern justification-relations between acts of judgments. My goal will be to determine the extent to which the intuitions and textual evidence that motivate each of these three positions are in fact incompatible, or whether there might not be a way to incorporate all three into a more nuanced (and more complete) picture of Frege's views.
3:30 Coffee Break
4:00 Patricia Blanchette (Notre Dame)
Talk Title: “Axioms in Frege"
Abstract: Frege’s conception of axioms is an old-fashioned one, especially as compared with the modern conception in terms of which the role of axioms is that of defining structure-types. In this talk, I discuss several important aspects of Frege’s conception of axioms, exploring particularly some of the ways in which such important modern notions as the independence and the categoricity of axioms do, and ways in which they do not, make sense from Frege’s point of view. Part of the purpose of this investigation is to gain some clarity about what we gain, and what we lose, when we turn away from a purely Fregean conception of axioms.
Saturday, 13 April
9:00 Continental Breakfast
Talk Title: "Definitions in Begriffsschrift and Grundgesetze"
Abstract: I investigate changes made by Frege in the definitions of key concepts (hereditary property, ancestral, many-one relation) between Begriffsschrift (1879) and Grundgesetze, vol. 1 (1893). I argue that the form of these definitions in Begriffsschrift is defective. This problem is fixed in Grundgesetze but in a way that depends on the introduction of courses-of-values, and so on the problematic Basic Law V. I end by considering the significance of these conclusions.
11:00 Coffee Break
11:30 Peter Hylton (University of Illinois, Chicago)
Talk Title: “Problems of Philosophy as a stage in the evolution of Russell’s views on knowledge”
Abstract: This paper considers Problems of Philosophy, and other works which Russell wrote in the same year (1911), as one stage in the evolution of his views on knowledge. The main focus is on our knowledge of physical objects. The stage is set by Russell’s rejection of the view that we are acquainted with such objects; this rejection is first stated in 1905 (perhaps following Moore’s paper of that year, “Nature and Reality of the Objects of Perception”) but not until 1911 does Russell argue for it and begin to work out its consequences. Since it is almost undeniable that we at least appear to have knowledge of physical objects, Russell, in Problems, tries to explain how we can have such knowledge. The explanation relies heavily on the theory of descriptions. It also requires us to have very extensive a priori knowledge of the relations of sense-data to physical objects. It may be that this requirement came to seem implausible to Russell, and that this is what led him to the next stage in his view of what passes for our knowledge of physical objects. In this next stage, he speaks of physical objects as logical constructions, but this metaphor disguises how radical the new view is. That view denies that we really have any knowledge at all physical objects, even that there are such things to be known. What appears to be knowledge of such objects does not in fact extend beyond our knowledge of our own sense-data and the purely abstract objects of logic.
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