Third UCI FregeFest, February 26-27, 2010
Location: Social and Behavioral Sciences Gateway, room 1517
Attendance is free, but registration with Patty Jones (firstname.lastname@example.org), preferably by Feb 12, is appreciated.
Friday, 26 February
9:00 Jeremy Heis, UC Irvine: “The Priority Principle from Kant to Frege”
In a famous passage, Kant writes that “the understanding can make no other use of […] concepts than that of judging by means of them.” Kant’s thought is often called the thesis of the priority of judgments over concepts. We find a similar sounding priority thesis in Frege: “it is one of the most important differences between my mode of interpretation and the Boolean mode […] that I do not proceed from concepts, but from judgments.” Many interpreters have thought that Frege’s priority principle is close to (or at least derivable from) Kant’s. I argue that it is not. Nevertheless, there was a gradual historical development that began with Kant’s priority thesis and culminated in Frege’s new logic.
11:00 Richard L. Mendelsohn, CUNY: “Sinn/Bedeutung with Scope”
Frege included no scope distinction for definite descriptions; none for any quantified expression in either modal or attitude constructions. Why not? The texts show, not that Frege was opposed to the de re, but that he was unaware of it. So appending scope turns out to require minimal revision of fundamental doctrine. I explore these matters by systematically deepening the sensitivity of the Sinn/Bedeutung theory to scope, first in extensional contexts, then in intensional contexts, and finally in hyperintensional contexts.
2:00 Sean Walsh, Notre Dame: “Logicism, Interpretability & Knowledge of Arithmetic”
In contemporary discussions of logicism, one can find claims to the effect that arithmetical knowledge can be based on knowledge of principles such as Hume's Principle and that Hume's Principle in turn has an epistemic status similar to that of truths of logic. Most of the recent discussion of logicism has focused on the epistemic status of Hume's Principle, and has neglected the question of how knowledge of Hume's Principle is supposed to support knowledge of arithmetical principles. The goal of this talk is to articulate and evaluate different accounts of how knowledge of arithmetical principles may be based on knowledge of Hume's Principle. In particular, we articulate syntactic and semantic versions of this account, and we suggest that both face deep problems. Roughly, the syntactic account cannot seem to exert an appropriate amount of control over the types of things which it counts as knowledge, while the semantic account is seemingly question-begging.
4:00 Aldo Antonelli, UC Davis: “The Nature of Abstraction”
The logical status of abstraction principles, and especially Hume’s Principle, has been long debated, but the best currently available tool for explicating a notion’s logical character – permutation invariance – has not received a lot of attention in this debate. This talk aims to fill this gap. After characterizing abstraction principles as particular mappings from the subsets of a domain into that domain, we explore several distinct notions of permutation invariance for such principles, assessing the philosophical significance of each.
Saturday, 27 February
9:30 William Demopoulos, Western Ontario: “Carnap’s Thesis and Frege’s Criterion of Identity”
By ‘Carnap’s thesis’ I mean the assertion that logic and mathematics are not factual. This is not simply a more general formulation of the well-known “Principle of Tolerance,” but a thesis that is capable of justifying that principle. I present two strategies for establishing Carnap’s thesis. The first is based on Wittgenstein’s notion of a tautology and his account of logical propositions in the Tractatus. The second is based on Hilbert’s development of the axiomatic method and the distinction between pure and applied geometry which it inspired. I argue that the second strategy yields a plausible defense of the thesis for a “narrow” conception of factuality, a defense that has eluded the first strategy. My discussion of Carnap’s thesis has a corollary: Among applications of mathematical theories, there are those that proceed via a mathematical theory’s physical interpretation, and those that do not. It has long been held that the distinction between these cases is well-illustrated by geometry and arithmetic. I show that the distinction can be traced to the role played by empirical constraints on criteria of identity—Frege’s criterion of identity in the case of applications of the theory of the natural numbers in counting, and the criterion of identity that controls physical applications of four-dimensional geometrical theories in the case of the theory of space and time.
11:30 Roy T. Cook, University of Minnesota: “In favor of strong stability: A solution to the Bad Company Objection”
The Bad Company Objection challenges the Neo-logicist to provide a principled division between abstraction principles that are 'good' (such as, presumably, Hume's Principle) and abstraction principles which are 'bad' (such as Basic Law V). The literature contains a number of proposals for drawing this distinction, but each of these either has been shown to be inadequate (e.g. consistency, conservativeness, unboundedness) or lacks substantial philosophical motivation (stability, irenicity, strong stability). Conservativeness, although failing as a sufficient condition, is nevertheless a plausible necessary condition for the acceptability of abstraction principles. After identifying an important insight regarding the correct 'behavior' of abstraction principles - an insight corresponding to the requirement that abstraction principles be conservative - I generalize this insight, arriving at a new condition which is a plausible necessary and sufficient condition for the acceptability of abstraction principles. I then show that this condition is equivalent to strong stability.