Workshop on Logicism
08.06.2024
Idea and Motivation
The workshop deals with classical and recent attempts at logicism, that is, the reduction of mathematics to logic, as well as closely related topics, such as abstraction, higher-order logic, and "thin“ accounts of objects.
Speakers
- Francesca Boccuni, University Vita-Salute San Raffaele
- Bruno Jacinto, Lisbon
- Øystein Linnebo, Oslo
- James P. Studd, Oxford
- Edward N. Zalta, Stanford
Program
| Time | Event |
| 09:00-10:30 | Edward N. Zalta: A Defense of Logicism |
| 10:30-11:00 | Coffee Break |
| 11:00-12:30 | Francesca Boccuni |
| 12:30-14:00 | Lunch Break |
| 14:00-15:30 | James P. Studd |
| 15:30-16:00 | Coffee Break |
| 16:00-17:30 | Bruno Jacinto |
| 17:30-19:00 | Øystein Linnebo |
| 20:00 | Workshop Dinner at "Conviva im blauen Haus" |
Abstracts
Edward N. Zalta: A Defense of Logicism
(Authors: Hannes Leitgeb, Uri Nodelman, and Edward N. Zalta)
Abstract: We argue that logicism, the thesis that mathematics is reducible to logic and analytic truths, is true. We do so by (a) developing a formal framework with comprehension and abstraction principles, (b) giving reasons for thinking that this framework is part of logic, (c) showing how the denotations for predicates and individual terms of an arbitrary mathematical theory can be viewed as logical objects that exist in the framework, and (d) showing how each theorem of a mathematical theory can be given an analytically true reading in the logical framework.
Francesca Boccuni: Fregean Object Theory
Authors: Francesca Boccuni & Sean Ebels-Duggan (Northwestern University)
Abstract: We will present a plural theory of Fregean objects (FAO+) based on Boolos' and Zalta's intuition that Fregean abstraction principles rely on explicit existential assumptions. The axioms of the theory are so regimented that the resulting system is consistent, but strong enough to derive some important Fregean abstraction principles (e.g. BLV and HP). We will also investigate the mathematical strength of FAO+ (in particular, if FAO+ interprets PA2 via definitions that parallel Frege's) and the philosophical problem of cross-sortal identity of Fregean abstracts.
James Studd: Caesar and Stipulation
Abstract: A neglected response to the Caesar problem maintains that the content of ‘mixed’ identity contexts such as ‘#X = Julius Caesar’ is just as open to stipulation as the content of ‘unmixed’ contexts such as ‘#X = #Y’. I defend this stipulative response against some objections, including those raised by Fraser MacBride and by Bob Hale and Crispin Wright.
Bruno Jacinto: Sets as properties
According to the iterative conception of set, sets are “built in stages” in a process to be pursued “as far as possible”. It is notoriously difficult to make sense of the “building” analogy unless the mind-dependence of sets is accepted. In this talk I will sketch the sets as properties view, according to which set theory is nothing but a part of cumulative (modal) type theory, and sets are just a specific kind of properties. I will offer some reasons for thinking that the sets as properties view, broadly based on (Linnebo & Rayo 2012, Degen & Johannsen 2000) delivers a more satisfactory and realist understanding of the iterative conception than those presently available. In addition, I will address Button and Trueman’s (2022) “no bootstrapping” objection to the sets as properties view. Finally, I will show how this reply paves the way to a modal and neoRussellian form of logicism which is thoroughly contingentist.
Øystein Linnebo: Abstraction and Critical Plural Logic
Dummett wished to solve the bad company problem by requiring that abstraction be predicative in some sense. The dominant way to pursue this idea has been to impose predicativity restrictions on the second-order logic. I review why this strategy has not been a success. I propose an alternative development of Dummett’s idea, namely that we obtain a large and natural class of permissible abstractions by (i) abstracting on pluralities of objects (rather than Fregean concepts), and (ii) use the Critical Plural Logic recently developed by Salvatore Florio and myself rather than traditional plural logic.
Organizer
Registration
Please register sending an email to Office.Leitgeb@lrz.uni-muenchen.de.
Venue
Prof.-Huber-Pl. 2, Room W 401.
Restaurant
Conviva im Blauen Haus, Hildegardstr. 1, 80539 München