PPP

"Plurals, Predicates, and Paradox: Towards a Type-Free Account"

Coordinatore	UNIVERSITETET I OSLO    more Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie.
Nazionalità Coordinatore	Norway [NO]
Totale costo	940˙655 €
EC contributo	940˙655 €
Programma	FP7-IDEAS-ERC Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
Code Call	ERC-2009-StG
Funding Scheme	ERC-SG
Anno di inizio	2010
Periodo (anno-mese-giorno)	2010-01-01   -   2013-12-31

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	BIRKBECK COLLEGE - UNIVERSITY OF LONDON  Organization address address: Malet Street city: LONDON postcode: WC1E 7HX contact info Titolo: Mr. Nome: Craig Cognome: Bryce Email: send email Telefono: +44 20 7380 3141 Fax: +44 20 7380 3221	UK (LONDON)	beneficiary	432˙885.66
2	UNIVERSITETET I OSLO  Organization address address: Problemveien 5-7 city: OSLO postcode: 313 contact info Titolo: Dr. Nome: øystein Cognome: Linnebo Email: send email Telefono: +44 20 7631 6383 Fax: +44 20 7631 6564	NO (OSLO)	hostInstitution	507˙769.34
3	UNIVERSITETET I OSLO  Organization address address: Problemveien 5-7 city: OSLO postcode: 313 contact info Titolo: Ms. Nome: Karen Cognome: Haugland Email: send email Telefono: 4722856928 Fax: 4722857551	NO (OSLO)	hostInstitution	507˙769.34

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 Obiettivo del progetto (Objective)

'This project aims to transform our understanding of the logical paradoxes, their solution and significance for mathematics, philosophy and semantics. It seeks to show that some of the key inferences in the paradoxes should not uncritically be blocked, as is customary, but rather be tamed and put to valuable mathematical, philosophical and semantic use. By adopting a richer logical framework than usual, the paradoxes can be transformed from threats to valuable sources of insight. When discovered at the turn of the previous century, the paradoxes caused a foundational crisis in mathematics. Many logicians and philosophers now believe the crisis has been resolved. This project denies that an acceptable resolution has been found and aims to do better. A strong push remains towards paradox. This push arises from the widespread use of (and need for) higher-order logics (HOL), which allow quantification into the positions of predicates or plural noun phrases. Phase I seeks to reveal greater similarities between HOL and set theory than generally appreciated. Phase II explores four arguments that HOL collapses to first-order logic, i.e. that every higher-order entity defines a corresponding first-order entity. These arguments are generally ignored as they threaten to reintroduce the paradoxes. But we show that a properly circumscribed form of collapse is a valuable source of mathematical and semantic insight. Phase III examines controlled forms of collapse using notions of modality and groundedness. This enables us to motivate ZF set theory and valuable semantic theories, explain the nature of cognition about sets and properties, and show that mathematics cannot be fully extensionalized. Phase IV applies these insights to solve the paradoxes and criticize influential uses of HOL.'