The strict-tolerant (ST) approach to paradox promises to erect theories of naïve truth and tolerant vagueness on the firm bedrock of classical logic. We assess the extent to which this claim is founded. Building on some results by Girard (Diss Math 136, 1976) we show that the usual proof-theoretic formulation of propositional ST in terms of the classical sequent calculus without primitive Cut is incomplete with respect to ST-valid metainferences, and exhibit a complete calculus for the same class of metainferences. We also argue that the latter calculus, far from coinciding with classical logic, is a close kin of Priest’s LP.
ST, LP, and tolerant metainferences
francesco paoli
;bogdan dicher
2019-01-01
Abstract
The strict-tolerant (ST) approach to paradox promises to erect theories of naïve truth and tolerant vagueness on the firm bedrock of classical logic. We assess the extent to which this claim is founded. Building on some results by Girard (Diss Math 136, 1976) we show that the usual proof-theoretic formulation of propositional ST in terms of the classical sequent calculus without primitive Cut is incomplete with respect to ST-valid metainferences, and exhibit a complete calculus for the same class of metainferences. We also argue that the latter calculus, far from coinciding with classical logic, is a close kin of Priest’s LP.
| File | Dimensione | Formato | |
|---|---|---|---|
|
Articolo versione bozza.pdf
Solo gestori archivio
Tipologia:
versione post-print (AAM)
Dimensione
385.02 kB
Formato
Adobe PDF
|
385.02 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I metadati presenti in IRIS UNICA sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono protetti da diritto d'autore, salvo diversa indicazione.
