Five observations concerning the intended meaning of the intuitionistic logical constants

Citation
G. Fernandez Diez, Five observations concerning the intended meaning of the intuitionistic logical constants, J PHILOS LO, 29(4), 2000, pp. 409-424
Citations number
27
Categorie Soggetti
Philosiphy
Journal title
JOURNAL OF PHILOSOPHICAL LOGIC
ISSN journal
00223611 → ACNP
Volume
29
Issue
4
Year of publication
2000
Pages
409 - 424
Database
ISI
SICI code
0022-3611(200008)29:4<409:FOCTIM>2.0.ZU;2-6
Abstract
This paper contains five observations concerning the intended meaning of th e intuitionistic logical constants: (1) if the explanations of this meaning are to be based on a non-decidable concept, that concept should not be tha t of 'proof'; (2) Kreisel's explanations using extra clauses can be signifi cantly simplified; (3) the impredicativity of the definition of double righ t arrow in terms of 'proofs from premises' results in a loss of the inducti ve character of the definitions of \/ and There Exists and (5) the same occ urs with the definition of For All in terms of 'proofs with free variables' .