Chapter

Systems with Propositional Constants and Functorial Variables

A. N. Prior

in Formal Logic

Published in print March 1963 | ISBN: 9780198241560
Published online October 2011 | e-ISBN: 9780191680373 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780198241560.003.0003
Systems with Propositional Constants and Functorial Variables

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If people are to build up a propositional calculus with a single undefined operator, it seems a pity that it should be an awkward one as ‘neither’ or ‘not-both’. Peirce gave expression in the nineteenth century to the feeling, shared by many logicians, that the ideal would be develop everything else in terms of implication. The first section of this chapter discusses the implicational calculus and Wajsberg's system in C and o. The second section considers Quine's completeness proof for the full calculus. The third section examines Wajsberg's completeness proof for the restricted calculus. The last section describes logic, metalogic, and functorial variables.

Keywords: full calculus; logic; metalogic; completeness; Quine; implicational calculus; Wajsberg's system

Chapter.  6496 words. 

Subjects: Philosophy of Mathematics and Logic

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