Logic and Truth: Some Logics without Theorems

  • Jayanta Sen Presidency College, 86/1, College Street, Kolkata - 73, INDIA.
  • Mihir Kumar Chakraborty University of Calcutta
Keywords: logical truth, logical consequence, lattice

Abstract

Two types of logical consequence are compared: one, with respect to matrix and designated elements and the other with respect to ordering in a suitable algebraic structure. Particular emphasis is laid on algebraic structures in which there is no top-element relative to the ordering. The significance of this special condition is discussed. Sequent calculi for a number of such structures are developed. As a consequence it is re-established that the notion of truth as such, not to speak of tautologies, is inessential in order to define validity of an argument.

Author Biographies

Jayanta Sen, Presidency College, 86/1, College Street, Kolkata - 73, INDIA.
Lecturer, Department of Mathematics
Mihir Kumar Chakraborty, University of Calcutta
Professor, Deapartment of Pure Mathematics
Published
2008-09-01
How to Cite
Sen, J., & Chakraborty, M. (2008). Logic and Truth: Some Logics without Theorems. Studia Philosophica Estonica, 104-117. https://doi.org/10.12697/spe.2008.1.1.06