Open AccessLogic and Truth: Some Logics without Theorems
Author(s) -
Jayanta Sen,
Mihir K. Chakraborty
Publication year - 2008
Publication title -
studia philosophica estonica/studia philosophica estonica.
Language(s) - English
Resource type - Journals
eISSN - 2228-110X
pISSN - 1736-5899
DOI - 10.12697/spe.2008.1.1.06
Subject(s) - sequent , argument (complex analysis) , mathematics , element (criminal law) , algebraic number , sequent calculus , algebra over a field , truth value , calculus (dental) , intuitionistic logic , matrix (chemical analysis) , classical logic , truth table , pure mathematics , order (exchange) , discrete mathematics , computer science , propositional calculus , algorithm , mathematical proof , mathematical analysis , law , programming language , geometry , dentistry , finance , economics , materials science , chemistry , composite material , biochemistry , political science , medicine
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.