Logic and Truth: Some Logics without Theorems | Zendy

Jayanta Sen | Zendy; Mihir K. Chakraborty | Zendy

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Logic and Truth: Some Logics without Theorems

Author(s) -

Jayanta Sen,

Mihir K. Chakraborty

Publication year - 2008

Publication title -

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.

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