Theodore Hailperin. Quantification theory and empty individual domains. The journal of symbolic logic, vol. 18 (1953), pp. 197–200. - W.V. Quine. Quantification and the empty domain. Ibid., vol. 19 (1954), pp. 177–179.

1955 ◽  
Vol 20 (3) ◽  
pp. 284-284
Author(s):  
John Myhill

1968 ◽  
Vol 32 (4) ◽  
pp. 480-504 ◽  
Author(s):  
J. Jay Zeman

The “traditional” method of presenting the subject-matter of symbolic logic involves setting down, first of all, a basis for a propositional calculus—which basis might be a system of natural deduction, an axiom system, or a rule concerning tautologous formulas. The next step, ordinarily, consists of the introduction of quantifiers into the symbol-set of the system, and the stating of axioms or rules for quantification. In this paper I shall propose a system somewhat different from the ordinary; this system has rules for quantification and is, indeed, equivalent to classical quantification theory. It departs from the usual, however, in that it has no primitive quantifiers.



2004 ◽  
Vol 10 (3) ◽  
pp. 438-446
Author(s):  
Michael Kremer


2008 ◽  
Vol 14 (4) ◽  
pp. 553-558
Keyword(s):  




2008 ◽  
Vol 14 (3) ◽  
pp. 418-437
Author(s):  
Chris Laskowski


2009 ◽  
Vol 15 (2) ◽  
pp. 237-245
Author(s):  
Ali Enayat
Keyword(s):  


2012 ◽  
Vol 18 (1) ◽  
pp. 142-149
Author(s):  
Michael Mislove
Keyword(s):  


Author(s):  
Andrea Henderson

The difference between the transcendent Coleridgean symbol and the unreliable conventional symbol was of explicit concern in Victorian mathematics, where the former was aligned with Euclidean geometry and the latter with algebra. Rather than trying to bridge this divide, practitioners of modern algebra and the pioneers of symbolic logic made it the founding principle of their work. Regarding the content of claims as a matter of “indifference,” they concerned themselves solely with the formal interrelations of the symbolic systems devised to represent those claims. In its celebration of artificial algorithmic structures, symbolic logician Lewis Carroll’s Sylvie and Bruno dramatizes the power of this new formalist ideal not only to revitalize the moribund field of Aristotelian logic but also to redeem symbolism itself, conceived by Carroll and his mathematical, philosophical, and symbolist contemporaries as a set of harmonious associative networks rather than singular organic correspondences.



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