Witold A. Pogorzelski. On the scope of the classical deduction theorem. The journal of symbolic logic, vol. 33 (1968), pp. 77–81.

1975 ◽  
Vol 40 (4) ◽  
pp. 606-606
Author(s):  
Mircea Tîrnoveanu
Keyword(s):  
Symbolic Logic ◽  
Deduction Theorem

The deduction theorem in a functional calculus of first order based on strict implication

1946 ◽  
Vol 11 (4) ◽  
pp. 115-118 ◽  
Author(s):  
Ruth C. Barcan
Keyword(s):  
Functional Calculus ◽  
Symbolic Logic ◽  
Deduction Theorem ◽  
Strict Implication ◽  
First Order ◽  
Fundamental Theorems

In a previous paper, a functional calculus based on strict implication was developed. That system will be referred to as S2. The system resulting from the addition of Becker's axiom will be referred to as S4. In the present paper we will shw that a restricted deduction theorem is provable in S4 or more precisely in a system equivalent to S4. We will also show that such a deduction theorem is not provable in S2.The following theorems not derived in Symbolic logic will be required for the fundamental theorems XXVIII* and XXIX* of this paper. We will state most of them without proofs.

Algebra

2018 ◽  
Author(s):  
Andrea Henderson
Keyword(s):  
Euclidean Geometry ◽  
Symbolic Logic ◽  
Associative Networks ◽  
Aristotelian Logic ◽  
Modern Algebra ◽  
Symbolic Systems ◽  
The Difference ◽  
Founding Principle ◽  
Conventional Symbol

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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