Robert E. Clay. A simple proof of functional completeness in many-valued logics based on Łukasiewicz's C and N. Notre Dame journal of formal logic, vol. 3 (1962), pp. 114–117. - Robert E. Clay. Note on Stupecki T-functions. The journal of symbolic logic, vol. 27 no. 1 (for 1962, pub. 1963), pp. 53–54.

1965 ◽  
Vol 30 (1) ◽  
pp. 105-105
Author(s):  
Arto Salomaa
Keyword(s):  
Simple Proof ◽  
Formal Logic ◽  
Symbolic Logic ◽  
Functional Completeness ◽  
C And N

Disarming Stove’s Paradox: In Defence of Formal Logic

1998 ◽  
pp. 127-134
Author(s):  
R. Rodrigo Soberano
Keyword(s):  
Main Part ◽  
Formal Logic ◽  
Symbolic Logic ◽  
Logical Contradiction ◽  
False Conclusion

The argument (d) ("All arguments with true premises and false conclusions are invalid.") is an argument with true premises and false conclusion. Therefore "(d) is invalid" seems to be formally valid. Thus presumably formal logic has to admit it as valid. But then formal logic finds itself in a bind. For the above argument is problematic and even paradoxical since it involves an internal logical contradiction. The paradox, aptly termed "Stove's paradox," is fully realized by demonstrating with the help of symbolic logic the contradiction within the argument. Then as the main part of this essays shows, the paradox is attacked by exposing the paradox's genesis. It is shown that by appeal to some not so obvious logical considerations regarding sound linguistic construction and usage, the above argument could not have been legitimately construction. For its construction must have involved either equivocation or hiatus of meaningfulness in the use of the symbol (d).

scholarly journals Czy logika formalna ma sens?

2018 ◽  
Vol 13 (3) ◽  
pp. 49-55
Author(s):  
Ludomir Newelski
Keyword(s):  
Critical Thinking ◽  
Formal Logic ◽  
Symbolic Logic ◽  
Logical Inference ◽  
Semantic Inference ◽  
Definition Of ◽  
Rational Reasoning

Does formal logic make sense?This text is a commentary on the book Logika i argumentacja. Praktyczny kurs krytycznego myślenia Logic and Argumentation. A Practical Course In Critical Thinking by Professor Andrzej Kisielewicz. Prof. Kisielewicz argues there, among other things, that formal symbolic logic is inadequate to explain practical rational reasoning. This commentary defends formal logic in this respect. In particular, Prof. Kisielewicz proposes in his book a definition of practical logical inference. According to him, a conclusion follows from a given set of premises if there is no situation, where the premises hold, while the conclusion fails. In this commentary it is pointed out that this is a well-known notion of semantic inference in formal logic. It is also well-known that semantic and syntactic inference in logic are equivalent, i.e. equally strong.

Model-Completeness and Elementary Properties of Torsion Free Abelian Groups

1974 ◽  
Vol 26 (4) ◽  
pp. 829-840
Author(s):  
Elias Zakon
Keyword(s):  
High Power ◽  
Abelian Groups ◽  
Elementary Theory ◽  
Complete Classification ◽  
Formal Logic ◽  
Predicate Calculus ◽  
Symbolic Logic ◽  
Model Completeness ◽  
Free Abelian Groups ◽  
Torsion Free

The decidability of the elementary theory of abelian groups, and their complete classification by elementary properties (i.e. those formalizable in the lower predicate calculus (LPC) of formal logic), were established by W. Szmielew [13]. More general results were proved by Eklof and Fischer [2], and G. Sabbagh [12]. The rather formidable "high-power" techniques used in obtaining these remarkable results, and the length of the proofs (W. Szmielew's proof takes about 70 pages) triggered off several attempts at simplification. M. I. Kargapolov's proof [3] unfortunately turned out to be erroneous (cf. J. Mennicke's review in the Journal of Symbolic Logic, vol. 32, p. 535).

Evert W. Beth. Preface. English translation of XL 256(1). Science a road to wisdom, by Evert W. Beth, D. Reidel Publishing Company, Dordrecht, Holland, 1968, pp. XI–XIII. - Evert W. Beth. Science as a cultural factor. English translation of XL 256(2). Science a road to wisdom, by Evert W. Beth, D. Reidel Publishing Company, Dordrecht, Holland, 1968, pp. 1–10. - Evert W. Beth. Natural science, philosophy, and persuasion. English translation of XL 256(3). Science a road to wisdom, by Evert W. Beth, D. Reidel Publishing Company, Dordrecht, Holland, 1968, pp. 11–20. - Evert W. Beth. Scientific philosophy: its aims and means. English translation of XL 256(4). Science a road to wisdom, by Evert W. Beth, D. Reidel Publishing Company, Dordrecht, Holland, 1968, pp. 29–34. - Evert W. Beth. Symbolic logic as a continuation of traditional formal logic. English translation of XL 256(5). Science a road to wisdom, by Evert W. Beth, D. Reidel Publishing Company, Dordrecht, Holland, 1968, pp. 42–61. - Evert W. Beth. Science a road to wisdom. English translation of XL 256(6). Science a road to wisdom, by Evert W. Beth, D. Reidel Publishing Company, Dordrecht, Holland, 1968, pp. 69–75. - Evert W. Beth. Modernism in science. English translation of XL 256(7). Science a road to wisdom, by Evert W. Beth, D. Reidel Publishing Company, Dordrecht, Holland, 1968, pp. 76–85. - Evert W. Beth. In retrospect. English translation of XL 256(8). Science a road to wisdom, by Evert W. Beth, D. Reidel Publishing Company, Dordrecht, Holland, 1968, pp. 95–105.

1975 ◽  
Vol 40 (2) ◽  
pp. 255-298
Author(s):  
H. L. Berghel
Keyword(s):  
Natural Science ◽  
English Translation ◽  
Cultural Factor ◽  
Formal Logic ◽  
Publishing Company ◽  
Symbolic Logic ◽  
Reidel Publishing Company ◽  
Scientific Philosophy ◽  
Science Philosophy
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