By Howard DeLong
Publish 12 months note: First released in 1971
This textual content explores the historic purposes for the formation of Aristotelian good judgment, the increase of mathematical good judgment, the character of the formal axiomatic process and its use, and the most result of metatheory and their import.
From 1971 edition
Includes 22 figures and 19 tables. Appendixes. Bibliography. Indexes.
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Additional resources for A Profile of Mathematical Logic (Dover Books on Mathematics)
P. 268) Later, after observing that “Mathematics is every bit as 4 Fuzziness as an Experimental Science: An Homage to Claudio Moraga 45 much an imaginative art as a logical science and the art of mathematics is the art of asking the right questions”, he asks the question of recognizing the interesting results among all that can be mechanically derived from the premises and answer by affirming that “This charge is entirely beyond the jurisdiction of logic, but the ability to discriminate between such trivial theorems and the really vital conclusions of a mathematical science is precisely that quality which the competent mathematician has and the incompetent mathematician lacks”.
1 Claudio Moraga, Enric Trillas, and Fatima Zohra Hadjam at the “1. International Symposium Fuzziness, Philosophy and Medicine” at the European Centre for Soft Computing, Mieres (Asturias), Spain, March 23–24, 2011; in the background, Mila Kwiatkowska; photograph by Rudolf Seising that it fails in many cases; it holds with f = id, T = W and N = 1 − id, and fails with f = id, T = pr od, T = min, and the same negation 1 − id . Carla. Yes, and without considering strong negations there are also positive and negative cases.
We are not questioning here the importance of the results of “fuzzy logic, taken seriously” in itself. What we want to ask is whether such a theory can be considered an applied logic and, more importantly, a general model of reasoning. We think that—independently from the value of the obtained results—it cannot provide any true help for applications in situations where uncertainty and fuzziness play a crucial role (see . And this for very simple and fundamental reasons; namely the central notions of mathematical logic, coherence and completeness, in the first place, lose their crucial role when we are concerned from the start with uncertainty and imprecision.
A Profile of Mathematical Logic (Dover Books on Mathematics) by Howard DeLong