I present three theses in passing: (1) logicians fail to fully appreciate the basic mathematical idea of truth and consequently push the semantic paradoxes aside. Otherwise they would have come to adopt the reflexive logic LR* right after Cantor (more on this briefly in Sect. 4 . For a ...
摘要: Stimulating, thought-provoking analysis of the most interesting intellectual inconsistencies in mathematics, physics, and language, including being led astray by algebra (De Morgan's paradox). 1982 edition.Bunch, Bryan 关键词: Logic, Symbolic and mathematical. 被引量: 40 年份: 1982 收藏...
paradox- (logic) a statement that contradicts itself; "`I always lie' is a paradox because if it is true it must be false" logic- the branch of philosophy that analyzes inference contradiction in terms,contradiction- (logic) a statement that is necessarily false; "the statement `he is brav...
They are part of the author's work on the Paradoxist Philosophy based on mathematical logic. The general cases exposed below are modeled on the English language structure in a rigid way. In order to find nice particular examples of such paradoxes one grammatically adjusts the sentences. 关键词...
between mathematical reality and physical reality becomes the subject of the book, while the ...
Here is a crude list, possibly summarizing the role of paradoxes within the framework of mathematical logic: 1. directly motivating important theories (eg type theory, axiomatic set theory, combinatory logic); 2. suggesting methods of pr... A Cantini - 《Handbook of the History of Logic》 被...
where our desire for airtight logic and mathematical precision runs headlong into a brick wall. Often they show some kind of previously misunderstood limitation in the logical structures we have been building, or some kind of fundamental disconnect between our human languages and the underlying ...
, From Frege to Gödel: A source book in mathematical logic 1879–1931, Harvard Univ. Press, Cambridge, Mass (1967) (ed. and trans.) Van Heijenoort, 1967b J Van Heijenoort Logical paradoxes The encyclopedia of philosophy, Vol. V (1967), pp. 456-461 Google Scholar Whitehead and ...
Examples of logical paradoxes, including the square root of two paradox, Achilles and the tortoise paradox, author paradox, Russell paradox, bibliomaniac paradox, and Berry paradox, are presented; some are resolved. (DT) 关键词: Instructional Materials Logic Mathematical Concepts Mathematical Enrichment...
and once I get there I have to cover half of that remaining distance,ad infinitum.There are an infinite number of halfway points, and so according to logic, I'll never be able to get there. But it's easy to prove this false by simply doing it, which we can all do. So we have...