Answer by none for How to tell a paradox from a "paradox"?
What you're describing as a "true paradox" is sometimes called an "antimony" and it means an actual logical inconsistency in the underlying theory. The Burali-Forti paradox is another example and it...
View ArticleAnswer by Andrej Bauer for How to tell a paradox from a "paradox"?
Many paradoxes are first expressed in a semi-formal way, for example "the least number not describable by fewer than eleven words". They are warning signs that lead us to further analysis and can be...
View ArticleAnswer by Marco Caminati for How to tell a paradox from a "paradox"?
Although I am not so good with philosophical subtleties, I have always found useful to make a distinction between an antinomy and a paradox.The first leads to a formal contradiction, i.e., a logical...
View ArticleAnswer by Andreas Blass for How to tell a paradox from a "paradox"?
Both the Russell paradox and the Banach-Tarski "paradox" show that certain ideas are contradictory. It seems to me that the key difference between the two is that, in Russell's case, the ideas in...
View ArticleAnswer by Florian for How to tell a paradox from a "paradox"?
I don't see how these two a so fundamentally different. Russell's paradox tells us that we have to think more carefully about what a set actually is, and Banach-Tarski tells us that we have to think...
View ArticleHow to tell a paradox from a "paradox"?
Russell's paradox showed that naive set theory leads to a contradiction. This was something that was taken seriously and caused a lot of work.Now, Banach–Tarski paradox is arises from a result that a...
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