Answer by user16974 for The sets in mathematical logic
I think this problem shows itself at many stages of the human thinking. So we can form the expression "This expression is wrong" and immediately the liar paradox appears. So really this has nothing to...
View ArticleAnswer by Buschi Sergio for The sets in mathematical logic
The old (Hilbert) idea was to have a foundation of mathematics on elementary concepts that have a "itself evidence", and there was a intuitive "halph-real" (platonic?) idea about mathematics, it live...
View ArticleAnswer by The Puzzled Logician for The sets in mathematical logic
I happen to realize the same apparent circularity in mathematical logic. If it purports to establish a foundation for mathematics, it seems to me its methods need to be different from mathematical...
View ArticleAnswer by Brendan Cordy for The sets in mathematical logic
There are a few problems you seem to be having. First of all, the statement "mathematical logic depends on ZFC" doesn't make sense.As mathematical logicians, when we study formal systems, we should...
View ArticleAnswer by Timothy Chow for The sets in mathematical logic
The short answer is that there is no way to be absolutely certain that mathematics is free from contradiction.To start with an extreme case, we all take for granted a certain amount of stability in our...
View ArticleAnswer by kakaz for The sets in mathematical logic
You cannot have any theory without metatheory. Opposite statement is not true and is simple kind of ideology in the fundamentals of mathematics. Of course You may use the same language for both of...
View ArticleAnswer by Sergey Melikhov for The sets in mathematical logic
That is to say, mathematical logic is using intuitive set theory. So, is there any paradox in mathematical logic?Yes, in set theory whose logic is based upon naive set theory there is Berry's paradox....
View ArticleAnswer by Michal R. Przybylek for The sets in mathematical logic
You cannot get anything out of nothing :-) But do not worry.Mathematics existed long before ZFC was formulated, and well before “formal reasoning” rose to a kind of religion. Mathematically, there is...
View ArticleAnswer by Stefan Geschke for The sets in mathematical logic
I have been asked this question several times in my logic or set theory classes. The conclusion that I have arrived at is that you need to assume that we know how to dealwith finite strings over a...
View ArticleThe sets in mathematical logic
It is well known that intuitive set theory (or naive set theory) is characterized by having paradoxes, e.g. Russell's paradox, Cantor's paradox, etc. To avoid these and any other discovered or...
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