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This question already has an answer here:

I was studying first order logic by a book and the author uses set theory to define some concepts like models, structures, etc. Everything fine here, but then i started to read about ZFC set theory and the author uses first order logic to prove some theorems. My question is if this is valid. Seems a little circular, we use set theory to study logic and logic to study set theory.

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marked as duplicate by Carl Mummert logic Mar 13 '18 at 0:39

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ Another duplicate question is at math.stackexchange.com/questions/769262/… with some comments $\endgroup$ – Carl Mummert Mar 13 '18 at 0:39
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    $\begingroup$ I have voted to close as a duplicate because, at the current level of detail in the question, nothing new is likely to be generated that is not already in the previous ones. That is not to say this is a bad question - it is a natural question that many people have thought of and asked in various settings. If there is a more specific question about the perceived circularity of first-order logic and set theory (beyond he fact that they may appear circular), that could make an excellt non-duplicate post. $\endgroup$ – Carl Mummert Mar 13 '18 at 0:41
  • $\begingroup$ @Carl: You can actually edit the duplicate list and add more duplicates. $\endgroup$ – Asaf Karagila Mar 13 '18 at 8:55
  • $\begingroup$ @Asaf: thanks, I didn't know that. Unfortunately in this case it won't let me add the other duplicate because the other one has no answers. $\endgroup$ – Carl Mummert Mar 13 '18 at 13:14