Is a course in Mathematical Logic necessary for a well-rounded Mathematical education? I asked a question about taking a Set Theory course before and was advised to do so. However the course offered at my institution this Fall is really in Logic and the Foundations of Mathematics, not Set Theory. The class uses Enderton's Textbook "A Mathematical Introduction to Logic" Second Edition. ISBN-13 = 978-0122384523 [amazon link][1]http://www.amazon.com/Mathematical-Introduction-Logic-Second-Edition/dp/0122384520/ref=cm_cr_pr_product_top

The professor teaching the course advised me to take Logic before Set Theory. He seemed to put a lot of emphasis on Logic as being very important. But again what kind of answer would you expect when you ask a barber if you need a haircut. :) BTW he is a Set Theorist.

What do you guys think? The textbook has mixed reviews, depending on whether the reviewer is a Mathematician or a Computer Scientist. My education is in Mathematics, however I am leaning towards teaching myself programming and will definitely study algorithms and complexity at a certain stage. Would this class help in this endeavor?

Thank you

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    $\begingroup$ Set theory really isn't logic. There are logics where sets aren't prominent at all. Further (and this may be an unpopular thing to say but a semester is a large enough investment to justify saying this) don't bother learning logic from someone who isn't involved in writing logic into software. It's like trying to learn car repairs from someone who has never gotten oil on his hands. I recommend looking from someone who takes logic seriously enough to actually face a compiler. $\endgroup$ – DanielV May 9 '14 at 0:03
  • $\begingroup$ @DanielV: could you please expand on your statement to: learn Logic from someone involved in writing logic into software? $\endgroup$ – Quester May 9 '14 at 0:24
  • $\begingroup$ "I recommend looking for someone who takes logic seriously enough to actually face a compiler" if you want to know that every well-formed formula has the same number of left and right parenthesis!!! $\endgroup$ – William May 9 '14 at 3:54
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    $\begingroup$ @DanielV Logic has a long history which predates compilers. Your last suggestion implies that logicians like Frege, Russell, Lukasiewicz, Skolem, Kleene, Tarski, Whitehead, Curry, Schonfinkel, and Heyting would make poor teachers. I see that you said this " There is no excuse for anyone living after 1990 to study logic without putting their ideas into software." in your profile. How would you put a proof like the one here math.stackexchange.com/questions/516912/… into software? $\endgroup$ – Doug Spoonwood May 9 '14 at 4:37
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    $\begingroup$ @DanielV - Putting aside your odd partiality to programming, calling category theory "a very foundational version of set theory" is somewhere between a gross misrepresentation and outright wrong. (What does "very foundational" even mean?) $\endgroup$ – Malice Vidrine May 9 '14 at 22:03

You might find it helpful to look at the opening chapters of the Teach Yourself Logic study guide which you can download here http://www.logicmatters.net/tyl/ These include a map of how various bits of the classic math. logic curriculum fit together. And yes, the content covered in Enderton's book is absolutely basic, whatever you later want to explore in the broad field of math. logic traditionally conceived (including set theory, computability theory, or other areas).

That doesn't quite answer your question whether a logic course is necessary for a rounded mathematical education more generally. There are plenty of working mathematicians who know next to zero logic, set theory etc. apart from how to use a bit of symbolism. But logic is intrinsically fascinating, foundational, and fun, so I'd say give it a go!


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