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Are truth tables seen as rigorous enough for proofs? I was just wondering because I am not sure if they suffice for a proof.

jasonL
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    They are legitimate, but a little brute force, if you like. In the end, truth tables convey all the information you need, so they are proofs. However, you can always simplify expressions using rules, so drawing up a truth table always seems a little elaborate. – Sarvesh Ravichandran Iyer Sep 29 '16 at 05:03
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    Thank you sorry! sorry about asking such a simplistic question. I'm new to math but am having fun! – jasonL Sep 29 '16 at 05:04
  • Have fun. Enjoy yourself. – Sarvesh Ravichandran Iyer Sep 29 '16 at 05:05
  • The biggest problem with relying on truth tables is when you get into spaces where the number of cases you have to check is large, or even infinite. When you're starting to learn, though, it can be good to check some of your proofs using truth tables along with other means. – ConMan Sep 29 '16 at 05:09
  • @астонвіллаолофмэллбэрг "You can always simplify expressions using rules": maybe, maybe not. When simplification doesn't work and truth tables are too big, there are SAT solvers. – Robert Israel Sep 29 '16 at 05:31
  • @RobertIsrael That's right. I was wondering for some time that I was wrong, and I was, but the statement still stands, namely truth tables are often huge to evaluate. They are not aesthetically pleasing too. But SAT solvers are also part-brute-force, aren't they? I'm not saying that's a sin or a crime, but really, things can get better than that,can they? – Sarvesh Ravichandran Iyer Sep 29 '16 at 05:35

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Yes they are a rigorous proof. A truth table is just iterating over all alternatives and showing that what you wish to prove holds for all of them.

Q the Platypus
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If you are doing a proof in a subject like complex analysis, or graph theory, or number theory, then truth tables are fine, and knowing how to do them should be encouraged.

If you are doing a proof about the theory of logic, then truth tables become problematic. For example, it can be the case that you can neither prove a statement, and you also cannot prove that the statement is false either. Truth tables have it implicit that "everything is either true or false", but unfortunately it isn't always the case in every logic that every statement must either be provable or provably unprovable.

DanielV
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  • Based on what you've said here and another comment of yours, I'm curious to know what exactly is your objection against classical logic. Do you (roughly) agree with my claim at http://math.stackexchange.com/a/1888389/21820 that LEM holds for totally precise and unambiguous statements about reality. (I know this claim itself is imprecise but we can't help it since there is no way we can say something about reality without invoking natural language at some point. However, I hope you get what I am conveying here.) Do you also agree with my justification that LEM fails for the Quine sentence? – user21820 Oct 14 '16 at 07:54
  • If you agree, then do you accept the absoluteness of the type of natural numbers in the sense that LEM holds for any arithmetical sentence? If so, do you accept LEM for things beyond arithmetical sentences? But if not, do you accept the notion of programs (ideal Turing machines) and that LEM holds for whether a given program halts? I really look forward to your answer, and feel free to come to http://chat.stackexchange.com/rooms/44058/logic to discuss further! – user21820 Oct 14 '16 at 08:01