Big Bang Theory Reference to Formal Logic

In the second episode "The Junior Professor Solution" of the 8th season of the Big Bang Theory, there exists a brief moment where Sheldon Cooper references one of his boards with what for a brief moment looked like a bunch of statements in some formal system which has modal operators and quantification. But there also exists an "ess" phrase in one of the strings of symbols. I also couldn't tell what the rules of the system they would have referenced or what the axioms were.

Did the Big Bang Theory reference a formal system or just write symbols that looked like a formal system to an untrained eye (my guess is the later)?

• Upon reinspection, this is Godel's proof for the existence of god. en.wikipedia.org/wiki/G%C3%B6del%27s_ontological_proof – Asaf Karagila Sep 23 '14 at 10:49
• @Joel: I've added a screenshot. – Asaf Karagila Sep 23 '14 at 10:53
• Doesn't this question fit nicely in the 'Understanding mathematical concepts and theorems' group? I think it should be reopened and @AsafKaragila should be awarded points for answering. – Jonas Dahlbæk Sep 23 '14 at 11:02
• The axiom A2 is missing a "not" in the screenshot, since of course it should say that $\varphi$ is positive just in case $\neg\varphi$ is NOT positive. This is what gives Goedel essentially an ultrafilter. – JDH Sep 23 '14 at 11:46
• @JDH: You're right! I didn't notice that. But I suppose this is just a typo. – Asaf Karagila Sep 23 '14 at 12:06

1 Answer

This is Gödel's ontological proof, which is fully explained on Wikipedia (see the link).

I find this to be an incredible easter egg, since the proof is something which Sheldon says he doesn't understand. And Sheldon has expressed more than once that he doesn't believe in the existence of god.

(Originally I thought this would be something pertaining to the many-worlds interpretation of quantum mechanics, which was brought up a couple of scenes before this showed up. But upon re-examination of the screenshot, it didn't seem that way anymore.)

• The co-executive producer Eric Kaplan was studying for a PhD in Philosophy before his career in television, so it's not hugely surprising that there is some easter egg like this. Still very cool, though. – Dennis Sep 23 '14 at 14:03
• Dennis, that's interesting. I saw some of their behind the scenes specials, and it only seemed that they had physicists as advisors in time of need (some part of the script would literally say something like "Insert physics joke here", and one of the physicists would put a joke there), so I figured one of them might have suggested that. But this makes much more sense! – Asaf Karagila Sep 23 '14 at 14:06
• I find it plausible enough that they just mistakenly forgot to put a "$\lnot$" in axiom 2. – Doug Spoonwood Sep 23 '14 at 15:35
• @Doug: Yes, me too. Thanks for asking, because I was wondering myself. – Asaf Karagila Sep 23 '14 at 15:58