# Is S5 the appropriate logic tool for examining existential supremacy? **URL:** \ **Category:** Great Debates\ **Created:** [December 14, 2007, 11:29pm UTC](https://boards.straightdope.com/t/is-s5-the-appropriate-logic-tool-for-examining-existential-supremacy/430050 "2007-12-14T23:29:00Z")\ **Posts on this page:** 20\ **Page:** 4
**Author:** ![Liberal](https://avatars.discourse-cdn.com/v4/letter/l/848f3c/32.png) [@Liberal](https://boards.straightdope.com/u/Liberal)\ **Post date:** [December 17, 2007, 1:53pm UTC](https://boards.straightdope.com/t/is-s5-the-appropriate-logic-tool-for-examining-existential-supremacy/430050/61 "2007-12-17T13:53:22Z")
[QUOTE=Bryan Ekers] Which leads to…? [/QUOTE] …the examination of existential supremacy with a suitable tool. I don’t understand what it is that you don’t understand. If what you’re saying is that examination of such things is unimportant or a waste of time, then why are you wasting your time (and mine)? Perhaps some other thread would be of greater interest to you. ---
**Author:** ![Bryan\_Ekers](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bryan_ekers/32/183_2.png) [@Bryan\_Ekers](https://boards.straightdope.com/u/Bryan_Ekers)\ **Post date:** [December 17, 2007, 7:25pm UTC](https://boards.straightdope.com/t/is-s5-the-appropriate-logic-tool-for-examining-existential-supremacy/430050/62 "2007-12-17T19:25:50Z")
[QUOTE=Liberal] …the examination of existential supremacy with a suitable tool. I don’t understand what it is that you don’t understand. If what you’re saying is that examination of such things is unimportant or a waste of time, then why are you wasting your time (and mine)? Perhaps some other thread would be of greater interest to you. [/QUOTE] I just figured if someone asked “Is a freeblemizer the proper tool for adjusting glimlicks?” they’d follow up by describing all the glimlicks they looked forward to freeblemizing and how properly-freeblemized glimlicks can be used to obtain better fuel economy, reduction of global warming, male enhancement or some other real-world application. Once you’ve successfully examined an existential supremacy (granting for the sake of argument that S5 is the correct tool to do so), what results do you expect to get? Even if the pursuit was a purely intellectual and academic one, I assume you expect S5 to give a different result than, say, S4 or S6[sup]\*[/sup] or some other **in** appropriate tool. If you see my asking about this difference as a waste of your time, you’re of course free to not respond. [sup]\*[/sup]labels used for illustration only ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [December 17, 2007, 7:34pm UTC](https://boards.straightdope.com/t/is-s5-the-appropriate-logic-tool-for-examining-existential-supremacy/430050/63 "2007-12-17T19:34:46Z")
Good lord, how did you find out about S6?! That’s classified information! ---
**Author:** ![Bryan\_Ekers](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bryan_ekers/32/183_2.png) [@Bryan\_Ekers](https://boards.straightdope.com/u/Bryan_Ekers)\ **Post date:** [December 18, 2007, 3:11am UTC](https://boards.straightdope.com/t/is-s5-the-appropriate-logic-tool-for-examining-existential-supremacy/430050/64 "2007-12-18T03:11:10Z")
Am I so far off-base here, asking these questions? ---
**Author:** ![Liberal](https://avatars.discourse-cdn.com/v4/letter/l/848f3c/32.png) [@Liberal](https://boards.straightdope.com/u/Liberal)\ **Post date:** [December 18, 2007, 9:11am UTC](https://boards.straightdope.com/t/is-s5-the-appropriate-logic-tool-for-examining-existential-supremacy/430050/65 "2007-12-18T09:11:03Z")
I don’t know whether you’re off-base. As I said, I don’t understand the nature of the question. Your “Is a freeblemizer the proper tool for adjusting glimlicks?” further confounds me. Is that your way of saying that you’d prefer a less technical vocabulary? If so, I can probably accomodate you, although it might be a very thick read. The terms serve as shorthand for much longer expressions. ---
**Author:** ![Czarcasm](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/czarcasm/32/4050_2.png) [@Czarcasm](https://boards.straightdope.com/u/Czarcasm)\ **Post date:** [December 18, 2007, 12:21pm UTC](https://boards.straightdope.com/t/is-s5-the-appropriate-logic-tool-for-examining-existential-supremacy/430050/66 "2007-12-18T12:21:55Z")
Would “Existential Supremacy” be another name for and/or a description of “God”? ---
**Author:** ![the\_PC\_apeman](https://avatars.discourse-cdn.com/v4/letter/t/ac8455/32.png) [@the\_PC\_apeman](https://boards.straightdope.com/u/the_PC_apeman)\ **Post date:** [December 18, 2007, 2:10pm UTC](https://boards.straightdope.com/t/is-s5-the-appropriate-logic-tool-for-examining-existential-supremacy/430050/67 "2007-12-18T14:10:50Z")
**Liberal** , It seems to me that the concept P (necessarily P) is a fundamental component of S5. It also seems that you’ve defined “existential supremacy” as a synonym for P. So the “Is S5 the appropriate tool for examining existential supremacy” question appears trivial and masturbatory for a substantial thinker such as yourself. That’s why there is suspicion here about where this thread is headed. -PC- ---
**Author:** ![Liberal](https://avatars.discourse-cdn.com/v4/letter/l/848f3c/32.png) [@Liberal](https://boards.straightdope.com/u/Liberal)\ **Post date:** [December 18, 2007, 2:30pm UTC](https://boards.straightdope.com/t/is-s5-the-appropriate-logic-tool-for-examining-existential-supremacy/430050/68 "2007-12-18T14:30:51Z")
[QUOTE=Czarcasm] Would “Existential Supremacy” be another name for and/or a description of “God”? [/QUOTE] I don’t think that’s relevant here. > [@the PC apeman](#): > > It seems to me that the concept P (necessarily P) is a fundamental component of S5. It also seems that you’ve defined “existential supremacy” as a synonym for P. So the “Is S5 the appropriate tool for examining existential supremacy” question appears trivial and masturbatory for a substantial thinker such as yourself. That’s why there is suspicion here about where this thread is headed. My _intention_ for where it is headed is just exactly what I’ve said (repeatedly now) — I’m looking for the best system for analyzing existential supremacy, and wondering whether there is a better system than S5, given its Euclidean frame and the nature of objectivity/subjectivity. Opinions vary on the matter. Hartshorne and Plantinga obviously think it is the correct tool. Suber thinks it is lacking because he is dubious about Becker’s Postulate. And \*\*Indistinguishable \*\* seems to have a problem that it is too universal to be useful. (Correct me if I’ve misunderstood you.) I just want to hear people’s opinions — if they have one — and hear debate one way or the other. ---
**Author:** ![Czarcasm](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/czarcasm/32/4050_2.png) [@Czarcasm](https://boards.straightdope.com/u/Czarcasm)\ **Post date:** [December 18, 2007, 2:36pm UTC](https://boards.straightdope.com/t/is-s5-the-appropriate-logic-tool-for-examining-existential-supremacy/430050/69 "2007-12-18T14:36:46Z")
[QUOTE=Liberal] I don’t think that’s relevant here. [/QUOTE] And I don’t think that’s an answer. ---
**Author:** ![Liberal](https://avatars.discourse-cdn.com/v4/letter/l/848f3c/32.png) [@Liberal](https://boards.straightdope.com/u/Liberal)\ **Post date:** [December 18, 2007, 2:48pm UTC](https://boards.straightdope.com/t/is-s5-the-appropriate-logic-tool-for-examining-existential-supremacy/430050/70 "2007-12-18T14:48:09Z")
[QUOTE=Czarcasm] And I don’t think that’s an answer. [/QUOTE] You’re right. That’s a deictic. ---
**Author:** ![Bryan\_Ekers](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bryan_ekers/32/183_2.png) [@Bryan\_Ekers](https://boards.straightdope.com/u/Bryan_Ekers)\ **Post date:** [December 19, 2007, 5:31am UTC](https://boards.straightdope.com/t/is-s5-the-appropriate-logic-tool-for-examining-existential-supremacy/430050/71 "2007-12-19T05:31:04Z")
Would it make any difference if another arbitrary label was used, like “existential normalcy” or “existential consistency”? And, sure, take a shot at dumbing it down, though my question wasn’t about the terminology, it was what you would do with the conclusion. Asking if you can analyze existential supremacy with S5 so you can use S5 to analyze existential supremacy is a touch circular. ---
**Author:** ![Czarcasm](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/czarcasm/32/4050_2.png) [@Czarcasm](https://boards.straightdope.com/u/Czarcasm)\ **Post date:** [December 19, 2007, 5:47am UTC](https://boards.straightdope.com/t/is-s5-the-appropriate-logic-tool-for-examining-existential-supremacy/430050/72 "2007-12-19T05:47:06Z")
[QUOTE=Liberal] You’re right. That’s a deictic. [/QUOTE] I ask because the term “Existential Supremacy” is used _quite_ often in spiritual circles, so I feel that my question is legitimate. ---
**Author:** ![Bryan\_Ekers](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bryan_ekers/32/183_2.png) [@Bryan\_Ekers](https://boards.straightdope.com/u/Bryan_Ekers)\ **Post date:** [December 19, 2007, 7:49am UTC](https://boards.straightdope.com/t/is-s5-the-appropriate-logic-tool-for-examining-existential-supremacy/430050/73 "2007-12-19T07:49:14Z")
[QUOTE=Czarcasm] I ask because the term “Existential Supremacy” is used _quite_ often in spiritual circles, so I feel that my question is legitimate. [/QUOTE] I thought about suggesting “Scoobiness” (i.e. an object that can be perceived by all of humanity has achieved the quality of Scoobiness) as a label, just to avoid any confusion of this with an attempted teleological proof of God. Meantime, I’ll wait for Liberal to explain why “existential supremacy” is the more appropriate term, assuming that’s how he feels. ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [December 19, 2007, 10:36am UTC](https://boards.straightdope.com/t/is-s5-the-appropriate-logic-tool-for-examining-existential-supremacy/430050/74 "2007-12-19T10:36:29Z")
I just wrote a fairly long response asking for clarification of the OP on several points. My hand then spazzed out, hit some random key combination, and caused my Netscape window to close, thereby causing me to lose everything I typed. I’ll return and try to reconstruct the post tomorrow. ☹ (What would I have pressed in order to cause Netscape to close like that?) Anyway, do I understand correctly that part of what you’re doing here involves using S5 as a tool for building a model, not of possible worlds, but rather of points of view? And also, what are: Existential supremacy Existential subjectivity esp: what is the word “existential” doing in those two phrases? Also, do you think God knows what it is like for me to be me? I’ve never answered this particular question to my own satisfaction. -FrL- ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [December 19, 2007, 10:42am UTC](https://boards.straightdope.com/t/is-s5-the-appropriate-logic-tool-for-examining-existential-supremacy/430050/75 "2007-12-19T10:42:56Z")
[QUOTE=Liberal] It’s \<\>A -\> \<\>A. One way of reading it is that if A is possible in actuality, then it is necessarily possible. [/QUOTE] Note: The Dual of that axiom scheme is the axiom scheme **MrDribble** was referring to, though I don’t know if he meant to refer to it under its description as “dual.” Anyway, whatever you can prove using \<\>A -\> \<\>A you could have proved under a system which used \<\>A -\> A instead, and vice versa. -FrL- (My crowning achievement, such as it was, when I took Modal Logic a few years ago was proving the dual theorem. I could not remember how the proof went even if you offered me five million dollars.) ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [December 19, 2007, 10:47am UTC](https://boards.straightdope.com/t/is-s5-the-appropriate-logic-tool-for-examining-existential-supremacy/430050/76 "2007-12-19T10:47:31Z")
Also, Hey **Liberal** , have you read much Kierkegaard? He’s got something to say somewhere or other about the logical problems that seem to be created by the notion of subjective beings being related to objective beings (and, I think, also the notion of subjective beings relating to each other by virtue of objective being, if I recall correctly!) I’ll try to remember where I saw that. Of course with Kierkegaard you’re going to get more problems than solutions, but there’s nothing wrong with that. -FrL- ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [December 19, 2007, 10:53am UTC](https://boards.straightdope.com/t/is-s5-the-appropriate-logic-tool-for-examining-existential-supremacy/430050/77 "2007-12-19T10:53:07Z")
[QUOTE=Liberal] Sure. Let’s prove that existential supremacy is true in S5. Definitions: Let A be “for every” Let E be “there exists” Let != be “not equal” Let ~ be logical negation Prove: AxEy(y=x) Premises: 1. x = x … Identity 2. Ay(y!=x) -\> x!=x … Quantifier Proof: 1. x=x -\> ~Ay(y!=x) … Contraposition on 2 2. x=x -\> Ey(y=x) … Definition of E on 3 3. Ey(y=x) … Modus Ponens on 1 and 4 4. Ey(y=x) … Rule of Necessitation on 5 QED: AxEy(y=x) … Rule of Generalization on 6 [/QUOTE] Wait. That last line doesn’t just say something exists necessarily (which is what I would have assumed you to be after) but rather, that _everything_ (in the domain of discourse) exists necessarily (which seems stronger than I would expect you to want, but am I wrong?). -FrL- ---
**Author:** ![Liberal](https://avatars.discourse-cdn.com/v4/letter/l/848f3c/32.png) [@Liberal](https://boards.straightdope.com/u/Liberal)\ **Post date:** [December 19, 2007, 11:05am UTC](https://boards.straightdope.com/t/is-s5-the-appropriate-logic-tool-for-examining-existential-supremacy/430050/78 "2007-12-19T11:05:26Z")
[QUOTE=Bryan Ekers] Would it make any difference if another arbitrary label was used, like “existential normalcy” or “existential consistency”? [/quote] No, because I didn’t choose the label arbitrarily. You could write it out longways, though, and say something like, “Is S5 the best tool for examining something that exists in every situation and circumstance where its existence is metaphysically possible?”. > [@](#): > > And, sure, take a shot at dumbing it down, though my question wasn’t about the terminology, it was what you would do with the conclusion. Asking if you can analyze existential supremacy with S5 so you can use S5 to analyze existential supremacy is a touch circular. There’s nothing wrong with circularity per se. After all, every circular argument is valid. But asking a question is not drawing a logical inference, so circularity doesn’t apply at all. I’m simply saying that I want to know whether a bat is the best tool for hitting a baseball so that I can hit a baseball with the best tool. What’s wrong with that? ---
**Author:** ![Liberal](https://avatars.discourse-cdn.com/v4/letter/l/848f3c/32.png) [@Liberal](https://boards.straightdope.com/u/Liberal)\ **Post date:** [December 19, 2007, 11:09am UTC](https://boards.straightdope.com/t/is-s5-the-appropriate-logic-tool-for-examining-existential-supremacy/430050/79 "2007-12-19T11:09:47Z")
[QUOTE=Frylock] Wait. That last line doesn’t just say something exists necessarily (which is what I would have assumed you to be after) but rather, that _everything_ (in the domain of discourse) exists necessarily (which seems stronger than I would expect you to want, but am I wrong?). [/QUOTE] I don’t think it’s necessary to take an actualist’s reading of it. I think it is more accurate to say that S5 can prove the necessary existence of anything that exists necessarily. In other words, it simply means that necessary existence is true in S5. ---
**Author:** ![Liberal](https://avatars.discourse-cdn.com/v4/letter/l/848f3c/32.png) [@Liberal](https://boards.straightdope.com/u/Liberal)\ **Post date:** [December 19, 2007, 11:14am UTC](https://boards.straightdope.com/t/is-s5-the-appropriate-logic-tool-for-examining-existential-supremacy/430050/80 "2007-12-19T11:14:28Z")
[QUOTE=Frylock] Note: The Dual of that axiom scheme is the axiom scheme **MrDribble** was referring to, though I don’t know if he meant to refer to it under its description as “dual.” Anyway, whatever you can prove using \<\>A -\> \<\>A you could have proved under a system which used \<\>A -\> A instead, and vice versa. [/QUOTE] There are very few axioms that cannot be derived from the General Axiom: \<\>[sup]h[/sup][sup]i[/sup]A → [sup]j[/sup]\<\>[sup]k[/sup]A. But again, my question is very specific. Is there a better tool? [Previous page](https://boards.straightdope.com/t/is-s5-the-appropriate-logic-tool-for-examining-existential-supremacy/430050.md?page=3) [Next page](https://boards.straightdope.com/t/is-s5-the-appropriate-logic-tool-for-examining-existential-supremacy/430050.md?page=5)