# Math Folks: Set Theory Question **URL:** \ **Category:** Great Debates\ **Created:** [August 25, 2005, 7:03pm UTC](https://boards.straightdope.com/t/math-folks-set-theory-question/318608 "2005-08-25T19:03:40Z")\ **Posts on this page:** 15\ **Page:** 2
**Author:** ![ITR\_champion](https://avatars.discourse-cdn.com/v4/letter/i/c67d28/32.png) [@ITR\_champion](https://boards.straightdope.com/u/ITR_champion)\ **Post date:** [August 28, 2005, 9:42pm UTC](https://boards.straightdope.com/t/math-folks-set-theory-question/318608/21 "2005-08-28T21:42:37Z")
> [@Dijon Warlock](#): > > Sorry about getting rid of God, folks. D’ya think Pat Robertson will shut up now? Finally, here’s a question that I can answer without the slightest hint of uncertainty. No. ---
**Author:** ![Bytegeist](https://avatars.discourse-cdn.com/v4/letter/b/9dc877/32.png) [@Bytegeist](https://boards.straightdope.com/u/Bytegeist)\ **Post date:** [August 28, 2005, 9:43pm UTC](https://boards.straightdope.com/t/math-folks-set-theory-question/318608/22 "2005-08-28T21:43:50Z")
> [@Mathochist](#): > > Fine. Now prove that Z-F obtains in the real world, and further that reductios are valid (no, it’s not a settled point). You do realize that my post was tongue-in-cheek, I hope. ---
**Author:** ![DarrenS](https://avatars.discourse-cdn.com/v4/letter/d/977dab/32.png) [@DarrenS](https://boards.straightdope.com/u/DarrenS)\ **Post date:** [August 28, 2005, 9:49pm UTC](https://boards.straightdope.com/t/math-folks-set-theory-question/318608/23 "2005-08-28T21:49:42Z")
This is headed for GD, but I have to wonder: why on earth would you think you’d be able to prove any theological or philosophical result using mathematical axioms and logic? It’d be like holding a protest rally against earthquakes. If god exists, why would he be bound by mathematical logic? It reminds me a little of the time I asked a devout, intelligent Christian friend if God could make 1+1 = 3, or true = false. He asserted that he didn’t think so - he believed that logic are “the mind of God”. I still never quite figured it out. In any case - suppose you were somehow able to string together a bunch of propositional logic or set theory, and reach some kind of conclusion which you arbitrarily interpret as “therefore, God [does|doesn’t] exist.” If God is supposed to be omnipotent, why would he be bound by your conclusion? This seems like some kind of logical fallacy - a ‘category mistake’, perhaps, like “multiplying Monday by Tuesday”. ---
**Author:** ![liberty3701](https://avatars.discourse-cdn.com/v4/letter/l/3d9bf3/32.png) [@liberty3701](https://boards.straightdope.com/u/liberty3701)\ **Post date:** [August 29, 2005, 2:08am UTC](https://boards.straightdope.com/t/math-folks-set-theory-question/318608/24 "2005-08-29T02:08:57Z")
> [@Dijon Warlock](#): > > Have a question (or two-ish, as it turns out) about set theory: > Every set has at least two subsets: the Empty Set (which contains NO elements of the original set), and the \_\_\_\_\_ Set (whose name escapes me…but which contains ALL elements of the original set). Of course, I’m sure someone already mentioned that the empty set has but one subset. Also, one college prof (Arunas) used to call the whole set “the whole damn thing” in this context ---
**Author:** ![xash](https://avatars.discourse-cdn.com/v4/letter/x/c6cbf5/32.png) [@xash](https://boards.straightdope.com/u/xash)\ **Post date:** [August 29, 2005, 4:16am UTC](https://boards.straightdope.com/t/math-folks-set-theory-question/318608/25 "2005-08-29T04:16:53Z")
Moving to GD for further discussion. - **xash** General Questions Moderator ---
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [August 29, 2005, 4:28am UTC](https://boards.straightdope.com/t/math-folks-set-theory-question/318608/26 "2005-08-29T04:28:33Z")
> [@DarrenS](#): > > This is headed for GD, but I have to wonder: why on earth would you think you’d be able to prove any theological or philosophical result using mathematical axioms and logic? It’d be like holding a protest rally against earthquakes. If god exists, why would he be bound by mathematical logic? Basically, what I already said. > [@](#): > > It reminds me a little of the time I asked a devout, intelligent Christian friend if God could make 1+1 = 3, or true = false. He asserted that he didn’t think so - he believed that logic are “the mind of God”. I still never quite figured it out. He’s implicitly assuming that there is a unique logic which does obtain, and that such logic is consistent and strong enough to model Peano’s axioms of arithmetic. > [@](#): > > This seems like some kind of logical fallacy - a ‘category mistake’, perhaps, like “multiplying Monday by Tuesday”. To a certain extent. It’s a little hairier than that, though… ---
**Author:** ![Dijon\_Warlock](https://avatars.discourse-cdn.com/v4/letter/d/a9a28c/32.png) [@Dijon\_Warlock](https://boards.straightdope.com/u/Dijon_Warlock)\ **Post date:** [August 29, 2005, 8:00pm UTC](https://boards.straightdope.com/t/math-folks-set-theory-question/318608/27 "2005-08-29T20:00:15Z")
> [@Mathochist](#): > > Okay, please stop with all the Capitalized Words. The more capitals you gratuitously throw in, the more psychoceramic you look. Unless you mean a specific concept differing from the normal definition of “existence” – a concept you would need to explicitly define – don’t capitalize the word. _Points frantically:_ Junior mod, junior mod! NO…kidding, really. I _did_ mean something different (at least to me), but I’m not convinced of how well I can communicate the distinction. To me, existence (with a small “e”) is the normal mundane type of limited existence…my vocabulary is going to fail me here, I suspect. There exists an apple in my refrigerator. There exists a number of “Far Side” collections on my bookshelf. There exists a healthy volume of beer in my stomach. However, Existence (with a capital “E”) refers (in _my_ brain, anyway) to existence at the universal level…as a totalistic concept. Things exist, but Everything Exists. With a small “e” it is limited; with a capital “E” it is limitless. The same goes for the rest of the terms. Sorry you don’t like them, but to me they denote a valid distinction. I was just trying to be clear. > [@Mathochist](#): > > Now, what I meant by assuming a dichotomy is that you haven’t given any reason that just because there is a supreme being (“God”) there must be an antithesis (“Satan”). Why should this be? The reason that I was playing with goes back to the “Why is there Something rather than Nothing?” question. If God exists (which, by definition, He must for everything else to exist), then there clearly IS Something rather than Nothing, and _that_ right there is a dichotomy. Therefore, the concept of Dichotomy in general must exist. Therefore, if there is a God, there must also be a “not-God”: i.e.: Satan (or possibly Pat Robertson). Proof? Nope, sorry. Don’t have it. But I’m not trying to start a church, here. Just thinking, is all. > [@Mathochist](#): > > I wouldn’t trust any mathematical “proof” of God’s non-existence any more than I would of His existence. The divine is simply beyond the scope of mathematical structures, which clearly delineate their own scope in their definitions. If you really want to attack theology with mathematics, for God’s sake go back to college and learn some real mathematics and how it works rather than just half-remembering a collection of formulas and factoids. Certainly not bad advice, but it isn’t really that important to me (for one thing, the SDMB is a hell of a lot cheaper than college). I just got thinking about this, and wasn’t sure if I remembered what I needed to answer the questions I had. Hence, my coming here. Fighting Ignorance, and all that, you know. > [@liberty3701](#): > > Also, one college prof (Arunas) used to call the whole set “the whole damn thing” in this context God in a nutshell, in my book…although perhaps not in the revised edition. ---
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [August 30, 2005, 12:08am UTC](https://boards.straightdope.com/t/math-folks-set-theory-question/318608/28 "2005-08-30T00:08:59Z")
> [@](#): > > I was just trying to be clear. And if you don’t define exactly what you mean by using the capital letter you’re _not_ being clear. You just make yourself look like a crank. You’re more than halfway there by trying to apply mathematics to theology to begin with, so I’d avoid as many such signals as possible. > [@](#): > > The reason that I was playing with goes back to the “Why is there Something rather than Nothing?” question. If God exists (which, by definition, He must for everything else to exist) WOAH! There are a _lot_ of people who would call you out right there. > [@](#): > > , then there clearly IS Something rather than Nothing, and _that_ right there is a dichotomy. Therefore, the concept of Dichotomy in general must exist. That some dichotomies exist is not under question. That _all_ things exist in dichotomy is. Just because light and dark are dichotomous doesn’t mean that everything has an opposite. As an example, there are _three_ “colors” of the strong nuclear force – a trichotomy. Do you mean that then there must be another figure besides God and Satan? Or maybe you’ll use this to justify the doctrine of the trinity, in which case where are the other two counterparts to Satan? You see how ludicrous that sort of reasoning very quickly becomes. ---
**Author:** ![Dijon\_Warlock](https://avatars.discourse-cdn.com/v4/letter/d/a9a28c/32.png) [@Dijon\_Warlock](https://boards.straightdope.com/u/Dijon_Warlock)\ **Post date:** [August 30, 2005, 12:34pm UTC](https://boards.straightdope.com/t/math-folks-set-theory-question/318608/29 "2005-08-30T12:34:18Z")
Sigh… > [@Mathochist](#): > > And if you don’t define exactly what you mean by using the capital letter you’re _not_ being clear. You just make yourself look like a crank. You’re more than halfway there by trying to apply mathematics to theology to begin with, so I’d avoid as many such signals as possible. Well…if I’m not being clear to someone, they are free to ask for clarification. You did so, and I answered you. I fail to see the problem with that. I make myself look like a crank? I’m more than halfway there by trying to apply mathematics to theology to begin with, so you’d avoid as many such signals as possible? Care to check the forum rules again? Are you pissed that I’m not sleeping with you, or something? My understanding of mathematics (which I freely admit–and have done so–is not complete) is that it is one of the more logically rigorous disciplines. If theology could stand up to _any_ test, it should be mathematical. That is my opinion, and _again_ I’m not trying to start a church, nor asking anyone to follow me. > [@Dijon Warlock](#): > > The reason that I was playing with goes back to the “Why is there Something rather than Nothing?” question. If God exists (which, by definition, He must for everything else to exist) > [@mathochist](#): > > WOAH! There are a lot of people who would call you out right there. Well, then they would be wrong in doing so. If the definition of God is: **That which must exist in order for anything else to exist** , then calling me out on the definition would indicate a misunderstanding of that definition. What’s my proof that this is the correct definition? Again, I don’t have any. That’s simply what I was taught to believe the word “God” meant. > [@Mathochist](#): > > That some dichotomies exist is not under question. That all things exist in dichotomy is. I’m not claiming that ALL things exist in dichotomy, because that seems clearly false to me. That (AUGH! Capital letter!) Dichotmy _itself_ (as a concept) exists seems clear. It is the most fundamental manifestation of plurality in general, and therefore must exist as a prerequisite to trichotomies, or any other higher -otomies. > [@Mathochist](#): > > Do you mean that then there must be another figure besides God and Satan? Or maybe you’ll use this to justify the doctrine of the trinity, in which case where are the other two counterparts to Satan? You see how ludicrous that sort of reasoning very quickly becomes. Nope, not claiming anything of the sort, so you see how ludicrous the condemnation of that sort of reasoning very quickly becomes. 😉 Look, I’m not sure why or how I’m pissing you off so bad. I am not advancing a theology, I am not reinventing mathematics, I am not trying to pull an Time Cube on anyone. I was just thinking, and was missing some details of set theory since I haven’t really studied it for close to a quarter-century. If you find it so irritating, I don’t understand why you keep posting. But I would ask that if you _do_ keep posting (and I appreciate the knowledge you’ve contributed), you might scale back the derision. Please. Thank you. ---
**Author:** ![Hypnagogic\_Jerk](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hypnagogic_jerk/32/4252_2.png) [@Hypnagogic\_Jerk](https://boards.straightdope.com/u/Hypnagogic_Jerk)\ **Post date:** [August 30, 2005, 1:20pm UTC](https://boards.straightdope.com/t/math-folks-set-theory-question/318608/30 "2005-08-30T13:20:14Z")
> [@Dijon Warlock](#): > > I make myself look like a crank? I’m more than halfway there by trying to apply mathematics to theology to begin with, so you’d avoid as many such signals as possible? Care to check the forum rules again? Are you pissed that I’m not sleeping with you, or something? My understanding of mathematics (which I freely admit–and have done so–is not complete) is that it is one of the more logically rigorous disciplines. If theology could stand up to _any_ test, it should be mathematical. That is my opinion, and _again_ I’m not trying to start a church, nor asking anyone to follow me. Well, the thing is that mathematics doesn’t really exist in the real world. It can only be used to prove things in an idealized world, under specific axioms. Of course, applied mathematics exist (this is what I do), but what they give you is an approximation to the real solution, which is usually good enough when you’re working with, for example, engineering problems. You will have trouble trying to apply mathematics to theology. I don’t think **Mathochist** is angry with you or anything. He’s just trying to make you realize that what you’re trying to do will in all probability not work, and does, in some ways, look like the work of a crank. I’m not saying this to insult you. It’s just that to me, what you’re doing is pretty similar to “applying” laws of modern physics to social sciences. Which doesn’t work and is pseudoscientific. I won’t try to criticise your arguments since I know next to nothing about philosophy and theology. I’ll just say that I had trouble following them, and that, as **Mathochist** said, they’re based on axioms that many people would disagree with. I wish you good luck. ---
**Author:** ![Dijon\_Warlock](https://avatars.discourse-cdn.com/v4/letter/d/a9a28c/32.png) [@Dijon\_Warlock](https://boards.straightdope.com/u/Dijon_Warlock)\ **Post date:** [August 30, 2005, 2:12pm UTC](https://boards.straightdope.com/t/math-folks-set-theory-question/318608/31 "2005-08-30T14:12:27Z")
> [@severus](#): > > Well, the thing is that mathematics doesn’t really exist in the real world. It can only be used to prove things in an idealized world, under specific axioms. Of course, applied mathematics exist (this is what I do), but what they give you is an approximation to the real solution, which is usually good enough when you’re working with, for example, engineering problems. I understand this, and have no problem accepting it. > [@severus](#): > > You will have trouble trying to apply mathematics to theology. I don’t think **Mathochist** is angry with you or anything. He’s just trying to make you realize that what you’re trying to do will in all probability not work, and does, in some ways, look like the work of a crank. I’m not saying this to insult you. It’s just that to me, what you’re doing is pretty similar to “applying” laws of modern physics to social sciences. Which doesn’t work and is pseudoscientific. Well, that might be part of the problem: I wasn’t really trying to do _anything_. It was just a thought experiment, and required a few details of set theory which I hadn’t studied for a quarter-century. That was really all it was. So I was kind of bewildered as to why his responses were (at least to me) over the top and unduly antagonistic. I’m not out to take offence unless it’s vehemently intended. It just started to seem as if he was trying to pick a fight. If he misinterpreted my intent, and lost patience with it, that might explain why he felt entitled to be a bit testy. But he DID misinterpret my intent. That’s what baffled me. > [@severus](#): > > I won’t try to criticise your arguments since I know next to nothing about philosophy and theology. I’ll just say that I had trouble following them, and that, as **Mathochist** said, they’re based on axioms that many people would disagree with. I wish you good luck. Of course, I would certainly apologise for not being clear; but the point of my original thread was not to propose a thesis, but to garner facts to determine the legitimacy of a(n) hypothesis. If you wish me to clarify my point of view further (which I am personally not thoroughly convinced of any longer), I would be happy to. Otherwise, I at least appreciate your good wishes. ---
**Author:** ![Mathochist](https://avatars.discourse-cdn.com/v4/letter/m/c89c15/32.png) [@Mathochist](https://boards.straightdope.com/u/Mathochist)\ **Post date:** [August 30, 2005, 5:38pm UTC](https://boards.straightdope.com/t/math-folks-set-theory-question/318608/32 "2005-08-30T17:38:03Z")
> [@Dijon Warlock](#): > > My understanding of mathematics (which I freely admit–and have done so–is not complete) is that it is one of the more logically rigorous disciplines. If theology could stand up to _any_ test, it should be mathematical. The problem is that you know a number of mathematical “words”, but your notion of mathematical “grammar” – not to mention “literature” – is very shaky. There simply _isn’t_ a mathematical test for theology. There isn’t even a consensus on to what extent mathematics describes the real world or not. You can’t just throw around a bunch of math words, plug in “God” here and “Satan” there and call it a proof. It doesn’t work like that. You can go ahead and play around all you want, but please don’t go thinking it’s mathematical. > [@](#): > > If the definition of God is: **That which must exist in order for anything else to exist** , then calling me out on the definition would indicate a misunderstanding of that definition. What’s my proof that this is the correct definition? Again, I don’t have any. That’s simply what I was taught to believe the word “God” meant. And again, this highlights your lack of understanding of what mathematics is. If you base everything on this premise, the best you can say is either “If this premise is true, God exists” or “If this premise is true, God doesn’t exist”. If you want a proof, you need to make no choices. > [@](#): > > I’m not claiming that ALL things exist in dichotomy, because that seems clearly false to me. So why does the something/nothing dichotomy imply that God has a dichotomous counterpart? You just used the mere existence of the something/nothing dichotomy as proof of the God/Satan dichotomy, which doesn’t follow at all unless you’re asserting universality. > [@](#): > > I am not trying to pull an Time Cube on anyone. Maybe not “trying”… > [@](#): > > If you find it so irritating, I don’t understand why you keep posting. I keep posting because your assertions are shot through with imprecisions and fallacies, and you seem to need someone to remind you how to make a coherent, logical argument ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [August 30, 2005, 6:07pm UTC](https://boards.straightdope.com/t/math-folks-set-theory-question/318608/33 "2005-08-30T18:07:35Z")
Sir, (a + b[sup]n[/sup])/n = x; hence God exists; reply! ---
**Author:** ![Dijon\_Warlock](https://avatars.discourse-cdn.com/v4/letter/d/a9a28c/32.png) [@Dijon\_Warlock](https://boards.straightdope.com/u/Dijon_Warlock)\ **Post date:** [August 31, 2005, 12:04am UTC](https://boards.straightdope.com/t/math-folks-set-theory-question/318608/34 "2005-08-31T00:04:48Z")
> [@Thudlow Boink](#): > > Sir, (a + b[sup]n[/sup])/n = x; hence God exists; reply! 1. There! Ran circles 'round you logically! ---
**Author:** ![Dijon\_Warlock](https://avatars.discourse-cdn.com/v4/letter/d/a9a28c/32.png) [@Dijon\_Warlock](https://boards.straightdope.com/u/Dijon_Warlock)\ **Post date:** [August 31, 2005, 12:20am UTC](https://boards.straightdope.com/t/math-folks-set-theory-question/318608/35 "2005-08-31T00:20:24Z")
> [@Mathochist](#): > > The problem is that you know a number of mathematical “words”, but your notion of mathematical “grammar” – not to mention “literature” – is very shaky. There simply _isn’t_ a mathematical test for theology. There isn’t even a consensus on to what extent mathematics describes the real world or not. No, the problem seems to be that you don’t get the fact that I simply was hazy on a few details of set theory (which I haven’t studied for 25 years–oh, and excuse the hell out of me for that). I have never claimed (nor do I believe) there is a mathematical test for theology, so your criticism is once again unjustified. I _have_ asked you to drop the antagonism, but evidently you don’t intend to. > [@](#): > > You can’t just throw around a bunch of math words, plug in “God” here and “Satan” there and call it a proof. It doesn’t work like that. You can go ahead and play around all you want, but please don’t go thinking it’s mathematical. Haven’t, and am not. Nowhere have I called ANYTHING a proof. Are you _trying_ to drag this into the Pit? > [@](#): > > And again, this highlights your lack of understanding of what mathematics is. If you base everything on this premise, the best you can say is either “If this premise is true, God exists” or “If this premise is true, God doesn’t exist”. If you want a proof, you need to make no choices. Good lord, this doesn’t even merit a response (but I don’t want you to feel ignored). > [@](#): > > So why does the something/nothing dichotomy imply that God has a dichotomous counterpart? You just used the mere existence of the something/nothing dichotomy as proof of the God/Satan dichotomy, which doesn’t follow at all unless you’re asserting universality. Okay, I’m going to try one more time here. First, I didn’t use ANYTHING as a proof of ANYTHING. Insofar as “asserting universality,” that was kind of what those pesky capital letters were for. > [@](#): > > Maybe not “trying”… Okay, you ARE trying to drag this into the Pit. > [@](#): > > I keep posting because your assertions are shot through with imprecisions and fallacies, and you seem to need someone to remind you how to make a coherent, logical argument \*::bangs head on desk::\*I am NOT TRYING TO MAKE ANY ARGUMENT AT ALL!!! Jesus Christ, what is wrong with your brain??? Mods: do what you want with this. The GQ was asked and answered. I don’t have the patience for this shit. [Previous page](https://boards.straightdope.com/t/math-folks-set-theory-question/318608.md?page=1)