# Does the Christian Trinity violate the Law Of Identity **URL:** \ **Category:** Great Debates\ **Created:** [December 14, 2014, 12:23pm UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200 "2014-12-14T12:23:51Z")\ **Posts on this page:** 20\ **Page:** 5
**Author:** ![Alessan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/alessan/32/465_2.png) [@Alessan](https://boards.straightdope.com/u/Alessan)\ **Post date:** [December 15, 2014, 11:28am UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/81 "2014-12-15T11:28:49Z")
> [@Half\_Man\_Half\_Wit](#): > > However, the view that quantum mechanics poses a challenge to the law of identity has certainly been expressed before, based on some other phenomena it gives rise to. It depends a little bit, however, on how exactly you understand identity: if, for instance, you understand it to include the identifiability of objects, their having some sort of individual existence that makes it possible to tell them apart, then it’s arguably violated in quantum field theory—two electrons are indistinguishable to the point that you can’t put a lable on each of them to say ‘that’s electron 1’ and ‘that’s electron 2’. This is in fact an important factor in the statistics ‘gases’ of electrons or photons follow, which are different from those of classical particles that you can imagine as being composed of tiny little balls that bounce off one another. > > It’s not something I’m ultimately really qualified to comment upon, but it’s a view that has some adherents, I think, and has been defended in [this book](https://ndpr.nd.edu/news/22989-identity-in-physics-a-historical-philosophical-and-formal-analysis/) a couple of years back. Thanks! I was hoping that someone who knew more than me about the subject would wander in and support my half-assed theory. It’s an approach that has served me well on this board. ---
**Author:** ![Jagermeister](https://avatars.discourse-cdn.com/v4/letter/j/f19dbf/32.png) [@Jagermeister](https://boards.straightdope.com/u/Jagermeister)\ **Post date:** [December 15, 2014, 12:02pm UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/82 "2014-12-15T12:02:31Z")
The problems have existed since Tertullian formulated the idea of the Trinity at the end of the second century AD or start of the third century AD. It was not original to the the first Christians, despite the attempt of many of them to twist what the New Testament actually says. These problems plagued the early church for centuries, with Christian chroniclers and theologians like Eusebius in the fourth century AD discussing such problems as God not being begotten while Jesus was begotten. Arian, the leader of a different sect of Christianity allegedly made such logical arguments against the notion of the Trinity, it nearly split the early Christian church in two. But rewards from Constantine for those who followed official policy, and excuses, sorry, arguments such as God not being amenable to logical analysis won the day. And that is the problem with the question, the Christians will either just declare their god to be above logical analysis, or will have such vague ideas about their god it will be impossible use logic on the idea. ---
**Author:** ![BigT](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bigt/32/12044_2.png) [@BigT](https://boards.straightdope.com/u/BigT)\ **Post date:** [December 15, 2014, 12:12pm UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/83 "2014-12-15T12:12:50Z")
> [@PlaceboTarget](#): > > I can see both the beauty and coherence of the analogy, but I still think this argument fails to logically support, for instance, the idea that the Father and the Son are distinct persons and yet make up the single person of God. Where does the idea come from that God is a single person? He’s one God, but three Persons. As for your symbols, I think the problem is with F = S = H. This is true in some ways but not in others. Specifically, it is not true that the Father is the same person as the Son is the same person as the Holy Spirit. They are equal in power, longevity, and essence, but they are not 100% the same. Statements of how the Son is 100% God are just due to the imprecision of language. We’re not dealing with a transitive property. God is not 100% the Son. So when you say the Son is 100% God, you are saying that every part of him is a part of God, not that every part of God is a part of the Son. It can be easily shown that S != F != H. The Son died on a Cross. The Father and the Holy Spirit did not. Right there is a property that the Son has that the other two don’t. Thus they are not 100% the same. I don’t think we need to appeal to infinity at all. It’s just an overlapping Venn diagram. ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [December 15, 2014, 2:25pm UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/84 "2014-12-15T14:25:57Z")
> [@Half\_Man\_Half\_Wit](#): > > Well, presumably, the idea is that a wave is ‘not a particle’, and that thus, a photon, being both a particle and a wave, is therefore a particle and not a particle. But of course, that’s debatable from a quantum-mechanical point of view: a photon manifests wave-like properties only in the context of a specific experimental arrangement, and particle-like properties likewise. They’re complementary properties, and part of this complementarity relationship is precisely that both aspects are not simultaneously observable. That’s basically what I was trying to get at. > [@](#): > > However, the view that quantum mechanics poses a challenge to the law of identity has certainly been expressed before, based on some other phenomena it gives rise to. It depends a little bit, however, on how exactly you understand identity: if, for instance, you understand it to include the identifiability of objects, their having some sort of individual existence that makes it possible to tell them apart, then it’s arguably violated in quantum field theory—two electrons are indistinguishable to the point that you can’t put a lable on each of them to say ‘that’s electron 1’ and ‘that’s electron 2’. This is in fact an important factor in the statistics ‘gases’ of electrons or photons follow, which are different from those of classical particles that you can imagine as being composed of tiny little balls that bounce off one another. I wouldn’t have equated identifiability with identity, but it will be good for me to keep in mind in the future that this may be what people have in mind. The logical law of identity, as far as I’ve ever been able to tell, remains just as valid as ever. ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [December 15, 2014, 2:27pm UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/85 "2014-12-15T14:27:17Z")
> [@Half\_Man\_Half\_Wit](#): > > They are all unambiguously H[sub]2[/sub]O, however. They’re substantially the same, but different individually—different ‘modes of presentation’ of the same thing, perhaps. You can make sense of the trinity in the same way—the Father, Son, and the Holy Ghost are all God, and there is only one God, in the same sense there is only one H[sub]2[/sub]O, but they’re different ways the substance of God may present itself, just as there are different ways H[sub]2[/sub]O may present itself, as a liquid, as a solid, or as a gas. Unfortunately, modalism, too, is considered to be a heresy in classical Christian circles. It really seems like the Trinity, while not inconsistent, just doesn’t model _anything other_ than the Trinity! ---
**Author:** ![PlaceboTarget](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/placebotarget/32/1073_2.png) [@PlaceboTarget](https://boards.straightdope.com/u/PlaceboTarget)\ **Post date:** [December 15, 2014, 8:22pm UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/86 "2014-12-15T20:22:53Z")
> [@BigT](#): > > Where does the idea come from that God is a single person? He’s one God, but three Persons. Let us discuss this then: “God is a collection of three Persons.” Above all, I can refrain myself from noting how much this concept resembles the Indian [Para Brahman](http://en.wikipedia.org/wiki/Para_Brahman). I hate initiating a tedious discussion on definition but it seems unavoidable. God is defined as a being with supernatural characteristics, and a being is defined as a person. Which means the contradiction is still there, that is: “The Person endowed with absolute supernatural characteristics in Christianity is a collections of three Persons.” ---
**Author:** ![Half\_Man\_Half\_Wit](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/half_man_half_wit/32/21766_2.png) [@Half\_Man\_Half\_Wit](https://boards.straightdope.com/u/Half_Man_Half_Wit)\ **Post date:** [December 15, 2014, 8:43pm UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/87 "2014-12-15T20:43:53Z")
> [@Frylock](#): > > The logical law of identity, as far as I’ve ever been able to tell, remains just as valid as ever. Well, to the extent that nobody can force you to give it up, certainly. But on the other hand, you can construct nontrivial logics in which it doesn’t hold, and some of those logics apparently can be used to describe certain aspects of quantum mechanics. It’s really the same with the other two classical laws of thought—which, interestingly, have all been at one point or another proposed to be abandoned in order to ‘make sense’ of quantum mechanics. But of course, you can just as well continue using classical logic, if you want to. The most straightforward way to do so, however, comes with some ontological baggage, quantities that are hidden from direct experimental observation, as for instance the position variable in Bohmian mechanics. It’d maybe be interesting to investigate whether such ontological baggage is a necessary addition if you insist on leaving all of classical logic intact, but I can’t offhand think of any research in that direction… > [@Frylock](#): > > Unfortunately, modalism, too, is considered to be a heresy in classical Christian circles. Damn, they’ve really thought of everything, haven’t they? But now I feel sort of cheated: the facebook test I took recently claimed my heresy was arianism, and now I find out I’ve been a modalist all along! ---
**Author:** ![Trinopus](https://avatars.discourse-cdn.com/v4/letter/t/2bfe46/32.png) [@Trinopus](https://boards.straightdope.com/u/Trinopus)\ **Post date:** [December 15, 2014, 8:44pm UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/88 "2014-12-15T20:44:20Z")
> [@PlaceboTarget](#): > > I can see both the beauty and coherence of the analogy, but I still think this argument fails to logically support, for instance, the idea that the Father and the Son are distinct persons and yet make up the single person of God. The ice/water/steam idea is only a metaphor, to enhance visualization of the ineffable. It is not an argument, and it bears no logical support at all. This is religion. It works only at the level of what people believe. Do Hindu Gods really have multiple arms, or is it just an artistic convention in portraits and statues? The answer is “both.” The answer may be contradictory, but, so it goes: that’s religion for you. Some of us hold that omniscience, omnipotence, and omnibenevolence cannot logically co-exist, but must be self-contradictory. Others shrug and go right on believing it. ---
**Author:** ![andros](https://avatars.discourse-cdn.com/v4/letter/a/e480ec/32.png) [@andros](https://boards.straightdope.com/u/andros)\ **Post date:** [December 15, 2014, 8:54pm UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/89 "2014-12-15T20:54:47Z")
> [@PlaceboTarget](#): > > God is defined as a being with supernatural characteristics, and a being is defined as a person. If those are your premises, then there’s arguably a contradiction. But other people might well begin with different premises, like f’rinstance that the being called God is _not_ definable as a person. Or indeed, definable. ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [December 15, 2014, 9:02pm UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/90 "2014-12-15T21:02:28Z")
> [@Half\_Man\_Half\_Wit](#): > > Well, to the extent that nobody can force you to give it up, certainly. But on the other hand, you can construct nontrivial logics in which it doesn’t hold, and some of those logics apparently can be used to describe certain aspects of quantum mechanics. Sure but at the lay level I don’t think this is what anyone means when they say that somehow QM “breaks” the law of identity. In such contexts, people seem to mean that (in so many words) when talking about QM using second order predicate logic with identity, certain contradictions involving identity turn out to be true. Which is not correct. > [@](#): > > It’s really the same with the other two classical laws of thought—which, interestingly, have all been at one point or another proposed to be abandoned in order to ‘make sense’ of quantum mechanics. > > But of course, you can just as well continue using classical logic, if you want to. The most straightforward way to do so, however, comes with some ontological baggage, quantities that are hidden from direct experimental observation, as for instance the position variable in Bohmian mechanics. It’d maybe be interesting to investigate whether such ontological baggage is a necessary addition if you insist on leaving all of classical logic intact, but I can’t offhand think of any research in that direction… I don’t see how ontological baggage would come along with using classical logic to talk about QM. Can you say something about why you suggested this might be so? I would have thought if anything that using classical logic to talk about QM would have sort of the opposite effect–you’d end up leaving some stuff out that is necessary for actually getting in there and making predictions. (But that’s just to say that classical logic isn’t a good (or at least, complete) model for QM, which to be clear I’m not denying.) ---
**Author:** ![JRDelirious](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jrdelirious/32/9531_2.png) [@JRDelirious](https://boards.straightdope.com/u/JRDelirious)\ **Post date:** [December 16, 2014, 12:26am UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/91 "2014-12-16T00:26:08Z")
nm ---
**Author:** ![PlaceboTarget](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/placebotarget/32/1073_2.png) [@PlaceboTarget](https://boards.straightdope.com/u/PlaceboTarget)\ **Post date:** [December 16, 2014, 5:39am UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/92 "2014-12-16T05:39:42Z")
> [@andros](#): > > If those are your premises, then there’s arguably a contradiction. But other people might well begin with different premises, like f’rinstance that the being called God is _not_ definable as a person. Or indeed, definable. It is theists that have come up with the concept of Trinity, which is supposedly employed to define and clarify. ---
**Author:** ![PlaceboTarget](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/placebotarget/32/1073_2.png) [@PlaceboTarget](https://boards.straightdope.com/u/PlaceboTarget)\ **Post date:** [December 16, 2014, 5:46am UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/93 "2014-12-16T05:46:17Z")
I’ve just realized that I made a mistake in my little formalization, which began with G=F+S+H. It was wrong of me to state F=S=H and claim that the equal sign stands for “identical with.” They say these three persons are equal, but not identical. There is an interesting implication, though, which I’ll produce a bit later. ---
**Author:** ![Half\_Man\_Half\_Wit](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/half_man_half_wit/32/21766_2.png) [@Half\_Man\_Half\_Wit](https://boards.straightdope.com/u/Half_Man_Half_Wit)\ **Post date:** [December 16, 2014, 6:25am UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/94 "2014-12-16T06:25:10Z")
> [@Frylock](#): > > Sure but at the lay level I don’t think this is what anyone means when they say that somehow QM “breaks” the law of identity. In such contexts, people seem to mean that (in so many words) when talking about QM using second order predicate logic with identity, certain contradictions involving identity turn out to be true. > > Which is not correct. Agreed. > [@](#): > > I don’t see how ontological baggage would come along with using classical logic to talk about QM. Can you say something about why you suggested this might be so? I would have thought if anything that using classical logic to talk about QM would have sort of the opposite effect–you’d end up leaving some stuff out that is necessary for actually getting in there and making predictions. [This is going to be a bit of a digression, so anybody not interested in nonclassical logics should skip this post] I think that if you tried to do it that way, applying classical logic in order to talk about QM in a sort of ‘coarse-grained’ way, then what you’d leave out would basically be all distinctively quantum phenomena, since it’s where the uncertainty principle becomes important that classical logic doesn’t model things well anymore. What I mean here is, roughly, that classical logic is a good model for classical physics because the structure of subsets of the state space of classical physics, that is, for instance, the subsets of configuration space (or equivalently phase space), form a Boolean lattice ordered by inclusion with the operations of set intersection and union. Furthermore, those subsets can be taken to correspond to propositions about the system—‘the system has such-and-such a configuration’ is just ‘the system is in this subset of the state space’. The analogous construction in quantum mechanics, where the state space is not a set, but a linear inner-product vector space called Hilbert space, is the algebra of sub-spaces of Hilbert space, which however does not form a Boolean, but merely an orthomodular lattice, which can nevertheless be understood as a logic—namely, the original quantum logic by Birkhoff and von Neumann. If you want to use classical logic to describe this, then you need basically something to turn this structure into something that more closely resembles the sets of classical mechanics. Now, at least one way to do this is to identify the uncertainty principle as the culprit of what makes QM non-classical: essentially, it means that if you try to describe QM in a set-like state space, you can’t localize the system to a point in that space, but merely to a subset whose area is dictated by the uncertainty relation—localizing the system to a point would mean knowing all its properties simultaneously arbitrarily well. In quantum mechanics, and quantum logic, basically, the tenet is that the system is not in fact localized better than the uncertainty principle allows—not all of its properties are simultaneously ‘sharp’. But what you then can do is to say that, actually, the system is localized sharply, but we’re prohibited from knowing those sharp values. This amounts to a hidden variable theory, such as Bohmian mechanics, where it’s simply the act of measurement that disturbs the value of the hidden variables in such a way as to uphold the uncertainty principle (via the nonlocal influence of the quantum potential). Then, you can reason about all quantum phenomena (Bohmian mechanics and ordinary QM are observationally equivalent) using classical logic, without leaving anything out—the state space of Bohmian mechanics is simply configuration space (augmented with a specification of the wave function at each point). However, this comes at the cost of introducing unobservable quantities (and nonlocal influences). In a sense, it’s ‘violating’ the uncertainty principle without that violation being obervable that makes this possible, so I’d guess that any similar ‘classicalization’ of QM would introduce similar additional structure or ontology (modal interpretations might be a candidate). ---
**Author:** ![PlaceboTarget](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/placebotarget/32/1073_2.png) [@PlaceboTarget](https://boards.straightdope.com/u/PlaceboTarget)\ **Post date:** [December 16, 2014, 6:25am UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/95 "2014-12-16T06:25:22Z")
They say [God is the Father], [God is the Son] and [God is the Holy Spirit]. They all share the same substance. At the same time, however, [the Father is different from the Son], [the Son is different from the Holy Spirit] and [the Holy Spirit is different from the Father]. Thus, God is a collective noun just like \*furniture \*for example. chair … table ------ …------- …/… …furniture… …----------… …|… …bed… …----… The difference is that in the case of God the number of instances is limited to 3, and these instances are persons. This is, in my opinion, just another relativization of the notion of monotheism. ---
**Author:** ![Buck\_Godot](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/buck_godot/32/6573_2.png) [@Buck\_Godot](https://boards.straightdope.com/u/Buck_Godot)\ **Post date:** [December 16, 2014, 5:07pm UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/96 "2014-12-16T17:07:31Z")
I’m not a Christian so take this with a grain of salt, but my take would be to say that the trinity represents different aspects and roles of the same person. For example I could be considered as two persons: 1. Buck Godot the husband 2. Buck Godot the statistician Both are Buck Godot, but they are in a way distinct. When my wife calls me at work, and I don’t notice who called, she will say that I answered in my professional voice, which is distinct from the voice I normally use with her. Similarly if we are being cuddly, I’m hopefully not on the top of my game with regard to negative binomial mixture models. But it is certainly the case that Buck the statistician is married to my wife, and my wife’s husband does statistics. ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [December 16, 2014, 5:36pm UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/97 "2014-12-16T17:36:44Z")
One of these days I need to get in there and get serious about learning what a Boolean lattice is, and learning all the stuff in the framework around that concept that will let me talk smart on the topic. Oddly enough, the concept keeps coming up in various conversations I have online. ---
**Author:** ![Hector\_St\_Clare](https://avatars.discourse-cdn.com/v4/letter/h/b5ac83/32.png) [@Hector\_St\_Clare](https://boards.straightdope.com/u/Hector_St_Clare)\ **Post date:** [December 16, 2014, 6:13pm UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/98 "2014-12-16T18:13:59Z")
> [@PlaceboTarget](#): > > They say [God is the Father], [God is the Son] and [God is the Holy Spirit]. They all share the same substance. At the same time, however, [the Father is different from the Son], [the Son is different from the Holy Spirit] and [the Holy Spirit is different from the Father]. > > Thus, God is a collective noun just like \*furniture \*for example. > chair … table > ------ …------- > ….…/… > …furniture… > …----------… > …|… > …bed… > …----… > > The difference is that in the case of God the number of instances is limited to 3, and these instances are persons. This is, in my opinion, just another relativization of the notion of monotheism. I think that’s a good analogy, and I like it. I’m not sure quite what you see as the problem here? ---
**Author:** ![Hector\_St\_Clare](https://avatars.discourse-cdn.com/v4/letter/h/b5ac83/32.png) [@Hector\_St\_Clare](https://boards.straightdope.com/u/Hector_St_Clare)\ **Post date:** [December 16, 2014, 6:16pm UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/99 "2014-12-16T18:16:06Z")
> [@Buck\_Godot](#): > > I’m not a Christian so take this with a grain of salt, but my take would be to say that the trinity represents different aspects and roles of the same person. > > For example I could be considered as two persons: > > 1. Buck Godot the husband > 2. Buck Godot the statistician > > Both are Buck Godot, but they are in a way distinct. When my wife calls me at work, and I don’t notice who called, she will say that I answered in my professional voice, which is distinct from the voice I normally use with her. Similarly if we are being cuddly, I’m hopefully not on the top of my game with regard to negative binomial mixture models. But it is certainly the case that Buck the statistician is married to my wife, and my wife’s husband does statistics. No, that kind of ‘distinction by roles’ is modalism, and certainly not anything I could sign on to. I don’t get why some people are so anxious to elide the distinction of persons, and collapse the three persons into one. ---
**Author:** ![Buck\_Godot](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/buck_godot/32/6573_2.png) [@Buck\_Godot](https://boards.straightdope.com/u/Buck_Godot)\ **Post date:** [December 16, 2014, 8:36pm UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/100 "2014-12-16T20:36:28Z")
> [@Hector\_St\_Clare](#): > > I think that’s a good analogy, and I like it. > > I’m not sure quite what you see as the problem here? But the same analogy could be used with regard to the Greek pantheon. Olympians is a collective noun, and Zeus, Hermes and Athena are instances, but we certainly wouldn’t call the Greeks monotheistic just because we can group all the gods together under one name. Would a better analogy be a troll with three arms that are controlled by three heads, each one acting independently but still part of the whole? [Previous page](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200.md?page=4) [Next page](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200.md?page=6)