# 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:** 4
**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:** [December 14, 2014, 8:35pm UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/61 "2014-12-14T20:35:29Z")
> [@Robert163](#): > > Law Of Identity: > In logic, the law of identity is the first of the three classical laws of thought. It states that “each thing is the same with itself and different from another”. > > Trinity: > Father, Son, Holy Ghost > > But can the Christian simply say it is one “power” with three parts??? Suppose I own a copy of _Moby Dick_ and you own a copy of _Moby Dick_. My copy is the same as your copy, meaning that they are both the same text. My copy is not the same as your copy, meaning that they are not the same physical object. Does this violate the law of identity? ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [December 14, 2014, 8:35pm UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/62 "2014-12-14T20:35:40Z")
> [@PlaceboTarget](#): > > Trinity can be summarized as follows: > > 1. God consists of his three hypostases: the Father, the Son, and the Holy Spirit. > > G = F + S + H > > 1. The Father, the Son, and the Holy Spirit are co-equal, co-eternal and cosubstantial. > > F = S = H > > 1. Each of the three (the Father, the Son, and the Holy Spirit) is God, whole and entire. > > F = G > S = G > H = G > This means: > F = F + S + H > S = F + S + H > H = F + S + H > > How can one aggregate 1), 2) and 3) without violating the Law of Identity? This was answered already–those equations can be solved by setting all the variables to either zero or aleph-null. If you don’t mean them to be interpreted numerically like that, then you need to explain how you mean them to be interpreted. Without having explained that, we have no way of knowing what the problem is supposed to be. ---
**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:** [December 14, 2014, 8:43pm UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/63 "2014-12-14T20:43:55Z")
> [@PlaceboTarget](#): > > Trinity can be summarized as follows: > > 1. God consists of his three hypostases: the Father, the Son, and the Holy Spirit. > > G = F + S + H > > 1. The Father, the Son, and the Holy Spirit are co-equal, co-eternal and cosubstantial. > > F = S = H > > 1. Each of the three (the Father, the Son, and the Holy Spirit) is God, whole and entire. > > F = G > S = G > H = G > This means: > F = F + S + H > S = F + S + H > H = F + S + H > > How can one aggregate 1), 2) and 3) without violating the Law of Identity? Let me offer a different way of thinking about it. I have two finite mathematical objects (sets, graphs, groups, …) Let’s call them A and B. Is it possible that A is properly contained within B, and B is properly contained with A? It is not possible. But what if I have two _infinite_ mathematical objects, C and D. Is it possible that C is properly contained within D, and D is properly contained within C? Yes, it is. Anyone who’s studied group theory, for instance, can easily give examples of infinite groups F and G such that F \< G and G \< F, while F and G are not the same group. So if the Father, Son, and Holy Spirit are infinite, one can imagine that the Father contains all properties of the Son and Holy Spirit, the Son contains all properties of the Father and Holy Spirit, and the Holy Spirit contains all properties of the Father and Son, while the three are not the same. This is not a direct correspondence to mathematics, but rather is using mathematics as an analogy to understand a theological concept which the human mind cannot grasp in its fulness. ---
**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 14, 2014, 8:58pm UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/64 "2014-12-14T20:58:34Z")
> [@Frylock](#): > > This was answered already–those equations can be solved by setting all the variables to either zero or aleph-null. > > If you don’t mean them to be interpreted numerically like that, then you need to explain how you mean them to be interpreted. Without having explained that, we have no way of knowing what the problem is supposed to be. If Trinity is summarized as follows: 1. God consists of his three hypostases: the Father, the Son, and the Holy Spirit. G = F + S + H 1. The Father, the Son, and the Holy Spirit are co-equal, co-eternal and cosubstantial. F = S = H 1. Each of the three (the Father, the Son, and the Holy Spirit) is God, whole and entire. F = G S = G H = G This means: F = F + S + H S = F + S + H H = F + S + H then aggregating 1), 2) and 3) would violate the Law of Identity. The Law of Identity states that A is identical only with A (i.e. itself). In light of the Law of Identity, 2) and 3) in the brief presentation of Trinity above make equivocal and contradictory statements. ---
**Author:** ![simster](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/simster/32/1047_2.png) [@simster](https://boards.straightdope.com/u/simster)\ **Post date:** [December 14, 2014, 9:06pm UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/65 "2014-12-14T21:06:07Z")
> [@Robert163](#): > > one god define ‘god’ - Christians (trinitarians anyway) define God as the combination of the three beings - all equal, all separate, all becoming (or being) the one thing called “GOD”. You could similarly call man a “three pronged being” - body, mind, soul - and it wouldn’t be that far off the mark. It is not a logical argument but one of faith - which does not require, by definition, any logic or reasoning. ---
**Author:** ![simster](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/simster/32/1047_2.png) [@simster](https://boards.straightdope.com/u/simster)\ **Post date:** [December 14, 2014, 9:16pm UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/66 "2014-12-14T21:16:07Z")
> [@PlaceboTarget](#): > > Trinity can be summarized as follows: > > 1. God consists of his three hypostases: the Father, the Son, and the Holy Spirit. > > G = F + S + H > > 1. The Father, the Son, and the Holy Spirit are co-equal, co-eternal and cosubstantial. > > F = S = H > > 1. Each of the three (the Father, the Son, and the Holy Spirit) is God, whole and entire. > > F = G > S = G > H = G > This means: > F = F + S + H > S = F + S + H > H = F + S + H > > How can one aggregate 1), 2) and 3) without violating the Law of Identity? You keep using ‘aggregate’ or a summation (plus ) - when it could be a multiplication issue - 1x1x1 still == 1 1 /1 still ==1 You’re also (like the OP) assuming “Identity” is something its not been defined as - at least as far as the Christian Trinity is concerned. ---
**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 14, 2014, 10:00pm UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/67 "2014-12-14T22:00:02Z")
> [@ITR\_champion](#): > > Let me offer a different way of thinking about it. > > I have two finite mathematical objects (sets, graphs, groups, …) Let’s call them A and B. Is it possible that A is properly contained within B, and B is properly contained with A? It is not possible. > > But what if I have two _infinite_ mathematical objects, C and D. Is it possible that C is properly contained within D, and D is properly contained within C? Yes, it is. > > Anyone who’s studied group theory, for instance, can easily give examples of infinite groups F and G such that F \< G and G \< F, while F and G are not the same group. > > So if the Father, Son, and Holy Spirit are infinite, one can imagine that the Father contains all properties of the Son and Holy Spirit, the Son contains all properties of the Father and Holy Spirit, and the Holy Spirit contains all properties of the Father and Son, while the three are not the same. This is not a direct correspondence to mathematics, but rather is using mathematics as an analogy to understand a theological concept which the human mind cannot grasp in its fulness. Mathematics is a language that I used to master relatively well before I went to university (i.e. long ago). I’m not against using math concepts, but I don’t see how this is useful in the case of Trinity. For instance, point (1) states that G=F+S+H whereas point (2) states that F=S=H. Whatever makes F, S and H different in point (1) should make it impossible for F, S and H to be the same in point (2). Accepting (1) and (2) at the same time leads to contradiction. > [@simster](#): > > You keep using ‘aggregate’ or a summation (plus ) - when it could be a multiplication issue - > 1x1x1 still == 1 > > 1 /1 still ==1 > > You’re also (like the OP) assuming “Identity” is something its not been defined as - at least as far as the Christian Trinity is concerned. A sylogism cannot be equated to a series of mathematical operations. In a logical argument, premises cannot be multiplied. (N.B. The Law of Identity belongs to formal logic.) ---
**Author:** ![Learjeff](https://avatars.discourse-cdn.com/v4/letter/l/94ad74/32.png) [@Learjeff](https://boards.straightdope.com/u/Learjeff)\ **Post date:** [December 14, 2014, 10:09pm UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/68 "2014-12-14T22:09:58Z")
> [@Thudlow\_Boink](#): > > What’s the part the doesn’t “make sense, logically speaking”? I don’t know whether you’re trying to use the + and = signs mathematically, but even then, equations like those you wrote all “work” mathematically if all the “letters” are equal to aleph-null. > [@Frylock](#): > > And, for that matter, zero. Great points! And it’s amusing that two valid answers are infinity and zero … which pretty much sums up how different people assign the values. 😉 (BTW, I believe any infinity works, aleph null merely being the smallest.) > [@Miller](#): > > How do you distinguish between what we _think_ is fair and right, and what _really is_ fair and right? What are the objective standards of justice? How do you define them, and how do you demonstrate that they are, in face, objective? > [@Robert163](#): > > I dont know. But just because I don’t know everything doesn’t mean I can’t identify something that is clearly wrong, ie, sending Fred to jail to serve the time for Tom’s crime, and letting Tom go free. You’re assuming that justice has an objective definition, which is a very unusual position among philosophers and scholars. Ayn Rand would agree with you, but she at least goes to the trouble of explaining why. Religious people can say that God decides what is just; that’s still subjective to God. > [@Robert163](#): > > really, and how do you know that’s correct, or is that just what you think??? When you say you feel something is just or not just, how do you know that’s correct, or is that just what you think? Sociobiologists will tell you that we have an evolved “moral sense” that emotionally informs us when something is fair or not. If they’re right, this moral sense is not based on some objective standard for right and wrong, it’s based on what works. We all use our moral senses as guides, but we should be careful not to assume it’s always the best judge. > [@PlaceboTarget](#): > > If Trinity is summarized as follows: > … Restatement doesn’t clarify. If you said this: F = G S = G H = G F != S != H then you’d have to be dealing with a situation where the equality operator is intransitive, or else you’d have an inconsistency. I’ll admit I have a problem with that; I can’t imagine any use for an intransitive equality operator. But is anyone actually saying that F != S != H? Perhaps. In any case, I don’t need the Trinity to find the concept of God illogical. To me, it’s illogical from the get-go. But then, the existence of anything at all is a bit illogical. Everything would be so much simpler if there were nothing! ---
**Author:** ![Learjeff](https://avatars.discourse-cdn.com/v4/letter/l/94ad74/32.png) [@Learjeff](https://boards.straightdope.com/u/Learjeff)\ **Post date:** [December 14, 2014, 10:18pm UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/69 "2014-12-14T22:18:20Z")
> [@PlaceboTarget](#): > > A sylogism /// Sylogisms aren’t valid logic in any case. Since it doesn’t treat existence specially, you can prove all sorts of silly stuff. For more info, see [Syllogism - Wikipedia](https://en.wikipedia.org/wiki/Syllogism#Existential_import) . ---
**Author:** ![simster](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/simster/32/1047_2.png) [@simster](https://boards.straightdope.com/u/simster)\ **Post date:** [December 14, 2014, 10:40pm UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/70 "2014-12-14T22:40:05Z")
> [@PlaceboTarget](#): > > A sylogism cannot be equated to a series of mathematical operations. Is that not what you are trying to do in your “summation” ?? You’re trying to construct a mathmatical model for “god” or the “trinity” - I’m simply showing that there is a mathmatical model that does resolve just fine for the trinity. > [@PlaceboTarget](#): > > In a logical argument, premises cannot be multiplied. (N.B. The Law of Identity belongs to formal logic.) And what part of ‘God’ or “The Trinity” is a logical argument? ---
**Author:** ![tomndebb](https://avatars.discourse-cdn.com/v4/letter/t/b9e5f3/32.png) [@tomndebb](https://boards.straightdope.com/u/tomndebb)\ **Post date:** [December 14, 2014, 11:29pm UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/71 "2014-12-14T23:29:59Z")
> [@Robert163](#): > > really? > > monotheism = one and only one true god > trinity= father, son, holy ghost > > it seems pretty clear cut. and to accept the “christian” explanation of a logical fallacy seems hardly worth even responding too. objective standards are what i am interested in. but i’m not a logician nor a linguist… let me put it another way… is there a non-christian justification of the logical fallacy between the law of identity and the trinity? Had you actually started out with this as the OP, we’d have been further along with less snark. The Trinity has been a point on which various Jews and Muslims have criticized Christianity as not monotheistic for a long time. Christians are aware of the criticism and it does not seem to have had any deleterious effect on their faith, but you are welcome to make your pleas as long as you remain civil in this thread. ---
**Author:** ![Trinopus](https://avatars.discourse-cdn.com/v4/letter/t/2bfe46/32.png) [@Trinopus](https://boards.straightdope.com/u/Trinopus)\ **Post date:** [December 14, 2014, 11:36pm UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/72 "2014-12-14T23:36:08Z")
Ice, water, steam. The co-exist at the “triple point” of water. Anyway, it’s religion. It means whatever the believer wants it to mean. ---
**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, 6:40am UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/73 "2014-12-15T06:40:50Z")
> [@Learjeff](#): > > Restatement doesn’t clarify. > > If you said this: > > F = G > S = G > H = G > F != S != H > > then you’d have to be dealing with a situation where the equality operator is intransitive, or else you’d have an inconsistency. I’ll admit I have a problem with that; I can’t imagine any use for an intransitive equality operator. But is anyone actually saying that F != S != H? Perhaps. > > In any case, I don’t need the Trinity to find the concept of God illogical. To me, it’s illogical from the get-go. But then, the existence of anything at all is a bit illogical. Everything would be so much simpler if there were nothing! I wonder if you have applied prepositional logic, which is a branch of mathematical logic (about which I have no idea). I don’t think math is the key to the Trinity logical problem. And even if it were, the propositions and their implications should have noncontradictory equivalents in plain English or else logical paradoxes can be invoked by anyone in order to justify just about any flapdoodle. It seems to me that the concept of the singleness of God’s person, who should be regarded as consisting of three distinct persons, violates the Law of Identity. ---
**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, 6:46am UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/74 "2014-12-15T06:46:16Z")
> [@Learjeff](#): > > Sylogisms aren’t valid logic in any case. Since it doesn’t treat existence specially, you can prove all sorts of silly stuff. For more info, see [Syllogism - Wikipedia](https://en.wikipedia.org/wiki/Syllogism#Existential_import) . True. The question then is should we invoke logic anymore in learning what there is or there isn’t or we should we uncritically accept every statement issued by some authority? ---
**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, 6:49am UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/75 "2014-12-15T06:49:30Z")
> [@simster](#): > > Is that not what you are trying to do in your “summation” ?? You’re trying to construct a mathmatical model for “god” or the “trinity” - I’m simply showing that there is a mathmatical model that does resolve just fine for the trinity. > > And what part of ‘God’ or “The Trinity” is a logical argument? I understand now that the way I was trying to formalize the ideas has made people think of a mathematical solution, but that was not my intention. I meant the equal sign to stand for “identical with.” ---
**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, 7:00am UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/76 "2014-12-15T07:00:12Z")
> [@Trinopus](#): > > Ice, water, steam. > > The co-exist at the “triple point” of water. > > Anyway, it’s religion. It means whatever the believer wants it to mean. The statement above (i.e. “Ice, water, steam.”) is misleading. I know that in informal logic water is the same as liquid water, but if we want to be rigorous it should be stated as “Ice, liquid water, and steam.” Since ice is solid water and steam, gaseous water, there is no contradiction in holding them all as water since non-contradictory modifiers do not turn a single object into a plurality. ---
**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, 7:06am UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/77 "2014-12-15T07:06:11Z")
> [@Frylock](#): > > Something can have both wavelike properties and particle-like properties, yes. What’s the contradiction (A & not-A) you think you see here? 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. 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. ---
**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, 7:12am UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/78 "2014-12-15T07:12:34Z")
> [@PlaceboTarget](#): > > The statement above (i.e. “Ice, water, steam.”) is misleading. I know that in informal logic water is the same as liquid water, but if we want to be rigorous it should be stated as “Ice, liquid water, and steam.” Since ice is solid water and steam, gaseous water, there is no contradiction in holding them all as water since non-contradictory modifiers do not turn a single object into a plurality. 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. ---
**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, 7:32am UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/79 "2014-12-15T07:32:41Z")
> [@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. 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. ---
**Author:** ![simster](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/simster/32/1047_2.png) [@simster](https://boards.straightdope.com/u/simster)\ **Post date:** [December 15, 2014, 11:08am UTC](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200/80 "2014-12-15T11:08:44Z")
> [@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. When steam leaves - its still ‘water’ although physically separate from the main body - it can even ‘stop being steam’ and rejoin the main body with no inherit change in either (other than state). [Previous page](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200.md?page=3) [Next page](https://boards.straightdope.com/t/does-the-christian-trinity-violate-the-law-of-identity/707200.md?page=5)