Complete Irrationality
May 7, 2005 § 30 Comments
I’ve probably been too cryptic in the discussions I’ve been having below with a few very bright mathematicians. Let me explain the pedantry in (hopefully) more layman-accessible terms. (At the same time please do keep in mind that pedantry is one of the founding principles of this weblog).
A “hermeneutical system” consists of a finite text (for example the Bible or the Koran**) which we will call scripture and some rational process for interpreting that scripture. Interpreting the scripture means, among other things, producing written doctrines which we say must be believed. When I say “true” in the remaining discussion, I don’t mean “happens to be true”: I mean “must be believed”. Lots of things happen to be true but do not have the character that they must be believed by Christians. The sort of “true/false” I am using here, though, is the “must be believed/need not be believed” sort.
Sola scriptura states that if a doctrine is proposed as true, its truth must be decideable from the text of scripture. To claim that whether a given proposition must be believed or not is decideable from the text of scripture is to claim that scripture is complete. Sola scriptura also claims that it is, itself, derived from the text of scripture. And so, via Godel’s Theorem (the proof/comprehension of which is left as an exercise), sola scriptura asserts its own logical inconsistency:
“The hermeneutical system of which this sentence is a theorem is complete.”
The only way for this not to be a logically inconsistent claim – and you will see the quibbling about this between myself and the real mathematicians in the comments – is if the hermeneutical system is expressly restricted not to be smart enough to do arithmetic. If any abstract concepts that can be used to build a functional arithmetic sneak into our hermeneutical system (we don’t have to actually do any arithmetic, we just have to make use of abstract reasoning capable of doing some), then sola scriptura asserts the inconsistency of the hermeneutical system. Sola scriptura asserts its own irrationality. Martin Luther was presciently right to decry reason as the mortal enemy of sola scriptura.
** An interesting bit of trivia in the history of theology is that the Moslem faith adopted a form of sola scriptura long before any Christian faith did. It may or may not be coincidence that John Wyclif (the inventor of Christian sola scriptura), his friend and patron John of Gaunt, and John of Gaunt’s secretary Geoffrey Chaucer were all quite familiar with the faith of the Moors.
Zippy Catholic 
Hi,I’m sure your intentions are perfectly fine, but it is preferred to use the term Muslims as opposed to Moslems (there is also Quran instead of Koran, but thats not a biggie). It is primarily because the pronunciation is quite incorrect (Moz-lem instead of Mus-lim) and when going from language to language; one must be careful because the meaning of a word are integrally tied with how you say it (as in any language).I am glad you clarified some terms as I did read the discourse between you and the mathematicians; but to be honest I did not understand most of the arguments. I simply enjoy being intellectually baffled. I tried reading <>Godel Esher Bach: An Eternal Golden Braid<>; but haven’t gone too far in the book because it requires me to pay close attention to it; and the lingo is very close to how you 3 have been talking.A few questions: what is sola scriptura? I have heard it in relation with Christianity, but never Islam.“The only way for this not to be a logically inconsistent claim – … – is if the hermeneutical system is expressly restricted not to be smart enough to do arithmetic.”Are you saying that the only way for the H.S. to be logically CONSISTENT (you had a double negative up there) is if the H.S. is not allowed to be represented mathematically? I do not understand why this is so; and what scripture has to do with mathematically representation. What do you mean by ‘smart enough’?What is the difference between an abstract or mathematical representation?A hermenuetical system can only possibly reinforce its own truth. Or dare I say that everything reinforces itself and its components ? And nothing is truly true but based on successive hierarchies of related assertions? (or is that what u all have been talking about :S)What is the argument about sola scriptura asserts the inconsistency of the hermeneutical system” really going to prove?I’m sorry I have so many questions, but I’m really quite interested 🙂You dont have to answer all of them, but I might be less confused if you do.
By the way, Zippy: you can still have -some- arithmetic and be complete (e.g. Pressburger arithmetic, which is decideable), just not all of “regular” first-order (Peano) arithmetic.More important: I think your argument would be more effective if, instead of appealing directly to GT, you extended your method of analogy (viz. dogma := theorem and scripture := axioms) you analogized Gödel’s proof directly.For example, could you construct by diagonalization a hermeneutical truth which wasn’t provable by scripture, even though it was in the “language” of scripture.AM
I’m afraid I’m quite wary of trying to analogize Gödel’s Theorem in this way, Zippy. It’s not robust enough to have compelling force in this context. Most importantly, the hermeneutical system lacks any apparent way to go about Gödel-numbering (or its equivalent) to produce statements of meta-doctrine from statements of doctrine. For another, the rules of derivation of theorems are not agreed upon in the least, the most necessary thing for any sort of Gödelian self-reference. And finally, a “Gödel sentence” of doctrine would in fact be such a complicated and abstruse statement (as G, without its metamathematical interpretation, is just an arcane and pointless statement about a really big integer) as to not merit the necessity of belief. In other words, we ain’t talking the Assumption of Mary here.If there’s a logical consistency in general with a hermeneutic of Luther-esque <>sola scriptura<>, showing it conclusively seems to be well beyond our powers. I prefer to concentrate on such points as that the Bible does not itself mandate <>sola scriptura<>.
I don’t suppose that Cornelius Van Til was much concerned with Goedel but I’m thinking that his “presuppositionalism” is one consistent way a Protestant biblicist might tackle your challenge.
fahd wrote:<>A few questions: what is sola scriptura? I have heard it in relation with Christianity, but never Islam.<>Well, Islam doesn’t generally say things in Latin :-).<>Sola scriptura<> is just the understanding that whether a proposed doctrine must be believed or not (including the doctrine of sola scriptura itself) is decideable from the text of scripture. If scripture does not say that a doctrine must be believed, then it does not have to be believed. My understanding is that < HREF="http://www.submission.org/hadith/bhadith.html" REL="nofollow">this sort of controversy over textual completeness<> has been around in Islam since at least the 800’s A.D., many centuries before John Wyclif latched onto the idea in order to undermine the sacrament of penance. (The sacrament of penance was inconvenient for Wyclif’s patron, since it implies that grace can be restored to a sinner like the Pope, and if grace can be restored to a sinner then it cannot be asserted that temporal authority flowing to that sinner from God has been forever severed by sin. And John of Gaunt really wanted to sever the Pope’s temporal authority, perhaps not appreciating that the same sort of trick would be used to sever aristocratic authority a few centuries later). Sola scriptura (that is, a Book, a finite written text, as the literal word of God and the source of all those truths which must be believed) is foundational to Islam. It found its way into the Christian religion in modified form many centuries later because of its political implications.<>Are you saying that the only way for the H.S. to be logically CONSISTENT (you had a double negative up there) is if the H.S. is not allowed to be represented mathematically?<> No, it is really much worse than that (or better, depending on whether you are pro- or con- <>sola scriptura<>). In order to do everyday arithmetic you only need a few relatively straightforward humdrum abstract concepts (sufficient to construct what mathematicians would call a <>ring<>: sets of things, correspondences between sets of things, ways of manipulating set members <>associatively<> and <>distributively<>). You don’t need to actually do anything with numbers or try to explicitly represent anything with what you would recognize as math. You just have to make use of abstract concepts that <>could be used<> to build an arithmetic capable of doing at least multiplication.If you can in principle do everyday arithmetic in your hermeneutic (even if you don’t do it in practice), and you claim that your written-text-plus-hermeneutic is <>complete<>, you have violated Godel’s Theorem. Basically you have contradicted yourself, although <>proving<> that you have contradicted yourself is fairly involved.<>What is the difference between an abstract or mathematical representation?<>None. I use the term “abstract” to point out that you don’t have to actually do anything explicitly with <>numbers<> in order to have invoked the sort of reasoning that would trigger Godel’s Theorem. You have to use a kind of reasoning that <>could<> be used to do math, but you don’t have to self-consciously recognize yourself as doing math. <>What is the argument about sola scriptura asserts the inconsistency of the hermeneutical system” really going to prove?<>Basically is shows that when one asserts something like “everything you have to believe about X, including this very proposition itself, is deduceable from this text”, if we take the claim seriously, then one has made an irrational (literally logically contradictory) statement. This would apply as much to (for example) constitutional interpretation as to scriptural interpretation.Perhaps I ought to do another post on what it means, as a practical matter, for people to attempt in good faith to reason their way through something when their premeses are contradictory.
AM wrote: <>More important: I think your argument would be more effective if, instead of appealing directly to GT, you extended your method of analogy (viz. dogma := theorem and scripture := axioms) you analogized Gödel’s proof directly.<>I don’t think it is an analogy. In order to write something rational without contradicting ourselves we have to follow the rules of logic and avoid semantic equivocation. That isn’t an analogy, it is a fact of life. And my major concern is not with whether this makes good apologetics, but with whether or not it is true. The question isn’t whether sola scriptura is irrational, since the levels on which it is irrational are not singular. The question is how epistemically deep that irrationality goes.<>For example, could you construct by diagonalization a hermeneutical truth which wasn’t provable by scripture, even though it was in the “language” of scripture.<>How about “be fruitful and multiply”? (Ha. I kill me).Even from a purely apologetical point of view though that sounds like something that would (1) be a lot of work and (2) would immediately degenerate into a shouting match. And it is entirely unnecessary from the standpoint of determining/demonstrating what is actually true, which is my main concern here. Patrick wrote:<>Most importantly, the hermeneutical system lacks any apparent way to go about Gödel-numbering (or its equivalent) to produce statements of meta-doctrine from statements of doctrine.<>In other words, the problem only arises if our HS has enough power to do arithmetic. If we are very careful to avoid any reasoning that could in principle be used to construct arithmetic, then sola scriptura is not self-contradictory. “Be sure to avoid thinking in this perfectly ordinary, valid way” is an odd doctrine, but it does seem to be a corrolary doctrine to sola scriptura.<>For another, the rules of derivation of theorems are not agreed upon in the least, the most necessary thing for any sort of Gödelian self-reference.<>Oh, but that doesn’t matter, because the question is whether <>any<> conception of sola scriptura could possibly be (non-tautologically) rational in principle. The question is whether (and under what conditions) sola scriptura can <>say something<> without contradicting itself. Various particular hermeneutics are not relevant except as examples; and in any case we don’t say that arithmetic is invalid because of disagreement about axioms.<>And finally, a “Gödel sentence” of doctrine would in fact be such a complicated and abstruse statement (as G, without its metamathematical interpretation, is just an arcane and pointless statement about a really big integer) as to not merit the necessity of belief. In other words, we ain’t talking the Assumption of Mary here.<>And again, that doesn’t matter, because the semantics we choose for our two-valued logic is “must be believed/need not be believed” not “happens to be true/happens to be false”. It most certainly isn’t “everyone would agree/everyone would not agree”. And I am not relying on the metamathematical <>truth<> of G, just its undecideability.Grateful Catholic wrote: <>I don’t suppose that Cornelius Van Til was much concerned with Goedel but I’m thinking that his “presuppositionalism” is one consistent way a Protestant biblicist might tackle your challenge.<>I don’t know anything about Van Til (other than what I just googled), but no amount of axiom-shuffling can take the wind out of Godel’s sails. GT applies in general to <>any<> formal system that is capable of representing arithmetic.
A couple things:1. You really should read Van Til.2. Your definition of Sola Scriptura is not one I’ve ever read: “a doctrine proposed as true must be decideable by scripture.” Rather, SS means that Scripture is the only infallible source of Divine revelation. Your definition focuses on how scripture is *used,* the doctrine actually focuses on what scripture *is*.3. Godel’s Theorem does not apply to the mind of God. There are no truths in God’s mind that cannot be derived from… God’s mind. His mind, because he is the Creator of all things, is complete, exhaustive, and is the principium of all truth. If God has revealed his mind in Scripture, Godel’s Theorem is just as non-applicable to God’s revelation as it is to God’s mind. To assert that GT applies to God’s mind or his revealed will (as opposed to applying to, say, human approximations of truth in mathematical systems) is tantamount to saying that mathematics, or Godel’s Theorem, or something, is more ultimate, more foundational than God himself – a fundamentally anti-theistic position.3. My limited understanding is that Godel’s Theorem applies to deductive systems, so as to show how they do not have the foundational “resources,” by way of axioms, to account for all the truths deduced by the system. The Christian Faith, along with its doctrine of Divine revelation, is simply not a deductive system in the sense of a mathematically deductive system. Nor is it strictly an inductive system. It is, in the final analysis, a transcendentally presuppositional system. That’s why picking up some Van Til may prove helpful. Your application of GT and Sola Scriptura are complete apples and oranges.4. An honest question, from a Reformed Protestant: as I’ve perused around the internet, seeing what my Roman Catholic colleagues are up to, I often find them involved in what they entitled “apologetics.” Sometimes I get excited, thinking to myself, “Hey, this will be interesting! I would love to see how modern-day Roman Catholics defend the faith against unbelievers today. Do they use Thomas’s Five Ways? What is the popular method?” Instead, I *invariably* find that what my Roman Catholic friends mean by “apologetics” is “presenting arguments against Protestants.” So th question: Where can I find examples of real apologetics by a Roman Catholic on the web? By “real,” I mean, the defense and vindication of the *Christian Faith* over against non-Christian religions; not the defense and vindication of *Roman Catholicism* over against other (arguably downgrade) Christian groups.Thanks for the stimulating thoughts.
You make logical inconsistency sound like a bad thing.I know what “inconsistent” means for a mathematical system, but what does it mean for any actual doctrine of <>sola scriptura<>?I don’t think it’s enough to say a Goedel sentence exists given any version of <>sola scriptura<> found in the world. I think you need to construct one and see what it means, if anything.You might also apply your argument to the Catholic position that the deposit of faith is complete as of the death of the last Apostle.
<>I know what “inconsistent” means for a mathematical system, but what does it mean for any actual doctrine of sola scriptura?<>It means that one can argue, with locally logical consistency, in favor of or against any proposition whatsoever. It means in more abstract terms that any orbit can be selected. It means in practical terms that people will choose whatever outcome they happen to like for reasons that don’t (and at the same time do!), in the end, follow from the text. We ought to expect a <>sola scriptura<> based religion or ideology to fracture into a large number of different factions, the denominations of which have nothing ultimately to do with what the text actually says.Asserting <>sola scriptura<> is (literally) asserting the meaninglessness of the text about which it is asserted.<>You might also apply your argument to the Catholic position that the deposit of faith is complete as of the death of the last Apostle.<>Godel’s Theorem doesn’t apply to the Deposit of the Faith generally, because the Deposit of the Faith is not a finite text. Showing that sola scriptura is deeply anti-rational is by no means the same as showing that Catholicism is true; but since Catholicism does not assert sola scriptura it dodges the bullet.
Rooster wrote:<>Rather, SS means that Scripture is the only infallible source of Divine revelation.<>That is precisely what I understand it to mean. SS means that if something <>must be believed<> then that fact – the fact that it must be believed – is derivable from the text of scripture. Sola scriptura means “scripture alone”, not alone as a source of all knowable truth in general, but alone as source of those knowable truths which must be believed.
Oh, and my remark above that GT doesn’t apply to the Deposit of Faith also applies to the Mind of God, personal revelations from God, etc. It does apply specifically to finite texts, and its implications are fundamental logical implications; they cannot be escaped simply by asserting that math doesn’t apply.
While I understand hermeneutics and sola scriptura, your comments are not clear to me so please allow me to re-state so you can clarify: (1) sola scriptura relies on an external system (hermeneutics) to support it? (2) sola scriptura is therefore self-defeating because it is not “sola” but relies on external thought? Please clarify.
Please disregard my question. The discussion on the DawnEden web site has oriented me toward the important points in the debate.
<>Godel’s Theorem doesn’t apply to the Deposit of the Faith generally, because the Deposit of the Faith is not a finite text.<>No, but it is a finite deposit, “contained in Sacred Scripture and Tradition” [CCC 84]. And the Church asserts completeness: “All that [the Magisterium] proposes for belief as being divinely revealed is drawn from this single deposit of faith” [CCC 86].There are four properties involved in Goedel’s theorems: completeness, consistency, formality, and Peano arithmetic. I’m not sure either <>sola scriptura<> or the Catechism asserts any of these, in the mathematical sense. Not even completeness, which is why I keep saying you should construct a statement whose need to believe is undecidable, or which both must and need not be believed, and see whether anyone says their hermeneutical system is intended to resolve that statement.
<>Not even completeness, which is why I keep saying you should construct a statement whose need to believe is undecidable, …<>That persistent request is what leaves me with the impression that you have not yet grasped the implications of a non-standard logic with semantic values of “must be believed/need not be believed” rather than “is true/is false”.
My apologize for any of my questions/comments that sound extremely kindergarden. 😛Zippy,Has it been proved that human logic in terms of hermeneutical systems is ‘mappable’ to ordinary mathematics? Which would then allow it to be analyzed using GT, otherwise we cannot make the comparison.Its just hard to get my mind around the fact that we have to think of the hermeneutical system as a mathematical construct without actually using any math operands on the text. Because, from what I get, the sola scriptura’s self-assertion makes it a hermeneutical system that has “crossed over” from being a regular jumble of words to those that now are contained within themselves. (I’m not sure what I mean by that. Since the statements are not claiming to be true on any system of logic but are ‘asked’ to be believed to be true on faith) However, I think that, technically, nothing is contained within itself explictly. Its like observing a quantum particle: the moment you observe it can change its nature. So when a human being looks at sola scriptura, it ceases being ‘sola’ because some form of external intelligence or logical structure is applied to this hermeneutical system. It still is ‘sola’ in terms of it stating that every statement in the text “must be believed” as valid/true.So from that, why should a <>doctrine<> that is proposed to be <>decideable <> from the text of scripture, if the nature of the scripture is that every text is believed to be true, regardless of its agreement within itself or between or whatnot? The sola scriptura does not have to answer to any form of logic; or anything actually. And it does not have to comment on every possible belief in existence, but states that the stated beliefs are to be believed.I’m kinda just rambling so you can correct me in all the places where I am talking nonsense.thanksfahd
This is mostly off topic, but I do get into logical framework and faith. I wanted to provide a little about the concern about apologetics. “I *invariably* find that what my Roman Catholic friends mean by ‘apologetics’ is ‘presenting arguments against Protestants.’ “The problem here is that christianity by its nature is a faith-based system, so it cannot be true by definition, lest we have complete knowledge, which leaves no room for faith. Therefore, our reasoning must have some kind of uncertainty to it, which makes the mathematitians of us somewhat uneasy. The choice as it applies to a person is one of two systems, if the truth is one, and there are two mutually exclusive choices, then one must be chosen. For to choose none implies that the choice is unimportant, and that is unacceptable if that choice pretains to religion. In this arena, come the apologists. Their job is to get people to choose A over B. There are two options in doing this: hold up A, knock down B. As christians, our job is to create a positive case for christianity. We know we cannot do this perfectly because our faith would become self-refuting, so it must be done imperfectly…some arguments are better than others, and they all need to be weighed according to their worth. I agree that apoligists should spend most of their time on the defense of christianity, but pointing out the errors in other systems is somtimes necessary whether or not the imperfect arguments are found persuasive. My own view of Magesterial Teaching is as an internally-consistent system of belief, and that sola scriptura is inconsistent. That belief is not defined by the ashes of the other system, but I have chosen it because it stands stronger. In other words, the primary job of an apoligist is to build up his own howse, not tear down the houses of others, but that doesn’t exclude criticism of the latter.
Surely there are better ways to make a doctrinal arguement. I posted < HREF="http://blogotional.blogspot.com/2005/05/religion-and.html" REL="nofollow">here<>
<>The problem here is that christianity by its nature is a faith-based system, so it cannot be true by definition, lest we have complete knowledge, which leaves no room for faith. Therefore, our reasoning must have some kind of uncertainty to it, …<>I would suggest that the basic epistemic point you are making here is not limited to Christianity, or religious knowledge, or moral knowledge. It applies to knowledge in general. It is the strangest thing that we know anything at all, and yet we do indeed know very much.
John Schroeder wrote:<>Surely there are better ways to make a doctrinal arguement. I posted here.<>I appreciate your speculations about my person, John. I agree that there are much better <>polemical<> ways to argue against <>sola scriptura<>. But that isn’t what interests me here. We are all about pedantry here, not polemics.
I have posted on this here:http://www.coffeeconversations.com/?p=63For those interested, I don’t believe Zippy has accurately described the doctrine he is critiquing nor do I think Godel’s theory is applicable at all. But you can read the blog entry and let me know what you think.
<>Goedel’s theorem here is most certainly irrelevant as it claims to evaluate human systems and not the mind or words of God.<>Not at all. I am merely assuming that when God reveals things to us, He does not contradict Himself.
Then don’t juxtapose Unam Sanctam with Lumens Gentium.JSG
Z: Your initial definitional statement is that “Sola scriptura states that if a doctrine is proposed as true, its truth must be decideable from the text of scripture”.Just like your imputation to M. Luther of a subjectivist hermeneutic, your definition of the term “sola scriptura” is inaccurate. Your entire polemic is based on a caricature.It is very easy in this electronic age to go to original sources and learn a prospective opponent’s posiiton from the original source. It would certainly make for clarity if you would do that.JSG
I may have more to say when I return, but for the present I will simply say this:I am perhaps more familiar with the writings of Luther than many seem to suppose. Luther’s writing on scripture is not univocal; indeed he at some points appears to embrace equivocation openly in his polemics against reason itself. If <>sola scriptura<> taken seriously is an inherently inconsistent concept, though, then < HREF="https://zippycatholic.wordpress.com/2005/05/whats-so-great-about-consistency.html" REL="nofollow">that should not really be surprising<>.Underneath the “this is a straw man” criticisms of my post lies the notion that (e.g.) Luther gets to tell us what his ideas do and do not imply. But nobody gets to tell us what his own ideas imply. What an idea implies is an objective matter, independent of whether the implication is endorsed by the propounder of the idea. If communism leads to material poverty then a communist cannot in an authoritiative fiat make it otherwise simply by claiming that <>his<> communism doesn’t lead to poverty.So even though there actually are places in Luther’s corpus where he seems to say himself that his ideas are anti-rational, his opinion on the matter is irrelevant. Even if he unequivocally denied the irrationality of his ideas, that would not in itself establish their rationality.
Gödel’s theorem could show that sola scripura is not inconsistent. It is well known that from Gödel’s incompleteness results follows the incompleteness of higher order logic. I.e. there us no deductive system able to completely formalize the logical consequence relation. Now interpret the sola scriptura thesis as saying that whatever is true is a logical consequence of something stated in the scripture. By the incompleteness of logic this does not imply the possibility of providing the scripture with a finite set of inferential rules, able to derive all logical consequences from it. Consequently, the sola scriptura claim is consistent with the scripture being impossible to render a deductive system. But if this is so, Gödel’s theorem won’t apply to it.Could humans then derive all logical consequences of the scripture? Only if the whole of human logical competence cannot be represented as a deductive system; an impossibility that is certainly a possibility 😉RegardsLaureano Lunahttp://www.criticadelarazon.com
To the extent I understand the comment (an important qualifier) I agree with it — that is, the ‘completeness’ criticism of SC applies to SC understood to mean that every essential Christian doctrine is deduceable from Scripture alone. Once we take the <>sola<> out of sola scriptura it is no longer inherently irrational, at least in this particular way.
Could you please elaborate more on how can we arithmetize the hermeneutical system of Sola Scriptura? In particular, how can we construct a concept of ring based on that system.
Also, have you thought of formalizing the proof, instead of operating on your analogy level? In current form, it is not usable to convince either convinced proponents of sola scriptura or professional logicians, as the proof is lacking. It would appeal only to those who already are skeptical about sola scriptura.
According to WordPress, the last time someone commented on this post was 2,843 days ago. Pretty cool.
(I mean, there are probably only about 40 days out of this whole year when that could have turned out to be a prime number.)