## It isn’t a Shotgun

December 26, 2006 § 38 Comments

*An Examined Life* has up another post on the development of doctrine. I made the following comment in the combox there:

My only objection – and it is important to understand how narrow an objection it is – is to this claim:

Ultimately, however, anything that is accepted as de fide will have some deductive proof following from other irreformable doctrines and the theorems that can be derived from them.

I object to this claim precisely because it is in the same class of claims as David Hilbert’s postulate (disproven by Godel) about mathematics: that every mathematical truth must admit of a deductive proof from primordial axioms. (In our logic we substitute “is de fide” for “is true” in the metalanguage, and the game is immediately over**). (I am leaving out what would be a nontrivial discussion of the implications of ruling out abstract reasoning capable of performing Peano arithmetic here, but this is after all just a combox).

Specifically, I do not object to this claim:

My second assumption is that whatever the Church teaches, at any time in history, will be logically compatible with everything else the Church has ever taught, or ever will teach, at any point in her history.

There is a difference between a relatively weak assertion of logical compatiblity (inductive inferences are not ruled out by a requirement for logical compatibility) and the strong assertion of the existence of a deductive proof for every theorem (where inductive inferences, and indeed all inferences which are not a matter of mechanical application of the [some] rules of logic, are ruled out).

And interestingly, both of our “stakes in the game” here are the same: we are both attempting to understand DD in a way which avoids *logical* contradiction. If my understanding is correct, insisting on the existence of a deductive (solely deductive) proof for every theorem results in a logical contradiction.

** I didn’t say this in the comment at AEL, but this can be expressed unambiguously at the formal level by making every statement take the form “It is de fide that X”.

<>If my understanding is correct, insisting on the existence of a deductive (solely deductive) proof for every theorem results in a logical contradiction.<>Not unless you insist on completeness, which would be impossible for dogmatic definitions- there are infinitely many true statements of theology, and not infinite time for the Church to define them!So the claim “Every defined doctrine is just a ratification of a deductive proof from the Deposit of Faith” isn’t contradictory at all. It merely fails to be true (well, as I understand it- and I haven’t read the post at <>Examined Life<> yet).

Ah, but Scott’s claim isn’t just that every presently defined doctrine actually has a purely deductive proof. (That may well be true, for all I know, though it doesn’t sound likely, and in any case proving “doctrine X has no deductive proof” for each and every presently defined doctrine would be nontrivial). It is that all possible defined doctrines, now and in the future, have a deductive proof. He is defining a class of possible doctrines (a class of theorems resting on some logic) and (as far as I can tell) making a completeness claim on that class.Or, that is to say, the claim I am arguing against is a completeness claim. It may well not be precisely what Scott intends to say.

Ah, but even that claim would be logically consistent.I mean, in mathematics, every theorem <>does<> have a deductive proof. That is simply what we mean by “theorem”.The point of Gödel’s Incompleteness Theorem is that this notion of theorem is not coterminous with the notion “holds in every possible model of the axioms”- or, more colloquially, that not every true statement expressible in the mathematical language is thereby a theorem.Again, there’s nothing logically fallacious about making an analogous claim for possible dogmatic definitions. You have to confront that hypothesis on the level of historical actuality.

How does one confront hypotheses about the nature of all possible future truth claims on the level of historical actuality? All possible future truth claims are not present historical realities.

Sorry for that last sentence- I realize it was kind of muddled.What I meant was that Gödel doesn’t give you a logical contradiction in Scott’s position, so you can’t shoot down his hypothesis in the abstract.You could, however, look at the <>actual<> doctrines that the Church has defined, and try to argue that in those cases the Church hasn’t appeared to simply ratify a deductive chain from a brightly delineated body of axioms in the Deposit of Faith. There are arguments that shed light on each doctrine, that make them compelling, but that’s not the same as what he’s suggesting.

OK, and I think I’ve realized where we differ on the applicability of Gödel here. You substitute “is de fide” for “is true”, and I think that’s invalid. Why should every true statement (pertaining to faith and morals) be potentially <>de fide<>?I mean, that may seem intuitive for the candidate staments we think of, but it breaks down by the time you reach the Gödelian sentence G, the interpretation of which is entirely self-referential (i.e. “G is not derivable by a deductive argument from the Deposit of Faith”). Why should such a statement, which speaks not of God or Man or anything outside the convoluted workings of potential doctrine, be eligible for <>de fide<> status?So “X is de fide” is more properly replaced by “X is a theorem”, whereupon it’s clear that Gödel’s Theorem gives you, not a contradiction, but incompleteness: not every true statement (pertaining to faith and morals) can be <>de fide<>.

<>Why should every true statement (pertaining to faith and morals) be potentially de fide?<>If statement Q is de fide <>because<> deduced from statement P, then P is necessarily also de fide. If Q is only de fide because P is de fide, and I don’t have to believe P, then I don’t have to believe Q.

Pardon? I’m afraid that doesn’t address the question.You’ll just get incompleteness and not inconsistency, <>unless<> you have some axiom of the form “Every true statement pertaining to faith and morals is a potential <>de fide<> statement.”Otherwise, the theological equivalent of the sentence G would get away scot free- it wouldn’t be potentially <>de fide<>, but neither would its negation.And need I say that there is no such axiom in the Deposit of Faith?

I agree with Patrick. Unless Scott is confusing “true” with “solemnly defined as a truth of Faith” — and, whatever his faults, he is not often <>that<> confused — your Goedel-Powered Assertion Disintegration Ray won’t work on non-ampliative inference.

I believe you are (both) hiding the ball by introducing “about faith and morals”. That category doesn’t exist at all in a proposed deductive system capable of producing proofs that certain propositions are de fide. A formal system capable of giving us deductive proofs of every possible de fide statement necessarily has logical true and false values which correspond to “is de fide” and “is not de fide”.

And my prior comment demonstrates why this is so: given a proposed de fide syllogism, if any necessary premise is not de fide then the conclusion is not de fide. If it is false that any premise is de fide, it is false that the conclusion is de fide. The deductive system has a two-valued logic, the semantic values of which are “true that it is de fide” and “false that it is de fide”.More generally, Godel’s theorem requires two-valued logic as a formal matter, and this criticism of my argument appears to be assuming that it requires something more than or other than that.

<>That category doesn’t exist at all in a proposed deductive system capable of producing proofs that certain propositions are de fide.<>Wait, who’s proposing <>that<> deductive system? I thought we we talking about the Magisterium of the Church.

<>Wait, who’s proposing that deductive system?<>Scott. And anyone else who claims that every de fide development of doctrine must in principle have a purely deductive proof starting from apostolic-time premeses, which is what I take his principle of non-ampliative inference to mean.This doesn’t mean that the Magisterium actually reaches conclusions in the development of doctrine in this way, even in Scott’s understanding. But once Scott insisted that every de fide developed doctrine must have a purely deductive proof from apostolic premeses, the game was over.Most people don’t realize that Godel applies any time this after-the-fact formal deductive verificationism is invoked, as A.S. Davis observed many years ago, “even though private intuition and creativity be involved in the invention of concepts and in the discovery of theorems and their proofs”.

Another couple of pertinent quotes from the Davis paper, which unfortunately is not on-line but of which I have an original typewritten copy in my hand:“In other words, every axiomatic theory is an example of a formal system.”“Godel’s Theorem asserts that every formal system must be inadequate in at least one of three ways: either the system harbors a contradiction, or there are questions** it can ask but cannot answer, or it is too weak to comprehend even the elementary theory of natural numbers.”** Specifically in this case questions of the form “is X de fide?”So when doctrine develops, the Magisterium must be doing something more in addition to proposing propositions which can in principle be proven deductively from primordial apostolic premeses; and the whole point to the principle of non-ampliative inference is to rule out that “something more”.I don’t think there is room for any compromise here. Either what the Magisterium is doing when it develops doctrine is in principle verifiable through a purely deductive process, or not. If we assert that it is verifiable through a purely deductive process, then what we have really asserted is that development of doctrine is literally nonsense.

Zippy:I say again, put down Goedel’s Theorem. It has absolutely no relevance to Scott’s position.He is quite simply <>not<> proposing a deductive system capable of producing proofs that certain propositions are de fide.Rather, he is saying that every de fide proposition has a[n at least implicit] deductive proof. That’s a claim that in no way bumps against anything Goedel proved — not least because “true” and “de fide” are different properties.

<>Either what the Magisterium is doing when it develops doctrine is in principle verifiable through a purely deductive process, or not. If we assert that it is verifiable through a purely deductive process, then what we have really asserted is that development of doctrine is literally nonsense.<>And here I think you betray a fundamental misunderstanding of the implications of Goedel’s theorem.What you’re saying boilds down to this, that a purely deductive system is nonsensical. But that’s nonsense.Your mistake, I think, comes from insisting that the system be used to ask questions it can’t answer. And I think you only insist on that because you haven’t much looked at the sorts of questions it can’t answer.I’ve pressed you on this point before, and will do so again now: Construct a Goedel sentence that demonstrates that Scott’s position is literally nonsense. Give me a <>specific question<>, in English, that a non-amplitative Magisterium might ask without being able to answer.The reason I’m challenging you on this is because I suspect that, if you were to actually read such a question, you’ll see that the differences between a formal system and a human system are such that nothing Goedel has to say has any practical significance for actual human systems as actually proposed and used by actual humans.

<>Rather, he is saying that every de fide proposition has a[n at least implicit] deductive proof.<>That is exactly what I understand him to be saying.<>…not least because “true” and “de fide” are different properties.<>All of the deductive proofs – deductive proofs which rule out underdetermination, and by the way of which not a single example is provided – which he claims must exist in principle for every possible legitimately developed doctrine are of the form “it is true/false that X is de fide”. A putatively universal axiomatic theory about the existence or nonexistence of a particular property is an axiomatic theory, and thus an example of a formal system.

<>I’ve pressed you on this point before, and will do so again now: Construct a Goedel sentence that demonstrates that Scott’s position is literally nonsense.<>Well, you think I don’t understand Godel and its implications and I think you don’t. You think it is a narrow mathematical point and I think it is a profound epistemic one. This is unlikely to be resolved until God tells us which one of is is wrong, or that both of us are wrong.In order to construct a specific proof that Scott’s claims are nonsensical he would have to first make his claims (both the logic and the complete set of primordial apostolic premeses) unambiguously explicit, so that the sort of purely deductive proofs he insists exist can be actually constructed. I tend to think that such an exercise would show the silliness of what he is claiming rather than the invalidity of what I am claiming.

Oh, and FWIW, Godel himself thought he was making a conclusive and profound epistemic point against positivism not a narrow mathematical point (see e.g. the recent book <>Incompleteness<> by Goldstein). That doesn’t mean he was right, of course, and he <>was<> a bit of a nutcase who eventually starved to death because he wouldn’t feed himself when his wife got sick.

<>…which he claims must exist in principle for every possible legitimately developed doctrine are of the form “it is true/false that X is de fide”<>That’s not what anyone has claimed, Zippy; if Scott is making any strong claim, it’s that every doctrine that has been (or could be) de fide has a deductive proof of the form “X follows from the Deposit of Faith”.

Look, I don’t want to impugn your intelligence, Zippy; you’ve had a lot of insights here that I admire. But it’s very easy to misuse Gödel’s Theorem in epistemology, and here I’m on turf that I know well.Starting in its mathematical context, and progressing toward its epistemological context:<>Theorem:<> Not every true statement of mathematics has a deductive proof- no matter what consistent schema of axioms you start from.<>Definition:<> A <>theorem<> is a mathematical statement with a deductive proof from a given set of axioms.<>Corollary:<> Not every true mathematical statement is a theorem. (Incompleteness.)<>Application:<> Not every <>truth<> can be derived from scientific experiment and logical deduction. (Refutation of positivism.)Now, you want to condemn the proposition that “every (possible) de fide statement has a deductive proof from the deposit of Faith”- or, equivalently, “every (possible) de fide statement is a theorem”.This statement may well be false. But, I repeat, it does not run foul of Gödel- <>unless<> there is some reason for believing that “every true statement (or every true statement in some expansive arena of knowledge) is potentially de fide”.Otherwise, faced with a Gödelian claim G, it might simply be the case that neither G nor its negation ~G is a candidate for being <>de fide<>. This is not contradiction but incompleteness.So, unless Scott has asserted that any true statement (in general, or limited to some arena) might be one day declared <>de fide<>, Gödel’s trap does not ensnare him. You’ll have to oppose him on other grounds.Zippy, this will be my last post on this topic. I worry I’m in danger of becoming condescending here, and there would be no excuse for that, however certain I am of my understanding on these points. I remain your friend in service of the truth.

<>…which he claims must exist in principle for every possible legitimately developed doctrine are of the form “it is true/false that X is de fide”<><>…if Scott is making any strong claim, it’s that every doctrine that has been (or could be) de fide has a deductive proof of the form “X follows from the Deposit of Faith”.<>I must be missing the distinction.At bottom there seems to be a difference of opinion about whether Scott is (implicitly, since almost all of his claims are implicit) asserting the existence of a formal system using two-valued logic. Or about whether the distinction “is de fide/is not de fide” formally establishes a two-valued logic. Or something.<>…”every true statement (or every true statement in some expansive arena of knowledge) is potentially de fide”.<>The “expansive area of knowledge” includes at minimum “every premise which is necessary to a proof that a proposition is de fide”. If Scott’s system capable of proving theorems de fide can comprehend the basics of numbers it follows that there necessarily exists a Godel statement which is potentially de fide. (Producing it would depend, as I said, on Scott actually showing us these de fide proofs and all of their premeses explicitly) We seem to disagree about that point in particular: that a formal system capable of producing proofs that certain statements are de fide (and capable of arithmetic etc) necessarily will produce a Godel statement which is potentially de fide.

And Patrick, I really wish you <>wouldn’t<> exit the discussion. Your insights and explanations on this particular subject have been very helpful to me.<>Theorem<>: Not every true statement of doctrine has a deductive proof- no matter what consistent schema of axioms you start from.<>Definition<>: A theorem is a doctrinal statement with a deductive proof from a given set of axioms.<>Corollary<>: Not every true doctrinal statement is a theorem. (Incompleteness.)I suppose what this raises is the question of whether it makes any sense to say that the reasoning which supports any doctrine is not doctrine: that the truths prerequisite to any doctrine are not themselves doctrine. I think saying that: (1) It is necessary to believe P in order for it to be necessary to believe Q; and(2) It is necessary to believe Q…implies that it is necessary to believe P. So unless “doctrine” means something other than “a truth it is necessary to believe” the game is up.

I’ll freely grant that Goedel’s work on incompleteness has significant implications about epistemology.What I’ll deny is that Scott in particular and most other folks in general make the sorts of epistemological claims that the incompleteness theorems quash.For example, a corollary of Scott’s principle of non-ampliative inference is that “potentially de fide” and “true” are different properties of statements, thus making [mathematical] incompleteness an uninteresting property of the Magisterium.And if you want “potentially de fide” and “true” to be identical properties, I again invite you to construct a true statement out of the deposit of faith that does not admit of deductive proof — you may disambiguate Scott’s claims however you like — and see whether it’s the sort of statement any sane Church would define as dogma.

<>And if you want “potentially de fide” and “true” to be identical properties…<>Maybe that is the misunderstanding, because that doesn’t resemble anything I recall claiming.And again, I can’t accept the invitation because only the person claiming that purely deductive conclusions are being drawn can disambiguate that claim. All I can do is observe that if he means it, the rest follows (independent of what specific premeses he chooses).I agree that any such exercise would look very alien to any actual human process (and alien specifically to any actual Magisterial process). But that isn’t a function of my counterclaims, it is a function of how alien the original claim in fact is.

Well, OK- as long as I’m not getting on your nerves.First, the distinction- between “proof that X follows from Deposit of Faith” and “proof that X is potentially de fide”- doesn’t affect the main argument, but it’s an important distinction nonetheless.The main claim we’re discussing can be phrased, somewhat sloppily, as “All potential de fide statements are theorems.” However, perhaps not all “theorems” are potential de fide statements- perhaps statements that are too far removed from the essentials of faith wouldn’t be fit matter for dogma, no matter how true they are. (“How many angels can dance on the head of a pin” isn’t perhaps the best example- there is, in fact, a point to the debate- but it gives the spirit of the idea. [Puns notwithstanding.])

Anyway, back to the main point.<>We seem to disagree about that point in particular: that a formal system capable of producing proofs that certain statements are de fide (and capable of arithmetic etc) necessarily will produce a Godel statement which is potentially de fide.<>Yes, this is where we disagree. When you put it back in the context of mathematics, here’s the actual Gödel’s Theorem:<>Theorem:<> Any sufficiently powerful formal system is capable of producing proofs that certain statements are theorems. Any such system is either inconsistent, or contains a Gödel statement G which is true but is not a theorem.The application to our current context, assuming (in your case, for a proof by contradiction) Scott’s (alleged) premise, which can be written as “All potential de fide statements are theorems proceeding from the Deposit of Faith”:<>Application:<> The system of doctrine is either inconsistent, <>or<> contains a statement G which is true but is not a theorem (and thus, by assumption, is not potentially de fide).Gödel’s Theorem has not eliminated the second alternative, Zippy. The system will indeed produce a Gödel statement, but it will not be potentially de fide, and neither will its negation.

<>Well, OK- as long as I’m not getting on your nerves.<>I often get on my own nerves, so that can’t be an excluding criteria for posting around here.<>Yes, this is where we disagree.<>Yah, if nothing else I at least better understand specifically where we each think the other is being a knucklehead 🙂<>The system of doctrine is either inconsistent, or contains a statement G which is true but is not a theorem (and thus, by assumption, is not potentially de fide).<>My own restatement: the system of doctrine is either inconsistent or contains a statement G which is de fide but not a theorem. By design, the formal system does not produce metamathematical logic values of “is true/is false” but rather metamathematical logic values of “is de fide/is not de fide”. At the formal level each WFF X could be placed in a textual wrapper “It is de fide that X” instead of in a textual wrapper “It is true that X” (for the sake of clarity, not because it is required). And I can do this because the only sort of theorems the formal system in question produces are semantically claims that X is de fide or X is not de fide; it does NOT produce theorems which semantically claim that X is merely true, since every merely true but not de fide proposition is both superfluous and is not de fide. Slightly more precisely, in the formal system in question an assertion of mere truth is not a WFF.But at any rate, it is really clear now that where we differ is in how we understand the requirement for a two-valued logic. It doesn’t mean I don’t like you or respect you, but we do disagree. FWIW, I discussed this for several years with a PhD who did his thesis on Godel before we concluded that formal assertions and negations of a property, when that property is the only property addressed by the formal system (an important constraint), constitute a two-valued logic subject to Godelian constraints. (One way to intuit this is to observe that assertions and negations of a property are assertions of set membership, and assertions of “true/false” are – as a <>formal<> matter – just a special case of assertions of set membership).Lots of trivial finite sets don’t necessarily run afoul of Godel (or of the fundamental truth about the nature of reason that he so dramatically exposed), of course. So where the rubber <>really<> meets the road is in whether the Deposit of the Faith as a set of premeses to a formal system (stipulating that that even makes sense, which I remind is the very point at issue) is the sort of set which can be unambiguously enumerated without remainder or mystery. I haven’t really addressed that specifically in any of my arguments, though in my defense I haven’t considered it a necessarily urgent point to address.

Another crack at it: would G’s theorem apply if the formal system we designed were intended only to produce theorems representing <>mathematically<> true statements, not <>all<> true statements? Yes it would (and indeed the specific formal system of Principia Mathematica was precisely the one Godel initially addressed). And in fact you can replace the set specifier <>mathematically<> with <>any<> set specifier whatsoever. In some cases we get trivial (and it is important to understand how trivial) finite sets when we do that, and avoid any Godelian trouble. But if we start doing anything even slightly intellectually interesting the game is up.<>Every<> axiomatic theory which relies on (any form of) logical deduction alone to produce its (inherently constrained as to subject matter) truth-claims is a formal system. <>Every<> such theory is subject to the constraints of GT. That all such theories are inherently topical does not insulate claims of logical completeness from GT and all of its corollaries.

One problem is that, as far as I know, no one has ever proposed the existence of a formal system that produces metamathematical logic values of “is de fide/is not de fide”. Popes and councils produce those values, and no one passingly familiar with popes and councils would take them to be [mathematically] formal systems.The Goedel argument may have something to say against projects like Ott’s <>Fundamentals of Catholic Dogma<>, but I don’t think even Ott was trying for mathematical formality.The deductive proofs Scott asserts do not produce values of “is de fide/is not de fide,” they produce values of “is true/is not true.”

<>The deductive proofs Scott asserts do not produce values of “is de fide/is not de fide,” they produce values of “is true/is not true.”<>He specifically < HREF="http://examinelife.blogspot.com/2006/12/again-with-non-ampliative-inference.html" REL="nofollow">says<>:<>I want to set at ease the hearts and minds of those Orthodox who worry that the principle of the development of doctrine warrants introducing radically new (and possibly heretical) belief-statements into the corpus of beliefs that must be held de fide. I think that this is a “valid” worry (non-technical use of “valid” here), and it is one that I share. The difficulty with any and all inductive inferences is that they are subject to (often massive) underdetermination, that is, the evidence can never establish the truth of any particular inference to the exclusion of all competing, non-consistent inferences. This is not a situation in which we want to find ourselves when trying to discover what must be believed de fide.<>…and…<>In short, I think that the homoousios doctrine does follow by strict deduction. This is not to say that every premise needed for that deduction is made explicit in Scripture; some premises are themselves intermediary conclusions of other deductions. But the inference itself needs to be deductive or else there is no rationally compelling reason to believe it.<>…and quite a few other things in a number of different posts which make it pretty clear what he is proposing. He is not proposing a formal system which verifies solely by deduction whether or not a given proposition is <>true<>, he is proposing a formal system which verifies solely by deduction whether or not a given proposition is <>de fide<>.Again, you and I are on the same page when it comes to the conclusion that what is being described is alien, bizarre, untenable, disconnected from any sane process of reasoning, etc. It is just that you seem to think that I introduced the bizarreness to the discussion by taking it seriously and invoking Godel. The bizareness isn’t a result of my invocation of Godel, it is a result of the initial assertion of <>sola deduction<>.And this is the case in all situations where positivism is at the root. Yes positivist epistemology is bizarre, inhuman, and disconnected from how human beings reason. The thing that makes Godel and its correlates so interesting is that they don’t just show how ridiculous things get when positivist claims are taken seriously, they refute positivism on its own terms. I do think someone can (and many people do) perfectly reasonably come to the conclusion that positivism and its manifestations are – despite a certain (paradoxically) intuitive appeal to us moderns – ridiculous, inhuman, unrelated to how people actually reason, etc without resort to formal deductive methods.

Zippy:Scott is <>absolutely not<> “proposing a formal system which verifies solely by deduction whether or not a given proposition is <>de fide<>.” He is proposing that, <>given<> a <>de fide<> proposition, there exists a deductive proof that the proposition <>is true<>.You yourself just quoted Scott pointing out that “inductive inferences … can never establish <>the truth<> of any particular inference.”It’s pretty clear that you are still misreading him.

<>…”inductive inferences … can never establish the truth of any particular inference.”<>Yes, and in context of his many posts it is clear that what he means is “establish the truth that any particular inference is de fide”. His whole thrust is to assure the Orthodox that there aren’t any non-deductive shenanigans going on in establishing “<>the corpus <>[that is, set]<> of beliefs that must be held de fide.<>“Of course it is always possible that he doesn’t mean what I think he means. All I can go by is what he has actually said, and the most reasonable interpretation of what he said. Which is kind of the point.

Zippy:Now I wonder whether we agree on what “<>de fide<>” means.I understand it to mean that a proposition has two properties: it is a truth contained in the Deposit of Faith; to deny it is heresy.In this understanding, to establish the truth that a particular inference is <>de fide<> necessarily entails two steps: 1) to establish the inference is a truth contained in the Deposit of Faith; 2) to establish that to deny it is heresy.The second step, though, is logically trivial: when the Magisterium teaches that to deny it is heresy, to deny it is heresy.If Scott has a similar understanding of “de fide,” and you’re right about what he means, then he’s spent untold hours over his Christmas break writing thousands of words to defend the validity of a one-line argument.

It seems to me that he is trying to establish the truth of that one-line argument based on something other than it being true by definition, and specifically by appeal to strictly deductive logical inferences from some fixed primordial corpus of premeses. In other words, he is more generally trying to assure the Orthodox that they can put their trust the Magisterium of the Church without actually putting their trust in the Magisterium of the Church: that there will always be a strictly deductive method for verifying what the Magisterium declares to be de fide, so that at the Parousia (if you will), in the eternal Platonic realm, there is guaranteed to be no logical underdetermination of the Deposit (or, equally problemmatic, there is guaranteed to be no logical underdetermination of those propositions arising from the Deposit which are in fact, at the Parousia, actually declared to be de fide).This is really just <>sola scriptura<> (only worse, becuase sola scriptura doesn’t necessarily explicitly rule out all kinds of inferences other than deductive ones) operating on an unspecified canon which happens to include the actual Canon and some other unspecified stuff.

The good news is your misreading seems much less bizarre than it did yesterday.I think you will find, if you ask him, that Scott is not telling the Orthodox that, by construction open to inspection, the Catholic Magisterium can’t blow a call on a <>de fide<> proposition. I think you will instead find that he is telling the Orthodox that the Catholic understanding of the development of doctrine is consistent with an Orthodox understanding of the Deposit of Faith. (Specifically, because they are both consistent with operating only within the domain of deductive proofs. Whether he’s right about that is a separate question, but one that has nothing to do with epistemological incompleteness.)I further think you will find your concerns about underdetermination basically put to rest (while recognizing that your concerns about underdetermination will never be fully put to rest in this life) if you look a little more into what Scott thinks about the interpretation of the Deposit of Faith.

<>Specifically, because they are both consistent with operating only within the domain of deductive proofs. Whether he’s right about that is a separate question, but one that has nothing to do with epistemological incompleteness.<>Every claim to be operating solely within the domain of deductive proofs has something to do with incompleteness, every bit as much as it has something to do with consistency. Consistency and completeness (i.e. their presence or absence) are inherent properties of deductive systems.As to whether all of Scott’s various claims are or are not mutually compatible, well, that isn’t for me to decide. I am addressing a specific one.

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