Wednesday, 4 June 2014

Of Infalability and Green Cheese

Brendan Burnett, a friend of mine, an Evangelical Protestant and a fellow blogger, has an argument which, he believes, disproves the authority claims of both the Roman Catholic and Eastern Orthodox Churches. The argument can be found here.

Brendan attempts to refute the claims of those Churches which claim infallible authority to interpret the Scriptures with a Reductio ad Absurdum. For those unfamiliar, this is a form of logical argument, sometimes called a "proof by contradiction". The essence of the argument consists in assuming, for argument's sake, that a given proposition is true, demonstrating that said assumption leads to a contradiction and, thereby showing that the initial assumption was false.

Brendan does a small thought experiment and asks us to imagine a possible scenario:

Imagine, then, that the Church says that John 3:16 means: “The moon is made of green cheese.” Imagine that all the respected, godly, knowledgeable church fathers and leaders forever since the first, second and third etc. centuries AD have always believed and interpreted John 3:16 as meaning “The moon is made of green cheese.” Church today holds it. Holy Tradition has always held it.

In such a circumstance, Brendan, argues, either Roman Catholic or Orthodox claims about the authority of the Church to interpret Scripture would lead to the conclusion that John 3:16 does teach that the moon is made out of green cheese. However, as Brendan quite correctly argues, John 3:16 is very clearly not saying anything about the composition of the moon but is, rather, a statement about God's love for humanity and His salvific purpose. From this, Brendan draws the conclusion that, Catholic and Orthodox beliefs about the infallibility of the Church logically lead to absurdity and are, therefore, proven false.

To clarify what he is and isn't arguing, Brendan writes:

Now for this argument to work, I don’t have to show that there is some real instance of it in the world. All I need to illustrate is that there exists some possible, logically consistent situation, which implies some absurd counterfactual (counter-to-fact proposition) from the premise, “Whatever the Church teaches about Scripture is true.” This proposition would be true if the facts turned out a certain way, This turns out quite easy to do.

The reason this argument may seem logical is because of an ambiguity in the term "possible" in the second sentence. Possible can mean a few different things in different contexts.

Some metaphysicians and logicians use possible simply to mean that given proposition has nothing that makes it logically absurd, it is true in some possible worlds. In this sense, it is possible that Julius Caesar died of old age and Brutus remained his faithful friend until death, since there is nothing about the essential nature of Caesar that logically required him to die of assassination at his former friend's hand.

On the other hand, the word "possible" may refer to real, concrete possibilities in the actual existing world. In this sense it is not possible that Julius Caesar died by any means other than assassination since, all the evidence clearly shows that that's the way he died.

Now, if, in the argument above, Brendan means "possible" in the first sense, true in some possible world, then I'll grant that his fathers and councils teaching John:316 is about moon cheese scenario is possible. I deny, however, that this proves what he thinks it does. To the best of my knowledge, no Catholic or Orthodox theologian has ever claimed that an infallible Church must exist in all possible worlds, as if God was somehow logically bound to operate in this way. If somebody ever did make such a claim, Brendan's argument might (I say might, I'd still have some issues) help to refute them. This, however, tells us nothing about what is and isn't the case in the world as it actually is.

On the other hand, if by, "possible" Brendan is talking about concrete possibilities in the actual world, then I'll agree, if you could prove the possibility of the Church teaching that John 3:16 is about moon cheese, then you would have disproven the Church's claims to authority. The problem here is that, a thought experiment is not, by any stretch of the imagination, enough to demonstrate such a real possibility.

Brendan then attempts to write his argument out formally. For those of you not familiar with philosophy and/or formal logic, what follows may be a little technical and difficult to follow. I'll simply say that I've already made clear my principle objections to his argument, what follows need only interest those concerned with the technicalities.

He writes:

P: Whatever the Church says about Scripture is true.
Q: The Church says that John 3:16 means ‘The moon is made of green cheese.’
R: John 3:16 means ‘The moon is made of green cheese.’

(1) If whatever the Church teaches about Scripture is true, then if the Church were to say that John 3:16 means ‘The moon is made of green cheese’, then John 3:16 really would mean ‘The moon is made of green cheese.’
(2) But the text of John 3:16 cannot possibly mean ‘The moon is made of green cheese.’
(3) Therefore, John 3:16 would not mean ‘The moon is made of green cheese’ even if the Church said that it did.
(4) Therefore, the proposition ‘Whatever the Church teaches about Scripture is true’ is false.

I assume (1) and (2) are premises, and I accept them both. (3) follows necessarily from (2). (4) However, does not directly follow from any combination of (1) (2) and/or (3). The only way it would do so is with the mediation of some premise along the lines of "There exists a real possibility that the Church would say the John 3:16 is about green moon cheese"

Finally, Brendan tries to write it out symbolically.

(1) If P, then if Q then R.
(2) Not-R.
(3) Therefore, not-Q. (Therefore not-’if Q then R’)
(4) Therefore, not-P.

QED. Modus tollens.

And at this point he's pretty much lost me. (1) and (2) obviously correspond to their counterparts in his non-symbolic argument. However, at (3) he gives two statements "Therefore, not-Q" and then, in brackets, "Therefore not -'If Q thenR'". These statements are not equivalent to one another, neither is equivalent to (3) in his non-symbolic argument and I don't see how either is derived from his premises. (4) Does follow as a Modus Tollens from (1) and from the brackets part of (3), but that only helps him if he can explain how he derives (3) from his premises.

In short, this argument will not work.

P.S. I don't believe it's possible to derive the conclusion "Not P" from Brendan's premises. It is, however, quite easily to derive the conclusion "If Q then not P". Absent, however, some proof of at least the real possibility of Q this doesn't help his case.

For anyone who cares, the relevant proof is as follows:

1. P > (Q > R)       (Premise)
2.  - R                    (Premise)
3.  Q                      (Assumption)
4.  P                       (Assumption)
5.  Q > R                (> E; 1,4)
6.  -Q                      (M.T.; 2,5)
7. Q & -Q               (&I; 3,6)
8. - P                       (-I; 4- 7)
9. Q > -P                 (> I; 3-8) Q.E.D.


  1. Interesting rejoinder, Jason.

    I think you're right in saying that there's an ambiguity on what I meant by "possible." By "possible I simply meant logical possibility. That's because I assumed that X is infallible just in case there is no possible world in which what X says is false. X therefore cannot say a false thing in any possible world. But if infallibility is relative to worlds, as you seem to be suggesting, then it follows that X can be infallible relative to a world W1, but be fallible relative to another world W2, so that there is a logically possible world where the Church says "John 3:16 means 'The moon is made of green cheese'," but simply be mistaken.

    If that's right, my question then is to say, Why think this world is the infallibility world?

    Granted, that's quite apart from what I specifically said, so I guess I won't say anything more about it.

    I will come out with a full response later. But for now let me try to clarify that small syllogism I made. (Note, I think I will need to specify the syllogism further than this, so as to make clear my modal assumptions. But I'm going to save that for later.)

    I think your main criticism of the syllogism as so formed was my confusing brackets in the premise (3) formulation. I didn't mean to say what was outside the brackets after (3) is supposed to be logically equivalent to what is inside them. I meant that the bracketed section to be a sub-premise following from (3) as a consequence of it. Let me write it out clearer:

    (1) If P, then if Q then R.
    (2) Not-R.
    (3a) Therefore, not-Q.
    (3b) Therefore not ’if Q then R’
    (4) Therefore, not-P.

    We can see that this is valid if we employ a simple method like a truth-tree. The idea is that, in premise (1), you have a conditional, which has as its consequent another conditional (Q → R). Then, what you do in premise (2) is falsify the consequent of that conditional (Q → R), not-R. So, in premise (3a), we spell out that not-R implies not-Q as per an ordinary conditional, and (3b) shows the whole conditional (Q → R) to be false, given the falsity of R. But then it follows that the consequent of (P → (Q → R)) is false. Therefore, as (4) says, P itself, being the antecedent of the whole conditional, turns out to be false.

    S I hope that's clear. But just in case it's not, what do you think I should address if I do another blog response? Did I miss anything essential that you're trying to communicate here?

    Thanks for taking the time to interact with me.

  2. Brendan, thanks for the response.

    On the possible worlds question, let me put it this way: There certainly exist possible worlds where there exists something called the Catholic Church and in which the thing called the Catholic Church has taught something obviously false about the meaning of Scripture. Obviously, the thing which is called "The Catholic Church" in this world would lack certain essential properties that I, as a Catholic, believe the Catholic Church has in the actual world.

    Let me put my claim this way: in order for your argument to work, you'd need to establish the existence of some possible world where there exists a body with the same essential nature as the Catholic Church has in the actual world and in which that Church has taught that John 3:16 is about green moon cheese.

  3. As for you attempt to rewrite your symbolic logical argument, I have to say, no, sorry, I still don't get it, I've read through your argument several times and still don't see how it logically follows.

    1. Okay, I think I made a mistake. Having enlisted the help of Anthony Bigg, let me try again:

      (1) If P, then if Q then R.
      (2) Not (if Q then R).
      (3) Therefore, not P.

      Okay should I clarify with you, then. How does Catholicism define its own infallibility? Is it that the Church just happens to say all the true things? Or is it stronger, namely, to say that the Church does not in fact have the power to say a false thing?

    2. Thanks Brendan, (and Anthony, long time no see)

      I'll split this into two separate responses, one on the logic, one on theology.

      On theology, the claim of the Church is not only that she hasn't taught error but that Christ promised (and, of course, Chrsit's promises are reliable) that the Holy Spirit will act to keep the Church free from error.

    3. On the formal logic, your reformulated syllogism is, obviously, logically valid, but I don't think that helps your case.

      In your original argument, your premises were "If P then (If Q then R)" and "Not R". I agreed with those premises.

      In your new argument, you've replaced your second premise with "Not (If Q then R)". I don't see any reason to accept that premise.

    4. actually Jesus never said the Church would be kept reliable, on the contrary, He warned about false teachers and false prophets IN the Church as did the Apostles!

      St. Vincent of Lerins Commonitory shows how to defeat such, what is held everywhere by all at all times? if it isn't held everywhere or if there is a history to it so it wasn't held everywhere, go back father, if this doesn't help look at the early writers and dogmatic definitions, if this doesn't help go to the Scriptures.

    5. Justina, Christ and the apostles both warned about false teachers in the body of the Church however, that is a very different thing from the suggestion that the Church its self (as opposed to individuals within it) can fall in error.

  4. I think the problem is, that while the Church's interpretation of Scripture in general as expressed in dogmatic definitions made by bishops steeped in study of Scripture and some individual holy writers ditto, this earlier fact, that the Church is infallible interpreter of Scripture because its leadership alone has the time and dedication and literacy to compare Scripture with Scripture and absorb and understand it all, has morphed into whatever nonsense from Origen or Basil's misunderstanding of the atom theory as positing chaos (which is doesn't) therefore it is false may have crept into the Patristic writers must be considered infallible truth, and RC took it even farther to church can indeed if it damn well pleases say John 3:16 means the moon is made of green cheese. well they didn't say that in so many words, but that is the attitude.

    Now, when protestants uphold Scripture against "tradition" it is usually a head on between things like predestination and free will, the latter opinion having been normative against pagan deterministic fatalistic philosophy until Augustine became so popular. But if you study the Scriptures you find that it is more nuanced, and predestination is limited and changeable by prayer (often by those individuals predestined to become Christian so they can start the ball rolling or restart or continue it).

    Purgatory and toll houses in RC and Orthodoxy, the error of purgatory is not that it defames Christ's once and for sacrifice for sin, since that is applicable when we repent, but both are issues of unrepented for sin. The error of purgatory is to posit it as a location separate from hell, and that the damned have no hope, even if prayed for, while Revelation last chapter only posits a finality of condition as being after The Last Judgement, so is inappropriate to apply to any time before that.

    Toll houses have two features, getting dragged into hell because your sins alienate you from God and his protection, an issue in prayers back to early times, and specific number of levels of judgement and demons having some office of judgement given from God, as opposed to lawless monsters who can get at other but weaker lawless absent intervention from God.

    Then there is prayer for the dead, remember St. Paul prays for mercy for the household of Onesiphorus, but what about him? why is it not Onesiphorus and his house? and adds a request that God have mercy on him on that day. What day? The day of judgement. Same prayer as the Jews made in I Maccabbees for their dead they discovered had hidden pagan amulets on their persons, and so made sin offerings for them and prayed God to be merciful to them on The Day of Judgement.

    So those steeped in Scripture operating with an open mind not through blinders, will get the truth, and this was done in early days of the Church and by those trained by the Apostles who then trained others.

    Immaculate Conception of Mary requires the same kind of allegorizing and jumping through hoops the classical gnostic and other heretics did, not to mention that the pre tribulation rapture crew who expect to not go through persecution do. Infallibility of the pope is so off the wall that even RC caveat it to where supposedly no pope since pronouncing these doctrines has spoken ex cathedra. Nonsense. Any formal pronouncement, a papal bull (so called by the bull design seal that used to be put on such when formally sent out for distribution), or whatever, if it deals with faith and morals is ipso facto ex cathedra.

    St. Vincent of Lerins in his Commonitory online discussed how to settle such disputes, what is held everywhere and by all and at all times? if this fails, look to earliest writers and Scriptures.