The First Vatican Council declared that when speaking ex cathedra, the Pope ‘enjoys the same infallibility that the Divine Redeemer wished his church to have’. What infallibility is that? The Council did not say, but a letter from Pius IX to the Archbishop of München-Freising in 1863 warns him that the obligation of Catholic teachers and writers to assent to doctrines of faith is not restricted to those doctrines which have been propounded for everyone to believe by ‘the infallible judgement of the Church’(Denzinger 2879), and this phrasing appears in the Syllabus of Errors of 1864: Error number 22 is to imagine that the obligation by which Catholic teachers and writers are bound is restricted to these dogmas of faith (Denzinger 2922). The Council, then, says that the Pope speaking ex cathedra has the same infallibility as the Church, whatever that may be, and the idea that the Church has infallible judgement in propounding doctrines of faith appears in Denzinger's gleanings from the 1860sFootnote ¹. Exactly what infallibility means is not explained either by the Council or by Pius IX, but the doctrine of Infallibility is generally understood to be that the Church's judgement cannot be wrong, and the Pope's statements ex cathedra cannot be false. Pius IX spoke of infallible judgement about doctrines of faith; the Council extended infallibility to morals as well.

The Catholic Church, then, teaches that certain judgements and statements cannot be false or erroneous. This differs from other religious doctrines in two ways. First, it is what philosophers call ‘second order’. What does that mean? Roughly speaking, a first order belief or statement is about things, while a second order one is about beliefs or statements about things. The following doctrines are first order: the universe exists because God wants it to; there are three persons in God; God became a man; Jesus was conceived without a human father; he died and came back to life; he gives a share in divine life to those who receive the Eucharist. These purport to tell us about people that exist and events that occur independently of anything we say or think. The doctrine of Infallibility, in contrast, concerns what certain people think and say about these things.

The second peculiarity of the doctrine is that it is what logicians call ‘modal’. Roughly speaking a modal statement is one that says, not just that something is the case, but that it must be or can be or cannot be. The other doctrines just mentioned are not modal: they say not that it is possible that the universe should exist because God wants it to, but that it does; not that it is necessary that Jesus rose from the dead, but that he did. The doctrine of Infallibility, however, is modal; it does not say that the Church never in fact makes a mistaken judgement or that the Pope never in fact says anything ex cathedra that is false. It says the Church could not possibly arrive at a false judgement or the Pope make a false statement.

What is the purpose of this exotic doctrine? Ronald Knox in The Belief of Catholics says:

Knox hoped people would satisfy themselves by ordinary reasoning first that ‘God is revealed in Nature, then that he is revealed in Christ and finally that Christ is revealed in his Church’; and says ‘This general outline of certainty is sufficient to make us (if we wish to do God's will) take the Church…for our guide on the rest of our journey; to let her teach us, knowing that her teaching must be his.’(p 163)‘Are we really more inconsistent’ he asks, ‘than the bather who steps out cautiously through the shallow water, and then, when it is breast-high, spreads out his hands to swim’(p 47).

Knox is clearly trying to make out that Catholics are rational in believing what the Church says. But there are two different lines he could be taking. He could be saying that it is rational to believe things Christ tells us or the Church tells us, even though we are not given good grounds for believing them; that it is rational for us to adopt this strategy if we have grounds for believing that Christ was God incarnate and that he founded the Church as a society which would have, among other functions, that of teaching. Or he could be saying that if we have good grounds for believing that Christ founded the Church and wanted it to teach, then that the Church tells us something is itself a good ground for believing that thing.

What is the difference between these suggestions? The first is that it can be rational to believe Christian doctrines without grounds. There are many things we believe without having grounds for believing them, that is, without inferring them from other things we believe. If everything we believed we believed because we inferred it from something else we believed, belief could not get started: we have a vicious regress. Our beliefs about objects in plain view are mostly without grounds, but form the grounds on which we believe other things. It would be madness not to believe our eyes and ears. It might also be foolish not to believe certain theological doctrines. The second suggestion is that Christian doctrines do after all have grounds: if the Church says something, that is a good ground for believing it. The Church's being instituted by Christ and Christ's being sent by God make the fact that the Church teaches something a good ground for thinking it true.

A parallel may bring out the point. Othello may wonder if Desdemona spent the night with Cassio. If Desdemona is in Cyprus and Cassio was engaged a seafight off Rhodes, that is a good reason for thinking he did not spend the night with Desdemona. It would be just about a physical impossibility to do both. But if Desdemona says he did not spend the night with her, that is not in itself a good reason for thinking he did not. She could perfectly well say this, and yet have spent the night with Cassio. What if Desdemona loves Othello and cares little for Cassio? Those are grounds for thinking she was not with Cassio, but they still do not make her words a ground for thinking that. The fact, however, that she is married to Othello gives Othello a reason for taking her word even though it is not a good ground. Marital trust consists in believing certain things one does not have good grounds for believing.

Perhaps this seems a quibble. If everything the Church teaches about theology is true, and the church teaches a certain theological doctrine, it follows logically that the doctrine is true. So if we have reason to believe the general proposition, ‘Everything the Church teaches is true,’ doesn’t the fact that the Church teaches, say, ‘Mary was conceived without sin,’ give us reason to believe that she was conceived without sin? This reasoning is fallacious. It is like the following:

We have here what logicians call a mistake of scope. Mistakes of scope are easily shown in modern symbols. There is a clear difference between

which may be read as ‘It is a necessary truth that P implies Q’, and

‘P implies that Q is a necessary truth’.

Modern formal logic had not got under way at the time of the First Vatican Council. The Council fathers were probably ignorant of the non-modal theorem:

which we may read ‘If two propositions together imply a third, then the first implies that the second implies the third.’ They would not have distinguished this from the dubious modal theorem:

which for present purposes we may read: ‘If two propositions together make it reasonable to accept a third, then if the first is true the second by itself makes it reasonable to accept the third.’ I suspect that the purpose of the doctrine of Infallibility is to make the Church's teaching a doctrine a rational ground for thinking it true. Its advocates thought it would enable Catholics to reason as follows: ‘Everything the Church teaches is true. It teaches so-and-so – the Immaculate Conception, for example. So the Immaculate Conception is true.’ This is bad reasoning and leads to bad theology.

How it leads to bad theology may be seen if we consider the following argument:

If the pamphlet in question is issued by the Government after consultation with the best doctors we have some reason to think the first premiss true, and we can see for ourselves that the second is. So it would not be irrational to visit the Off Licence. But if it is a serious question whether or not wine counteracts heart disease, nobody would think it a rational way of finding out, to see if there is a Government statement that says it does. A rational way of finding out is to set up a full-scale research programme, with force-feeding of chimpanzees, control groups of medical students and the rest of it. Our confidence in the statement by the government is rational just insofar as we have reason to believe that such a programme has actually been carried out. The Government statement gives no rational grounds for belief apart from this; it cannot be more trustworthy than the work of the scientists on which it is supposed to be based. And if it turned out that the scientists, instead of engaging in genuine medical research, had done a document-scan to see if any Government paper in the past declared that wine counteracts heart disease, it would be completely irrational to accept the conclusion of our argument. For it is not in general a reliable way of discovering whether a regimen is beneficial or harmful, to see if there is some kind of statement saying it is.

The moral is obvious. If the doctrine of Infallibility leads theologians to try to answer doctrinal questions by searching through Denzinger or the Acta Apostolicae Sedis they will have abandoned theology and it will be irrational to believe what they say. It is rational to believe what the Church teaches just so long as there is reason to think that the teaching is arrived at by reliable methods.

What about the Cumaean Sibyl? It is not a reliable method of ascertaining the future to write on leaves and let the wind blow the leaves about. Suppose, however, she predicted the winners of horse-races in this way and her prophecies always turned out true, would it not be rational to believe what she says in spite of the unreliability of her method? It might be rational to believe what she says, but not because she says it; rather, her success rate gives reason to suspect there is more to her method than appears. But the position with the Church's teaching is not quite like that. We do not know that everything the Church has taught hitherto is true in the way we could know that every past racing prediction by the Sibyl (had she made such predictions) was true.

I said that that reasoning which began with the premiss ‘Everything the Church teaches is true’ not only led to bad theology but was bad in itself. It has the same defect as a fallacy identified by Lewis Carroll and called, in memory of him, the fallacy of ‘What the Tortoise said to Achilles.’ Carroll imagines the Tortoise setting out the following argument:

1. (A) Things that are equal to the same are equal to each other.

2. (B) The two sides of this triangle are things that are equal to the same.

3. (Z) The two sides of this triangle are equal to each other.

Achilles and the Tortoise agree that someone might accept the premisses but still not accept the conclusion on the grounds that it does not follow from the premisses. And the Tortoise shows that it will not then help to add the further premiss

If A and B are true, Z must be true.

No matter how many such further premisses are added, the recalcitrant reasoner will not be forced to accept (Z). The reason is that what (C) asserts, that the form of the inference is valid, must not itself be a premiss of the inference. That the form of the inference is valid is implicit in any argument, not a premiss of it. The same is true of other things that are implicit, that the objects talked about exist and that the premisses are true. Everything which anyone states is stated as true. Nobody, unless trying to set out the Cretan Liar paradox, says ‘What I am saying is false’. Every doctrine of the Church is put forward as true, but that every doctrine of the Church is true ought not itself to be a doctrine of the Church or a premiss of any argument.

Perhaps this criticism of the doctrine of Infallibility may be felt not to do justice to its modal character. For the doctrine is not that everything the Church teaches is true, but that the Church could not possibly teach anything false. This doctrine is grounded on considerations about the purposes of Christ. ‘In order to preserve the Church in the purity of the faith handed on by the Apostles’ says the Catechism of the Catholic Church s. 889, ‘Christ who is the Truth willed to confer on her a share in his infallibility.’ This is a perfectly proper theological conjecture, which needs to be judged on its own merits like any other. Theologians may argue that it would be silly for Christ to intend the Church to teach if he was not going to ensure that they never taught anything false. But one way of deciding whether this is true, is to see if the Church ever has taught anything false. Some people think it has, particularly in the area of morals – that it has taught, for instance, that it is all right to keep slaves, or that it is wrong to join in prayer with non-Catholics.

It may be that the Church has never taught anything false. Suppose, however, that we are not sure whether some particular thing it has taught is false or not. The more reason we have for thinking this particular doctrine false, the more we have for thinking false the doctrine of Infallibility. The reasons for doubting the suspect doctrine have to be weighed against the reasons for accepting the doctrine of Infallibility; we cannot automatically give the latter precedence over the former. The position is similar to that over miracles. People sometimes argue that God would never allow the laws of nature which he himself instituted to be violated by miracles; but their arguments have to be weighed against the evidence that miracles have in fact occurred. It is as arbitrary to make it a fundamental principle that the Church cannot err, as to make it a fundamental principle that miracles cannot happen.

As a matter of fact it is not unreasonable to give people a mission to teach even if you are unable to ensure they will never teach anything false, and perhaps that is as impossible to ensure as that they will never misbehave. Outside the Christianity of Western Europe attaining truth about God and about good and evil would not normally be thought independent of good character and even sanctity. Jews look for truth to humble devout rabbis, Hindus and Buddhists to what it is natural to describe as holy men. The doctrine of Infallibility depends on a conception of truth that hardly goes back beyond the seventeenth century. The age that invented telescopes and microscopes conceived the mind as a mirror of nature and modelled truth on accurate mirroring. Mirrors have no moral qualities. If truth consists in exact mirroring all that is needed to ensure the Church against error is that Christ should keep the minds of its teachers smooth and well polished.

Classical Latin contains no such words as fallibilis or infallibilis, but Victorian England was always being offered ‘infallible’ remedies for this or that. Recourse to the Holy Office was then, as recourse to the Congregation for the Doctrine of the Faith is now, an infallible means of resolving controversies: whatever question you put you can be sure of a definite answer. One has to admire the spirit of Pio Nono and his cardinals when, pinned down in a corner of Rome, they replied to the triumphalism of secular scientists and political theorists with equally bombastic counterclaims. But today the doctrine of Infallibility seems a little dated: a Victorian extra, an additional protection with which one could dispense, like goloshes.