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Those who advocate for a change in Church teaching on certain moral issues, such as contraception, or sexual expression between two people of the same sex, or even the ordination of women, etc., must seriously consider the implications of the idea. There are a number of angles from which to explore this. I would like to consider what the implications of a change in Church teaching (i.e., in matters of sexual ethics and some basic life issues) would imply with respect to the Church's moral authority, but I would like to do so from a mathematical point of view. I will attempt to show that a simple Bayesian probability calculus might be all we need to demonstrate that the Church would lose almost all of her moral authority if she were to proceed in this direction, a direction the German synodal path seems to be taking.

First, a word about cognitive dynamics. There are a number of ways that cognitive changes occur, and thus a number of ways that Church teaching can, theoretically, change, not all of which are problematic. The first way I will refer to as **truth status determination** . Here, we come to learn the truth condition of a previously indeterminate position (p changes from I to T or F). For example, at one time we were unable to determine whether space and time are separate "entities"; now, as a result of certain pieces of evidence, we have determined that space-time is the fabric of the universe (i.e., it is more than just a thought experiment).

A different cognitive dynamic is what we will call **issue acquisition** . What takes place here is that new concepts needed to formulate a contention that could not previously be entertained at all are developed (p changes from U to T or F or I). For example, Newton never asked the question about the nature of space-time; it could not have arisen. Only after certain questions were posed could these issues arise, that is, after Einstein's thought experiment regarding the speed of light and relativity.

A third cognitive dynamic is simply a matter of **truth status revision** . Here we simply change our mind as to the truth status of a thesis in light of "new information" (p changes from T to F, or F to T). And finally, what we will call **reopening** : here new information leads us to become unsure of the truth-status of a proposition we had previously classed as true or false, thus, the truth-status of the proposition at issue is reopened (p changes from T or F to I).[1]

The Church's teaching can of course change in the first two modes above: **truth status determination** and **issue acquisition** . For example, the Church did not adopt a position on in vitro fertilization in the first three centuries of her history; for it was simply not an issue. When in vitro fertilization eventually did become an issue as a result of new technology, the body of Catholic moral teaching expanded accordingly. The issue of usury (charging interest on a loan) is somewhat trickier, for the Church did condemn usury, but there was a clear development of the teaching on usury by virtue of a more profound understanding of economic theory, specifically the concept of time preference. This means that a good in the present (i.e., my money today) will be valued more than the same quantity of that good in the future. The idea of time preference implies that a future good ($1000) is valued less than the same good ($1000) in the present, and so if the borrower were to repay only the nominal sum he originally borrowed (i.e., $1000 that he borrowed from me five years ago), the repayment would constitute a defect of justice, for they are not the same good, but different goods (this is especially the case in light of inflation). Patrick O'Neil explains this rather well. He writes:

The error concerning the charging of interest is an example of correct moral principles (against economic exploitation and so forth) mistakenly applied on account of the inadequacies of early economic theory. When better economic theory became available (along with lessons of practical experience), the Church could change its position because the fundamental form of her judgment was: "If W is the economic function involved in the charging of interest, then the charging of interest is immoral, because economic activities must adhere to rule X (or rules X, Y, & Z)." Changes under these circumstances do not threaten the claims of the magisterium of the Church in any way. The discovery that the charging of interest does not (necessarily) involve exploitation, but represents instead legitimate payment for the time-value of money and for the risk factors endured by the lender, denies the antecedent of the hypothetical.[2]

The issue of usury is, in this light, fundamentally a matter of **issue acquisition** ; the new economic concepts needed to formulate a contention that could not previously be entertained at all are later developed--a question that depends on the concept of time preference simply does not arise until much later in history, permitting a better understanding of what charging interest on a loan really is and what it is not.

**Truth status revision** and **reopening** are, in the context of Church history, an entirely different matter. What was at one time clearly taught as true is now seen as false (or possibly indeterminate), or an assertion that was at one time clearly taught as false is now regarded as true or indeterminate. For example, the assertion that "it is morally permitted to for two people of the same sex who love one another to engage in sexual acts (which are necessarily both non-procreative and non-unitive)" has been clearly taught by the Church to be false. For that to change would constitute a **truth status revision** . Moreover, it is true that according to authentic Catholic moral teaching, to intentionally change the significance of the conjugal act by willingly taking steps to prevent a possible baby from becoming an actual baby is morally impermissible; were that to become false, we would have an instance of **truth status revision** . Furthermore, the Church clearly teaches that she cannot ordain women to the priesthood; were that claim to move from true to indeterminate, we would have an example of **reopening** .

I have no intention of treating any such moral or theological issues in this article. Instead, I would like to explore what a **truth status revision** or **reopening** with respect to such Catholic moral teachings would imply in terms of the Church's moral authority. To do so, I would like to use a tool of inductive logic, namely Bayes Theorem, which is the mathematical formula that attempts to determine *the probability of a hypothesis, given certain pieces of evidence* . What I would like to determine is the probability that the Church possesses the charism of infallibility on matters of faith and morals, given certain actual or possible pieces of evidence. For example, what is the probability that the Church enjoys the charism of infallibility in matters of faith and morals, given that Humanae Vitae was mistaken all these years? Or what is the probability that the Church enjoys the charism of infallibility in matters of faith and morals, given that her teaching on sexual ethics, in particular sex between persons of the same sex, was mistaken all these years? Or what is the probability that the Church enjoys the charism of infallibility in matters of faith and morals, given that her teaching on the ordination of women was, for all these years, mistaken? I believe it can be shown that for each of these questions, the probability would be very low.

The formula for Bayes Theorem is the following: p(h|e) = p(h) **x** p(e|h) **divided by** p(h) x p(e|h) **+** p(-h) **x** p(e|-h). To illustrate how this works, consider a simple and straightforward scenario involving shipments of bananas from Honduras and Guatemala and the likelihood that the consignments have a tarantula or two crawling around. Let us say that 3% of consignments of bananas from Honduras were found to have tarantulas on them, and 6% of the consignments from Guatemala were found to have tarantulas on them. Let us also establish that 40% of the consignments came from Honduras, while the remaining 60% came from Guatemala. A tarantula was found on a randomly selected lot of bananas. What is the probability that this lot came from Guatemala? Thus, we want to know the probability of the hypothesis that this lot came from Guatemala, given the evidence available to us (we found a tarantula).

To calculate that probability, we will need to know the base rate, that is, the probability of the hypothesis without any reference to evidence. The notation for the base rate is simply p(h). The probability that this consignment came from Guatemala as opposed to Honduras is 60%, and so the probability that it did not come from Guatemala, but Honduras, is 40%, and its notation is p(-h).

The probability that we will find a tarantula, given that the consignment is from Guatemala, is 6% (since this is what we have found in the past). This is called the likelihood, and its notation is the following: p(e|h). The probability that we will find a tarantula, given that the consignment is from Honduras, is 3% (since 3% of them were found to have tarantulas on them). We have everything we need to calculate the probability that this randomly selected lot, on which was found a tarantula, came from Guatemala.

p(h|e) = p(h) **x** p(e|h) **divided by** p(h) **x** p(e|h) **+** p(-h) **x** p(e|-h).

p(h|e) = 60% **x** 6% **divided by** 60% **x** 6% **+** 40% **x** 3%.

p(h|e) = .6 **x** .06 **divided by** .6 **x** .03 **+** .4 **x** .03

p(h|e) = 0.036 **divided by** 0.036 **+** 0.012

p(h|e) = 0.036 **divided by** 0.048

p(h|e) = 0.75 or 75%

Hence, the probability that this lot came from Guatemala, given the evidence, is 75%.

Let us now calculate the probability that the Church enjoys the charism of infallibility in matters of faith and morals, given that Humanae Vitae was mistaken all these years (i.e., the culture was right all along). To do so, we need a number of priors. Hence:

p(h) = Our base rate probability that the Church is infallible in matters of faith and morals. For this, let us assume that the average Catholic is unsure: 50/50, or 0.5. Hence, p(-h) would also be 50%, or 0.5.

p(e|h) = the probability that Humanae Vitae is wrong, given that the Church is truly infallible on matters of faith and morals. On such an important matter, and given the Church has the charism of infallibility, one would have to say the likelihood is quite low, if not zero. Let us agree on 10%, or 0.1.

p(e|-h) = the probability that Humanae Vitae is wrong, given the Church is not infallible on matters of faith and morals. It is reasonable to assume that it is very likely that the Church got it wrong on this matter, given that the Church has no charism of infallibility, and that the teaching originated from a group of unmarried clergy, and that virtually every other voice in the world finds nothing morally objectionable about contraception. A reasonable number is 90%, or 0.9. We now have what we need to calculate a probability.

p(h|e) = p(h) **x** p(e|h) **divided by** p(h) **x** p(e|h) **+** p(-h) **x** p(e|-h).

p(h|e) = 50% **x** 10% **divided by** 50% **x** 10% **+** 50% **x** 90%.

p(h|e) = 0.5 **x** 0.1 **divided by** .5 **x** 0.1 **+** 0.5 x 0.9

p(h|e) = 0.05 **divided by** 0.05 **+** 0.45

p(h|e) = 0.05 **divided by** 0.5

p(h|e) = 0.1 or 10%

This gives us a 10% probability that the Church is infallible, given that Humanae Vitae was mistaken, and that popular culture got it right. If we were to change the base rate from 50% to 70%, that is, a person believes that for the most part, the Church has the charism of infallibility, that still leaves us in the end with a 21% probability that the Church enjoys the charism of infallibility in matters of faith and morals, given that Humanae Vitae was mistaken all these years (and that popular culture got it right). In other words, for anyone with an intuitively Bayesian mind, the Church's moral authority would virtually disappear.

- [1] Nicholas Rescher. Empirical Inquiry . London: The Athlone Press, 1982, pp. 90-91.
- [2] Patrick M. O'Neil, "A Response to John T. Noonan, Jr., Concerning the Development of Catholic Moral Doctrine," Faith & Reason (Spring/Summer 1996), quoted in Thomas Woods, The Church and the Market: A Catholic Defense of the Free Economy . New York: Lexington Books, 2005, p. 122.

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