A theological argument that justified true belief is not knowledge

My 13-year-old daughter came up with a rather nice argument against taking knowledge to be nothing but justified true belief.

Jesus tells us that no one knows the day or the hour of his return. But now for each of the 24 possible hours, we can arrange for someone to have reason to believe that that hour is the hour of return. One of these 24 people will then have a justified true belief as to the hour when Jesus returns. If justified true belief is knowledge, then this would contradict what Jesus told us.

Of course, likely, when Jesus said that no one knows the hour, he was probably talking of a specific hour on a specific date—next Tuesday noon, say, rather than a noon in general. But the argument adapts. If the second coming is somewhere in the next 900,000 years, we could divide up the 8 billion people on earth, give each one reason to believe the second coming is during a specific hour during the next 900,000 years, and then one would be right, and would know, if knowledge is justified true belief.

That said, Jesus didn’t say that no one can know the hour, but only that no one knows the hour. Thus as long as no one actually lucks out and has a justified true belief, we have no contradiction to Scripture even if knowledge is justified true belief.

However, apart from the theological ramifications, I think this argument shows that pretty much anything that could be put into language could be known if knowledge is justified true belief. And that is implausible.

This line of argument also damages this line of thought of mine.

Two decreases in tension between faith and science

Over the past two hundred years or so, one new tension point arose for the relationship between Christianity and science due to scientific progress—namely, evolution. At the same time, several tension points disappeared due two other instances of scientific progress.

The first instance of this scientific progress was the general abandonment of the Aristotelian eternal world model of the universe with Big Bang cosmology. In the middle ages, Jewish, Islamic and Christian thinkers struggled with the tension between the science/philosophy of the day strongly tending towards a universe that always existed and the theological commitment to a creation a finite amount of time ago. That problem is gone.

The second instance is our scientific understanding of the continuity of organic development from zygote to embryo to infant to adult, which has made quite implausible the old view of discontinuous transition in utero from vegetable to animal to human. This old view was the dominant scientific view of human origins until fairly recently, and it had serious tensions with Christian theology.

The first of these embryological tensions was with Christian moral views about abortion. While traditionally Christians opposed both contraception and abortion, abortion was morally seen as a form of homicide. But on the discontinuous transition view, abortion prior to human ensoulment would only be contraception.

The second embryological tension was a technical problem in Christology. Suppose that in the Incarnation we have the vegetable, mere animal and rational animal sequence. Then Aquinas observes there are two possibilities, neither of which is theologically appealing.

First, it could be that God becomes incarnate as a vegetable or a mere animal. But this seems, as Aquinas says, “unbecoming”. And he seem to be right. The Incarnation reveals to us the person of the Logos, and it would be unbecoming that the Logos become a non-personal being.

Second, it could be that the Incarnation happens only at the beginning of the third stage of development, namely once everything is ready for a rational animal. But then Aquinas says “the whole conception could not be attributed to the Son of God”. Indeed, don’t we even have a tension with the Apostles’ Creed line that Christ “was conceived by the Holy Spirit”? For on this option, Christ was not conceived at all. What was conceived was a vegetable, not Christ. (Indeed, none of us were conceived on this view.) Moreover, one might worry that then there would be a sense in which the flesh of Christ would pre-exist the Incarnation. And that makes it difficult to say that the Word became flesh—for the flesh that Scripture says he “became” would already in a sense have been there, and one can’t become this flesh, since this flesh already has its own identity. (Granted, there may well be some Aristotelian metaphysics one can do to lessen this last worry.)

Aquinas solves the problem by supposing that Christ is conceived fully formed in Mary’s womb, and hence has the rational soul from the first moment of his existence. But this solution is itself problematic. Absent gradual development from a zygote, is this conception at all? If God were to create an adult human either ex nihilo or out of some pre-existing matter, we would not consider that a conception. But neither should we then consider it a conception if God creates a fully-formed fetus, even if he does that out of the pre-existing matter of Mary. So we still have a problem with the Apostles’ creed’s “was conceived by the Holy Spirit”. Moreover, it seems that this deprives Mary of a significant chunk of her motherhood.

But the problem entirely disappears once we think that the human beings begin their existence at conception. Christ is conceived by the Holy Spirit, presumably in that Mary’s ovum is transformed into a zygote by the infinite power of the Holy Spirit, which zygote is the Christ who then grows in utero like we all do.

(Catholics also note that the new scientific understanding of human embryonic development also helps with the doctrine of Mary’s immaculate conception—for only a rational being can be immaculately conceived, since original sin or freedom from it can only apply to a rational being.)

Open theism and the Incarnation

Here is a very plausible pair of claims:

1. The Son could have become incarnate as a different human being.

2. God foreknew many centuries ahead of time which human being the Son would become incarnate as.

Regarding 1, of course, the Son could not have been a different person—the person the Son is and was and ever shall be is the second person of the Trinity. But Son could have been a different human being.

Here is a sketch of an argument for 1:

1. If the identity of a human being depends on the body, then if the Son became incarnate as a 3rd century BC woman in India, this would be a different human being from Jesus (albeit the same person).

2. If the identity of a human being depends on the soul, then God could have created a different soul for the Son’s incarnation.

3. The identity of a human being depends on either the body or the soul.

I don’t have as good an argument for 2 as I do for 1, but I think 2 is quite plausible given what Scripture says about God’s having planned out the mission of Jesus from of old.

Now add:

3. If the Son could have become incarnate as a different human being, which human being he became incarnate as depends on a number of free human choices in the century preceding the incarnation.

Now, 1, 2 and 3 leads to an immediate problem for an open theist Christian (my thinking on this is inspired by a paper of David Alexander, though his argument is different) who thinks God doesn’t foreknow human free choices.

Why is 3 true? Well, if the identity of a human being even partly depends on the body (as is plausible), given that (plausibly) Mary was truly a biological mother of Jesus, then if Mary’s parents had not had any children, the body that Jesus actually had would not have existed, and an incarnation would have happened with a different body and hence a different human being.

Objection: God could have created Mary—or the body for the incarnation—directly ex nihilo in such a case, or God could have overridden human free will if some human were about to make a decision that would lead to Mary not existing.

Response: If essentiality of origins is true, then it is logically impossible for the same body to be created ex nihilo as actually had a partial non-divine cause. But I don’t want the argument to depend on essentiality of origins. Instead, I want to argue as follows. Both of the solutions in the objection require God to foreknow that he would in fact engage in such intervention if human free choices didn’t cooperate with his plan. God’s own interventions would be free choices, and so on open theism God wouldn’t know that he would thus intervene. One might respond that God could resolve to ensure that a certain body would become available, and a morally perfect being always keeps his resolutions. But while perhaps a morally perfect being always keeps his promises, I think it is false that a morally perfect being always keeps his resolutions. Unless one is resolving to do something that one is already obligated to do, it is not wrong to change one’s mind in a revolution. I suppose God could have promised someone that he would ensure the existence of a certain specific body, but we have no evidence of such a specific promise in Scripture, and it seems an odd maneouver for God to have to make in order to know ahead of time who the human that would save the world is.

What if the identity of a human depends solely on the soul? But then the identity of the human being that the Son would become incarnate as would depend on God’s free decision which soul to create for that human being, and the same remarks as I made about resolutions in the previous paragraph would apply.

On monkeys and exemplar theories of salvation

On “exemplar” theories of salvation, Christ’s work of the cross saves us by providing a deeply inspiring example of love, sacrifice, or the like.

Such theories of salvation have the following unsavory consequence: they imply that it would be possible for us to be saved by a monkey.

For imagine that a monkey typing on a typerwriter at random wrote a fictitious story of a life in morally relevant respects like that of Christ, and people started believing that story. If Christ saves us by providing an inspiring example, then we could have gotten the very same effect by reading that fictitious story typed at random by a monkey and erroneously thinking the story to be true.

Of course, that’s just a particularly vivid way of putting the standard objection against exemplar theories that they are Pelagian. I have nothing against monkeys except that they are creatures, and so that if it is possible to be saved by a monkey, then it is possible to be saved by creatures, which is Pelagianism.

Jesus's "unknown years"

Here is something that struck me about Jesus’s “unknown years”—the years not expressly described in the Gospel. Jesus was a Jew under the Torah. The Torah suffuses all aspects of life. Thus, in virtue of the fact that Jesus was sinless and hence perfectly fulfilled the Torah, we can know a lot more about his daily life than we know about the daily life of any ordinary historical figure. In Jesus' case, "ought" implied "is".

A Biblical argument for epistemicism

1. If God knows the exact number of hairs we have on our head, then there is a definite number of hairs we have on our head.

2. If there is a definite number of hairs we have on our head, vagueness is at most epistemic.

3. God knows the exact number of hairs we have on our head. (Luke 12:7)

4. So, vagueness is at most epistemic.

Premise 2 is based on observing that the number of hairs we have on our heads involves similar kinds of vagueness to more paradigmatic cases of vagueness. Think here about these questions:

• What’s the cut-off between hairs on the head and hairs on the upper neck?

• How much keratin needs to come out of a hair follicle before that keratin counts as a hair?

• How far must the molecules of a hair separate from the molecules of the skin before the hair counts as no longer attached?

One might worry that Premise 3 relies on biblical data too literalistically. Jesus is emphasizing the impressiveness of God’s knowledge. Suppose that instead of God knowing the exact number of hairs on my head, God knew the exact vagueness profile for the hairs on my head. That would be even more impressive. I see some force in this objection, but it implies that epistemicism holds at the level of vagueness profiles, and it seems (but perhaps isn’t?) ad hoc to go for epistemicism there rather than everywhere.

On reflection, I think premise 1 might be the most questionable premise. Perhaps God’s knowledge definitely matches the number of hairs: for every natural number n, it’s definitely true that: God believes I have n hairs if and only if I have n hairs, but there is no natural number n such that God definitely believes I have n hairs. In other words, the vagueness profile concerning God’s beliefs exactly matches the vagueness profile in reality. I am sceptical of this solution. It doesn’t feel like knowledge to me if it’s got this sort of vagueness to it.

Faith and belief

Christians are called to have faith in Jesus Christ.

The Old Testament, however, is big on not putting our faith in anything other than God.

Thus, someone who has faith in Jesus Christ but does not believe that Jesus Christ is God is risking violating a central principle of the Old Testament.

Moreover, faith in Jesus requires submission to Jesus. But Jesus wants his followers to obey the central principles of the Old Testament.

Thus, for someone aware of these observations, it is not possible to have faith in Jesus Christ without believing that he is God. This is a serious problem for accounts of faith that claim that a Christian need not have any doctrinal beliefs.

Beliefless Christianity

A number of authors have claimed that it is possible to practice the Christian faith without assigning a high epistemic probability to central doctrines of Christianity. Here is an interesting problem with such a practice. A central part of Christian practice is to worship Jesus Christ as God. Now, Jesus Christ is uncontroversially a man. Christianity adds that he is also God. If that additional belief is false, then we who worship Jesus Christ as God are idolaters. But it is wrong to undertake a serious risk of idolatry. Thus, it is only permissible to practice the Christian faith if by one's lights the risk of idolatry is not serious. And the only way that can be is if one assigns a high epistemic probability to the doctrine that Jesus Christ is God. Thus, it seems, at least this central doctrine of the Incarnation needs to have a high epistemic probability if one is to be morally justified in practicing the Christian faith.

There is, however, a hole in the argument. Idolatry is only a great evil if God exists. Now imagine someone who assigns a high conditional probability to the Incarnation on the condition that God exists, but who assigns a low unconditional probability to both the Incarnation and the existence of God. Such a person can reason as follows. Either God exists or not. If God does not exist, there is not much evil in idolatry, and so not much harm in worshiping Jesus as God. If God does exist, however, then probably the Incarnation is true, and the value of worshiping Jesus outweighs the risks, since the risks are small.

So, what I think my overall argument shows is that it is wrong to practice the Christian faith without assigning a high epistemic probability to the doctrine of the Incarnation if one assigns a significantly higher epistemic probability to theism. Thus, someone who comes to be convinced that theism is true but assigns a low epistemic probability to Christianity should not practice Christianity.

Objection: Perhaps it is just as morally evil to fail to worship as God someone who is in fact God as it is to worship as God someone who is not. In that case, by not practicing Christianity, one also takes on a great moral risk, and perhaps the risks cancel out.

Response: I think it not just as morally evil to fail to worship as God someone who is in fact God. As far as we know, John the Baptist did not worship Jesus as God, but we have no reason to think that this was a great evil, on the par of idolatry.

Let your "yes" be yes

Jesus seems to have forbidden swearing, insisting that our “yes” should be a yes, and our “no” a no and that everything else is “from the evil one” (Matthew 5:34-37). A strong reading of this would take Jesus to be forbidding all oaths. By and large, the Christian tradition has not taken that to be the correct reading. In the US, many people who accept the Bible, including presumably this text in Matthew, swear in court on the Bible.

A plausible reading is that Jesus is engaging in hyperbole to command an integrity such that there be no need for oaths. For Christians, the same norms of integrity apply to simple assertions as to sworn depositions. I will assume that this is the correct reading.

Suppose one thinks, contrary to the main line of the Christian tradition, that it is sometimes permissible to lie. Then one has to think that it is also permissible to lie under oath in precisely the same circumstances in which it would be permissible to lie without oath. But this is an implausible consequence.

Let’s say that it’s permissible to lie to save an innocent life—that’s one of the most given criteria. Then, we have the consequence that it is permissible to swear to a false alibi for someone whom you know to be innocent in a capital case if you foresee that otherwise he will be convicted. This is already implausible. But it also means that, implausibly, even in a good and free society one might have good reason to keep one’s moral views secret. For if it were known that according to one’s moral views it would be permissible to provide a false alibi when one took oneself to know that the accused is innocent in a capital case, then one’s true alibi would be of little worth in such cases, too.

Second, whatever criterion one has is going to admit of borderline cases. For instance, in the case of “saving an innocent life”, at one end, there is the case where it is certain that the person will live if and only if one lies. Near the other end, the probability of survival is slightly bigger if one lies. It is implausible that one can permissibly lie just to give someone the slightest increase in probability of survival. If that were so, then it would be permissible to swear to a false alibi (assuming, as per my reading of what Jesus said, that swearing falsely is permissible whenever false assertion is) even when it is very likely that the innocent accused in the capital case will be let off, as long as it slightly increases the innocent’s chance of survival, and that can’t be right. And somewhere in between there will be borderline cases.

But now consider a borderline case of the permissibility of lying. If it is only borderline whether it is permissible to engage in a simple lie, to swear falsely in such a case would be simply wrong, not just borderline wrong. But this violates Jesus’s principle that the norms regarding simple lies are the same as the norms regarding false oaths.

It seems to me that the best reading of the situation is that:

1. Lying under oath is always wrong.

2. And so, lying is always wrong.

Faith and credence

Alice: I just saw a giraffe in my yard.
Bob: I always trust you about what's in your yard. So I think it's 55% likely there is a giraffe in your yard.

No, Bob doesn't trust Alice. If he trusted her, his credence that she's telling the truth would have been high.

I am not claiming that we always assign high credence in the assertions of someone we trust in a given matter. This dialogue is perfectly sensible.

Alice to Carla: I just saw a giraffe in my yard.
Bob to Dave: I always trust Alice about what's in her yard. I think I might have just overheard her saying that she saw a giraffe in her yard. So now I think it's 25% likely there is a giraffe in her yard.

In the second dialogue, the reason Bob's credence that there is a giraffe in Alice's yard is lowish has little to do with not trusting Alice about these matters. Rather, it is that he doesn't trust his hearing--he's far from sure that he heard her report a giraffe. I assume in the first dialogue, Bob is quite confident that Alice reported a giraffe--if he isn't, there is no problem.

Trust doesn't require high credence in the assertions of the person we trust. But:

1. If one trusts x with regard to p-type propositions, one assigns high credence to non-exclusive disjunctions like: p is true or x did not assert p.

When I started thinking about this, I also thought it required a high conditional probability P(p | Alice asserted p). But it doesn't require that. Suppose I trust Alice about mathematics and I hear her confidently say something that vaguely sounded like "The derivative of a sine function is a tangent." My unconditional probability that the derivative of a sine function is a tangent is very low (I can just see in my mind that the slope of a sine is bounded and a tangent is unbounded), but even my conditional probability on Alice's asserting it is very low. It's not that I actually don't trust Alice. Rather, it's that if she asserted that the derivative of a sine were a tangent, I would lose my trust in her mathematical knowledge. (It might be a bit more complicated. Trust might be compatible with accepting minor occasional slip-ups. So I might think it's one of those. So maybe even if she said this, I would be trusting her in general--but not in this circumstance.) And it's compatible with trust that there be possible circumstances where one would rationally stop trusting.

Now, here is a question that has had some discussion in the literature: Is it rationally possible to have explicit Christian faith (I am using "explicit" to distinguish from the kind of faith that an "anonymous Christian" might have) and assign only a modest (not at all high) credence to the proposition that God exists? I think that given fairly uncontroversial historical evidence, this can't happen. Here is why:

2. One has explicit Christian faith only if one trusts Jesus in central parts of his teaching.
3. The historical evidence clearly shows that Jesus existed and that a central part of his teaching is that God loves us.

Given the uncontroversial historical evidence, a rational person will accept with very high credence that a central part of Jesus's teaching is that God loves us. By (1) and (2), if she has explicit Christian faith, she will also assign a high credence to the disjunction that God loves us or Jesus didn't centrally teach that God loves us. Since the second disjunction is uncontroversially historically false, the credence will transfer to the first disjunct, and she will assign a fairly high credence to the claim that God loves us. But that God loves us obviously entails that God exists. So she will assign a fairly high credence to that, too. And hence her credence won't be modest (i.e., not at all high).

Interestingly, as far as arguments like this go, it might be possible to have faith in God while only assigning a modest credence to the existence of God. Someone who has faith in God will trust God. So she will assign a high credence to disjunctions like: God loves us or God didn't say God loves us. But while it's uncontroversial that Jesus said God loves us, it's controversial that God said God loves us, since it's controversial whether God exists, but the existence of Jesus is an uncontroversial historical matter (I understand that even the Soviet historians eventually stopped saying that there was no Jesus).

It is more blessed to give than to receive

On the one hand, Jesus tells us that it is more blessed to give than to receive. On the other hand, Socrates tells us in the Gorgias:

And what sort of a person am I? One of those who are happy to be refuted if they make a false statement, happy also to refute anyone else who may do the same, yet not less happy to be refuted than to refute. For I think the former a greater benefit, in proportion as it is of greater benefit to be oneself delivered from the greatest harm than to deliver another. No worse harm, it is true, can befall a man than to hold wrong opinions on the matters now under discussion between us.

We thus have two plausible and apparently conflicting claims: it is better to give than to receive and yet it is better to receive a refutation than to give it. If the conflict is real, then of course we go with Jesus. But is the conflict real? After all, Jesus' saying has the form of a proverb, and we know that proverbs, biblical and otherwise, are not meant to have universal applicability. Wisdom is needed to figure out which proverb applies when.

Jesus' saying seems to me to apply to cases where the giving is a sacrifice, either of the thing given or of one's time and energy in giving it. Socrates, however, is clearly not talking of that sort of giving. Socrates obviously finds it fun to give refutations. There is no sacrifice for him in refuting another. Well, at least in the Gorgias. Eventually, his practice of refuting others costs him his life. At that point it seems that Jesus' proverb applies: giving refutation to others becomes a sacrifice, and it is better for one to make that sacrifice than to be on the receiving end of another's sacrifice.

Maybe a similar thing can be said about another case. We tend to feel that it is better to work on one's own virtue, and to receive virtue from others, than to work on the virtue of others. I think this is because working on one's own virtue tends to be costlier personally, tends to be more of a sacrifice. It is often easier to preach than to do. (And while preaching without doing is often ineffective, that's not universally true. There are many people whose lives have been turned to virtue by the preaching of people whose own lives turned out to be a fraud. One must, though, remember that the preaching is not all that was going on--there was also grace.) So giving virtue to others need not be a sacrificial gift of the sort that Jesus is talking about on my interpretation. But it also can be, in which case the proverb seems to apply.

Aquinas on why the incarnation is fitting

I find it striking and interesting that in the article where Aquinas officially addresses whether the Incarnation is fitting, his argument in favor of the fittingness of the Incarnation makes no mention of salvation. In other words, it's clear that the Incarnation would be fitting whether or not we sinned, though Aquinas is inclined to think that had we not sinned, the Incarnation would not have occurred. The focus on epistemic benefits is particularly interesting:

On the contrary, It would seem most fitting that by visible things the invisible things of God should be made known; for to this end was the whole world made, as is clear from the word of the Apostle (Romans 1:20): "For the invisible things of God . . . are clearly seen, being understood by the things that are made." But, as Damascene says (De Fide Orth. iii, 1), by the mystery of Incarnation are made known at once the goodness, the wisdom, the justice, and the power or might of God--"His goodness, for He did not despise the weakness of His own handiwork; His justice, since, on man's defeat, He caused the tyrant to be overcome by none other than man, and yet He did not snatch men forcibly from death; His wisdom, for He found a suitable discharge for a most heavy debt; His power, or infinite might, for there is nothing greater than for God to become incarnate . . ."
I answer that, To each things, that is befitting which belongs to it by reason of its very nature; thus, to reason befits man, since this belongs to him because he is of a rational nature. But the very nature of God is goodness, as is clear from Dionysius (Div. Nom. i). Hence, what belongs to the essence of goodness befits God. But it belongs to the essence of goodness to communicate itself to others, as is plain from Dionysius (Div. Nom. iv). Hence it belongs to the essence of the highest good to communicate itself in the highest manner to the creature, and this is brought about chiefly by "His so joining created nature to Himself that one Person is made up of these three--the Word, a soul and flesh," as Augustine says (De Trin. xiii). Hence it is manifest that it was fitting that God should become incarnate.

Of course, in the next article, Aquinas does talk of the need for the Incarnation for our redemption. It's not an absolute need, but it is necessary for our redemption to be worked in a better and more fitting way (Aquinas compares it to the necessity of a horse for a journey--presumably, one could always walk, but a horse is better). In that article, Aquinas gives ten benefits for the sake of which the Incarnation was fitting in respect of our redemption. It is interesting that penal satisfaction is only one of the ten.

And then Aquinas adds: "And there are very many other advantages which accrued, above man's apprehension." How does he know? Is it just a confidence that God does many, many good things for us? Could one argue that the Incarnation of an infinite being must somehow bring infinitely many benefits, of which only finitely many will be understandable to us?