A variant of the preface paradox

Imagine being given a list generated as follows, without being told how it was generated:

1. A randomly chosen set of 2000 mutually consistent propositions that you justifiedly believe, subject to the constraint that they are consistent.

Given your fallibility, it’s highly probable that the list contains multiple falsehoods. As you look over the list, you say to yourself about each one: “Yup, that sounds right.” However, given what you know about your fallibility, you should also say: “I think some of these are false, though.” You will thus incline to disbelieve the conjunction of these propositions.

But suppose instead you were handed a list generated as follows, again without being told how it was generated:

2. A randomly chosen set of 2000 propositions that you know.

This list would look to you just like the first one. Thus, you would say about it exactly what you would have said about the first one. To each one, you would say: “Yup, that sounds right.” But then on reflection you would say: “I think some of these are false, though.” You will thus incline to disbelieve the conjunction of these propositions, just as in the first case. However, while in the first case you are correct in disbelieving, in the second you are mistaken in disbelieving.

But in any case, if you incline to disbelieve something, then you don’t know it. Hence, you do not know the conjunction of the 2000 randomly chosen propositions that you know, and so knowledge is not closed under conjunction.

Justification and units of assertion

It’s clear to me that each of two assertions could individually meet the evidential bar for assertibility, but that their conjunction, being typically less probable than either conjucnt, might not. But then there is something very strange about the idea that one could justifiably assert “S₁. S₂.” but not “S₁ and S₂.” After all, is there really a difference in what one is saying when one inserts a period and when one inserts an “and”?

Perhaps the thing to say is that the units of assertion are in practice not single sentences, but larger units. How large? Well, not whole books. Plainly, as the preface paradox notes, one can be justified in producing a book while thinking there is an error somewhere in it (as long as one does not know where the error lies). I think not whole articles, either. Again, we expect to be mistaken somewhere in a complex article. Perhaps the unit of assertion is something more of the order of a paragraph or less, but more than a sentence.

If so, then in typical cases “S₁. S₂.” will be a single unit of assertion, and to be justified in asserting the unit, one needs to be justified in the conjunction. This gives us a pretty precise definition of a unit of assertion: a unit of assertion is an assertoric locution that is lengthwise maximal with respect to needing to be justified.

What in practice determines the unit of assertion is probably determined by a mix of content, context, intonation, length of pauses, etc. For instance, a topic switch is apt to end a unit of assertion, and it may sometimes make a difference how long the pause between the sentences in “S₁. S₂.” with respect to whether the sentences form a single unit of assertion.

Surely people have written on this.

Magda the spy

Magda is a spy. Her handler gives her a spiel consisting of ten statements that she is to make to her enemy contact. Magda has no personal knowledge of whether the statements are true or false, and with a smile asks her handler: "I take it these are mostly false, but there is probably a truth or two tucked in just to mislead them even more?" Her very reliable and honest (she lets Magda do all the lying) handler responds: "Actually, this time it's the other way around. Eight of these statements are true, and two are false."

When Magda tells the spiel to her enemy contact, each of the ten assertions that she makes is an assertion that she thinks is likely, indeed 80% likely, to be true.

Does Magda lie to her enemy contact?

No one of the ten statements on its own seems to be a lie. When I think something is 80% likely to be true and I assert it, I may not be entirely sincere, but surely I am not lying.

Are the ten statements put together, into a spiel, a lie? After all, Magda knows that the conjunction of the ten propositions is false. But a series of statements does not become a lie just because one knows that one of them is false. Just about any non-fiction author of a decent level of humility knows that at least one of the statements in her book is false. So one doesn't utter a lie just because one utters a series of statements at least one of which one knows to be false. For exactly the same reason, the fact that the ten statements make up a single literary unit, a spiel, does not make them a lie, since typical books make a single literary unit and yet are not lies.

At this point, one might react as follows: Who cares whether Magda is lying? Whether she is lying or not, she is clearly dishonest, and her dishonesty is of the same sort as lying.

Here's another case. Magda is one of ten spies, each of whom is given a statement to convey to the enemy. They all know exactly two of the ten statements is false. Is Magda lying? I feel that she's not. She's simply saying something that she thinks is 80% likely to be true, in support of a deceptive plan by her organization.

If Magda isn't lying in the case where the statements are spread out between the spies, I think she isn't lying in the case where she makes all the statements. I do feel that in the case where the statements are spread out, Magda's dishonesty is less. But she is, nonetheless, being dishonest by supporting a deceptive communicative plan.

And maybe that is all we can say about the original case. Magda isn't lying. She is engaging in a dishonest communicative plan that is roughly morally on par with lying. Surely it makes little moral difference that unlike the ordinary liar, Magda doesn't know which of her statements is false. After all, ceteris paribus, there is little moral difference between the person who sets up a trap to kill one particular person and the person who sets up a trap to kill a random person.

But what makes her communicative plan be morally on par with lying? What moral norm applies equally to Magda's activity in the original case and to a variant where she knows which two of the ten statements are false?

I am inclined to think that the basic rough-and-ready moral rule behind the prohibition of lying is something like:

• Strive to assert only truths.

That's very rough. But it marks a difference between Magda and the non-fiction author. Both foresee that they will assert falsehoods. But the non-fiction author is, or so we hope, striving to avoid every instance of this. Not so Magda.

Not every violation of the rule to strive to assert only truths has the same moral weight. Lying is, perhaps, morally graver than BS—speaking with no regard for truth or falsity. And both of them are definitely morally graver than putting some effort into asserting only truths but not enough, say because one isn't being sufficiently careful to follow the evidence.