Infinite conjunctions

Field claims that our desire that we only believe truths can be understood as a desire for the infinite conjunction that

1. I believe "p₁" only if p₁, and I believe "p₂" only if p₂, and ...,

where I go through all the sentences. But one cannot replace a universally quantified desire with a conjunctive desire. Here is one way to see this. Suppose I falsely believe that "Eats jabberwocky sits" is a sentence. If I desire to believe only truths, then this desire together with my false belief explain why it is that I am motivated to ensure first that "Eats jabberwocky sits" is a truth before trying to believe it. (Think here of a case when an authority says "Eat jabberwocky sits", and we have prima facie reason to think that what she is true and hence a sentence, so I then investigate, for instance checking the authority's reliability.) But if what I desire is the infinite conjunction, then it is unclear why my desire has any explanatory bearing on my investigation into whether "Eats jabberwocky sits" is true, since my desire has nothing to do with the sentence.

What Field might try to do is, I suspect, to posit in me a mistaken belief that one of the conjuncts in my desire is 'I believe "Eats jabberwocky sits" only if eats jabberwocky sits', which somehow explains my activity. There are two problems with this. First, it is not clear how it is that the belief that something is a conjunct in something I desire is motivating. But the more serious puzzle is this. The mistaken belief that one of the conjuncts is 'I believe "Eats jabberwocky sits" only if eats jabberwocky sits' is supposed to motivate me. Motivate me to do what? Presumably, to believe "Eats jabberwocky sits" only if eats jabberwocky sits. But that is not an answer, because it is ungrammatical. So there seems to be no way of formulating what it is that I am motivated to do!

One might try to do better as follows. What I am motivated to do is to believe "Eat jabberwocky sits" only if what the (alleged) sentence "Eat jabberwocky sits" says is true. But 'What "p" says is true' is a quantification that Field will want to expand again into an infinite disjunction:

2. ("p" says that p₁ and p₁, or "p" says that p₂ and p₂, or ...).

So what I am motivated to do is to

3. believe "Eat jabberwocky sits" only if "Eat jabberwocky sits" says that p₁ and p₁, or "Eat jabberwocky sits" says that p₂ and p₂, or ....

But how does that motivate me to investigate whether "Eat jabberwocky sits" is true? After all, "Eat jabberwocky sits" does not in fact occur among "p₁", "p₂", .... If anything, I should be directly motivated not to believe "Eat jabberwocky sits", since it does not satisfy any of the conditions. Now, it is true that I believe that "Eat jabberwocky sits" is in the list of all sentences. Let's be more explicit about what I believe in believing that. What I believe is that a sentence of the form '"Eat jabberwocky sits" says that p and p' is one of the disjuncts on the right hand side of (3). This motivates me to believe "Eat jabberwocky sits" only if p, it seems. Well, not quite. For I haven't picked out p. Alright, let's pick it out. Stipulate that p_n is the first sentence in the list of all sentences (e.g., alphabetically ordered) such that "Eat jabberwocky sits" says that p_n. Now it seems that the content of my desire is getting clearer. As a result of my false belief that there is such a p_n, I desire to believe "Eat jabberwocky sits" only if p_n. But that doesn't make any sense unless I can actually spell out what "p_n" is. I can't have a belief with a variable sentence baldly inserted. Besides, how could that desire guide my action when in fact I don't know what "p_n" is?

I might try to do something with definite description in place of "p_n". I desire to believe "Eat jabberwocky sits" only if the first sentence that says what "Eat jabberwocky sits" says. But that's again ungrammatical. OK, so I desire to believe "Eat jabberwocky sits" only if the first sentence that says what "Eat jabberwocky sits" says is true. However, the last clause becomes, once again, an infinite disjunction: I desire to believe "Eat jabberwocky sits" only if "s₁" is the first sentence that says what "Eat jabberwocky sits" and s₁ say, or .... We once again see that we are back where we were.

But of course the above is a bit silly, because I have a very clear belief about what "p_n" is. But if I have such a belief, then what I desire is to believe "Eat jabberwocky sits" only if eat jabberwocky sits. And that's ungrammatical.

This problem shows an interesting problem for deflationist theories of truth. The theorist who says that truth is a property has no difficulty with the sentence "'Eat jabberwocky sits' is true." The sentence is, simply, false: it ascribes to a string of words that do not form a sentence a property that only strings of words that do form a sentence can have. But the deflationist's take on what it is to believe that 'Snow is white' is true is seems to be that it is, simply, to believe that snow is white. And if so, then to believe that 'Eat jabberwocky sits' is true is to believe that eat jabberwocky sits. But that's ungrammatical. So, either the deflationist must make a difference between what it is to believe that 'Snow is white' is true and what it is to believe that 'Eat jabberwocky sits' is true, which seems problematic, or she must give a more complex account of what it is to believe that 'Snow is white' is true. That more complex account is probably going to have to be something like the disjunction: 'Snow is white' is (or says the same as) 'p₁' and p₁, or 'Snow is white' is (or says the same as) 'p₂' and p₂, or .... That does not seem very plausible.