I before E: Getting Snowed

'Tis the night before Christmas, in a small desert house. Coyotes are stirring. And I am thinking about disquotation (with bourbon at hand, in front of a good fire). It is, as I write, snowing. And at least where I am, the snow really is white. But I am wondering why we were ever supposed to believe that sentences like (1) are true.

                        (1)  ‘Snow is white.’ is true if and only if snow is white.

Imagine someone who doubts that sentences of a Human Language have truth conditions, say because he thinks that sentences have meanings that constrain without determining the truth conditions of judgments/assertions made by using sentences in contexts, and that truth is related to judgments/assertions and to contexts in complicated ways not fully tracked by linguistic meaning. This person, call him ‘Scrooge’, doubts that the previous sentence—or the shorter sentence (2)—has a truth condition.

            (2)  Most people who know the Ghost of Christmas Past

know that Hesperus is Phosphorus.

Likewise, Scrooge doubts that (3) has a truth condition.

                        (3)  The third numbered example in this post is not true.

And he is unlikely to be impressed if someone insists that (2) and (3) must have truth conditions, on the grounds (4) and (5) just have to be true.

            (4)  Sentence (2) is true if and only if most people who know the Ghost of

                         Christmas Past know that Hesperus is Phosphorus.

                        (5)  ‘The third numbered example in this post is not true.’ is true 

                                     if and only if the third numbered example in this post is not true.

Someone might say that all instances of (6) are true;

                        (6)  S is true if and only if S.

where ‘S’ is to be replaced by an English declarative, and S is to be replaced by that same declarative quoted, as in (1). But Scrooge has his reply ready: Humbug. So why should Scrooge grant that (1) is true? Maybe (1) is a sentence that speakers can use to say that (7)

                        (7) Snow is white.

can be used to make claims that are (in their respective contexts) true if and only if snow is white (at least by the contextually relevant standards). Scrooge, who has a fondness for Austin and Strawson, might also note that ordinary speakers don’t often ascribe truth to sentences (or even utterances). The folk may speak of what someone said or what most people believe as being true or false. On special occasions, they may speak of propositions being true. Sentences, not so much. Though they do speak of true friends, true north, and true walls. Scrooge thinks it’s all a bit of mess. So why should he grant that (1) is true?

By way of saying why I think this matters, let me flash back to my own past. As a lad, I was taught that instances of (6) are true, modulo a bit of context sensitivity. There are endlessly many such instances. So if each one corresponds to a truth concerning the truth condition of the declarative sentence in question, there are endlessly many such truths crying out for explanation. (That’s what explananda did back then. They cried out for a good explanans.) This dire situation called for action, and the remedy was clear: provide a finite theory from which the truths in question—truths reported with instances of (6)—could be deduced. Of course, literally disquotational biconditionals like (1) aren’t derivable from remotely reasonable axioms. But one can try to derive instances of (8);

                        (8)  True[SD(S)] ≡ p

where ‘SD(S)’ is to be replaced by a structural description (as opposed to a quotation) of the object language sentence S, and ‘p’ is to be replaced by a sentence of the metalanguage that is at least truth-conditionally equivalent to S, and ideally a “good translation” with the same logical implications. That is, one can try to derive instances of (9);

                        (9)  True[SD(S)] ≡ Log(S)

where ‘Log(S)’ is the logical form of S, not to be confused with the LF of S. Indeed, if LFs can serve as structural descriptions, one can try to derive instances of (10).

                        (10) True[LF(S)] ≡ Log(S)

            I came to know and love the project of trying to derive instances of (10). Still do love it. But when it comes to understanding the theories that have emerged, and what they tell us about how humans understand sentences like (11) and (12),

                        (11)  Snow is white.

                        (12)  It is snowing.

I find myself wondering, Scrooge-like, why we should think that instances of (10) are true.

            We all know that neither (12) nor (13) is true.

                        (13) ‘It is snowing.’ is true if and only if it is snowing.

It may not be snowing where you are when you read this. But even if it is, there are many other snowless regions of spacetime; and at each such region, (12) is not true. Sentence (12), a sentence of (some version of) English, differs from the arithmetic sentence (14)

                        (14)  3 + 4 = 7

in this respect. Correlatively, while (15) is true, (13) is not.
                        (15)  True(‘3 + 4 = 7’) ≡ (3 + 4 = 7)

The spacetime-sensitivity of (11) is less obvious, but still there. Maybe snow will be green in the future, or the snow that sits on city streets will become the norm. Of course, even given a sentence like (12), we can construct more “eternal” variants. I’m not far from a place called ‘Ghost Ranch’, and it’s snowing there too. So consider (16).

                        (16)  It snowed (or will snow) at Ghost Ranch on Christmas Eve, 2012.

The parenthetical allows for uses at different times, and uses by confused time travelers. Or consider (17), which has a more “headline” feel;

                        (17)  Snow falls at Ghost Ranch on Nickday.

where ‘Nickday’ is, by stipulation, a name for the first December 24th after the end of the Mayan calendar. Having thus eternalized, one might say that (18)—

                         (18)  ‘Snow falls at Ghost Ranch on Nickday.’ is true if and only if

                                    snow falls at Ghost Ranch on Nickday.

or the analog for (16), or some fussier variant—is true.

If that’s right, then even a sentence like (12) corresponds to an explanandum initially characterized by some instance of (19), and potentially by some instance of (20).

(19)  S is true relative to C if and only if F(S, C).

(20) True[LF(S), C] ≡ F[Log(S), C]

But let’s pause a moment, and ask why we should think that (18) and endlessly many instances of (20) are true. Let’s agree that the most obvious reason for denying that (13) is true does not apply to examples like (18). But the most obvious reason needn’t have been (and wasn’t ever) the only reason. Scrooge’s question remains. Why think (1) is true?  

                        (1)  ‘Snow is white.’ is true if and only if snow is white.