Are the Laws of Logic Propositions?

Justin Taylor has posted a link to the Anderson-Welty paper. Predictably enough, the comments weren’t too inspiring, but one criticism (by Derek DeVries) invited a reply:

The laws of logic are rules. And these rules can, but need not, be stated on proposition form according to which they would be truth-apt. The laws of logic, in themselves, are not the kind of thing that has any truth value; only propositional statements expressed in the some language is capable of having any truth-value. Thus, saying that the laws of logic are truths is false, or sloppy at best. Therefore, the conclusion that the laws of logic are metaphysically dependent on the existence of God does not follow necessarily. The argument is deductively unsound.

I posted the following reply:

Your criticism is dealt with (implicitly) on page 4 of the paper. Just substitute “truths about the laws of logic” for “laws of logic” and the argument goes through just as well. If there’s at least one necessary truth, that’s enough for the argument. Do you want to deny that there are any necessary truths?

Derek posted a reply, which deserves further comment. However, since I don’t want to clutter Justin’s combox with technical discussion, I’m copying Derek’s reply here, with my comments interspersed:

The discussion on propositions in page 4 is found wanting. Here’s why: The English statement “Snow is white” and the German statement “Der Schnee ist weiß” are two different sentences about the same proposition.

This isn’t quite correct, at least on the conventional understanding of the sentence-proposition distinction. The sentences aren’t about a proposition; they’re about snow. Rather, the sentences express or contain a proposition: one and the same proposition, to be sure.

This is pretty elementary. If indeed snow is white, then the fact that snow is white is a proposition that merely obtains, without its needing to be expressed in any language whatsoever in order for it to obtain.

As I see it, this confuses propositions with facts (or states of affairs). Propositions can be true or false; they don’t ‘obtain’. Facts ‘obtain’; they aren’t true or false. Generally speaking (problem cases aside) a proposition is true if and only if the fact which serves as its truth-maker obtains.

Now in that case, the fact that snow is white — the proposition — is the *truthmaker*. It is a truthmaker for the possible truth of the sentence “Snow is white” or “Der Schnee ist weiß”, which are truthbearers; they are truth-apt sentences, which may have a truth-value assigned to them. This is a fairly non-controversial, standard way of parsing out the distinction between propositions and sentences.

I dispute this. Conflating facts and propositions is not at all a “fairly non-controversial, standard way” of distinguishing propositions from sentences, at least not in the literature I’m familiar with. To take one representative example:

The term ‘proposition’ has a broad use in contemporary philosophy. It is used to refer to some or all of the following: the primary bearers of truth-value, the objects of belief and other “propositional attitudes” (i.e., what is believed, doubted, etc.), the referents of that-clauses, and the meanings of sentences. . . .

Propositions, we shall say, are the sharable objects of the attitudes and the primary bearers of truth and falsity. This stipulation rules out certain candidates for propositions, including thought- and utterance-tokens, which presumably are not sharable, and concrete events or facts, which presumably cannot be false. These consequences fit well with contemporary usage.

McGrath’s definition is quite standard: propositions are truth-bearers, not truth-makers (facts). So Derek’s usage is idiosyncratic, not ours. Of course, he’s free to define words as he pleases. But we defined ‘proposition’ in an entirely conventional fashion in our paper, and our usage is consistent throughout. So if Derek wants to take issue without our definition, he’s out on a semantic limb. In any event, none of this has anything to do with the cogency of our argument.

Continuing with Derek:

I think it is *far more* controversial to claim that propositions (1) are truthbearers, since this unnecessarily multiplies the amount of truthbearers in question (beside the truth-value for proposition p, you also have a truth-value for sentence “p”), and that propositions (2) have a “nature” to them, namely that it is their “nature” to bear truth-values. This metaphysical view of propositions must be defended: that propositions have a “nature” to them is not self-evident. This “nature” of propositions sounds like a rather spooky property, if it is. Or is it that, more nominally, “nature” merely describes class-membership?

If Derek thinks that characterizing propositions as primary truth-bearers is controversial, he’ll need to take that up with the dozens of contemporary philosophers who do just that. Again, this is a standard definition in the literature. What’s more, that definition doesn’t carry any “spooky” metaphysical implications. Derek is reading more into the definition that he ought to. All we claim in the opening section of the paper is that propositions are primary truth-bearers, which means only that propositions are those things (whatever exactly they turn out to be) that (1) bear truth-values and (2) do not bear those truth-values in virtue of something more fundamental (hence primary truth-bearers). By dint of definition, then, propositions must be distinct from both sentences (which don’t bear truth-values fundamentally, as Derek’s “snow is white” example illustrates) and facts (which don’t bear truth-values at all).

As for multiplying entities beyond necessity, Derek’s own example proves our point. Sentences can’t serve as primary truth-bearers precisely because two different sentences (one English, one German) can express one and the same truth. What is that one truth? A proposition.

At any rate, page 4 could have been more precise about these issues. By the time it is said in page 4 that the laws of logic are propositions, we already have prima facie reasons to doubt that. Without a clearer account of propositions, it becomes hard to see in what sense *rules* such as the laws of logic are propositions. A rule, properly speaking, is the kind of thing that one follows. It is unlike a proposition, which is the kind of thing that one represents, say, by the utterance of a linguistic expression. A proposition is not a rule for the reason that one does not follow a proposition. A proposition is a proposition. A rule is a rule. To say that “the laws of logic are propositions” (page 4) is to problematically conflate rules with propositions.

There are a number of things to note here. First, we were very precise about our definition of ‘proposition’ in the paper. The problem is simply that Derek doesn’t like our definition. Well, he can substitute whatever word he prefers to refer to primary truth-bearers, but none of this is relevant to the cogency of our argument.

Second, Derek claims that the laws of logic are better construed as rules rather than propositions, but he gives us no reason to accept that. He simply asserts it. We, on the other hand, give a good reason for construing the laws of logic as propositions: the laws of logic are language-independent truths (see section 1 of the paper).

Third, as I already pointed out, even if we prefer to construe the laws of logic as rules, that doesn’t affect the argument, because we can simply reformulate the argument in terms of “truths about the laws of logic”. Derek simply ignored this point; but it shows why his criticism is superficial.

Finally, observe that Derek also didn’t answer my question about necessary truths. If he agrees that there are some necessary truths, that’s enough to fuel the argument; in which case, he’ll need to come up with a more substantive criticism. If he denies that there are any necessary truths, he’s even further out on a philosophical limb than his non-conventional definitions would suggest.

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