This post is inspired by this discussion.
Is the following sentence true?
(1) If the borogoves were mimsy, then the borogoves were mimsy or green.
The following is, after all, true:
(2) If the kings of Antarctica were spherical, then the kings of Antarctica were spherical or green.
It seems like (1) unproblematically expresses an analytic truth. But of course it's not so simple. In order for (1) to express an analytic truth in the obvious way that it seems to, both occurrences of "borogoves", as well as of "mimsy", must have the same meaning. But "borogoves" and "mimsy" have no meaning, and hence in particular the multiple tokenings do not have the same meaning, and so (1) is not guaranteed. Unlike (2), which is unproblematically true, whether we read it as material or subjunctive.
Well, here is a puzzle. Take a bunch of ontological terms of art: "substance", "trope", "accident", "mode", "property", "universal", "relation", "essence", "form", "participation" and "bundle". These terms figure in different theories, some ancient and some modern. It is plausible that if one of these theories is false, then it is not only contingently false, but necessarily so. Moreover, it seems likely that if one of these theories is false, then the terms of art from it not only lack reference, but are actually nonsense. But if this is right, then how can we argue against one of these theories?
The typical way is by reductio: we assume the theory and derive a contradiction. Yes, but derive how? Obviously: logically. Yes, but how can we apply logic to nonsense? We get exactly the problem we saw in (1). It seems, thus, that if our argument against the theory succeeds, it cuts off the branch it was sitting on. And why should our opponent listen to an argument that, according to its own conclusion, makes no logical sense?
Maybe we can reason conditionally. If the words "borogoves" and "mimsy" had meaning, and if they were used univocally, then sentence (1) would be true. If so, then when we engage in a reductio of a theory that we think will ultimately be non-sense, we are really making a semantic statement. If theory T is true, then terms A, B and C have meaning. But if they have meaning, then theory T entails a contradiction. Hence, theory T is not true.
But getting the logic of this reductio right is a difficult affair, I think. Consider the first part, viz., the claim that if the theory were true, then certain words would have meaning. Where do we get that claim? From the theory itself? Typically not. Consider Platonism and its technical terms, "Form" and "participation". Platonism is a set of statements about Forms and participation. It is not a set of statements about the words "Form" and "participation". It is false to say that Platonism says that the words "Form" and "participation" (in the technical sense) make sense. Perhaps the most obvious way to see that it is false is to note that in Plato's time, the words "Form" and "participation" didn't make sense because there was no English language back then. Could we say that Platonism says that "eidos" (in the technical sense) makes sense? No, for Platonism would not have been a different theory had it been developed by people who spoke Hittite instead of Greek, but "eidos" (in the technical sense) would not have made sense.
A more complicated way of looking at this is that in the reductio, we look not at a theory considered as a set of propositions, but at a set of texts, or maybe of mental acts, and we are constructing an argument that if these texts follow the standard grammar of our language, then they contradict themselves and hence are false. But, the argument continues, these texts cannot merely be false--they can only be true or nonsense; so they must be nonsense. I think this kind of works if one is careful.
Our old friend the reductio is a complex beast.