I think that the idea of ‘adding up to normality’ is incoherent, but maybe I don’t understand it. There is a rule of thumb that, in general, a theory or explanation should ‘save the phenomena’ as much as possible. But Egan’s law is presented in the sequences as something more strict than an exceptionable rule of thumb. I’m going to try to explain and formalize Egan’s law as I understand it so that once it’s been made clear, we can talk about how we would argue for it.
If a theory adds up to normality in the strict sense, then there are no true sentences in normal language which do not have true counterparts in a theory. Thus, if it is true to say that the apple is green, a theory which adds up to normality will contain a sentence which describes the same phenomenon as the normal language sentence, and is true (and false if the normal language sentence is false). For example: if an apple is green, then light of such and such wavelength is predominantly reflected from its surface while other visible wavelengths are predominantly absorbed. Let’s call this the Egan property of a theory. A theory would fail to add up to normality either if it denied the truth of true sentences in normal language (e.g. ‘the apple isn’t really green’) or if it could make nothing of the phenomenon of normal language at all (e.g. nothing really has color).
t has the property E = for all a in n, there is an α in t such that a if and only if α
t is a theoretical language and ‘α ‘is a sentence within it, n is the normal language and ‘a’ is a sentence within it. E is the Egan property. Now that we’ve defined the Egan property of a theory, we can move on to Egan’s law.
The way Egan’s law is articulated in the sequences, it seems to be an a priori necessary but insufficient condition on the truth of a theory. So it is necessary that, if a theory is true, it has the Egan property.
If α1, α2, α3..., then Et.
Or alternatively: If t is true, then Et.
That’s Egan’s law, so far as I understand it. Now, how do we argue for it? There’s an inviting, but I think troublesome Tarskian way to argue for Egan’s law. Tarski’s semantic definition of truth is such that some sentence β is true in language L if and only if b, where b is a sentence is a metalanguage. Following this, we could say that for any theory t to be true, all its sentences α must be true, and what it means for any α to be true is that a, where a is a sentence in the metalanguage we call normal language. But this would mean that a and α are strictly translations of one another in two different languages. If a theory is going to be explanitory of phenomena, then sentences like “light of such and such wavelength is predominantly reflected from the apple’s surface while other visible wavelengths are predominantly absorbed” have to have more content than “the apple is green”. If they mean the same thing, as sentences in Tarski’s definition of truth must, then theories can’t do any explaining.
So how else can we argue for Egan’s law?