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?
Again, you have to remember that your 'observation of a bent stick' does not match all of the observations we have for bent sticks. If you put your fingers in the water and felt the stick bend, you would conclude that water bends sticks.
I don't speak for EY, but I will try to answer:
First, in that particular quote, I hold that to be a promisary note (one that you might not feel he delivered on) that once you are done reading, it shouldn't conflict with your normal intuitions. That said, I will try to answer your more specific worry.
QM's straightforward reading endorses a many-world thesis, or something much like it. One can attempt to reject MW because we do not experience this "splitting," or because it breaks down their notions of personal identity, or because they are unclear how it should alter their planning.
Saying that 'It all adds up to normality' here doesn't mean that your intuitions about, say, personal identity can't or shouldn't change on the basis of what you learn about QM or MW. What it means is that if you suddenly conclude something like "... so we don't exist" either you made an error somewhere or the theory is wrong.
Let me try to make this more concrete: Say that I decide that because of QM and MW, that buckling my seatbelt and driving safely is either useless (quantum immortality) or maybe even unethical. (because other versions of you will decide differently)
The odds are good that I've made a mistake somewhere. Probably, I've made the errors where I am thinking of my consciousness as something that is "sitting on" the quantum processes, riding them around and not getting off unless no Everett branch can support me (which is false, I am those same processes) or by not mapping onto the fact that those other Everett branches will be like me in many ways, because I am a complex system. (so if I decide to not buckle up and drive recklessly, it stands to reason that most of them will too)
Now, it is also possible that my intuitions are wrong: after all, I've never experienced meeting anyone with quantum immortality, but I don't experience all Everett branches either. But it would seem odd for quantum immortality to be true and to never find myself down an Everett branch where someone has lived for 300 years, although I haven't met every individual person either. If I did, I would conclude that consciousness did have some way of funnelling itself toward Everett branches where it was conserved. But I don't conclude that QM or MW is wrong, I conclude that the bridge theory is wrong. One matches our observations, the other does not.
Thanks again for the excellent reply. It seems to me that the work of egan's law is essentially the recommendation of this assumption once I have concluded something counterintuitive:
That this recommendation triggers with claims (which I take it may nevertheless turn out true) like quantum immortality seems to be a function of the fact that quantum immortality theory does more explaining away and less endorsing of past observations and intuitions than a rival theory. Would you say that's a fair descr... (read more)