-4 [deleted] 13 July 2012 07:24PM

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?

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Comment author: 13 July 2012 07:57:39PM 15 points [-]

I think you're arguing up the entirely wrong tree. Normality is what you've seen before: your history of previous observations. Egan's law is that any new theory must predict what you've already seen. Einsteinian mechanics must predict roughly Newtonian behavior, otherwise it's already falsified!

Comment author: 13 July 2012 09:52:12PM *  2 points [-]
• "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."

This pretty much sums it up; if you're looking for more, you won't find it. Egan's Law doesn't guarantee a theory has explanatory power, it only sets a restriction on what theories might. Suppose a new theory (using the term loosely) is proposed, and the theorist helpfully provides tests to falsify it. If the theory contradicts current (in the sense of currently known) observations (distinct from current -explanations- of those observations), you don't need to perform those tests, because it has already been falsified.

To use an example brought up in the comments, any theory which predicts that the stick should appear the same to you when dipped into the water can be discarded under Egan's Law, because this wasn't the case.

Consider Egan's Law this way: Existing observations should be treated as falsification tests. In Bayesian terms, existing observations should be used in calculating your priors. (Egan's Law appears to be used on these boards most specifically to refer to the observations made in falsification tests of the theory you intend to supplant; since I can't find a formal formulation, I'm not sure if this is a strict part of its use.)

Comment author: [deleted] 13 July 2012 10:20:07PM 0 points [-]

Consider Egan's Law this way: Existing observations should be treated as falsification tests.

Observations are intensional in this sense: when I observe something, I observe that something is such and such. So I observe that the stick is bent. The trouble is, that this observation can't be included in the 'normal' since it can be overturned. It's theory laden, and on a correct theory, this theory laden observation is false.

If Egan's law (on a strict reading) is true, however, mere observations must be un-overturnable. So in fact I never observed that the stick was bent, rather I observed that it appeared bent, or I observed such and such a sense-datum which I interpreted (falsely) to indicate a bent stick. These 'appear that...' sentences or sense data sentences look promising because they don't look falsifiable. I can't be mistaken about what appears to be so, only about what actually is so.

The problem with this, I think, is that the 'normal' now looks quite narrow. If this is normality, nothing prevents external world skepticism, say, from preserving normality. Nor is anything interesting actually preserved: a physical theory needn't preserve the rising of the sun, the blueness of the sky, or free will so long as it preserves or explains the appearance of these things. But to explain that the sky appears blue is consistant with denying, ultimately, that it is blue.

Comment author: 14 July 2012 01:03:42AM *  2 points [-]

You seem to be confusing your observation that a stick was bent with an actual stick bending.

The difference being that the mere observation of a stick that is bent does not have (in the case of it being in a glass of water) all of the other observational properties of a bent stick.

If, when you put a stick in water, it had all the other observational properties of a bent stick (example: you put your hand in the water and feel the bend in the stick) then you would conclude that "water bends sticks" and this would add up to normality.

But that's not what happens, so you conclude that the stick didn't actually bend. But you don't just throw away your observation of "I saw the stick bend" either. Instead, you use another theory that can explain the visual appearance of a bent stick without the stick needing to actually bend.

The fact that you observed X is not overturned by a theory that says you couldn't have. Instead, the observation overturns the theory.

As to external world skepticism, etc. Egan's law does not, strictly speaking, falsify them. But it renders them improbable. External world skepticism does not predict a blue sky as well as physics does. It doesn't make the statement that the sky will be blue. Physical realism combined with out knowledge of physics does make this statement. This makes physical realism more probable than external world skepticism. If it did not seem that, in principle, experiments regarding reality were able to explain it than we wouldn't use experiments and probably would be required to believe something like external world skepticism.

Incidentally, physics DOES deny, in some senses, that "the sky is blue," without denying that it appears blue. Blueness, as it turns out, is not a primary property (and it is only by not looking at history that we don't realize that this is a revolutionary discovery) the sky doesn't have "blueness" inside of it. Nevertheless, optics can tell us why the sky appears blue, without some blueness being inherent in the sky.

Comment author: [deleted] 14 July 2012 01:41:51PM 1 point [-]

You seem to be confusing your observation that a stick was bent with an actual stick bending.

I may be confusing them, but it was my intention to draw out a distinction between 'appearance' sentences and 'fact stating' sentences, so as to show that 'normality' couldn't include any of the latter. That's the whole substance of my argument against Egan's law.

Egan's law does not, strictly speaking, falsify them. But it renders them improbable.

This depends on how you read Egan's law: as a heuristic or (as I put it in my original post), an a priori necessary condition on the truth of a theory. I think the sequences present that latter, stronger reading. I don't have any problem with the weaker reading.

Comment author: 14 July 2012 05:30:31PM *  2 points [-]

I don't follow why that distinction is important in this case: Egan's law (combined with some observation) can act both as a falsification criteria for some theories and to adjust the probability of other theories.

Take three theories regarding your stick:

A: There is no real stick, only the illusion of a stick. (Roughly, external world skepticism) B: There is a real stick, and it did not bend but appeared to bend. (Physical realism regarding the properties of sticks and optics) C: You never observed a stick bending.

C is falsified, given Egan's law and the observation. A is not falsified, but A doesn't predict that you'd see a stick bend in water. B does predict this, as B incorporates optics and physical theories of light into itself. If A violated Egan's law, it would violate the "necessary condition" and be falsified. It doesn't, it is just rendered less probable while B is made to be more probable.

Remember that 'falsify' really only means 'renders highly improbable.' So there is no contradiction in saying that Egan's law will sometimes render something highly improbable (reduced it's probability by several sigma) and will sometimes only render something slightly less probable. Even the probability that something is false given that it is a logical contradiction is only the prior probability of that thing being true, times the probability it is true given that it is a logical contradiction, divided by the probability of logic being true. That P(A|B) is very near zero and P(B) is very near 1 in this case does not change this.

Comment author: [deleted] 14 July 2012 06:07:43PM 0 points [-]

I like your analysis here, thanks. I remain unsure about what it means to combine egan's law ith some observation, as opposed to just testing a theory against an observation. Does Egan's law mean nothing more than 'theories ought to be tested against past, as well as future observations'? I admit, I find this hard to disagree with, but I'm not sure what this has to do with adding up to normality. Again, thanks for the excellent explanation.

Comment author: 14 July 2012 10:47:13PM 1 point [-]

What 'adding up to normality' means here is that 'theories should match observations, past and present.'

See, sometimes people encounter weird theories that are also true, quantum mechanics being the classic example here. So people make the mistake of thinking that the strangeness of the theory equates to the truth of it, and they end up believing weird things because they are weird and not because they are consistent with their experiences.

Example: I once encountered a group who tried to convince me that a 2x2 square should have an area of 2. They agreed that the area of a 1x1 square should be one, that 2 divides into two 1s, and that when you divided a 2x2 square this way you got four 1x1 squares. They then went on to say that I was just using the 'standard' definition of a 2x2 square. One of the mistakes they made was ignoring when their theory did not match their observations.

If that behavior seems intuitively like a mistake to you, then good. You probably don't have to worry too much about it, relative to other common mistakes that people make.

Comment author: [deleted] 14 July 2012 11:13:29PM *  0 points [-]

'theories should match observations, past and present.'

But you must mean 'theories should take account of observations, past and present' since no theory should have to match my observation of a bent stick (though, we agree, it should explain why I think I see a bent stick). Theories shouldn't be bound to endorse past observations, just bound to either endorse them or explain them. (Unless we assume all observations are necessarily true, and to do this I assume we would have to move into a language of sense data or something...but thar be dragons).

So people make the mistake of thinking that the strangeness of the theory equates to the truth of it, and they end up believing weird things because they are weird and not because they are consistent with their experiences.

That's not the work Egan's law seems to do in, say, "Living in Many Worlds". There, Egan's law is invoked to dispel seeming implausibility or surprisingness of quantum physics. Here:

Some commenters have recently expressed disturbance at the thought of constantly splitting into zillions of other people, as is the straightforward and unavoidable prediction of quantum mechanics.

Others have confessed themselves unclear as to the implications of many-worlds for planning: If you decide to buckle your seat belt in this world, does that increase the chance of another self unbuckling their seat belt? Are you being selfish at their expense?

Just remember Egan's Law: It all adds up to normality.

What's EY using Egan's law to say here? It's not that quantum physics shouldn't be accepted because it's weird (though, of course, it shouldn't be accepted for that reason), but rather that one shouldn't worry about the interaction of the theory of quantum physics with everyday phenomena like choice, deliberation, personal identity, and free will. Further, EY will claim that the theory does in fact interact with these things. Quantum mechanics isn't entirely irrelevant to the question of personal identity, for example, because it actually helps show why a certain view of personal identity (the 'same atoms' view) is nonsense.

Egan's law is used to argue that even though quantum mechanical theory is relevant to phenomena like identity and free will, it is somehow guaranteed endorse these phenomena to the extent that our ethical intuitions get preserved.

But of course, on your (if you accept my amendment) understanding of Egan's law, namely

What 'adding up to normality' means here is that 'theories should account for observations, past and present.'

A theory can (though is unlikely to) add up to normality without endorsing any of our past observations. So nothing at all prevents quantum mechanics from simply denying that we have free will or personal identity (so long as it explains why we think we do) to an extent that renders our ethical intuitions moot. Just to be clear, I doubt that quantum mechanics can or does do anything of the kind. But at any rate, on that understanding of Egan's law, its argumentative use in the sequences is wholly illicit.

Comment author: 14 July 2012 11:42:30PM 1 point [-]

But you must mean that 'theories take account of observations, past and present' since no theory should have to match my observation of a bent stick.

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.

That's not the work that Egan's law seems to do in, say, "Living in Many Worlds".

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.

Comment author: [deleted] 15 July 2012 04:16:23PM 0 points [-]

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:

The odds are good that I've made a mistake somewhere.

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 description of Egan's law then: a theory should be preferred if it endorses rather than explains away a greater proportion of past observations. If so (this seems very plausible to me), then egan's law is a statement about the iterative nature of theoretical activity, rather than a statement about adding up to some absolute sphere of normality. After all, if we dragged a Cartesian physicist through time to learn some quantum physics, I doubt he would admit that it adds up to anything normal, all the way down to meta ethical concerns.

So is that egan's law? That theoretical activity should always be an interation on past theory?

Comment author: 14 July 2012 11:51:22AM *  0 points [-]

I just want to reiterate what asparisi said above, because it's an awesome point. "The sky is blue" is just a short-hand for "my brain converts this specific wavelength that enters into the eyes into an experience of blue". And then you realize that most (or even all) observations are of this type, they start with a subjective experience. Luckily these subjective experiences are more or less persistent over time and across humans, so we assume a shared persistent "reality".

Comment author: [deleted] 14 July 2012 01:46:47PM 0 points [-]

I just want to reiterate what asparisi said above, because it's an awesome point. "The sky is blue" is just a short-hand for "my brain converts this specific wavelength that enters into the eyes into an experience of blue".

I'm not sure this is relevant. I'm happy to just use variables for these sentences, since their content isn't important to my point.

Comment author: 13 July 2012 07:49:20PM *  2 points [-]

I don't understand most of what you said (did you really need Greek letters to spell English names of logical predicates derived from German words?), but here is my instrumental understanding of this idea. If you perceive an apple as green, any model of apples/colors/light/perceptions/truths should output "green" in reply to "what color is this apple?".

Comment author: [deleted] 13 July 2012 08:28:31PM *  1 point [-]

I don't understand most of what you said (did you really need Greek letters to spell English names of logical predicates derived from German words?)

All my greek letters are just variables standing in for sentences, not logical predicates (and none of them have english names). I explained that here:

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.

-

If you perceive an apple as green, any model of apples/colors/light/perceptions/truths should output "green" in reply to "what color is this apple?".

Right, or some translation of 'green' like 'such and such a wavelength'.

Comment author: 13 July 2012 09:32:17PM 4 points [-]

All my greek letters are just variables standing in for sentences, not logical predicates (and none of them have english names).

Comment author: [deleted] 13 July 2012 09:36:48PM 3 points [-]

Yikes, that's not what I see. But I think I know what the problem is, and I'll try to fix it. Thanks for pointing it out.