I'm Eliezer Yudkowsky! Do you have any idea how many distinct versions of me there are in Tegmark Levels I through III?

ℵ1?

(Continued)

Page 20:

According to my proposal, what characterizes the empirical method is its manner of exposing to falsification, in every conceivable way, the system to be tested. Its aim is not to save the lives of untenable systems but, on the contrary, to select the one which is by comparison the fittest, by exposing them all to the fiercest struggle for survival.

[a number of indicative, but not decisive quotes omitted]

I had hoped to find some decisive sound bite in part one, which is a brief discussion of the epistemological problems facing any theory of scientific method, and an outline of Popper's framework, but it looks like I shall have to go deeper. Will look into this over the weekend.

I also found another, though much more recent candidate, David Deutsch in The Beginning of Infinity, Chapter 1 on "The Reach of Explanations". Tough I'm beginning to suspect that although they both point out that "you have to look at things to draw accurate maps of them...", and describe "causal processes producing map-territory correspondences" (for example, between some state of affairs and the output of some scientific instument) both Deutsch and Popper seem to have omitted what one may call the "neuroscience of epistemology." (Where the photon reflects off your shoelace, gets absorbed by your retina, leading to information about the configuration of the world becoming entangled with some corresponding state of your brain, and so on.) This is admittedly quite a crucial step, which Yudkowsky's explanation does cover, and which I cannot recall to have seen elsewhere.

A (very) quick attempt, perhaps this will suffice? (Let me know if not. )

I begin with the tersest possible defense of my claim that Popper argued that "you actually have to look at things to draw accurate maps of them...", even though this particular example is particularily trivial:

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(Thus the statement, ‘It will rain or not rain here tomorrow’ will not be regarded as empirical, simply because it cannot be refuted; whereas the statement, ‘It will rain here tomorrow’ will be regarded as empirical.)

To paraphrase: You have to look actually out the window to discover whether it is raining or not.

Continuing, page 16:

The task of formulating an acceptable definition of the idea of an ‘empirical science’ is not without its difficulties. Some of these arise from the fact that there must be many theoretical systems with a logical structure very similar to the one which at any particular time is the accepted system of empirical science. This situation is sometimes described by saying that there is a great number—presumably an infinite number— of ‘logically possible worlds’. Yet the system called ‘empirical science’ is intended to represent only one world: the ‘real world’ or the ‘world of our experience’.*1

Various objections might be raised against the criterion of demarcation here proposed. In the first place, it may well seem somewhat wrong-headed to suggest that science, which is supposed to give us positive information, should be characterized as satisfying a negative requirement such as refutability. However, I shall show, in sections 31 to 46, that this objection has little weight, since the amount of positive information about the world which is conveyed by a scientific statement is the greater the more likely it is to clash, because of its logical character, with possible singular statements. (Not for nothing do we call the laws of nature ‘laws’: the more they prohibit the more they say.)

My proposal is based upon an asymmetry between verifiability and falsifiability; an asymmetry which results from the logical form of universal statements.*4 For these are never derivable from singular statements, but can be contradicted by singular statements. Consequently it is possible by means of purely deductive inferences (with the help of the modus tollens of classical logic) to argue from the truth of singular statements to the falsity of universal statements. Such an argument to the falsity of universal statements is the only strictly deductive kind of inference that proceeds, as it were, in the ‘inductive direction’; that is, from singular to universal statements. *4 This asymmetry is now more fully discussed in section *22 of my Postscript.

(Oops, comment too long.)

Could you please quote the part of Popper's book that makes the explicit connection from the correspondence theory of truth to "there are causal processes producing map-territory correspondences" to "you have to look at things to draw accurate maps of them..."?

Right, this is the obvious next question. I started looking for the appropriate "sound bites" yesterday, but encountered a bit of difficulty in doing so, as I shall explain. Popper's embrace of (Tarskian) correspondence theory should be at least somewhat clear from the footnote I quoted above.

It seems clear to me, from my recount of the book that "you have to look at things to draw accurate maps of them" is one of the chief aims, and one of the central claims of the book; a claim which is defended, by a lengthy, but quite convincing and unusually successful argument - the premises to which are presented only one at a time, and quite meticulously over at least several chapters, so I'm not exactly sure how to go about quoting only the "relevant parts".

My claim that his argument was convincing and successful, is based on the historical observation that popperian falsificationism (the hypothetico-deductive framework) won out over the then quite prevalent logical positivist / verificationist view, to such an extent that it quickly became the default mode of Science, a position it has held, mostly uncontested, ever since, and therefore is barely worthy of mention today. Except when it is, that is; when one encounters problems that are metaphysical (according to Popper), such as Susskind's String Landscape of perhaps 10^500 vacuua, the small (but significant) observed value of the cosmological constant, the (seemingly fine tuned) value of the fine structure constant, and other observations that may require anthropic i.e. metaphysical explanations, since these problems are seemingly not decidable inside of standard, i.e. popperian science.

I feel faced with a claim similar to "I don't believe any mathematician has convincingly proven Fermat's last theorem." To which I reply: Andrew Wiles (1995) The obvious next question is: "Can you please quote the part where he proves the theorem?" This is unfortunately somewhat involved, as the entire 109 page paper tries and succeds at doing so around as concisely as Wiles himself managed to go about it. Unfortunately, in the Popper case, I cannot simply provide the relevant Wikipedia Article and leave it at that.

I suppose that having made the claim, it is only my duty to back it up, or else concede defeat. If you're still interested, I shall give it a thorough look, but will need a bit of time to do so. Hopefully, you'll have my reply before monday.

I also can't think of a philosopher who has made an explicit connection from the correspondence theory of truth to "there are causal processes producing map-territory correspondences" to "you have to look at things to draw accurate maps of them..."

Karl Popper did so explicitly, thoroughly and convincingly in The Logic of Scientific Discovery. Pretty influential, and definitely a part of "Mainstream Academia."

Here's an interesting, if lengthy, footnote to Chapter 84 - Remarks Concerning the use of the concepts 'True' and 'Corroborated'.

(1) Not long after this was written, I had the good fortune to meet Alfred Tarski who explained to me the fundamental ideas of his theory of truth. It is a great pity that this theory—one of the two great discoveries in the field of logic made since Principia Mathematica—is still often misunderstood and misrepresented. It cannot be too strongly emphasized that Tarski’s idea of truth (for whose definition with respect to formalized languages Tarski gave a method) is the same idea which Aristotle had in mind and indeed most people (except pragmatists): the idea that truth is correspondence with the facts (or with reality). But what can we possibly mean if we say of a statement that it corresponds with the facts (or with reality)? Once we realize that this correspondence cannot be one of structural similarity, the task of elucidating this correspondence seems hopeless; and as a consequence, we may become suspicious of the concept of truth, and prefer not to use it. Tarski solved (with respect to formalized languages) this apparently hopeless problem by making use of a semantic metalanguage, reducing the idea of correspondence to that of ‘satisfaction’ or ‘fulfilment’. As a result of Tarski’s teaching, I no longer hesitate to speak of ‘truth’ and ‘falsity’. (...)

A (short) footnote of my own: Popper's writings have assumed the status of mere "background knowledge", which is a truly great achievement for any philosopher of science. However, The Logic of Scientific discovery is a glorious book which deserves to be even more widely read. Part I of the book spans no more than 30 pages. It's nothing short of beautiful. PDF here.

Yep. Gloriously lucid and quite readable book.
Encapsulates good chunks of the sequences.

Much more accessible than I had anticipated.

But we can claim every star that now burns.

No, we can't. As I said, distant galaxies that we can see today are receding, such that no probe we send can ever reach them. Barring aliens already nearby, they will burn unclaimed.

Ouch! I had originally written "every star that burns in the night sky". But that sounded cheesy and pompous even in the context of the comment above. Apparently I failed to replace it with something reasonable before hitting the button.

Perhaps only every star and planet in every galaxy within a sphere centered at earth with a radius of at least a couple of billion light years will be in reach of our technologically mature descendants.

Even as distant civilizations trillions of years hence are lost to each other, forever separated by the expansion of space, their neighbors receding over the cosmological horizon, there can still be rich life in those bubbles. If we survive this eon, life can flourish for the next hundred trillion years.

After that we may be in trouble. After that the cynics may win.

We'll fill the stars and conquer death. The spark of intelligence and sentience will not extinguish.

No we won't, barring new physics. Even if our civilization avoids catastrophe and invents great improvements in therapies for aging, or brain emulation, that won't let us change the 2nd law of thermodynamics, or prevent the distant galaxies from accelerating out of our reach.

But we can claim every star that now burns. Even if in the vast, long, unimaginably long future of this universe, complexity itself must someday die, we should at least do what we can in the meantime. Perhaps we can't beat physics, but we do have some headroom still!

I found this thread to be "vapid and melodramatic" at first, but I now recognize that humanity did indeed lose something highly valuable with the death of Neil Armstrong, outside and beyond the tragedy that is inherent to the death of any mind.

A spark of intelligence and sentience, a very keen observer, but also, literally the first member of our species to transcend to another world, even if it were for a very brief time. Within a decade or two, human kind will likely no longer have visitors to other worlds among us. Were I a journalist, I would write: "A small death for a man, a giant leap backwards for mankind."

Armstrong, and his fellow Apollo astronauts are to us like the astronauts in Carl Sagan's novel Contact. Ambassadors from the Blue Dot to the vast dead Cosmos. Humanity no longer has it's eyes facing outwards to the other pebbles, to the other stars that burn with unspent opportunity. With their deaths we lose the steady gaze of those who look up, since they have been there, whereas we have not. We lose their voices, and their dreams of someday returning, of someday going beyond 1969.

O you who turn the wheel and look to windward,
Consider Phlebas, who was once handsome and tall as you.

May his footprints someday be lost to the footprints of many.

Someday going beyond 1969 is a crazy ambitious idea today, but seemingly wasn't so crazy before the late seventies/mid-eighties. I'm too young to tell, but it seems this ambition went from bold to crazy somethime around end of the cold war, perhaps as the salient threat of thermonuclear doom faded.

What do you think of contemporary theoretical physics? That is also mostly "arguing on the Internet".

Some of it yes. At the end of the day though, some of it does lead to real experiments, which need to pay rent. And some of it does quite well at that. Look for example at the recent discovery of the Higgs boson.

These theoretical physicists had to argue for several decades until they managed to argue themselves into enough money to hire the thousands of people to design, build and operate a machine that was capable of refuting, or as it turned out - supporting their well motivated hypothesis. Not to mention that the machine necessitated inventing the world wide web, advancing experimental technologies, data processing, and fields too numerous to mention by orders of magnitude compared to what was available at the time.

Perhaps today's theoretical programmers working on some form of General Artificial Intelligence find themselves faced with comparable challenges.

I don't know how things must have looked like at the time, perhaps people were wildly optimistic with respect to expected mass of the scalar boson(s) of the (now) Standard Model of physics, but in hindsight, it seems pretty safe to say that the Higgs boson must have been quite impossible for Humanity to experimentally detect back in 1964. Irrefutable metaphysics. Just like string theory, right?

Well, thousands upon thousands of people, billions of dollars, some directly but mostly indirectly (in semiconductors, superconductors, networking, ultra high vacuum technology, etc.) somehow made the impossible... unimpossible.

And as of last week, we can finally say they succeeded. It's pretty impressive, if nothing else.

Perhaps M-theory will be forever irrefutable metaphysics to mere humans, perhaps GAI. As Brian Greene put it: "You can't teach general relativity to a cat." Yet perhaps we shall see further (now) impossible discoveries made in our lifetimes.