“The Ruliad”: Wolfram in Borges’ Library

I think people have mostly stopped taking Stephen Wolfram very seriously. He did some great work early in his career, at CalTech and the Institute for Advanced Study, and (with a certain amount of intellectual property mess) went on to create Mathematica, which was and is very cool.

Then in 1992 he disappeared into a garret or something for a decade, and came out with the massive A New Kind of Science, which got a lot of attention because it was Wolfram after all, but which turned out to be basically puffery. And a certain amount of taking credit for other people’s earlier work.

Being wealthy and famous, however, and one imagines rather surrounded by yes-folks, Wolfram continues in the New Kind of Science vein, writing down various things that sound cool, but don’t appear to mean much (as friend Steve said when bringing the current subject to my attention, “Just one, single, testable assertion. That’s all I ask”).

The latest one (or a latest one) appears to be “The Ruliad”. Wolfram writes:

I call it the ruliad. Think of it as the entangled limit of everything that is computationally possible: the result of following all possible computational rules in all possible ways.

It’s not clear to me what “entangled” could mean there, except that it’s really complicated if you try to draw it on a sheet of paper. But “the result of following all possible computational rules in all possible ways” is pretty clearly isomorphic to (i.e. the same thing as) the set of all possible strings. Which is to say, the set of all possible books, even the infinitely-long ones.

(We can include all the illustrated books by just interpreting the strings in some XML-ish language that includes SVG. And it’s probably also isomorphic to the complete graph on all possible strings; that is, take all of the strings, and draw a line from each one to all of the others. Or the complete graph on the integers. Very entangled! But still the same thing for most purposes.)

Now the set of all possible strings is a really amazing thing! It’s incomprehensibly huge, even if we limit it to finite strings, or even finite strings that would fit in a reasonably-sized bound volume.

And if we do that latter thing, what we have is the contents of the Universal Library, from Borges’ story “The Library of Babel”. As that story notes, the Library contains

All — the detailed history of the future, the autobiographies of the archangels, the faithful catalog of the Library, thousands and thousands of false catalogs, the proof of the falsity of those false catalogs, a proof of the falsity of the true catalog, the gnostic gospel of Basilides, the commentary upon that gospel, the commentary on the commentary on that gospel, the true story of your death, the translation of every book into every language, the interpolations of every book into all books, the treatise Bede could have written (but did not) on the mythology of the Saxon people, the lost books of Tacitus.

Borges — The Library of Babel

It also contains this essay, and A New Kind of Science, and every essay Wolfram will ever write on “the Ruliad”, as well as every possible computer program in every language, every possible finite-automaton rule, and to quote Wolfram “the result of following all possible computational rules in all possible ways.” (We’ll have to allow infinite books for that one, but that’s a relatively simple extension, heh heh.)

So, it’s very cool to think about, but does it tell us anything about the world? (Spoiler: no.) Wolfram writes, more or less correctly:

it encapsulates not only all formal possibilities but also everything about our physical universe—and everything we experience can be thought of as sampling that part of the ruliad that corresponds to our particular way of perceiving and interpreting the universe.

and sure; for any fact about this particular physical universe (or, arguably, any other) and anything that we experience, the Library of Babel, the set of all strings, the complete graph on all strings, “the Ruliad”, contains a description of that fact or experience.

Good luck finding it, though. :)

This is the bit that Wolfram seems to have overlooked, depending on how you read various things that we writes. The set of all strings definitely contains accurate statements of the physical laws of our universe; but it also contains vastly more inaccurate ones. Physicists generally want to know which are which, and “the Ruliad” isn’t much help with that.

Even philosophers who don’t care that much about which universe we happen to be in, still want correct or at least plausible and coherent arguments about the properties of formal systems, or the structure of logic, or the relationship between truth and knowledge, and so on; the Universal Library / “Ruliad” does contain lots of those (all of them, in fact), but it provides no help in finding them, or in differentiating them from the obviously or subtly incorrect, implausible, and incoherent ones.

There is certainly math that one can do about the complete graph over the set of all strings, and various subgraphs of that graph. But that math will tell you very little about the propositions that those strings express. It’s not clear that Wolfram realizes the difference, or realizes just how much the utter generality of “the Ruliad” paradoxically simplifies the things one can say about it.

For instance, one of the few examples that Wolfram gives in the essay linked above, of something concrete that one might study concerning “the Ruliad” itself, is:

But what about cases when many paths converge to a point at which no further rules apply, or effectively “time stops”? This is the analog of a spacelike singularity—or a black hole—in the ruliad. And in terms of computation theory, it corresponds to something decidable: every computation one does will get to a result in finite time.

One can start asking questions like: What is the density of black holes in rulial space?

It somewhat baffles me that he can write this. Since “the Ruliad” represents the outputs of all possible programs, the paths of all possible transition rules, and so on, there can be no fixed points or “black holes” in it. For any point, there are an infinite number of programs / rules that map that point into some other, different point. The “density of black holes in rulial space” is, obviously and trivially, exactly zero.

He also writes, for instance:

A very important claim about the ruliad is that it’s unique. Yes, it can be coordinatized and sampled in different ways. But ultimately there’s only one ruliad.

Well, sure, there is exactly one Universal Library, one set of all strings, one complete graph on the integers. This is, again, trivial. The next sentence is just baffling:

And we can trace the argument for this to the Principle of Computational Equivalence. In essence there’s only one ruliad because the Principle of Computational Equivalence says that almost all rules lead to computations that are equivalent. In other words, the Principle of Computational Equivalence tells us that there’s only one ultimate equivalence class for computations.

I think he probably means something by this, well maybe, but I don’t know what it would be. Obviously there’s just one “result of following all possible computational rules in all possible ways”, but it doesn’t take any Principle of Computational Equivalence to prove that. I guess maybe if you get to the set of all strings along a path that starts at one-dimensional cellular automata, that Principle makes it easier to see? But it’s certainly not necessary.

He also tries to apply terminology from “the Ruliad” to various other things, with results that generally turn out to be trivial truths when translated into ordinary language. We have, for instance:

Why can’t one human consciousness “get inside” another? It’s not just a matter of separation in physical space. It’s also that the different consciousnesses—in particular by virtue of their different histories—are inevitably at different locations in rulial space. In principle they could be brought together; but this would require not just motion in physical space, but also motion in rulial space.

What is a “location in rulial space”, and what does it mean for two things to be at different ones? In ordinary language, two things are at different points in “rulial space” if their relationships to other things are not the same; which is to say, they have different properties. (Which means that separation in physical space is in fact one kind of separation in “rulial space”, we note in passing.) So this paragraph says that one human consciousness can’t get inside another one, because they’re different in some way. And although you might somehow cause them to be completely identical, well, I guess that might be hard.

This does not seem like a major advance in either psychology or philosophy.

Then he gets into speculation about how we might be able to communicate between “different points in rulial space” by sending “rulial particles”, which he identifies with “concepts”. The amount of hand-waving going on here is impressive; Steve’s plea for a falsifiable claim is extremely relevant. In what way could this possibly turn out to be wrong?

(It can, on the other hand, easily turn out to be not very useful, and I think so far it’s doing a good job at that.)

He also proceeds, hands still waving at supersonic speed, to outline a Kantian theory that says that, although “the Ruliad” contains all possible laws of physics, we seem to live in a universe that obeys only one particular set of laws. This, he says, is because “for observers generally like us it’s a matter of abstract necessity that we must observe general laws of physics that are the ones we know”.

What “observers like us” means there is just as undefined as it was when Kant wrote the same thing only with longer German words. He goes on like this for some time, and eventually writes:

People have often imagined that, try as we might, we’d never be able to “get to the bottom of physics” and find a specific rule for our universe. And in a sense our inability to localize ourselves in rulial space supports this intuition. But what our Physics Project seems to rather dramatically suggest is that we can “get close enough” in rulial space to have vast predictive power about how our universe must work, or at least how observers like us must perceive it to work.

which is basically just gibberish, on the order of “all we have to do is find the true physics text in the Universal Library!”.

It’s hard to find anyone but Wolfram writing on “the Ruliad” (or at least I haven’t been able to), but the Wolfram essay points to an arxiv paper “Pregeometric Spaces from Wolfram Model Rewriting Systems as Homotopy Types” by two authors associated with Wolfram Research USA (one also associated with Pompeu Fabra University in Barcelona, and the other with the University of Cambridge in Cambridge, and one does wonder what those institutions think about this). That paper notably does not contain the string “Ruliad”. :)

I may attempt to read it, though.

God is not a source of objective moral truth

I mean, right?

I’ve been listening to various youtubers, as mentioned forgetfully in at least two posts, and some of them spend considerable time responding to various Theist, and mostly Christian, Apologists and so on.

This is getting pretty old, to be honest, but one of the arguments that goes by now and then from the apologists is that atheists have no objective basis for moral statements; without God, the argument goes, atheists can’t say that torturing puppies or whatever is objectively bad. Implicit, and generally unexamined, is a corresponding claim that theists have a source of objective moral statements, that source being God.

But this latter claim is wrong.

What is an objective truth? That is a question that tomes can be, and have been, written about, but for now: in general an objective truth is a true statement that, once we’re clear on the meanings of the words, is true or false. A statement on which there is a fact of the matter. If Ben and I can agree on what an apple is, which bowl we’re talking about, what it means to be in the bowl, and so on, sufficient to the situation, then “there are three apples in the bowl” is objectively true, if it is. If Ben insists that there are six apples in the bowl, and we can discover that for some odd reason Ben uses “an apple” to refer to what we would think of as half an apple, we have no objective disagreement.

What is a moral truth? Again, tomes, but for now: a moral truth is (inter alia) one that provides a moral reason for action. A typical moral truth is “You should do X” for some value of X. In fact we can say that that (along with, say, “You should not do X“) is the only moral truth. No other fact or statement has moral bearing, unless it leads to a conclusion about what one should do.

(We will take as read the distinction between conditional and categorical imperatives, at least for now; we’re talking about the categorical imperative, or probably equally well about the “If you want to be a good person, you should X” conditional one.)

What would an objective moral truth look like, and where would it come from? We would have to be able to get to a fact of the matter about “You should do X” from things about which there are facts of the matter, modulo word meanings. The theist is almost certainly thinking that the argument is simple and looks like:

• You should do what God wants,
• God wants you to do X,
• You should do X.

Since we’re talking about whether the theist’s argument works, we stipulate that God exists and wants you (me, us, etc.) to do X for some X. And if we should do what God wants, we should therefore do X.

But is it objectively true that we should do what God wants?

If I disagree, and say that I don’t think we should do what God wants, the theist can claim that we differ on the meanings of words, and that what they mean by “should do” is just “God wants you to do”. But that’s not very interesting; under those definitions it’s just a tautology, and “you should do X” turns out not to be a moral truth, since “should do X” may no longer be motivating.

To get further, the theist will have to claim that “God wants you to do X” implies “You should do X” in the moral sense of “should”; that it’s objectively motivating. And it’s not clear how that would work, how that claim is any stronger than any other. A utilitarian can equally say “X leads to the greatest good for the greatest number” is objectively motivating, a rule-utilitarian can say that “X follows the utility-maximizing feasible rules” is objectively motivating, and so on.

(“You should do X because God will punish you if you don’t” can be seen as objectively motivating, but not for moral reasons; that’s just wanting to avoid punishment, so not relevant here.)

Why would someone think that “You should do what God wants you to do” is any more objectively true than “You should do what maximizes utility” or “You should do what protects your family’s honor”? I don’t find myself with anything useful to say about that; because they grew up hearing it, or they’ve heard it in Church every Sunday or whatever, I suppose?

So that’s that. See title. :) Really we probably could have stopped at the first sentence.

Flash-loan attacks, also LegalEagle on crypto

If you type “flash” into the search box on good ol’ Web3 Is Going Just Great, it’s very likely that you’ll get a lot of hits; at the moment there are nearly a dozen just in the last two months.

I haven’t studied these all in detail, but I think I can outline a representative flash-loan attack in enough detail and generality to be instructive and/or amusing.

Consider this small recipe, embodied as a piece of code:

1. For a small fee, borrow a jillion FooCoins for a very small period of time, like the time that this program will take to run.
2. Use those FooCoins to purchase 51% of the FooAdmin coins that determine who gets to vote on actions of the FooDAO (Distributed Autonomous Organization).
3. Having control of the FooDAO, transfer all of the five-jillion FooCoins owned by the DAO to yourself.
4. Sell the FooAdmin coins purchased in (2), for some amount of FooCoins, probably less than a jillion, maybe zero, I’m not clear on this part, see below.
5. Pay back the jillion FooCoins borrowed in (1).
6. Make off with a net profit of four-jillion FooCoins, minus the small fee in (1), plus the possible proceeds from selling the empty husk in (4).

One interesting fact about this is that every step appears to be using some feature of the overall system exactly as it was intended to be used: there are no stolen passwords, no impersonation, no stack overflows. Prosecutions or lawsuits seem relatively unlikely; it would be interesting to see how one goes!

Another interesting fact about this is that it’s basically the way that Mitt Romney and other “Vulture Capitalists” got rich: find a company whose assets are worth more than it would take to buy the company, get a loan, buy the company, sell off the assets, pay off the loan, and profit, leaving an empty husk of a company behind.

Only it’s much, much faster.

People have talked about various ways to keep these things from working:

Flash loans seem bizarre; I don’t know what non-nefarious uses they have. On the other hand, since they are really just programs, it’s unclear how (especially in the Free and Decentralized Web3 World) one would prevent people from creating them, in order to profit by supplying services to even nefarious uses.

It’s also not clear to me that the DAO administrative coins should just be sitting around for sale to anyone with enough money; given what they do, perhaps one would like actual human judgment involved. On the other hand, that also goes against the basic Code Is Law And Everything Is For Sale principles of Web3.

Perhaps, even if flash loans have to be allowed and buying DAO administrative coins has to be allowed, maybe they shouldn’t be allowed to intersect. In the traditional market, you aren’t supposed to buy big things like cars and houses (and down-payments on loans) using borrowed money, to prevent this sort of privilege-amplification via cash. That seems like it would be hard to enforce without significant additions to the relevant protocols; like, a FooCoin would have to remember that it’s borrowed and will need to be paid back, and who wants to clutter up the free simple Web3 world with stuff like that?

Perhaps someone should have to have owned a DAO administrative coin for more than a millisecond before they can vote the share that it represents. A few days maybe even. I think this is being seriously considered by some DAOists. (Haha “DAOists”; have you read “The Confessions of a Taoist on Wall Street”? Good book, long predating cryptocurrencies.)

Perhaps in general FooDAO shouldn’t own more FooCoins than the value of 51% of the FooAdmin coins that exist. But, as with the traditional companies, it’s not all that unusual for a company to own more assets than the company (or just a controlling interest in it) would cost, it just means that they’ve been accumulating stuff to use to make money by doing whatever the company is in business to do, but haven’t made that money yet. And in the area of DAOs, it’s not clear to me whether it’s perhaps possible to get enough by reselling the husk in step (4) that this isn’t actually necessary anyway. Also there are “liquidity pools” that I should read about sometime.

This here above is a specific type of flash loan attack; the most impressive and amusing kind that I know of. More generally, there are various kinds of flash loans where someone pays a small fee to acquire a jillion FooCoins, uses those FooCoins to play fun lucrative tricks in the market (all the more feasible where liquidity is low, things are generally unstable, unregulated, etc), and then pays back the loan with a fraction of the resulting booty.

So that’s that Fun Idea o’ the Day! :)

Relatedly, the very interesting Legal Eagle YouTube channel / person / lawyer recently had a (what do you call them?) thing called “NFTs are legally problematic“, all about how NFTs are legally problematic, for reasons including the contract and copyright things that we wondered about back in previous posts here in the weblog, and benefiting from actual real legal concepts like “privity of contract”, which says that a contract can’t confer rights or impose obligations on anyone who hasn’t signed it (and which leads us to wonder for instance how someone who uses Opensea to buy some NFT that I’ve put up for sale, can acquire any rights in that, since I’ve never heard of them, let alone signed a contract with them; I dunno).

Anyone interested in the vaguely-legal NFT stuff that I’ve talked about here will probably be interested in that Legal Eagle video. There’s another one, also by Legal Eagle, about the usefulness (or otherwise) of NFTs for creators, and it’s over on Nebula and/or CuriosityStream; here is a link that probably requires some kind of membership in something.

I don’t entirely understand Nebula and/or CuriosityStream (including, clearly, being able to tell them apart), but there seem to be various interesting videos (that’s the word: videos!) on it/them, and various people that I like to listen to (including Legal Eagle and Jordan Herrod I think it is) talk about it/them and seem to be somehow involved, so that’s cool.

I wanted to write about something else, what was it? Oh, right, the objectivity or otherwise of God-based moral systems. That sounds like a different post :) so maybe later.

AkuDreams: Code Still Not Law

This is adapted from a twitter thread. Like the thread, I’ll start off talking based mostly on a simplification of what actually happened, and at least point to the somewhat more complicated but more accurate account lower down. I’m virtually sure that I have some of the technical bug details wrong here, so don’t take this as gospel, but the overall lesson is clear.

Hah, I love this SO MUCH. Because I am a terrible person only slightly bothered by the people who are actually suffering as a result.

$34 million, or 11,539 eth, is permanently locked into the AkuDreams contract forever. It cannot be retrieved by individual users or by the dev team.

The refund processing, which is complete, sets each bid status to 1. pic.twitter.com/6GnQPnddC6

— foobar (@0xfoobar) April 23, 2022

This is an auction run by code on the Ethereum blockchain. You make a bid by sending the “contract” some money (in the form of ETH cryptocurrency; every Ethereum “contract” basically has a built-in escrow agent), and if you send more than the ultimate price (it’s a “modified Dutch auction”), it’s supposed to refund that money. But!

Due to a little bitty bug (and a relatively typical one; thousands of bugs like this one are written every day), the program (roughly) thinks that it’s already done that, and doesn’t do it “again”. And all the overrides in the code aren’t low-enough level to slip past that check.

Also (due to another bug, where it falsely assumes that every “minting” transaction “mints” exactly one token-thing, but in fact some minted multiple) the program can never reach a state in which it will allow the owners of the thing(s) being auctioned to withdraw the funds; those ETH will stay in escrow forever.

Yet another example of why “Code is Law” is silly and false.

I can think of three basic things that could be done about this:

First, they could tell the victims “too bad, code is law, that’s what you get for sending money to a contract that might have bugs”. That’s imho unlikely; the publicity would be terrible, which is to say, accurate.

Second, they could fork the Ethereum blockchain, and get 51% of the system to agree to swap in an altered chain reflecting what the program should have done. Forks are also terrible publicity; I think this is unlikely too.

The main reason I think a fork is unlikely is that, third, some number of unjustly wealthy crypto-whales can just step in and make up the lost funds out of their own pockets. This will superficially make it look like “the system works”, and the donors will get clout. I kind of suspect that this is what will happen (although if in fact only the owners, and not the bidders, have lost money, see below, the first option might be more likely, in that “it’s your fault for having deployed buggy code” doesn’t sound all that bad maybe.)

I was actually dreaming about all this this morning, between waking up briefly and checking Twitter for amusing things since I was awake anyway, and actually waking up an hour or two later. (And now I have a headache :P.)

It was a fun dream, reminiscent of the early anti-virus days before it all got boring, sitting around in a War Room with various Important People on the phone, trying to decide the best mitigation for a weird code thing.

Mostly I thought / dreamed about how to fix it with a fork-but-not-really. A brute-force fork (“install this new Blockchain!”) would be boring, but what if we hacked the Ethereum bytecode interpreter? The bytecodes may be all fancily embedded in the blockchain, but their meaning isn’t!

We (note I’m saying “we” here because now I’m talking about something cool) could just (“just”) add code to the interpreter saying “if between time0 and time1 you’re interpreting these bytecodes [buggy program], then pretend that they say [fixed copy of program]”. Sweet, eh? 😁

Then you get enough nodes to install the new EVM sometime before time0, and Bob is your Uncle.

Would enough nodes object, and refuse to run the hacked code, that there would be a fork-in-practice? Good question, and I have no idea. I’m just doing this for the mental exercise. :)

Here’s a history of the most famous (unplanned) Ethereum fork. That one was due to an active attack on a bug to steal stuff, not a bug simpliciter, and differed in other interesting ways. The amount of money at stake, though, was arguably comparable.

Here’s the more detailed analysis alluded to above, which says that the bidders’ money getting stuck was due to someone intentionally exploiting that bug (by, I think, having a “contract” send a bid, and then refusing the attempt to send it a refund, or something), and they turned the exploit off (by signaling the contract to accept the refund now), after which (some? all?) refunds went through, but then due to the other bug all by itself with no exploitation, the owners are unable to withdraw the rest of the funds forever.

And here’s Web 3 is Going Great on the situation for completeness. :)

I’m fascinated by the details of the bugs that led to this, but in fact they don’t really matter; the moral is that code will have bugs, bugs will cause things to happen that no one wanted and/or that violated someone’s rights in some way, and that therefore code is not law, and must never be law.

(Speaking of which, I had a long and… somewhat memorable Twitter discussion (apologies about how hard it will be to read that anything like linearly) about this with one Vinay Gupta, who is apparently something of a Force in this space, having 37.5K Twitter followers. Among other things, he calls me all sorts of names, and declares that he himself is “a different kind/calibre of smart. Possibly a once in a generation transformational intelligence.” So that happened. :D

But if I start weblogifying all of my Twitter exploits, you’ll get bored. Heck, I’ll get bored! So I won’t.)

And that’s the end of Today’s Episode of Code Is Definitely Not Law So There. Not a podcast.

Those mysterious scrawls and drawings

Just because I haven’t done this for awhile…

Still enjoying this, but I feel like I’ve sort of explored quite a bit of the space already.

How about that Kalam argument?

While we’re talking about philosophical arguments for the existence of God, we should apparently consider the so-called Kalam argument.

In its simplest form it’s nice and short:

1. Whatever begins to exist has a cause of its beginning.
2. The universe began to exist.
3. Therefore, the universe has a cause to its beginning.

This is, obviously, an argument for the existence of God, only if God is defined as “A cause of the beginning of the universe” and nothing further, which doesn’t seem all that significant, but still. There are further associated arguments attempting to extend the proof more in the direction of a traditional (i.e. Christian) God, being “personal” and all, but let’s look at the simple version for now.

I think it’s relatively straightforward that the conclusion (3) follows from the premises (1) and (2), so that narrows it down. Now, are (1) and (2) true?

First we should figure out what we mean by “the universe”, because that matters a lot here. Three possible definitions occur immediately, in increasing size order:

(U1) All of the matter and energy that’s around, or has been around as far back in time as we can currently theorize with any plausibility. All of the output of the Big Bang, more or less.

(U2) Anything transitively causally connected in any way to anything in U1. Everything in the transitive closure of past and future light-cones of me sitting here typing this (which is, at least arguably, the same as everything in the transitive closure of past and future light-cones of you standing there reading this).

(U3) Anything in any of the disjoint transitively-causally-connected sets of things that are picked out in the same way that U2 is, starting from different seed points that aren’t transitively-causally-connected. The “multiverse”, if you will, consisting of all those things that aren’t logically (or otherwise) impossible.

It’s interesting to note here that “the universe” as used in the Kalam can be at most U1. This is because nothing outside of U2 can be causally connected to, can create or cause or otherwise have any effect at all on, anything in U2. Anything that claims to be a cause of U2 or U3 is either not actually a cause, or is part of U2 or U3 by virtual of being causally connected to it.

This works, I think, via (2) in the argument above; U1 might plausibly be said to have begun to exist, but it’s hard to see how U2 or U3 could.

Or, I dunno, is that true? We can certainly imagine U2, that is, this universe right here, somewhat broadly construed but still undeniably this one, did just start up at some time T0. That it could, I suppose, turn out to be a fact that at all times T >= T0 there are some facts to write down about this universe, but at times T < T0 there simply aren’t.

The reaction of Kalam proponents to that suggestion seems to be just incredulity, but in general I don’t see anything wrong with the idea; a universe simply coming into being doesn’t seem logically contradictory in any way. We can certainly write down equations and state transitions that have a notion of time, and that have well-defined states only at and after a particular time; it’s not hard.

So I guess, even if the Kalam must mean U1 by “universe” even in its first premise, (1), there’s no strong reason to think that (1) is true even then. This universe right here, this collection of matter and energy, could have just sprung into existence eight billion years ago or whatever, without any particular cause. Why not?

Premise (2) is less ambitious, and therefore more plausible. Did this particular batch of matter and energy, U1, begin to exist at some time? Could be. I mean, I can’t prove it or anything, and neither can anyone else, but I might be willing to stipulate it for the sake of argument.

(Even U2 might have, although the Kalam proponent probably has to disagree with that: since they want to have a backwards-eternal God creating U1, that means that that God counts as part of U2, which means that U2 is backwards-eternal, and never came into being. So the Kalam folks are still stuck with U1.)

U3 has the interesting property that it doesn’t have a common clock, even to the limited relativistic extent that U1 and U2 have common clocks. Since U3 contains disjoint sections that have no causal connections to each other, it’s not really meaningful to speak of the state of U3 at “a” time, so referring to it beginning to exist (i.e. at “a” time) turns out not to really mean anything. I think that’s neat. :)

If we’re willing to stipulate (1) and (2) as long as “the universe” means only U1, the conclusion isn’t very powerful; we find out only that this particular batch of matter / energy that existed shortly after the Big Bang (or equivalent) must have been caused by something. And fine, maybe it was, but if it was that something was just some earlier and likely quite ordinary piece of U2. Calling that “God” just because it happens to be so long ago that we can’t theorize about it very well seems very far removed from what “God” is usually supposed to mean.

I’ve read various things on the Kalam argument, including the Craig piece linked above, and the counterarguments both don’t seem to actually understand physics and cosmology very well, and are mostly of the “proof by incredulity” variety; Craig writes, for instance,

To claim that something can come into being from nothing is worse than magic. When a magician pulls a rabbit out of a hat, at least you’ve got the magician, not to mention the hat! But if you deny premise (1′), you’ve got to think that the whole universe just appeared at some point in the past for no reason whatsoever. But nobody sincerely believes that things, say, a horse or an Eskimo village, can just pop into being without a cause.

— William Lane Craig

“Worse than magic” is hardly a logical argument, it’s just ridicule. And to state as a raw fact that no one seriously believes the argument one is attacking is, again, content-free. (The bit about Eskimo villages is a silly evasion; what may have come from nothing is for instance an unimaginably hot and dense ball of energy, not a horse. But even for a horse, expressing incredulity that one might appear spontaneously is not a logical argument; more work is required!)

This reminds me of the rather popular fundamentalist Christian statement that everyone knows deep down that God exists, and atheists are simply in denial. This is of course false and silly.

This also reminds me, now that I think of it, of an excellent lecture that I saw the other week, “God is not a Good Theory“. Among other things, the speaker here makes a similar move to my positing a universe that simply springs into being and seeing no contradiction in it; he describes various simple universes and shows that they can be explained perfectly well with no reference to any external God. “All I need to do is invent a universe that God does not play a role in” (a bit before the 10 minute mark). He also talks about the issue of causes with respect to the universe, and briefly mentions the Kalam. Definitely worth a listen.

On the Kalam in general, then, I find it extremely non-compelling. It doesn’t even have a sort of verbal paradox in it to have fun with, the way the Ontological argument does; it’s just weak. So I do wonder why it’s so popular. Thoughts in the comments are most welcome.

Why the Ontological Argument doesn’t work

Back in the Rocket Car posting, we (following ol’ Gaunilo) showed, via a kind of reductio ad absurdum, that the Ontological Argument for the Existence of God doesn’t work (unless I have a really cool rocket car in my basement, which does not appear to be true).

Reductio arguments of this kind can be a little unsatisfying, because they just show that a thing is false, by showing that it being true would imply other things being true that we aren’t prepared to say are true. But they don’t tell us how the thing is false; in this case, the lack of a Z2500 Rocket Car in my basement doesn’t tell us how the argument fails, only that it fails.

But the other day, somewhere, I saw hints of an old refutation of the Ontological Argument that showed where it went wrong. I only glimpsed a few words of it, while looking for something else, and then forgot where or what it was, but a while later my brain said, “Hey look, I bet this is what that argument was saying!”, so here is that subconscious reconstruction. If anyone knows who made this argument, or an argument like it, anciently, do let me know!

Conversationally, the Ontological Argument goes something like:

A: Let’s define ‘God’ as that entity which has all perfections.

B: Okay.

A: Now, existence is a perfection, therefore since God has all perfections, God has existence, ergo God exists.

B: Wow!

The present argument against the argument changes the conversation, by having B point out problems in the underlying frame:

A: Let’s define ‘God’ as that entity which has all perfections.

B: We should be careful here, since there might not be any such entity. Let’s say instead that ‘God’ is defined as that entity which, if it exists, has all perfections.

A: Why do we have to do that? I can define ‘Humpty’ as a square circle, and that definition holds even though there are no square circles

B: Not really. If we define Humpty simply as a square circle, then if someone says “there are no square circles,” we can reply “sure there is; there is Humpty!”, and that’s wrong. It’s better to say that, strictly speaking, Humpty is a thing that, if it exists, is both a square and a circle. If it doesn’t exist, then of course it’s neither a square nor a circle, so we can hardly define it that way.

A: Hm, Oh. Well, if we define ‘God’ as something which … I guess … has all perfections if it exists, and then note that existence is a perfection —

B: We can conclude that God exists, if it exists! Much like everything else, really. :)

A: Wait, no…

The underlying observation here is that, strictly speaking, when we define or imagine something, we are defining or imagining the properties that that thing would have if it existed. If it doesn’t exist, of course, it has no properties at all. So when we imagine a seven-storey duck, we are imagining what one would be like if it existed. We aren’t imagining what it’s really like, because it doesn’t really exist at all, so it isn’t like anything; it isn’t a duck, doesn’t have seven storeys, and so on.

Therefore when we define God as having all perfections, we are actually saying that for any property which is a perfection, God would have that property if God exists.

And then the conclusion of the Ontological Argument will be just that God exists, if God exists; and that isn’t very interesting.

This isn’t an utterly formal (dis)proof, but I find it attractive.