Why Is There Something?
And is there everything?
not the src |
Jim Holt is the author of the modestly titled book, Why Does The World Exist? He has—as his book’s back cover says—written on string theory, time, infinity, numbers, truth, and even stercus taurinum, to use a learned translation of what the back cover actually says.
Today Ken and I thought it would be fun to ponder the main question he raises in his book.
The book is beautifully written, ponders deep questions, yet is fun to read. Holt is clearly a great writer who can make metaphysics seem accessible to those of us who are complete novices. The structure of the book is a tour, a literal tour, around the world; he talks to various great minds about his questions. This approach makes the book readable, accessible, and real. Grounding such a philosophical question in discussions with real people is a cool idea.
As you read the chapters, you journey around the world and get to hear from among others: David Deutsch, Andre Linde, Alex Vilenkin, Steven Weinberg, Roger Penrose, and the late John Updike.
The Question
Holt is most interested in the question:
Why is there something rather than nothing?
A pretty basic question. Perhaps more fundamental that our simple question like ? I guess if there were nothing, then who would care whether equals or not?
A Quick Proof
He gives a “proof” for those who are busy at the very front of the book:
Suppose there were nothing. Then there would be no laws; for laws, after all, are something. If there were no laws, then everything would be permitted. If everything were permitted, then nothing would be forbidden. So if there were nothing, nothing would be forbidden. Thus nothing is self-forbidding.
Therefore, there must be something. Q.E.D.
Another Argument
One proof I found especially interesting is based on the subtraction argument. Apparently pioneered in the 1990’s by British and American philosophers, this argument attempts to show that there could be a complete void—nothingness.
The arguments makes three assumptions. The world consists of a finite number of objects: people, tables, chairs, and so forth. It also supposes that each object is contingent. That is although the object does exist, it could actually have not existed. Holt says: “This too seems plausible.” Finally the argument assumes independence: the nonexistence of one object does not force the existence of another object.
The subtraction argument is now easy. Just start imagining that each of the objects does not exist. This is not meant in a literal sense, but one can perhaps imagine that each object in turn does not exist. Clearly, given the assumptions this eventually leads to a void of nothingness.
This seems a pretty simple argument from the math viewpoint. Holt asks:
But are the premises of the subtraction argument true?
He points out that the first two assumptions seem okay to him. But the independence one is, as he says, “more dubious.” He worries that the removal of one object might force the existence of other objects. This clearly would destroy the argument.
But Wait…
What I like about the subtraction argument is that there is a repair if independence is weakened. Suppose that the removal of an object actually forces the existence of another object. This seems like a strong obstacle to the argument. But suppose that the situation is this: The world consists of a finite number of objects
If you remove—mentally—the object then a finite number of new objects can be added to the world. However, we assume that these new objects are lower under some measure. Even though the number of objects has increased, provided the measure is proper, the subtraction process will eventually halt. That is the subtraction will eventually removal all objects and yield a void.
A simple concrete example is to imagine that objects are divided into a finite number of types. The independence rule now says that the removal of an object of type can add any finite number of objects of types less that . Then it is easy to see that the subtraction process works provided you remove the highest types first.
This is nothing more than an argument about ordinals. Of course there are ways to order the objects of the world so that the subtraction always stops, but that this is hard to prove. See this note by Andrej Bauer on “The hydra game” for a discussion of such situations.
According to a paper by Aviv Hoffman, the “Existential Subtraction” (ES) premise is expressed via possible-worlds semantics as:
There is a finite world such that for every possible world that shares some objects with , there is an object in both and such that there is a world whose objects are those of , minus .
Granting this allows one to iterate from to nothing. With weakened independence, however, the premise only says there is an and a which might have other objects besides , such that the ordinal measure of is less than that of . The choice of itself might be to minimize this measure.
Ken’s Takes
First, I (Ken) take the Platonist position that mathematical structures have objective existence, and witness the same laws throughout creation. This begins already with the empty set. I agree with this deduction by the philosopher Wesley Salmon (emphasis in original):
The fool saith in his heart that there is no empty set. But if that were so, then the set of all such sets would be empty, and hence it would be the empty set.
Creation then follows ex-{nihilo}, either by standard set-theoretic means, or the way Donald Knuth ascribed to “J.H.W.H. Conway” in his book Surreal Numbers.
Hence the question is really about whether “mathematical something” entails “physical something.” What I find missing from the above arguments, and even from the Stanford Encyclopedia of Philosophy’s article on “Nothingness” (from which the Salmon quote is taken), is information. John Wheeler’s dictum “It From Bit” doesn’t necessitate physical presence from the fact that information exists mathematically, but I believe it channels the question.
Since the subtraction argument presumes a finite universe, it presumes one with a finite number of physically realized bits of information. That is well-defined follows from the principle conceded by Stephen Hawking in 2005, that the amount of physical information in the universe cannot be changed by any physical process. Note that this already rules out any idea that “subtraction” could be a process applied to our own world.
The All-or-Nothing Argument
It strikes me, then, that when the subtraction argument is made attentive to information, it goes this way:
- Starting Premise: It is possible to have a finite world.
- Hence it is not the case that for all , at least bits of physically-realized information are entailed in any world.
- Hence there exists an such that some world has bits of information.
- Information Subtraction (IS) Premise: In any world with physically realized information, there is a physically realized bit whose removal leaves a possible world.
Granting both premises allows us to iterate from bits of information down to zero. We can give IS a formal statement like ES above, and also weaken it to say the bit is replaced by one or more other bits but reducing some ordinal measure. The weaker form still iterates down to zero.
The IS form helps one think of ways “independence” might be false. Perhaps every particle in some possible world reached in the argument is entangled with another particle, or is part of a virtual pair that disappears. These eventualities do not defeat the conceptualization in terms of information, however. Virtual pairs are actually the agents that conserve information in the resolution of the “black-hole information paradox” that Hawking accepted. An entangled pair of particles may represent just one bit of information, so removing that bit may mean removing both. A real-world example of a “substrate” in which physical elements may have less information than their number is the hashing scheme used by chess programs, as I described here. Thus it may be possible to answer objections to IS.
In my opinion, however, what the information view does best is raise a point of aesthetics that antecedes trying to make ES or IS work via points of contingency and possible worlds. I guess I should say “humble opinion,” but an argument from aesthetics about ultimate matters is the polar opposite of humble:
Denying the conclusion says there is an such that every possible world must have at least bits of information. From the starting premise, there must be a finite that is the greatest such , and then IS fails for some world of size . But why should any particular be analytically special in this way?
We can imagine being special, or… we could have . Thus I hold that the “subtraction” argument actually rebounds to speak about infinite addition:
Either the world is necessarily infinite, or it is possibly void.
Using symbols from modal logic, we can call this the ▯All-or-◇Nothing Argument.
This leads in turn to what I (Ken) think are the three questions that really matter.
Something Versus Everything
The first question is technical, and many regard it as already answered yes.
In an infinite cosmos, must every possible finite configuration of matter occur infinitely often?
If quantum fluctuations can generate configurations on human-sized scales—which is a premise of the still–current argument over Boltzmann Brains—then yes. Then the following main question becomes equivalent to whether the cosmos is finite or infinite.
Is there something rather than everything? And either way, why?
Unlike the original question of something-versus-nothing, this one is not counterfactual—and we honestly don’t know the answer, let alone why. At least the infiniteness question may be answerable: even this month there have been claims of new evidence from the Planck Project analysis of the cosmic microwave background. Note also that “everything is permitted” was already a step of Holt’s “proof” forbidding nothing above.
The third question is a mash-up of a quotation by Hawking and one by Wheeler, both noted as-here by cosmologist Max Tegmark. I read it as presuming a negative answer to “everything,” but it can be asked also about our particular region of an infinite cosmos:
What ‘breathes fire’ into one set of equations, and not another?
For myself, I am partial to “something,” in either a finite cosmos or an infinite one with the first question answered “no.” Else we have to face down the reality of infinitely many “copies” of ourselves—as blithely asserted in articles by Tegmark—and of Earths that are exactly like ours or differ in arbitrary ways. Such variety applies also to paths of histories: infinitely many worlds would be as up-to-now except that I actually go out and commit the unspeakable act I’m thinking of for the purpose of this sentence. The common “I” among my minions could still be “preponderantly moral” in a sense described mathematically by Deutsch in his book The Fabric of Reality, but such lack of parsimony strikes me as degrading rationality. However, I must concede that denying “everything” entails a limitation of scale for the principle that “everything not forbidden is compulsory,” which is observed to hold at quantum scales.
Open Problems
Why indeed is there something? Is there everything? Or as Christopher Hitchens said on the back cover of Holt’s book:
P.S. What makes you so sure that there’s anything? Love, Hitch.
→ Rolf Schock (1968), Logics Without Existence Assumptions
A few questions came to mind —
What is meant by Physically Realized Information (PRI)?
What is meant by Physically Realized Bit Of Information (PRBOI)?
Are you invoking the Physical Symbol System Hypothesis (PSSH) of Newell and Simon in speaking of such things, or something else entirely?
some ~2000 yrs ago, people were contemplating on exactly this question. Sometimes their entire lives…often silently in caves. Their focus was not on in terms of today’s physics terminology, but never the less, its the ultimate question. There was ground breaking realization. They started to call it “god”, “nirvana”, and more loosely self-realization. The conclusion ? Human mind itself is a relative thing. It is an avatar(manifestation) of existence. how can existence understand existence. IT has to realize “it is”.
I digress.
To do proper justice to this topic, below literature by Nagarjuna (Central figure for the middle-way/mahayana buddhism) should be studied. He is a master of logic. His central topic is nothingness/void (“illusion”/”maya”), and he deals with this topic in detail, in very practical terms, often with indepth logic. He identifies 4 states – nothing, everything, neither nothing nor everything (what if its an illusion, human incapacity to comprehend), both nothing and everything (“oneness”/maya).
1. Mulamadhyamakarika
http://www.stephenbatchelor.org/index.php/en/verses-from-the-center
http://www.amazon.com/Fundamental-Wisdom-Middle-Mulamadhyamakakarika-ebook/dp/B003ID7A54
2. Ratnavali (tailored for kings at that time, but has some tidbits. Ignore the mumbo-jumbo)
http://www.thezensite.com/ZenEssays/Nagarjuna/Garland_of_Ratnavali.html
Unless people transcend this important topic, its impossible to self-realize – particularly modern humans with all their logical material thinking. Some humans, with pure devotion/meditation reached this realization without understanding/transcending this topic, but if they get off track the mind surfaces these questions again and again. There is no peace/bliss, unless “the search/quest” ends. And it only ends when it fully realizes.
Many more ways to have something than nothing. Something is much more likely.
But the something that is overwhelmingly the most probable–nearly empty de Sitter space (which has the largest entropy)–is very close to nothing. By your probability argument, then, the most likely form for reality to take is near-nothingness.
Thanks for the comment! One of my interests is whether algorithmic probability, rather than probability based on Lebesgue measures, might make a difference to the cosmological measure problem. My quip is, perhaps the salient way the “universal prior” distribution is actuated is as a prior for universes. This goes into the territory of Jüergen Schmidhuber’s “Everything” talk.
Reminder for new visitors (is that a self-contradiction?): first comment is moderated, rest are immediate, except for the Nth comment where N is congruent to zero mod K, where K is variable and unknown to us :-).
With a constraint on computational resources, what is overwhelmingly most probable is the output of simple programs. And lo, we’ve found that natural phenomena tend to be well described by simple programs.
(Looks like Ken has beaten me to the punch whilst I was trying to remember my WordPress password!)
He said “If there were no laws, then everything would be permitted.”
But if there were nothing – the starting assumption – the word ‘everything’ loses its reference, so the sentence has no meaning, and the proof breaks down.
Am i wrong?
See ya Julio
I like it.
Another way to look at “If there were no laws, then everything would be permitted” is that “everything is permitted” is a law and therefore we have a stopper paradox before he gets to pull the rabbit out of the hat.
Cheers,
Alan
Or alternatively: if there were nothing then the very notion of a law would be meaningless because – by definition – laws are always about something.
Look at it this way – let “L” be a Boolean variable denotes the existence of laws. So, if the statement there are some law true the L is true. let “X” be any variable and P(X) denotes X is permitted. Then the statement becomes –
L is false => for all X P(X) is true
if the above statement is true then the below statement is also true
there exist X P(X) is false => L is true
in simple English the above statement would be –
Something is not permitted implies there are some laws ……………(a)
Now statement A is an axiom and true by the definition of law which is a set of rules that governs the universe.
‘Everything’ doesn’t lose it’s reference. It just becomes nothing.
It’s not just that. In the sentence “If everything were permitted, then nothing would be forbidden.”, the word “nothing” doesn’t mean that “nothing” itself is forbidden. It means that all scenarios are possible, including the lack-of-existence meaning of the word “nothing”. In the sentence “So if there were nothing, nothing would be forbidden.”, we again have the same play on words. The two words “nothing” mean different things in this context. The first one means literally lack of existence. But the second means something quite different. It is saying that all possibilities are permitted INCLUDING “nothing” (w/ the meaning of lack of existence).
That makes “Thus nothing is self-forbidding.” a non-sequitur and the proof fails.
This is an English language failure. Nothing more.
Anyways, I hope I missed the part where it’s claimed this was all a bad joke because this is pretty bad.
Heh, I also thought of the same thing when I read that “proof”.
The “proof” was offered at the very beginning of the book in the spirit of a joke, or a pun. It obviously commits the fallacy of equivocation. A seriously intended “proof” (with a rather different conclusion) comes near the end of the book.
> “P.S. What makes you so sure that there’s anything? Love, Hitch.”
Cogito ergo sum.
I note Daniel Kahneman’s conclusion quoted here: “Odd as it may seem, I am my remembering self, and the experiencing self, who does my living, is like a stranger to me.”
As also noted there, Jim Holt wrote the NY Times review of Kahneman’s book. I’m intending soon to resume a debate with Mark Braverman and his Princeton undergrad advisee Leo Stedile on whether a scaling effect of player error in my chess data is best explained by one of Kahneman-Tversky’s psychological conclusions (as I’ve said) or a rational one involving the marginal cost of error.
Indeed I’m intending to run more games played by computers to investigate things like that. I’m beginning to think already that I’m looking at an overlay of two (or more) causes.
Thanks for your reply. From the percentages in your final paragraph, it seems people are playing uniformly worse when at a disadvantage, rather than making a few blunders. That’s good information.
Regarding your second paragraph… I think you (and slides 17-18) are saying that the error rate of human players is higher when they’re playing at a disadvantage. My question here was about the game itself, regardless of humans. Maybe there are more nonoptimal moves close to the best move in favorable positions than in poor positions. In other words, does consistently playing the 2nd-best move when you’re a pawn up give you lower AD than playing the 2nd-best move when you’re a pawn down? You’d have to look at lots of positions rated +e and -e and take the AD between the best two moves. If so, it would mean humans do not have an asymmetry at all, but instead, the errors of any agent with constant playing strength will ’round’ (given available moves) to a greater AD when losing than when winning. At any rate, it is something to control for.
I have a few questions/comments on this:
* Are players making more Nth-best moves when they’re at a disadvantage, or are they making relatively few Nth-best moves with high N? e.g. Are they making lots of 2nd-best moves, or a few 5th-best moves?
* Is the histogram for the AD between the PV and Nth-best move symmetric? e.g. What is the average eval. difference between best and 2nd-best moves in +e positions vs -e positions?
* How do you address concerns about having to make the second-best move to evaluate it (rather than using multi-PV analysis)?
These are great questions. On the third, doing that was suggested to me by Rybka’s designer, but tests by me and others show Multi-PV mode to be stronger by about 100 points—said to be because it disables heuristics that trade accuracy for speed.
To the second question, it is definitely not symmetric—an example is in slide 17 of this talk. That’s why I’ve tried “correcting” by integrating a metric dmx giving the marginal value of an extra tick when the eval is x (and this I assume to be symmetric). The idea is if you make a one-pawn error when you are +0.50 up, you integrate from -0.50 to +0.50, while if it’s when you are already half a pawn down, you integrate from -1.50 to -0.50 which gets more of a correction. Right now I’m using dmx = 1/(1 + cx) where the constant c for Rybka 3 is “accidentally” close to 1, but Houdini 3 seems to want c > 1.5; I’ve also tried taking dmx from the probability curves in Stedile’s paper (which are fitted by hyperbolic trig functions), but so far with less avail.
The first question will take more work, but in last year’s master set of just over 600,000 Multi-PV moves, the overall percentages 52.7%-17.9%-8.9%-5.2%-3.4% for the top five moves become 52.1%-17.7%-8.9%-5.4%-3.7% for the 51,400-and-change moves with the player to move behind by 1.00 or more. Perhaps unsurprisingly, 31,400 of those moves are when Black is the player behind, but this all makes little difference to the percentages. For 16,100 turns with the player to move behind by 2 or more it’s 51.8%-17.4%-8.8%-5.4%-3.7%. I don’t know whether the decrease of 1% in the first-move-match in this sample is significant. Houdini and Stockfish are free of quirks that led me to enable a 4.00 cutoff (called “multipv_cp”) in the Rybka program parameters, so I hope to amass better data with them before too long.
The version of this that I subscribe to is Je me souviens, donc je suis. I have a few layers of meaning on the poetry there, but the top-level meaning is that the reason it is I that am, not just some thinking that is going on, is that I remember myself.
Not sure I get the various Subtraction Arguments, but they do remind me a little of the Exclusion-Inclusion Method or the Principle of Inclusion-Exclusion (PIE❢) that we use to find the number of elements that have none of a given list of properties.
In Rudy Rucker’s comic masterpiece Master of Space and Time (1984), the “big-name establishment physicist” Dana Baumgard commissions the novel’s (sporadically) omnipotent yet comedically feckless scientist-hero Harry Gerber to discover “Why do things exist?“
Wonderful fun, and highly recommended! :)
Here is another one of those eternally recurring ideas echoed inimitably by C.S. Peirce in his sketch of a Cosmogonic Philosophy.
“It would suppose that in the beginning,—infinitely remote,—there was a chaos of unpersonalised feeling, which being without connection or regularity would properly be without existence. This feeling, sporting here and there in pure arbitrariness, would have started the germ of a generalising tendency. Its other sportings would be evanescent, but this would have a growing virtue. Thus, the tendency to habit would be started; and from this with the other principles of evolution all the regularities of the universe would be evolved. At any time, however, an element of pure chance survives and will remain until the world becomes an absolutely perfect, rational, and symmetrical system, in which mind is at last crystallised in the infinitely distant future.”
The above quotation is taken from one of several discussions where Peirce introduces his idea that natural laws themselves evolve. That idea has enjoyed yet another revival in recent days, notably by Lee Smolin in Time Reborn.
Oddly enough, I dashed out my own thoughts about this book mere moments ago. Just before I hit ‘Publish’ I noticed that your piece was noted at the bottom of my screen. (I trust you know what I mean. I’m rather new to this ‘WordPress’ thing, so I don’t really know the correct terminology.) I enjoyed both the book and your observations, even if they’re both likely to give me a headache if I think about them too much.
If all there was was nothing, why would I be interested in it? :-)
On my crazier days I tend to get inspired by what I read in “A Short History of Nearly Everything”. There’s a section in that book that discusses the idea that we are basically physically replaced approx every 7 years. Matter goes in and goes out. Our cells die off and are regenerated. Gradually we leave a trail behind ourselves as we go forth and consume. We’re more of a cloud perhaps than ‘finite’ beings.
If you twist that around somewhat, it isn’t unlike ‘waves’ upon the ocean. We — action set in motion — simply form, propagate and eventually disperse. Stepping back a bit, everything around us can be seen with the same perspective. Perhaps there are no ‘finite’ objects, least not relative to the fabric of space-time? Everything is just relative actions sent forth long before we can imagine. The ocean exists perhaps, but the waves are far from independent. From that angle there is just one thing whose surface has numerous relative differences. If it wasn’t there, then neither are the waves. If the waves are there, then it must exist.
Paul.
The answer depends very much on whether you believe the real world is uncountable or not. If it is uncountable, then there is nothing (measure 0), which is quite something sometimes (countably infinite) ;)
Another analogy. Ideal is a place of nothing, but it gives you structure of everything. I’m here at childish removal argument – If you have two apples on the plate and you remove 2 apples from the plate you get zero apples on the plate, or nothing.
I guess I don’t see how to formulate any sort of statement comparing something that exists with non-existence– in particular, non-existence precludes satisfying -any- predicate, so how, exactly, do you compare anything that exists (including the empty set) with non-existence?
Good point I think almost of all contemporary mathematicians talking on the existence of “object”/mathematical object. They assume as a fiction the idea of empty set, and later they forgot about it is a ..fiction or a construct though useful and talk fiercly against each other.
Cantor himself was not sure if the term “set’ means “one” or “many” !
Just like we can’t fully simulate a system within itself (e.g. assuming the universe was perfectly deterministic, we still wouldn’t be able to predict the future because we’re part of it, and it would require as many resources as the universe itself to simulate it), I guess one cannot empty a system within itself.
Also, the empty set still requires the concept of set (and the concept of “concept”), etc.
Nice thought about “cannot empty”.
General note in this thread, to remind about something that Dick and I obscured by having the Hitchens quote at the end and imputing that nothing-vs-something was “counterfactual”: The point is not whether there “is” nothing, but whether having nothing was ever possible. Is there something about the world that necessitates its existence? This is sharper than the question of whether there must have been a “First Cause” for the world we have, as opposed to something like the Hartle-Hawking-et-al. proposal. In modal logic terms, the question is “Diamond Nothing?”
I’m pretty sure the world of nothing exists. The only question is how to measure it ;) The rest is psychological/sociological question of believes in logic, philosophy and sociologically convincing arguments – i.e. is the question of human perception!
There is always the Anthropic Argument: if there was nothing we would not be here to be aware of the fact. One could argue that the universe could exist but with such conditions that we would not be here, but one cannot argue that nothing could exist and we still be here to take notice of the fact. The proposition “nothing exists” is unverifiable in some cases and is therefore unverifiable in toto.
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> “A pretty basic question. Perhaps more fundamental that our simple question like P=NP? I guess if there were nothing, then who would care whether P equals NP or not?”
However, I can see a connection with P?=NP. The problem whether there’s something rather than nothing looks like the question why there’s some complexity instead of generalized easiness. So much so that the complexities we can’t explain should perhaps be taken for granted – just like the existence of something in this world.
wow, thats some pretty philosophical/metaphysical stuff there. I agree with the poster who suggested looking into hinduism which has pondered the topic for decades. also, even descarte the ur-rationalist seemed to have the basics right. existence seems to be constructed out of consciousness.
sorry weird typo there! correction, I meant millenia! its only I who have been pondering the nature of reality for decades! more on the nature of reality in this post incl a ref to hinduism at the end, solitons, cellular automata, quantum mechanics, and disagreeing with scott aaronson
Jan Lukasiewicz, Warsaw-Lvov School of Logic pointed the best I think the il-logicity of the Descartes mantra! You can find it I suspect on web or I can give you his article.
ps descartes saying updated to modern age/cyberspace is, “I post therefore I am” or “I have a blog, and it gets hits and/or comments, therefore I am”… and also close to an answer to that old riddle, “if a tree falls in a forest, does anyone hear it”?
Not boring? Does the above sentence: with letters (a,b,c..) not exist? Go to Aristotle and St.Thomas Aquinas or play in Hell
to make a sense because the missing sentence ‘the above sentence” is just the last one: P.S. What makes you so sure that there’s anything? Love, Hitch.
All the article’s Problem is in: Does mr.Ch.Hitchens exist at all in his own opinion? Does his own opinion exist?….etc!
A philosopher takes on “Why is there something rather than nothing?” and finds it to be ill-posed.
http://www.ontologia.net/studies/2009/gruenbaum_2009.pdf
I can raise a point that may help with one issue raised on page 169 of Holt’s book, on Leonard Susskind’s identification of the Many-Worlds and eternal-inflation multiverses, in which I regard the “Landscape” as his mediating picture. I analogize Many-Worlds to a nondeterministic finite automaton (NFA) whose states represent configurations of matter-&-spacetime—“worlds” or at least causally-connected subworlds. The equations of quantum mechanics analogously describe the deterministic finite automaton (DFA) that simulates this NFA via the sets-of-states construction taught in a CS theory course, whose computations update the status of all legal paths through the NFA. In our human “frog’s-eye view” we experience just one path through the NFA.
Now without involving my personal view that the one path of transitions is distinguished, the point regardless is that the states are already held to exist—they are not multiplied a zillionfold per instant. How they are “arrayed” is a matter for geometry we may not have conceived yet, but from the little I know, eternal inflation does not force them to be arrayed in contiguity that would preclude the transitions.
So we’re all going to be tortured infinitely horribly forever? I’m sure everyone else is fine with that but I’m less than happy about it.
As someone said: some people would complain even if there was nothing.
[I apologise in advance for the length of this coment]
I think some distinctions might help clear some things up here. For starters, I think the question, “Why is there something rather than nothing?” should be stated with more clarity. You guys mentioned Platonism. Now, on Platonism, the abstract objects (mathematical objects, universals, etc.) are typically taken to exist necessarily (that is, it is impossible for them to fail to exist, or in possible world semantics, they exist in every possible world). If we include these abstract objects in our “something”, then the answer is obvious: there is something because there could not fail to be something (ie. abstract objects). To avoid such triviality, I suggest the question be rephrased to what I imagine was being asked all along: “why does at least one concrete thing exist, as opposed to none?” (here “concrete” is taken to be “not abstract”, so examples are humans, tables, cities, planets, particles, etc.) If we’re not Platonists, then we can stick with the original question, since the only things that exist (or could exist) are concrete objects. (I’m taking Platonism here to be a blanket view of all realist views of abstract objects)
Now already we see that the “Quick Proof” doesn’t really help us answer this question: if we’re Platonists, then laws exist only as abstract objects and so they don’t exist in the relevant sense; and if we’re not Platonists, then the laws don’t exist at all, even though they still describe how reality works.
In fact, the second bit of this proof could also be cleared up by distinguishing between nothingness (the state of affairs where no objects exist) and nothing as it’s used elsewhere in the proof. Consider this rephrasing with the relevant clarifications: “If there were no laws, then everything would be permitted. If everything were permitted, then nothing would be forbidden. So if there were nothingness, nothingness would be forbidden. Thus nothingness is self-forbidding.” We can see that halfway through it just changes from talking about nothing being forbidden (that is, “everything is permissible”) to nothingness being forbidden (that is, “nothingness is impossible”). Nevermind the fact that the argument starts by saying there would be no laws, and ends with a law :P
Next, I think the independence premise is misunderstood a little. It’s originally stated very well: “the nonexistence of one object does not force the existence of another object.” The problem comes when this is interpretted as talking about the *removal* of the relevant object. You see, possible worlds are typically understood in terms of how things could have have been. When as say some object exists in some possible world but not another, we don’t necessaily mean that the object can be removed. What we mean is that things could’ve been such that that object didn’t exist. To get clearer, perhaps there’s a contingently existing object in the actual world which cannot be removed. Since it’s contingent, however, we know that things could have gone differently such that it never existed (or at least, didn’t exist at this time). So while the removal of some object A might bring about the existence of another object B, it might still be possible for reality to have been such that everything was the same yet where neither A nor B existed, and as such the non-exitence of A doesn’t force the existence of B even though the removal of A does. This is what the independence premise says.
I personally find the premise, when properly understood, to be exteremely plausible. After all, if we denied it, say, in the case of unicorns, then the non-existence (not removal) of everything but a single unicorn would entail that unicorn’s existence. Very strange.
Now, I think this means that the information substraction argument *can* be applied to the actual world. After all, we aren’t talking about the removal of information, but possible ways reality could have gone with less information. As such, I think the Information Subtraction Principle can also be stated with more clarity: “In any possible world w1 with physically realized information, there is a physically realized bit b and a possible world w2 such that w2 agrees with w1 on all physically realized information with the exception of b.”
As an aside: I understand it that some philosophers answer the question of why there is someting rather than nothing by saying that there exists a necessary being. In this case, the reason something exists is that nothingness is impossible. And perhaps to answer your question about what makes some finite m >= 1 special can be answered by saying that this being involves m bits of information. Besides that answer, the other most common one is to deny that there is an answer at all. While this doesn’t seem like a nice response, the idea of a necessary being smells too much like theism to many non-theistic philosophers (although, of course, there are theists who don’t answer with the necessary being either. Peter van Inwagen, for example, is a theist who doesn’t like some principles typically involved in getting to the necessary being answer and so gave a novel answer to this question a while back).
Now, not so much a distinction as a question: with your repair of the independence principle as you understood it, does it really lead to a void? Surely it just leads to a negligible set of objects (that is, negligble with respect to the measure being used). But surely such a set could be non-exmpty?
Aristotle in Metaphysics undermined once and forever the “Ideas” of his teacher, Plato. What’s the Hell with mathematicians not knowing this? All these controversies the objects of mathematics, many universies, are Plato-science fictions “creations”
Thanks, Roland. I did try to attend to some of the points you raise in choosing how to phrase things in the post, including my note about the question really being whether “mathematical something” entails “physical something”, and saying that subtraction/removal cannot be a process applied to our world. I chose to give just an informal statement of IS together with a pointer on how to make a formal one, such as you give. On your last question, the ordinal measures are discrete (unlike Lebesgue measure), so at least in the hydra-related instances we intend for analogy, iteration does go all the way to the base (that the ordinals are well-ordered matters in specific cases). Your tricky question before it seems to bear on whether a God is held to be a necessary being or “the supreme brute fact” as Holt puts it. If the former, and the necessary being is finite—in the sense of being specifiable by a finite amount m ≥ 1 of information—then we’re still left with my question of why the greatest analytically necessary m has that value.
Especially thanks for the reminding pointer to Peter van Inwagen—there are certain videos by him which I’ve earlier intended to watch, but no time yet.
If everything were permitted, then nothing would be forbidden. So if there were nothing, nothing would be forbidden. Thus nothing is self-forbidding.
‘That’s a great deal to make one word mean,’ as Alice said to Humpty Dumpty in a thoughtful tone.
Suppose there were nothing. Now, since flammable and inflammable mean the same thing, we have derived a contradiction. Therefore, something exists.
1.
This is very interesting. I was wondering if there was a possible interaction with Solomonoff probability. For example, can we say that necessarily-All is more or less probable than possibly-Void?
Indeed, this is something IMHO very important that I left out of the post to keep the length down, but commented above. Holt’s book verges on this in its treatment of “Simplicity”, especially regarding his own “proof” of Derek Parfit’s answer which we also left out. IMHO algorithmic probability (in any of Kolmogorov/Solomonoff/Levin/Rissanen/Chaitin/Schmidhuber’s forms) may solve at least the “Boltzmann Brains” aspect of the “measure problem”. But note also the apparent implication of this paper that it is impossible to gain any statistical advantage against any observable obeying a Kolmogorov distribution unless faster-than-light signalling is possible. Beyond that, it amuses me that the one saliently visible argument I know by a popularly recognized scientist that is predicated on the validity of Solomonoff probability in Nature is not about anything in Nature, but rather about God—Chapter 2 of Richard Dawkins’ The God Delusion. (And I think it has problems because in a multiverse with infinitely many causally independent viable regions, its predicate is subject to a zero-one law.)
Ken referred to Wesley Salmon’s beautiful quote: “The fool saith in his heart that there is no empty set. But if that were so, then the set of all such sets would be empty, and hence it would be the empty set.” I have a few remarks on that.
First, Salmon actually spoke of the null set… Not that that makes any difference of course. By the way, the real source of this quote is a book by Martin Gardner (Mathematical Magic Show) where Gardner printed a letter he received from Salmon in answer to Gardner’s question if the existence of the empty set could be proven.
Second, we should note that this ‘proof’ of the empty set invokes a principle of comprehension, which is of course problematic in formal set theory. Salmon appears to reason as follows: if E is a property such that Ex means “x is an empty set” then there must be a set S containing all objects of which E is true (= principle of comprehension). So if -∃x(Ex) then S must be (the) empty (set).
Comprehension is of course shunned in formal set theory because it leads to self-inclusion and paradox, like Russell’s paradox. From Salmon’s proof, too, a paradox seems to follow: if S is defined as the set of all empty sets, then (assuming S is empty) S ∈ S, so that S is not empty, hence a contradiction.
I wonder if this contradiction can be generalized to other notions of nothingness and if this is ontologically significant:
The philosopher David Lewis had a very simple way to show the contradictory nature of nothingness using truthmaker semantics: Suppose that nothing exists. In that case p is true iff p says “nothing exists”. But then there must be a fact which makes p true, namely the fact that nothing exists. Hence there exists something, namely this fact.
Rudolf Carnap also famously argued (in his polemic against Heidegger) that the concept of nothing is contradictory. His argument was very curt: “For even if it were admissible to introduce “nothing” as a name or description of an entity, still the existence of this entity would be denied in its very definition.” In semi-formal terms: if Nothing = N such that if x exists then x ≠ N, then if we say “Nothing exists” we substitute N for x and we get N≠N.
Carnap, of course, took this contradiction as proof that the concept of nothing is nonsensical. But why not take it to be a true contradiction, in the spirit of Graham Priest’s dialetheism? Then, perhaps, we can say: something exists because nothingness is contradictory…
Poor boys (logicians). Learn Aristotle’s 10 categories and that “relation’ is not a substance; consequently, all paradoxes will ‘evaporate” and the “wars” formalists with constcrutivists with….. ps. Answer: the term “set” is a being (substance) or not?
Actually, the assumption that everything could possibly not exist is suspect. Look at Godel’s Ontological Proof: http://en.wikipedia.org/wiki/G%F6del%27s_ontological_proof which proves the existence of at least one entity given equally resonable assumptions as those given above.