Modal Logic and the Ontological Proof

By Sean Carroll | March 10, 2011 7:56 am

The ontological proof for the existence of God (really “proofs” or perhaps “arguments,” as there are various versions) has popped up in the blogs a few times recently: e.g. Ophelia Benson, Josh Rosenau, Jerry Coyne. You’ve probably heard this one; it was most famously formulated by Saint Anselm, and most famously trashed by Immanuel “Existence is not a predicate” Kant. A cartoon version of it would be something like

  1. God is by definition a perfect being.
  2. It is more perfect to exist than to not exist.
  3. Therefore, God exists.

Now, this is a really cartoonish version of the argument — it’s not meant to be taken seriously. This kind of ontological proof is a favorite whipping-argument for atheists, just because it seems so prima facie silly. Just ask Jesus and Mo.

This kind of mockery is a little unfair (although only a little). What’s important to realize is that the ontological proof is perfectly logical — that is, the conclusions follow inevitably from the premises. It’s the premises that are a bit loopy.

It’s instructive and fun to see this in terms of formal logic, especially because the proof requires modal logic — an extension of standard logic that classifies propositions not only as “true” or “false,” but also as “necessarily true/false” and “possibly true/false.” That is, it’s a logic of hypotheticals.

So here is one formalization of the ontological argument, taken from a very nice exposition by Peter Suber. First we have to define some notation to deal with our modalities. We denote possibility and necessity via:

Just given these simple ideas, a few axioms, and a fondness for pushing around abstract symbols, we’re ready to go. Remember that “~” means “not,” a “v” means “or,” and the sideways U means “implies.” Take “p” to be the proposition “something perfect exists,” and we’re off:

There is something beautiful here, even if it’s somewhat silly as a proof for the existence of God. It’s silly in an illuminating way!

As Suber says, the argument is “valid but unsound.” He pinpoints three premises with which reasonable people might disagree: 1 (“if perfection exists, it necessarily exists”), 2 (“perfection possibly exists”), and 5 (“if something is necessarily true, then it is necessarily necessarily true”). That last one is not a typo.

For me, the crucial mistake is some mixture of 1 and 2, mostly 2. The basic problem is that our vague notion of “perfection” isn’t really coherent. Anselm assumes that perfection is possible, and that to exist necessarily is more perfect than to exist contingently. While superficially reasonable, these assumptions don’t really hold up to scrutiny. What exactly is this “perfection” whose existence and necessity we are debating? For example, is perfection blue? You might think not, since perfection doesn’t have any particular color. But aren’t colors good, and therefore the property of being colorless is an imperfection? Likewise, and somewhat more seriously, for questions about whether perfection is timeless, or unchanging, or symmetrical, and so on. Any good-sounding quality that we might be tempted to attribute to “perfection” requires the denial of some other good-sounding quality. At some point a Zen monk will come along and suggest that not existing is a higher perfection than existing.

We have an informal notion of one thing being “better” than another, and so we unthinkingly extrapolate to believe in something that is “the best,” or “perfect.” That’s about as logical as using the fact that there exist larger and larger real numbers to conclude that there must be some largest possible number. In fact the case of perfection is much worse, since there is not single ordering on the set of all possible qualities that might culminate in “perfection.” (Is perfection sweet, or savory?) The very first step in the ontological argument rests on a naive construal of ordinary language, and the chain is no stronger than its weakest link.

CATEGORIZED UNDER: Philosophy, Religion
  • Tony Konrath

    I get this one put to me time and again.

    Just stop the perpetrator by saying that you don’t accept that “It is more perfect to exist than to not exist.”

    Where does that come from?

    Moreover you can argue with them that since we can imagine a perfect unicorn that also must exist.

  • john

    I’m confused by the displayed argument by Prof. Suber. In particular, I don’t think Line 5

    ~[]P –> []~[]P

    is derivable by substituting ‘~[]P’ for ‘P’ in

    []P –> [][]P.

    Instead, maybe we are supposed to substitute ‘~P’ for ‘P’ in

    ~[]~P –> []~[]~P

    and then apply double-negation elimination on the resulting sentence.

    By the way, Sean, is you interest in logic and metaphysics a new thing? Any interesting connections to your interest in physics?

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  • TheBlackCat

    I haven’t looked at your proof closely yet, but I think you are being unfair by calling the first version you listed a “cartoon version”. My understanding is that this is the original formulation of the proof and that the idea of “necessary existence” was a later addition. Further, I have seen many instances where the original version of the proof is used to support the idea of God rather than one the later revisions.

    So rather than being the strawman you imply, it was originally intended to be take seriously, and still is be many religious people.

  • Stuart Brown

    Spinoza’s take on the perfection argument is pretty awesome. He gives a definition of perfection: he equates it with with reality. The more perfect something is, the more real it is. He does away with modality in the ontological argument: perfect things necessarily exist; imperfect things necessarily do not. God is (infinitely) perfect and (infinitely) real: thus (and through other arguments too) Spinoza arrives at total pantheism. This appears to be a slightly odd concept of perfection, given that it would appear to be comparative rather than superlative — can things be more or less perfect/real? But the argument concerns knowledge, and knowledge of God, so is better put as:

    — God is perfect, therefore God is everything.
    — Some things appear imperfect to us.
    — Imperfect things cannot exist.
    — Imperfect things therefore appear so due to a limited knowledge of God.
    — To someone with a full knowledge of God, nothing appears imperfect.

    Highly unusually, he argues that a full knowledge of God *is* possible for human minds. Why? Well because they are, of course, part of God, as is everything.

    Spinoza is barmily wonderful.

  • Sean

    John– I think you’re right. Looks like a ~ and a [] were carelessly commuted. But as you say, I think it can be fixed up.

    Not really a new thing, just something that doesn’t come up very often. I went to a Catholic university, and was assured by one of my religious-studies professors that the ontological proof could be cast in terms of formal logic, but only with the help of the internet did I finally get around to looking it up.

  • Rodrigo

    I think it is much simpler. The thing is, when you state the premises:

    # God is by definition a perfect being.
    # It is more perfect to exist than to not exist.

    you are already stating the conclusion. Not in a deduction way, but inside the premises. If I ask what is “perfect” according to those, one should say something like:

    “Perfect is something that is [bla bla bla] and exists”

    Since the second premise states that existing is “more perfect” than not. Then, what the first premise is really saying is:

    “God is by definition a being that is [blablabla] and exists”.

    Therefore, God exists? Of course, it’s almost (if not entirely) tautological.

    Of couse we could just challange the premises (as the article did in a way):

    1. Who said God is perfect? If I say an unicorn is perfect, than it exists?
    2. Why existing is more perfect than not? What is perfect, for that matter?

    The last phrase from the article said it all: “The very first step in the ontological argument rests on a naive construal of ordinary language, and the chain is no stronger than its weakest link.”

    But my point is that EVEN if we accept the premises, the conclusion is meaninless, since it were already hidden in the premises (not in a good, deduction way). “God exists (is perfect), therefore god exists”.

  • Peter Ellis

    Just stop the perpetrator by saying that you don’t accept that “It is more perfect to exist than to not exist.”

    Even better, argue the converse. It is more perfect not to exist. However good something is in reality, you can always imagine something better – something that goes to eleven. Therefore, God is imaginary.

    Put enough fancy clothes on that and you can probably disguise it as a consequence of the diagonal argument.

  • RawheaD

    I agree with Rodrigo. It’s not “almost” but entirely tautological, because under the premise, the concept of “perfection” includes “existing”. I’d also point out the logical instability of the phrase “more perfect”. If something is perfect, it should, by definition, unable to be “more perfect.”

  • Ophelia Benson

    I found, when thinking about this, that the more you think about “perfection” the loopier it seems, at least in relation to anything actual in the actual familiar world. Very good, very very good, very very very good; those all make sense; but perfection is just absurd.

    I wonder if engineers see it differently.

  • Eric Habegger

    Without being an expert in philosophy I would say the proposition stated in the cartoon is pretty accurate. It also pretty well sums up much of Eastern Philosophy. If you can imagine it then it is perfect. What causes problems is when you try to imagine an entity separate from that system, that does not experience happiness and/or desperation and suffering. People traditionally think of a god or gods that is somehow removed a bit from the experience of the world. If you think of desperation and suffering as the yang to the yin of happiness, then you can’t have either without the other. And if you define the world in that way why would a god be in any way separate and removed from that. A formal separate anthropomorphic God isn’t really necessary. One should just assume a lower case god as the totality of what is, suffering and happiness together. And it is perfect, but only in it’s combined totality.

  • Matt Tarditti

    #1: God is perfect
    #2: Perfect would be a tolerance to infinite precision
    #3: An extra digit of precision (going from .001 to .0001) usually involves a 10 fold increase in modeling or machine time.
    #4: God is infinitely expensive
    #5: Double the factor of safety and settle for a 90% God

    By the way, I noticed that the blog banner changed from a blue ball to a….blue ball. Way to break the mold.

    (I know, I know. It wasn’t Sean’s design. Consider yourself lucky that some guy going EVA isn’t relieving himself instead.)

    -Matt (an engineer)

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  • Jim Cross

    As a Buddhist, I’ve always felt that non-existence was more perfect than existence.

  • BL

    For a really nice take on what goes wrong with (a version of) the argument, see David Lewis’s “Anselm and Actuality.” Lewis takes an informal version of the argument and claims that there are four different ways we can read: “Something exists in the understanding, than which nothing greater can be conceived”. Under two of those ways, the argument is valid, but the premise in question is not plausible. Under the other two ways, the premises all look true, but the conclusion doesn’t follow. Lewis also nicely avoids using any modal logic at all by quantifying over possible worlds directly. (Don’t read the final section of the paper, though, where Lewis goes off the rails with his idiosyncratic metaphysical views.)

  • réalta fuar

    I think I’ll go stare at my navel now.

  • Gordon Willis

    If we take the notion of something which is perfectly blue, we can claim to conceive of something than which nothing can be more blue: a pure blue, containing not the faintest admixture of any other tint. Do we conceive of a dark blue, or a light blue? Obviously, though the OA claims that we can conceive of the greatest possible something-or-other, we can’t. Perfection is a mere superlative, and as such is something on a scale between “a bit” and “absolutely”. But we cannot conceive of “absolutely”. As Ophelia points out, it’s a case of good, “very good, very very good”……most perfect…even more perfect…(!) So it’s basically just a word, meaningful only in relation to some context, and meaningless as an attempt to describe accurately some sort of “absolute” (whatever that might be).

    Clearly, only an entity can be perfect, or at least perfectible (or just improvable), because perfection must be some condition of the properties of an entity. Also, an entity must be a sort of sum total of its properties, otherwise there would be no entity. This means that “perfection” is contingent, so immediately the OA seems to contradict itself, considering that a perfect being isn’t supposed to be contingent. After all, the OA is correct in claiming that something that exists is more perfect than something that doesn’t, for the banal reason that there is no thing that doesn’t exist.

  • Jumblepudding

    I would further like to posit that everybody goes to Shakey’s pizza, because Shakey’s is the place to go.

  • Russy

    I’ve always had a few problems with this argument. Mainly:

    1. Existence as an attribute of perfection.
    One could make an argument that says something like: God is perfect. Perfection is an ideal. No thing in existence correctly matches it’s ideal. Therefore God does not exist.

    2. The vagueness of “perfection”.
    People just tend to throw it in there as a catch-all abstract, but what is perfection exactly? What makes a perfect blue, for example, perfect? Now add in the fact that not everyone will agree on what constitutes perfection. Can we ever arrive at an objective definition of perfection?

    3. Logically paradoxical.
    When people do give some explanation of God’s attributes, they tend to throw in omnipotence, omniscience, omnibenevolence, etc., all of which come with their own internal contradictions. Can God make a rock too heavy for himself to lift? Either answer put limits on his power, and thus his perfection. In fact the very idea of omnipotence is illogical, therefore not possible, hence not perfect.

    It seems just sophistry to mask the lack of data on the subject. Like Sherlock Holmes said: can’t make bricks without clay.

  • jparfit

    Is the crude version of the argument above perfectly logical? Yes, but only in the sense that-

    God exists, therefore God exists

    -is perfectly logical. Validity occurs when the truth of the premise(s) means that the conclusion must be true, on pain of contradiction. So an argument which “begs the question” can be valid. If one is going start talking about “X” in the premises of an argument, and then conclude with the existence of X, the “X” in the premises has to refer to the “concept of X” not X itself, if it is not to beg the question. If one then admits that the “X” in the premises refers to the “concept of X” then the argument will be equivocating between the “concept of X” and “X”, so it will not be valid. I can’t see how any modal version of the argument would alter this. So the argument seems to be doomed from the beginning. Am I missing something?

  • ernie keller

    The only way I know to decide if something exists is by reasoning about observations. I’m sure that’s not “perfect” but it appears to be “necessarily’ the case.

    For that reason I think the Design argument was a better challenge. You really had to think about that one in the days before science began to show that primeval simplicity could lead to levels of complexity you’d need to produce conscious beings.

  • ernie keller

    The only way I know to decide if something exists is by reasoning about observations. I’m sure that’s not “perfect” but it appears to be “necessarily’ the case.

    For that reason I think the Design argument was a better challenge. You really had to think about that one in the days before science began to show that primeval simplicity could lead to levels of complexity you’d need to produce conscious beings.

  • Ebonmuse

    What Rodrigo said, at #7. The conclusion of the ontological argument is contained in its premise. It’s hidden a little more sneakily than in your average circular argument, but that’s all.

    Also, to play off what Sean said about perfection not being a well-ordering relation on the set of all objects: Who says the axis of perfection has to run in only one direction? Couldn’t you use the ontological argument to prove the existence of an all-powerful, all-knowing, perfectly evil being – one that’s exactly as powerful as God, but always has the opposite desire in any situation? (You could call this “the Manichaean Reductio”.)

  • Eric Habegger

    Why even define God as being perfection in the form of good or evil. It seems even western atheists are steeped in the traditions of good and evil. Couldn’t perfection be something altogether different from that? Use some imagination!

  • onymous

    I forget who to attribute it to, but back in my undergrad days I remember a discussion of this where someone pointed out that, just as a perfect God who exists is even more perfect than a perfect God who doesn’t, a perfect God who exists and tastes like delicious ice cream is even more perfect still. Mmm, delicious ice cream.

  • Brian Too

    No, the problem is that there is a point before #1. Let us call it point 0, and as such it should be defined as:

    0. A being named God is asserted.

    Only then can you continue on to point #1. And if you do not accept point #0 then the whole logic chain falls apart.

    I don’t take this stuff too seriously. Logicians are still debating the outcome of Zeno’s Paradox and that one is simple by comparison.

  • miller

    I’ve blogged about the modal ontological argument, explaining exactly why the premises do not say what they appear to say. Occasionally I’ve gotten trained philosophers trying to attack my arguments, and every time it becomes apparent that they don’t understand logic. (Come on! It’s just like math!)

    Long story short, I once got Plantinga himself to respond to me, and in his response he suggested that the parallel postulate might be necessary. Does he not know about non-euclidean geometries? And thus my respect for “sophisticated” theology dropped to an all-time low.

    When I have more time I’ll be happy to jump into the details of above comments.

  • Curious Wavefunction

    If Kant were on Facebook, I wonder if he would be expounding on the lolcategorical imperative

  • Craig McGillivary

    Hume’s general objection to this argument is the most important. You can’t prove the existence of a being with an apriori argument.

  • miller

    @Sean #6
    The problem is you stated Becker’s postulate incorrectly. It says that if something is necessary, then it is necessarily necessary AND if something is possible then it is necessarily possible. Note that ~[]p is equivalent to <>~p, so Becker’s postulate can be applied to it.

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  • Chris

    I exist.. therefore I must be perfect!

  • Kevin

    Yes, I think it’s quite clear that the notion of “perfect” is conditional, and therefore irrational per se.

    What’s more perfect than god? God with a pizza. What’s more perfect than god with a pizza? God with a pizza and a 6-pack of really good beer. And on and on.

    Nothing defined as “perfect” can exist because the concept is necessarily limited to non-existent things. Except Natalie Portman, of course.

    But it’s quite possible to redefine god as “not quite perfect”, and then the game’s on again. This notion of god as omni is a fairly recent invention, I think.

    For the purposes of Anselm, it borks the argument, however.

  • David George

    Still looking for not-God? Or not-good? Nothing is perfect — Mother Nature is not perfect, but she is harmonic — not by implication, but by operation.

  • semkath

    In a similar fashion, but different:
    It’s a proof for the neccessary existence of god.
    If anyone has interest for the details:

  • Simon

    I like Dan Dennett’s demonstration of the silliness of the OA: proof of the perfect ice-cream sundae!

    But Hume also nailed this one, didn’t he? When he pointed out that nothing ‘necessarily exists’ if it is possible to conceive of it’s non-existence without contradiction: “Nothing is demonstrable, unless the contrary implies a contradiction.” (Dialogues, part IX)

  • Axxyaan

    IMO the big problem is line 2. The fact is, that if we talk about something possible being true, we normally imply that it is also possibly false. But that possibility is not explicitly mentioned here.

    So what would happen if we introduced line 2a: <>~p or ~[]p which would state that the not perfect was possible.

    It would lead via modus tolens of line 1 directly to ~p.

    So by line 1 we have introduced a context in which <>p ^ <>~p is a contradiction and in which the choice of <>p or <>~p leads to p or ~p respectively.

    Now if I have to choose between the perfect is possible and the not perfect is possible, I’ll choose the second every time. Because that is not only possible, we see it’s existence every minute.

  • Aleksandar Mikovic

    My problem with taking seriously the proofs of existence/non-existence of God is that the idea of existence is not well defined and that one only uses the classical logic, where the rule of the exclusion of the third is valid (i.e. p or not p). Given the ideas from modern physics, i.e. quantum mechanics and parallel universes, it is clear that the outcome of such a proof depends on the context which one assumes. Note that the logic of quantum mechanics does not have the exclusion of the third rule (an electron passes through both slits in the double-slit experiment) but in all profs the validity of classical logic is assumed, and this is not justified, since the ontological features should apply to all domains. Another observation is that existence can be relative, if one accepts multiple universes (i.e. something does not exist in our universe bat it can exist in another universe). If one enlarges the domain of existence even further, one can say that there are abstract ideas outside of the universes, one arrives at the platonic ontology. For me the platonic ontology is the most general context in which various general questions can be analyzed. Then the idea of God exists, so that God exists, but what is interesting is to find out what is the relation between God and our universe.

  • ObsessiveMathsFreak

    Things like this are what make me believe that logic is about as far away as you can get from mathematics without actually leaving the subject.

  • sievemaria lucianus

    …. even those things that have gone bad or become broke – were once *perfect*

  • Dan L.

    You can break it pretty easily by asking the person to define “existence.” Most things that we think of as “existing” are contingent, temporary configurations of matter. We think about chairs “existing” without taking into account that there’s a definite time at which the chair is constructed and almost certainly a time at which the chair will be destroyed or dismantled.

    I have yet to hear of anything that “exists” in any sort of eternal way. Even electrons and other “fundamental particles” can be “destroyed” in nuclear reactions. One might be able to plausibly claim that electrons necessarily exist, but one can’t claim that of any particular electron.

    I think that, based on the sample so far investigated by human beings, one could make a pretty good case that anything that exists does so contingently (essentially by definition of “exists”). After all, if something existed necessarily, it would be eternal, and I simply can’t think of an example of ANYTHING that exists eternally.

  • Tom

    If the Ontological Argument is correct then the opposite would also be correct.

    1. George W. Bush is by definition an imperfect being.
    2. It is more imperfect to not exist than to exist
    3. Therefore, George W. Bush does not exist.

  • Aleksandar Mikovic

    Theoretical physics offers a way to define timeless existence: a particle trajectory in the spacetime (worldline) is such an object. The particle worldlines constitute the so called “block universe” interpretation of reality and time. In this interpretation the passage of time is an “illusion”, i.e. the time passage is an emergent phenomenon. Personally I subscribe to the “evolving block universe” interpretation, where the passage of time is identified as a moving Cauchy surface ( a section of the block universe).

  • Jim Kakalios

    I believe it was Woddy Allen who put for the syllogism:

    1) Socrates was a man

    2) All men are mortal


    3) All men are Socrates

    Put that in your pipe and smoke it!

  • John Harvey

    Some responses:

    To TheBlackCat

    “My understanding is that this is the original formulation of the proof and that the idea of “necessary existence” was a later addition.”

    And to


    “I’d also point out the logical instability of the phrase “more perfect”. If something is perfect, it should, by definition, unable to be “more perfect.” ’

    The original formulation, that of Anselm in the Proslogion, refers not to perfection but to “something than which nothing greater can be conceived”, aliquid quo nihil maius cogitari possit. This is not a quibble in the present context since everything depends on exactly how the argument is worded.

    To Ernie Keller
    “The only way I know to decide if something exists is by reasoning about observations.”

    There are many cases in which we use other methods to determine existence. In order to determine whether there is an integral square root of 181 we could , for example, try squaring all numbers within a certain range: this would not even require observing a piece of paper and ink marks if you were good at doing math in your head.

    To Simon:
    “But Hume also nailed this one, didn’t he? When he pointed out that nothing ‘necessarily exists’ if it is possible to conceive of it’s non-existence without contradiction: “Nothing is demonstrable, unless the contrary implies a contradiction.” (Dialogues, part IX)”

    It is exactly Anselm’s contention that the non-existence of God involves a contradiction: therefore the quote from Hume here begs the question (I am not presuming in this brief comment to refute Hume’s complete presentation, which see.)

    To Dan L.:

    “If something existed necessarily, it would be eternal, and I simply can’t think of an example of ANYTHING that exists eternally.”

    It is at least arguable that the number three exists necessarily and eternally, that is, timelessly. I would suggest that the burden of proof would be on anyone who thought 3 was temporary and contingent.

    To Tom:

    “If the Ontological Argument is correct then the opposite would also be correct.
    1. George W. Bush is by definition an imperfect being.
    2. It is more imperfect to not exist than to exist
    3. Therefore, George W. Bush does not exist.”

    I cannot tell to what extent this was meant seriously, but in any case this would apply only to the most imperfect being, not merely some imperfect being.

  • justawriter

    The problem is see is that you can prove anything if you pull your axioms out of thin air. If I assert as an axiom that two perfect things are greater than a single perfect thing, doesn’t that prove there are an infinite number of Gods? And by extension doesn’t that prove that monotheism must be wrong? Those lucky Hindus must have the only valid religion, I just proved it.
    If I were to run into old Anselm himself, I would ask him that since I can conceive of a conception of being than which no greater can be conceived that no other conception of that being can be made, that description must be the only true conception of that being and all other conceptions of that being, including Anselm’s are wrong? (He would weasel out, I’m sure, how humans are imperfect, blah, blah, blah)

  • Rosmary LYNDALL WEMM

    If god exists then he is perfect
    Men are perfectly male.
    Black is perfectly colorless
    Therefore god is a black male.

  • Rosmary LYNDALL WEMM

    The real first line of the argument should read:

    1. We will assume that god exists and that he is perfect.

    Lines 2 and 3 are thus built upon pure conjecture.

  • Guido

    The Greeks made fun of these silly arguments 2000 years ago. And how you can prove or disprove that God is when God is by definition undefinable.
    The bottom line is: look around – if it makes sense to you then God is – if it doesn’t then you are another piece of garbage in your own mind. So sorry.

  • TimG

    I’ve heard it said that the reason perfection must be possible is that we can imagine it. But that’s silly. We can imagine all sorts of impossible, self-contradictory things, because our minds don’t need a coherent description of something to imagine it. We tend to interpret any sequence of words that *sounds* coherent to be a coherent idea, whether it is or not. For instance, I can imagine “a stone so heavy that an omnipotent God cannot lift it”, even though this is self contradictory (you can’t simultaneously have an omnipotent God and a limit to his power). But because I can imagine it, I could say such a thing is possible. And if an omnipotent God is necessary, and yet it is possible for there to be a limit on his power, then he’s not necessarily omnipotent at all, so we arrive at a contradiction. This is an unsound argument, but the flaw in its premises is much the same as the flaw in this version of the Ontological Argument.

  • Anchor

    Sorry I came so late onto this.

    Based on 55 years of observational (if anecdotal) experience, I’ve never once encountered anything that existed that I could characterize as “perfect” or for which I could ever even remotely determine or confirm the presence of perfection. Never.

    Here is another ‘cartoon’ argument to refute those first three points Sean passes along, which are indeed, largely based on the tripe of Anselm which I have myself steamed over for decades, those purported “proofs” which so easily elevates premise to the status of self-evident fact.

    The following come about from my logical deductions based on what I’ve personally observed as well as what I’ve absorbed from formal theoretical AND observational work conducted by – and as far as I can determine – totally consistent work performed by distinguished physicists that do in fact make sense of the real world:

    Conjecture A (soft version): existence bears no relationship or obligation to our conceptual notions of the ideal, and since our ability to observe is (from many other lines of compelling observational evidence) anything but ideal, we can’t ever attribute perfection to anything that exists even if IT IS REALLY THERE, or merely if we suspect it is present based on preconceived premises of the ideal, however preciously we may harbor them. Nature works independently of our minds (which explains why we are so chronically if not obnoxiously in error).

    Conjecture B (hard version, encompassing the soft version): there is no such thing as perfection in anything that exists. Existence is by definition a state of imperfection definable as an inevitable consequence of order subject to changes of state or attrition through interactions with time (entropy inducing disorder according to the 2nd Law of Thermodynamics). The notion of existence being an attribute of perfection is therefore ridiculous.

    That last part is a conclusion of the “harder version” of the conjectures presented here. (But I’m not quite finished…bear with me).

    Since observational evidence seems in excellent agreement with one form of “idealistic” theoretical understanding available to us (quantum theory), it seems consistent to conclude that the existence of anything is predicated on its interactions with other things that too exist, rendering anything that exists in particular to inevitably depart from its ostensible state of perfection the instant we attempt to observe it or whenever anything else which happens to interact with it takes up the baton of ‘observership’ (Anthropic Principles thereby be damned and scrapped).

    It is reasonable to conclude that since perfect ‘isolation’ (in space) or ‘stasis’ (in time) defines non-existence by definition, the corollary – of constant potential exposure to interaction in spacetime full of other particular objects or things which co-define each other – necessarily demands the attribute of existence.

    So where is the putative “perfection” in existence?

    CHANGE or PROCESS is the fundamental barometer and attribute of existence, and the moment anything that ‘is’, once investigated to determine its integrity through observational bombardment, immediately becomes something that ‘was’, and therefore something completely different boggles the mind, not in terms of how nature does her thing, but in terms of stubbornly reluctant we are in taking her at her word at face value.

    Things get altered and ordered things fall apart all the time. One does not even have to observe a thing to ‘know’ (from our idealistic understanding of quantum theory) that there are other things in profusion throughout the universe that perform the task of ‘observation’ through interactions that are quite serviceable in our sentient stead. (So much for the specific CONCEIT associated with the Anthropic Principle).

    How can that be reconciled with “perfection”? If something – ANYTHING – was ever once perfect, it must perforce become imperfect the moment it gets ever-so-gently clobbered by any photon in the ambient cosmic medium that might have the wavelength-energy so much as to at least jostle it about. True, it COULD ‘change’ from one state of perfection to another, but the initial state of perfection is destroyed. How ‘perfect can anything possibly be – including any particular state – that is subject to modification, let alone destruction?

    There’s another way out of all this.

    Perfection may only be satisfied by the absence of change or process. In other words, only the absence of interaction can provide perfection. The absence of space and/or time satisfies the ‘condition’…or, more accurately – at the risk of introducing further semantic confusion – the LACK of condition satisfies ‘perfection’. To be ‘perfectly’ blunt about it, NOTHING is the ONLY POSSIBLE reservoir of ‘perfection’, as long as one does not place too high a priority on the term “reservoir” as a ‘something’ with the potential to exist.

    I’m talking about a null reservoir – a non-existent NON-PLACE – the NOTHING – which is not anything. It isn’t even ‘anything’ that may be described or referred to from our position of existence, which seeks meaning out of RELATION. There isn’t any relationship with NOTHING or NON-EXISTENCE to be had from our point of view. ‘It’ is a non-representational non-artifact unalloyed to any reference frame we might bring to bear, even in principle. ‘It’ isn’t even an ‘it’. That pesky ‘thing’ of NOTHING that does not (at least in principle) even exist is almost impossible to extricate from the arena of ‘thingness’ in our minds, because we have no recourse but to refer to something to RELATE to or otherwise semantically INTERACT with. But ‘it’ is not ‘there’. There isn’t even a ‘there’ there for ‘it’.

    But let’s amuse ourselves by assuming a reference anyway, and refer to it as something we can get a handle on: let’s just call it ‘non existence’. (Be forewarned that I speak in terms of quantum-scale entities, lest I be accused of hideous New Age tendencies):

    Conjecture C (ultra-hard version, although it is really just an addendum to the ordinary hard-version, with the extra baggage of explanation, because I’m by now bleary-eyed and this is a cartoon): Given the profuse and well-documented examples of IMPERFECTIONS in existence, and the theoretical bases outlined above that takes care of the rest even without observation (with some measure of uncertainty, to be sure, but that’s why this is called a ‘conjecture’ which may or may not be ‘proved’ in this cartoon) the only possible perfection that can possibly be had is in non-existence.

    If there is any meaning in the notion of a system’s state ‘in between’ successive interactions, that ‘state’ must be considered non-existent and may only be appreciated by another (‘observational’) interaction. There is NOTHING we can see of ANYTHING that exists unless we or something else in the universe bother it through some interaction, and what we do in the act is see something that isn’t what it used to be. Literally, in the meanwhile (so to speak) ‘between’ interactions, it doesn’t exist. There isn’t any ‘in between’. On the strictly quantum scale, there simply isn’t any existence of any particular state between one interaction and the next.

    What can we deduce from this so far?

    Conjecture D (the super-duper ultra-hard version, personally preferred by yours truly): Perfection being an attribute not only unknown in the realm of existence, but a requirement of NON-EXISTENCE, demands that the popular notion of THE perfect being – otherwise known as ‘God’ – is NOTHING. Non-Existent in purist perfection, unbridled by any issues presented by the constant turmoil of interaction existence demands.

    Conclusion: Prayer to Perfection is literally tantamount to praying at nothing. There isn’t even any interaction of any kind that can possibly take place, even in principle.

    Quite aside from the puerile pop-estimation of the profundity expended in making sure that the MOST POPULAR OMNISCIENT, OMNIPRESENT AND OMNIPOTENT BEING in all the world ought not properly to be given a name, according to the most excruciatingly fundamentalist. And yet they invariably go right ahead and point out one, as in “Yahweh” – notice the capitalization indicating a proper noun NAME…even though “God”, though likewise capitalized, ironically does a considerably better job of un-naming ‘Him’ through millennia of anonymity, in the collective population of generic “GODS” – and distinguishing THIS one simply by the expedient of singling out the particularity: it’s “The One and Only” and “The” god that NAMES the IDEA of it. Personally? I’d would find it more charming if He was referred to with a decent name like the rest of us, who are all supposedly Products of His Infinite Creative Ability that can only be ushered forth by such Perfection. Ralph might be a good name. So would Fido (as so many who invoke Him to terrorize their followers might as they would with an attack-dog). But any Perfect Creator who fashions, out of His Infinite Perfection of Talent, a world that produces the horror of the Japan earthquake and tsunami of March 11, and the ensuing horrific deaths and incomprehensible suffering, I would rather name something like, say, “Arschloch”. Monumentally so. Stinking tothe highest heavens so.

    There isn’t any “god” that isn’t an artifact of people’s minds. Like their ideals of what constitutes “perfection”. What possible harm could it inflict to apply a moniker to nothing at all?

    The IDEAL of the perfection of God is quite evidently EVERYTHING in the MINDS of the penitent. The REALITY is that perfection is incompatible if not impossible with existence, which is where we are, evidently, in spades (as I so clumsily relate above). The peculiarly funny thing is that we have cultivated cultures of people that find it so simple and easy to abrogate their own interactive responsibilities in favor of investing huge amounts of time, energy and resources in order to solicit assistance from NOTHING IN PERFECTION.

    Anybody want to wager that the same irrational mindset doesn’t rule the actions of people when they ostensibly act on BEHALF of God? Like obnoxiously wealthy people and corporate interests?

    Yeah, I’ll agree that “God” exists as long as it is understood it is NOTHING BUT an existing CONCEPT that infects the minds of a troublingly preponderant number of people. No, I will not entertain any notion of a perfection of being that exists anywhere in the actual reality of the universal realm of nature, which indubitably EXISTS…UNLESS one posits that non-existence (never mind ‘perfection’ for the moment) has some legitimately non-trivial bearing on existence besides its basic penchant for framing existence in the cockles of people’s minds…which seems to pose something of an impasse. In any case, it isn’t beyond the stretch of ordinary imagination to confine its trajectory to what is either demonstrably observable, or via theoretical excursions consistent not only with observational evidence, but with itself.

    [The above remarks are certainly contingent not only on a ‘premise’ that may or may not hold up to scrutiny, and of whether or not I can correctly identify things that exist, properly distinguish between the idealistic artifacts of the mind and the artifacts of the real world we acquire through our senses, and whether or not I understand what existence even means in terms of any workable definition that conforms to what nature screams at us through our well-documented scientific successes so far. But this cartoon certainly isn’t very much harder to appreciate than any ridiculous religion. Is it?]

  • David George

    #49 Guido — How right you are. I believe the universe can be understood as a system for making sense. But physics has followed a path by which many physicists find the universe to be “pointless”, i.e. making no sense. Maybe wounds from the battle for free thought are not healed, or maybe the physical model is incomplete. But there is something pathological in using sense to make nonsense out of sense. (Physicist, heal thyself!)

  • Alan

    You can’t have consciousness in the universe without quantum mechanics, period. Who ordered that ? – quantum mechanics (not muons).
    Well it’s some topology of spaces just before the universe began so the multiverse goes. But doesn’t that beg the question – why a life-mind universe got selected. OK, you can say it was Martin Rees’s infinite coatshop, eventually you will find a coat that fits.

    But if this is true (I knew the some of the investigators, several distinguished Professors of physics, psychology and electrical engineering) – It was a three year international study:


    Doesn’t this mean life-mind universes are massively important, in that those are selected in which consciousness, or some kind of heightened awareness, continues after death? Inescapable. And this puts meaning back into life, notwithstanding Weinberg.

    It also arguably makes the universe very very God-like. Just as in Solaris (the recent film), when you die the universe looks after you – keeping your meaning going. Beautiful.

    All this occured in a bare stone cellar with other witnessess.

    It is from the 300 page Scole Report (1999)

    This is a report from an academic psychologist (a witness) – actually from The Scole Report – 1999:

    “The first phenomena that I saw were small points of golden light dancing in the corner of the room…They danced animatedly upwards and downwards…. Shortly following this, there appeared a ball of diffused light, which I estimated to have a diameter of about 20 cm, close to the ceiling in the same corner…as the lights. The ball had no physical boundary: it was simply a three-dimensional orb of diffused golden light. It hung suspended for a moment in the corner about 30 cm beneath the ceiling. Slowly the orb moved toward the centre of the room, pausing above the centre of the table round which we were all sitting. It lowered itself by about 17 cm, remained still, then retreated slowly upwards and backwards into the corner…There were no beams of light to the orb, and the light was not reflected onto a surface; it moved independently in space. This occurred twice in succession, and I became aware of an overwhelming feeling of gentleness and love which seemed to accompany this phenomenon or, more accurately, which this phenomenon seemed to embody.”

    Very, very challenging.

  • Herman Newticks

    Alvin Plantinga made a nice modal ontological arg for the existence of God in The Nature of Necesssity. I recall that it started from the premise that God is the being such that none greater can be conceived. Then plowed into the same modal arg. Fun!

  • Joseph Smidt


    I enjoyed reading this. Two things:

    1. I have been told the Godel’s version of this proof is more difficult to critique than Anselm’s. It would be fun to see you rip that version apart.

    2. Your numbers analogy gives theologians fuel for their cause. They might point out that there isn’t a largest finite number but that as numbers get bigger they approach infinity and then tie this into an argument that not only does a most perfect being exist but that, by analogy, he must be infinite. (By analogy)

  • Joseph Dowdy

    This whole argument rests on one major flaw. There is no such thing as perfect. Any mathematician will tell you that there are no perfectly straight lines in reality. There can be no perfect lines thus there can be no perfect objects or things with names. Perfection is an illusion just as measuring 5 inches is more accurately measured as 5.00000000000029. It depends on the perception and logic dictates that while there is assumed truth to things there can be no perfection.

  • Matt B.

    1. I’m thinking of a spacecraft that travels faster than light and is blue.
    2. Things that are blue reflect blue photons.
    3. Things that don’t exist don’t reflect photons. (“It is more blue to exist than to not exist.”)
    4. Therefore anything blue exists.
    5. Therefore the blue faster-than-light spacecraft exists.
    I created something from nothing. Yay, me!

    Just because a combination of traits (including existence) is conceivable, doesn’t mean it is actual. It just means your brain is not restricted to conceiving true concepts.

  • Matt B.

    I think there’s a problem with treating existence as a characteristic. Any other characteristic of an entity (whether conceived or actual) might be alterable, but you can’t just add or subtract existence.

  • Daniel

    I think all these reasoning about God are so non-sense; I don´t waste my time on that.
    That is so useless… It´s so wrong….

    Several non-sequitur arguments: in the argument, in the comments…

    Though there´re some comments containing quantum mechnics, topology and about inteligent consciousness. Hmm, MAYBE these are worth to be read until the end.

    P.S.: from someone who believes in God.

  • Tim

    Has anyone in this discussion read St. Anselm’s book from which the proof comes, “The Proslogion”, along with the Reply to Gaunilo? The second is an addendum which sketches out the ontological argument in its completeness. While many have disagreed with St. Anselm (including Gaunilo, to whom the aforementioned letter was addressed, as well as St. Thomas Aquinas), his argument is actually subtler than the way it’s portrayed here. Gaunilo had said what some say here, namely, that you can use can use the argument to prove that a perfect island (for example) exists. Anselm explains how his argument can only apply to God.

  • Carneades Thales Strato

    Sean, Aquinas himself, whilst against this argument, unwittingly and surreptitiously, uses the notion of perfection in his fourth way-the degrees of perfection. Michael Scriven leaves to the reader to solve it as a silly argument in his “Primary Philosophy.”
    And the ” Star Trek’ argument is that as He is perfect and the Cosmos is imperfect, then He cannot exist!
    Plantinga the purveyor of solecistic, sophisticated sophistry of woeful, wiley woo- ignorant, complicated nonsense, claims that omni-God cam use flourishes-imperfections- in designng matters whilst limited God must use what little He has- the perfect in effect.
    He claims to have evisicerated the logical problem of evil, but he uses the unknown defence argument, which itself is the argument from ignorance and which makes topsy-turvy morality!
    No wonder then that Keith Parsons,except for stuff @ Secular Ouptpost, has gotten out of the philosophy of religion!
    Sir, please check out that blog of mine!

  • tamurphy

    Perfection emerges as an artifact of awareness within an organically individuating perceptual node. How might perfection thus be envisioned? It would lack nothing/include everything — eternal infinity. Coherence, often described as shared existence, may be the closest approach of science to such a conception. Indeed, Sean enlists ‘coherence’ as his criteria for judgment.

    Is perfection possible? Certainly not in the finite world of individuating perception, ubiquitously animated by awareness. But as sages have noted through the ages, awareness is everywhere capable of shucking its local trappings, thereby exposing underlying coherent superposition of boundlessly evolving probabilities. Shorthand for this might be coherent awareness.

    Note that ‘boundlessness’ acquires meaning only within the purview of a distinct perspective hosted by an evolving organism.

    Necessary versus contingent existence? This is a perversion of the very notion of existence. Clearly, only existants may be regarded as either necessary or contingent. Existence IS…period!

    In endlessly localizing perception, color, taste, smell and feel subsume organic domains, evoking recognition, anticipation, articulation and memorialization. The collective of all such local perceivables comprises a consensus universe, within which notions of creator and supreme-being inevitably percolate.

    Perfection is uniquely inclusive of all instances of existence. That’s a singularity. Inclusion of every instance of existence is essential to perfection, as any deficit is naught but imperfection.

    In the realm of scientific thought, it’s perhaps most eloquently articulated as an infinite and eternal multiverse, embodying all shimmering perspectives of fractally proliferating perception.

    Instances of existence boil down to awareness. Bacteria are less filtered from awareness than plants and animals. Humans deploy filters that subtly surf experience in domains of recognizing, anticipating and articulating — with memorializing as the ultimate articulation. Without situational recollection of present remembrance nothing can ever happen. That’s the organically based engine of time — present moment remembrance of experience coupled with situationally induced recollection. Even as experience pumps up remembrance, circumstantial recollection conditions recognition, anticipation and articulation.

    Symmetry is irrelevant to a non-dimensional singularity such as perfection.

    No-thing may be regarded as shorthand for all existants.

    Perfection isn’t a ‘largest possible number’ but infinity — again a singularity.

    So how might such an entity be described? I’d suggest labeling it ‘coherent awareness,’ as awareness — the animating force of perception — illuminates the meanings of local entities.

    Coherent awareness is non-dimensional; or, equivalently, omni-dimensional. It’s coincident with inflating probabilities entangling with boundlessly propagating perception. Coherent awareness is an eternal superposition condensing as endlessly individuating organisms on scales ranging from Planck to cosmic.

    The inevitable question of will arises here. Without feedback, all notions of anything are randomly generated artifacts of imagination.

    I’d propose that while coherent awareness encompasses all-that-is, it also occasions myriad singularities of local perception. The unique relationship of each such perceptual node to all others inflates its own bubble universe.


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Cosmic Variance

Random samplings from a universe of ideas.

About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] .


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