The Ontological Argument for God (“OA”) is not only infuriating in itself—the hauteur of thinking you can demonstrate the existence of something by logic (and bad logic) alone, without any reference to observation!—but also by its persistence: that generation after generation falls for this philosophical scam. The OA embodies the worst aspects of both theology and philosophy, which it straddles.
In case you don’t know how it runs, the OA goes roughly like this (there are several variants):
- God is the greatest being conceivable.
- One of the qualities of the greatest being conceivable is existence in reality, for something that exists is surely greater than something that does not exist.
- Ergo, God must exist.
If you want to hear this claptrap dissected in extenso, listen to a new 43-minute program hosted by Melvyn Bragg on BBC Radio 4 :”The Ontological Argument.” Here’s the BBC precis:
Melvyn Bragg and his guests discuss the Ontological Argument. In the eleventh century St Anselm of Canterbury proposed that it was possible to prove the existence of God using reason alone. His argument was ridiculed by some of his contemporaries, but was analysed and improved by later thinkers including Descartes, Spinoza and Leibniz. Other philosophers have been less kind, with the Enlightenment thinker David Hume offering one possible refutation. But the debate continued, fuelled by interventions from such heavyweights as Immanuel Kant and Kurt Gödel; and it remains one of the most discussed problems in philosophy.
With: John Haldane, Professor of Philosophy at the University of St Andrews; Peter Millican, Professor of Philosophy at the University of Oxford; Clare Carlisle, Lecturer in Philosophy of Religion at King’s College London.
Actually, I recommend listening to this if you have time, because it’s largely a critique of the OA, and it’s incumbent on every atheist learn something about this important but impotent weapon in the arsenal of Sophisticated Theology™. And kudos to BBC 4 for taking up such an arcane topic. The discussion is quite clear and absorbing.
It starts off very badly, though, when Bragg introduces the enduring popularity of the Ontological Argument in this way:
“The young Bertrand Russell experienced a philosophical ephiphany on the way to the tobacconist, declaring, “Great God in boots—the Ontological Argument is sound!”
He fails to mention that the older Bertrand Russell totally rejected the argument on the grounds (adduced earlier by Kant), that “existence” is not part of the definition of any entity (i.e., existence is not a “predicate”), but after an entity is defined, then you can go out and see if it does exist.
Dr. Carlisle makes the telling point that you can prove the existence of anything with this tomfoolery, conceiving of “the most perfect island” or “the most perfect pizza”, and then then adding existence as part of each entity’s perfection. Ergo, we have a new island and a great pizza. Theologians, of course, then come back and say that God is the only entity for which existence must be a predicate. That’s hilarious!
In the end, it’s simply impossible to prove the existence of anything through the power of thought alone. One needs to observe the thing! At least for the OA, then, science beats philosophy and logic as a “way of knowing.”
To learn more about the OA, read the section on “Ontological arguments” at The Stanford Encyclopedia of Philosophy.
h/t: Dom
Did they mention Plantinga’s rehash of this as the modal argument?
That one might be worth discussing. Even though it’s probably also unsound, it’s better than the original Anselmian and Cartesian ontological arguments.
Here’s a version of Plantinga’s, one that skips a couple of subtleties in the interest of clarity:
The support for (1) is supposed to be mostly intuitive, which is how we decide whether a nonexistent object is at least possible. There’s no obvious logical contradiction in claiming that a maximally great being exists, and most logically consistent objects are possible, right?
The support for (2) is that it’s a substitution-instance of a theorem of modal logic: that
Part of maximal greatness is supposed to include non-contingency: that if God exists at all, God is a de re necessary being. So if a necessary God possibly exists, then a necessary God actually exists. This theorem can be proven if we assume that modal accessibility is universal: that no matter which possible world turns out to be actual, all other possible worlds are still possible. (It even works if accessibility is just Euclidean.)
TL;dr: If we think God is possible and we think that all possible worlds are possible relative to all other possible worlds, then God exists.
Worng.
A maximally great being (“Jesus,” in our cast of characters) could test a lesser being (Satan) by making the lesser being falsely convinced of superiority. For example, Jesus might wish to give Satan a shot at redemption by letting Satan have the keys to the kingdom, but wisely keeps a hidden leash on Satan. Does Satan prove himself worthy, or does he go right back to his evil old ways?
The mechanism by which Jesus tests Satan is irrelevant. Jesus could construct a virtual reality for Satan, or Jesus could follow Satan around and help him out, or whatever.
Satan is no fool. The first thing he does is test to see if Jesus is yanking his chain. But Satan doesn’t merely use his own means of investigation; that’s too obvious. Rather, he uses Jesus’s super all-knowingness.
…and this is where things break down.
Either Jesus gives Satan the full monty and Satan discovers the ruse, or Jesus tricks Satan and withholds the full power of omniscience.
Either Jesus can’t prevent Satan from learning the truth, or Jesus can’t create an honest test that’ll survive five minutes of Satan’s probing.
Worse…Jesus himself is in the exact same situation. He doesn’t know if he really is the bee’s knees, or if he’s a bit of indigestion manifesting itself in the Red King’s dream in Alice’s trip down the rabbit hole.
If there were such a world…but there isn’t. We know this to be true because of overwhelming piles of empirical evidence that, for example, Jesus is not ringing my doorbell and delivering the perfect pizza. He’s also not at the hospital alleviating the suffering of a little girl dying an excruciating death from leukemia.
If your premises are fallacious, you can conclude anything at all. This here is a perfect example.
b&
Ben Goren,
Thanks for your reply.
Re (1), I agree that there are interesting epistemological problems about omniscience. But if omniscience is impossible, then we just say a maximally great being isn’t omniscient, right? It seems, then, that we can at least preserve the logical consistency of a maximally great being.
Re (2), that premise is not suggesting that the actual world contains a maximally great being. It’s merely suggesting that if such a being could have existed, then it does exist. And as I mentioned, this follows from the view that every world is possible relative to every other world.
I agree, also, that the Problem of Evil is very good evidence against the (actual-world) existence of a maximally great being. But that’s not really an objection to Plantinga’s argument directly; it’s an attempt to perform a G. E. Moore shift on the argument. I think that’s a perfectly respectable tactic, but it should be noted that it doesn’t challenge the premises of the original argument. (And of course the theist will just say that the world is better for some reason if Jesus isn’t delivering a perfect pizza to your door, or that a perfect pizza is impossible, etc.)
First, I’ve yet to meet somebody who espoused any type of an ontological argument who didn’t also claim that the entity being ontologized into existence has all the omni-properties. Indeed, it’s exactly the omnimax god that’s the proposed definition / example whose existence is being argued is “maximally necessary” or whatever.
Second, if we’re going to set limits on greatness, then that defeats the whole purpose. A Jesus who can trick Satan is greater than a Jesus who can’t; if we’re settling, though, for the Jesus who can’t trick Satan, then we’re no longer arguing for the maximally greatest being, but for an also-ran.
Worse…once you take impossibilities off the table, you have a race to the bottom. It’s every bit as impossible for me to run a two-minute mile as it is for Jesus to trick Satan. But if Jesus is still maximally great despite his incompetence at his prime function (i.e., judging the living and the dead), then my own claim of maximal greatness can’t be discounted simply because I’m not faster than Usain Bolt.
Unless, of course, we’re going to throw some special pleading into the pot….
b&
Ben Goren,
Yes, in practice, Anselmians will claim that God has the omni-properties. I would suggest that the Anselmian view God as the greatest metaphysically possible, not greatest conceptually possible, being. (Then it would have the most power, knowledge, and goodness consistent with each other.)
I guess it still seems plausible that whatever the greatest metaphysically possible being is, it would be far, far greater than any other being we know of, and likely to be some kind of god. I imagine that God ends up far better than any human at running a mile, for example. The theist might say something like this: ‘If God cannot do something, that is only evidence against His maximal greatness if it’s something that someone else can do, and if that thing intuitively contributes to a being’s greatness.’ (This is similar to what actual theist philosophers have said in defense of the omni-properties.)
So, again, inevitably, we see that God is just Superman for adults. And this is deserving of respect…how?
Oh, that’s trivial.
God cannot draw inspiration from his deficiencies sufficient to expand his horizons and grow to become something more — exactly what it is that we are to believe from theists is the ultimate God-given purpose in human life.
God cannot abdicate his powers, in whole or in part, in order to let a child / student / apprentice / whatever blossom into full potential. God is the parent who never takes the training wheels off the bicycle, the king who never dies or steps down from the throne. (If he were to abdicate his powers, he’s no longer maximally great, even by theistic definitions.)
God can never personally experience the kind of love that comes from drawing strength from another.
Need I continue?
Had theists been paying attention when Russell, Gödel, and Turing all made their brilliant discoveries about the power of diagonalization proofs, they wouldn’t still be parroting such patent nonsense.
Cheers,
b&
Don,t tell me Ben that you weren’t aware Godel made his own ontological proof for God…
http://en.wikipedia.org/wiki/Gödel's_ontological_proof
And if God is just all the consciousness that is, well he surely does a lot of things you claim he can’t do, like limiting himself when trapped into an organic machines like a human.
That wouldn’t affect its unity because the separation that is felt by the individuals would be an illusion caused by the physical sensation who gives rise to all egotic perception. We would be like whirlpools in the ocean who would feel separated from the ocean.
God could be just a natural phenomenon who is actualized on earth within the limits of the material universe, but at the same time, beyond those limits, but in a way that we can’t see or understand because our biological limits prevent us to do so.
Bebop, I’ve repeatedly addressed Gödel’s ontological argument in this very thread.
I’m afraid I can’t make sense of the rest of your post. Sorry.
b&
It ‘s ok.
Plantinga’s version has one of the same problems the original has:
Anselm and Plantinga both need to define their terms. What constitutes “maximally great”? What is meant by “greatest conceivable”? Until their arguments include specifics about these terms, they can be dismissed without further consideration.
You know that old saying about what happens when you assume something.
“Plantinga’s version has one of the same problems the original has”
.
see also: ‘polishing a turd.’
musical beef,
In this context, Plantinga defines God as a maximally great being. We’ll certainly disagree about the details, but it’s not difficult to see how a maximally great being–that is, the best or greatest metaphysically possible being–would probably qualify as some kind of god.
Some Native Americans at first perceived European explorers to be some kind gods too. Boy were they wrong.
Your reply has to do with the definition of “god”, not the definition of “maximal greatness.” Which prompts me to ask: is there a specific, concrete, universal definition of god?
You can’t use vague premises to establish something conclusively. If the theologian hasn’t “line itemed” what she means by “god” or “maximally great”, how on earth can she make any conclusions. “God” and “maximally great” are hopelessly vague, as good as meaningless in this context. Which is greater: ice cream or doughnuts? Consider this analogy:
“Bludge is maximally flimflamular, therefore Bludge exists.”
An open-minded individual’s response would be: “well, what do you mean by “Bludge” and “flimflamular”?” If a useful, specific definition is not forthcoming, the open-minded individual can dismiss the assertion as nonsense.
Or as we logic geeks would put it:
Is not a theorem in every system of modal logic. In fact, it’s quite easy to come up with a counterexample to Plantinga’s step two using any system of modal logic where R is allowed to be non-symmetric.
Of course, this just makes it an argument about which system of modal logic is best. But I think there are good reasons to use a non-symmetric system of modal logic when discussing the Ontological Argument. If God exists and we should care about that, then God interacts with the physical aspect of some possible world. If God interacts with the physical aspect of a world, God is a physically possible thing. As far as people who do modal logic can tell, modal logics that have non-symmetric accessibility relations are best for dealing with physical possibility. Therefore, symmetry in R should not be assumed in the Ontological Argument.
So, there’s my refutation, but I think Kant and Jerry did a better job, they both agree that the proper way to find out about this sort of thing is to look. That some thing exists can’t be part of the definition of that thing.
I wish we had a preview page here. I just have to hop my gnarly HTML code up there works.
bacopa,
I agree that one of the argument’s weakest points is that it depends on accessibility being symmetric. I think there are initially good intuitive reasons to think accessibility might be symmetric, but I think they start to erode when we consider the MOA itself. (Why should some merely possible thing in some merely possible world “affect” the actual world?)
Thanks for responding to my comment. I tried to summarize as best I could the whole S4 vs S5 controversy. Frankly, I can’t remember the distinction between the two systems without looking it up. But I do know that the OA relies on a symmetric accessibility relation, and that accessibility is non-symmetric in the logic of physical possibility. Without symmetry, God could be present in some world, even physically necessary in some world, yet absent in our world.
I see no reason to believe that there is a possible world in which a god exists. The concept of god is incoherent, therefore it is not possible that a god exists anywhere.
Marella,
I agree that there are many potential problems with the logical consistency of God. However, proponents of the ontological arguments can retreat to define God simply as the greatest being metaphysically possible. If, say, omnipotence and necessary moral perfection are logically incompatible, then we just have to say (for example) that God has the most power one can have consistent with necessary moral perfection. Such a being would still seem to qualify as a ‘god.’
And that sort of unlimited-yet-limited power is different from what we mortals have, ourselves…how, exactly?
b&
“Greatest being possible” is not a definition. Not even with “metaphysically” thrown in to make it look legit.
On the greatness continuum, who’s closer to the maximum: a person with blonde hair or a person with brown hair?
“Greatness” is neither universal nor absolute. It depends upon specific contexts for meaning. There is no place on that continuum occupied by some abstract, universal, Platonic “maximum greatness.”
Step 2 is wrong and really stupid.
It says, if god can exist, then it exists.
It draws a false conclusion by simply stating it and hoping no one is awake enough to see that it is just an assertion without proof.
This is pathetic!!!
(1) There is a possible world in which dragons exist. (I.e., Dragons could have existed.)
(2) If there is a possible world in which dragons exist, then dragons exist in the actual world.
(3) Therefore, dragons exist in the actual world. (I.e., dragons exist.)
This isn’t even logic.
It’s a trivial word game.
You can use it to prove that anything and everything exists. We now know that god, Invisible Pink Unicorns, and dragons exist. Next up, just substitute UFO aliens and Bigfoot for…god.
raven,
As I mentioned in the original comment, the argument depends on a maximally great entity being metaphysically non-contingent. Presumably dragons are not defined as maximally great. However, I think you’re right that there’s a parody argument in the vicinity, if we were (à la Rowe) to begin talking about nunicorns, which are necessarily existing unicorns. (Plantinga would probably say that he doesn’t think there’s a possible world in which they exist, but Kripkean worries aside, I don’t think he can really make that case convincingly.)
This is meaningless bafflegab.
FWIW, all imaginary entities can be defined as being metaphysically non-contingent, whatever that means. Dragons, UFO aliens, werewolves, and fairies are metaphysically non-contingent.
What’s more perfect that god? God with a pizza.
What’s more perfect that god with a pizza? God with a pizza and a 6-pack on my front doorstep.
And on and on. There’s no such thing as something that is infinitely perfect, because you can always, always, always improve upon it.
For the gods currently bandied about, actual real unambiguous action in the present moment would be a good first step. How about — let’s see, something simple for a god to do that doesn’t interfere with free will — eliminating childhood leukemia with a whisper.
Absent that or some other similar demonstration and you’ve got a less-than-ideal god. Ergo, no god at all.
What’s more perfect than god? God without river blindness, leprosy, earthquakes, tsunamis, etc. etc. etc.
The problem of evil, especially natural evil, can be recast as a rebuttal of the Ontological Argument, since surely “perfection” extends to one’s handiwork. A creator of imperfection, or who allows imperfection in its work, can’t be perfect.
Does anyone trying to shore up the argument bother answering that with “obviously we don’t understand perfection”?
Which then invalidates the argument.
/@
It is not that we don’t understand perfection. The problem is that we assume God thinks like us and is limited by what we can say about it.
Perfection is a human word and a concept.
And God, if he exists, doesn’t have to care about it. The problem of good and evil only exists in a human perspective. And from that human perspective, good and evil are seen as 2 opposites facing each other. But God as to be beyond the opposites by which we grasp the world and can talk about it. Otherwise he couldn’t be an Uncreated One.
But if we insist on God’s perfection, it would then mean it is a good-without-opposition, a concept our human mind can’t deal with because we grasp the world through opposites and God is beyond those opposites.
So your god drowned all but a handful of people over a matter of perspective? He had his own son killed over perspective? He condemns people to infinite eternal torture over perspective?
If you’re god is so far beyond human comprehension, why bother worshipping it? If your god is so inscrutable, how do you even know it’s benevolent, or even thinks of humans at all? Such an incomprehensible god might as well be Cthulhu.
You’re engaging in the very common Theological Two-Step. On the one hand we should worship a loving and caring fatherly creator, but when that concept is undercut by argument, that anthropomorphic god turns into a philosophical abstraction that has no recognizable human qualities, and whose motives are so opaque as to call into question why we would even worship it, instead of seeing it as an eldritch, inconceivable monster. It’s an intellectually dishonest maneuver.
Your conception of God is very biblical. I don’t pray and go to church by the way. I believe that consciousness is uncreated. I think that this is God. And when consciousness is experienced on a material level, it has no choice to come with good and bad sides. But those opposites doesn’t exist from the “natural” uncreated perspective, a perspective we all belong right now at the same time.
What is the opposite of gravity? What is the opposite of time? What is the opposite of chair?
These things are easier to think of as themselves without placing them in an opposition. You need to engage in contrived thinking to place these things in oppositions. We only think of things as oppositions when we project some value system on to them, positive and negative, or generally as presence or absence.
What would you call the opposite of water? Ice? Steam? Dryness? Which is good and which is bad? Only a context dependent human value judgement can make any of these things good or bad. Sometimes I like to swim or shower, other times I long to be dry. Ice can be soothing or deadly, as can water or dryness.
I’d say the problem is not assuming god thinks like us; the problem is assuming god is. There is a reason people think god thinks like us, that he can be jealous or angry or loving. It is because we invented god. If horses could draw, they would draw their gods as horses.
The opposite of time is eternity, which means beyond time otherwise it wouldn’t be eternal. What is eternal has no beginning. That is why it has no end. That is why it is beyond opposites. And if it is true that not everything have a clear opposite, it is also true that things are what they are because of what they are not, otherwise we wouldn’t be able to talk about them or feel them.
All our sensations are based on that discontinuity. It is on that base that our ego can arise. And because our mode of perception is based on discontinuity, we believe that it is an absolute condition and we can’t imagine, conceive that our ego borrows from an uncreated source its consciousness, that because the ego uses it on a mode made of discontinuity. We can only see and believe we are limited to our body.
“If horses could draw, they would draw their gods as horses.”
I find that horses generally draw carts.
/@
Funnily enough I came to the same conclusion – rather like there being an infinite number of infinities. Another, more human flaw that I can see, is what _exactly_ is meant by conceivable? My version of conceivable might be – and probably is – very different to Fred Bloggs down the road. Why should a theologian to tell me what I mean by “conceivable” ? I have a science background and my vision of what is “conceivable” would be bound and limited by my scientific training.
Will listen to the R4 programme when I get a mo though!
(Must admit I always liked the late, great Spike Milligan’s comment: “Contraceptives should be used on every conceivable occasion!”)
And taking your argument to it’s perfectly logical conclusion, you achieve the pinnacle of deistic evolution, having a god with (optional pizza), a beer volcano (obviating such mundane considerations as a “six pack”, even of Schrodinger’s wineglasses), stripper factory (including the “Sven” model as well as the classical “Samantha”).
All hail the FSM and his ineffably noodly appendage.
Yep, it’s in there. It’s a good and thorough discussion if you have 45 minutes to spare.
I remember first hearing the ontological argument in my college intro to philosophy class. It sounded like some kind of joke. My reaction was along the lines of, “OK, that was cute. Let’s move on to the real arguments for God’s existence now.”
Even though I couldn’t come up with any kind of formal logic to dispute it at the time, it should set off the BS detector of any normal person.
Also, don’t forget another property of the most perfect pizza in the world: it should be mine already. Otherwise it’s not doing me a whole lot of good and therefore not the definition of perfect!
And you shouldn’t have to do any work to eat and digest and taste it, because that would be a limitation. What if your jaws were wired shut? You wouldn’t be able to enjoy it, and that would be an imperfection in the pizza! So a perfect pizza should be one which everyone is constantly in a state of eating and tasting and enjoying, regardless of whether or not they can open their mouths. And it shouldn’t make you feel full, because then you wouldn’t want to eat anymore and that would be another limitation! So it shouldn’t actually take up any room in your belly!
Not really interested in this argument, I’m just a big fan of pizza.
And it shouldn’t make you fat! Fatteningness is a huge limitation of pizza!!
You know, I once thought of an infinitely perfect refutation of the ontological argument… so there it is!
+ 17
“In the end, it’s simply impossible to prove the existence of anything through the power of thought alone”
This may be very slightly too far. 🙂
“I think therefore I am.”
I think of the tooth fairy therefore she is.
From what we know of how consciousness seems to work (your brain is a pile of subsystems, what I picture as “consciousness” appears to come and go in awareness and then retcon a story about how I was actively aware the whole time, etc.), I’d start questioning the degree to which I “am”.
(Again, something held to be a philosophical dilemma turning out to be a matter for cognitive psychology.)
In fact, we know effectively nothing about how anything even approaching “consciousness,” which is really just talk, happens, let alone whether it means anything. It probably doesn’t.
Descartes just played with language conventions which are merely local social norms.
Natural language words and claims do not have to mean anything or carry any information value. Why math is used when real information is needed.
Look up the Turning Consciousness Conference for chapter and verse.
Although I appreciate all of the other problems with the OA pointed out by others, this is the basis of my non-acceptance of it–that it can be used to “prove” the existence of objects known to be non-existent, of which the tooth fairy might be the best example. I mean, after all, a tooth fairy that exists must be greater than one who does not, QED!
My other favorite argument is that the OA “works” just as well if you replace the word “God” with “Allah,” “Cthulhu,” “Thor,” “Make-make” or “The Flying Spaghetti Monster.”
Well, now, that’s not the same thing.
I think the cogito delivers, at a basic level. It won’t give you any details about what kind of thing you are, or what it means “to be”, but if you’re having subjective experience, I think it’s safe to say you exist.
You can’t have subjective experience on behalf of anyone else, tooth fairy included. That’s the difference.
No, that’s self-referential talk and only tells us about local language conventions not physical existence.
To prove existence means stepping well outside of natural language.
As I mentioned elsewhere, your awareness of your thoughts are empirical evidence of the fact that there’s something doing some form of thinking.
If observation of an apple falling from a tree is valid evidence for gravity, then metacognition is valid evidence for the existence of self.
Proof? Pfft. Who needs proof when you’ve got evidence?
Cheers,
b&
Why, thank you, Ben! I was just about to make the very same point.
You’re welcome! Glad to help.
I do owe a tip o’ th’ hat to Torbjörn, though. He’s the one who’s finally drilled into me the importance of empiricism and the utility of examining all arguments, no matter how abstract, for evidence of empirical foundation.
Not to dismiss the importance or utility of logic, of course!
b&
That’s absolutely right. Descartes’ first step in this line argument was sound, although everything that followed was fallacious for various reasons.
Wrong. If you presume the “I” you have already started a fallacious argument.
Since it has such strong face validity and presumptive truth — it’s likely ideology. Only beliefs/ideology works this way using natural language.
NO:
‘For all x, if x thinks, then x exists.
There exists an x which thinks.
Therefore, there exists an x which exists.’
Nothing fallacious in that logical argument (or please point it out if there is). And do not waste my time by criticizing the content of the two hypotheses. That has nothing to do with logic, which is about the validity of arguments, not the ultimate validity of their conclusions.
You must realize that the word “exists” is poorly used by me in the conclusion, in that the first time, it is the formal backwards ‘E’ of 1st order logic, whereas in the second case it is one of the two properties in general dealt with in the argument. I suppose I should have replaced “x thinks” by “P(x)”, and “x exists” by “Q(x)”, and then explained afterwards what to replace P and Q by when trying to convert to natural language.
I think you’re making too much of the distinction between “natural language” and more formal languages, like math.
“Natural language” is just less efficient and less precise. Math can be done with “natural language”: think of word problems.
I don’t see why the efficiency/precision (or lack thereof) of the language with which we normally communicate should imply anything about existence.
Your position sounds dangerously close to pomo bafflegab, to me.
I am suggesting something very different. I am saying that natural language, and perhaps most verbal signaling of other species, is mainly local social norm dependent/ideology and deceptive.
Further it carries little information – predictive usefulness.
Not sure what the name calling means other than deception.
So…you’re trying to communicate the ineffectiveness of communication?
b&
Also, although Descartes uses the “I” conjugation of both verbs, the general thrust of the argument doesn’t necessarily entail positing an “I”. It only shows that if thinking is happening, something must be doing the thinking.
All Descarte’s “cogito” proves is that thinking exists, and people who try to prove the existence of something a priori are like the people Wittgenstein described, who try to figure out what time it is by imagining a clock Also,”exists” is not a predicate; “there exists an x such that x exists” says nothing. “Being” means “being something.” You philosophy-bashers out there might get a new outlook on philosophy by reading Quine’s essay “On what there is”; it’s available free online.
My point exactly, this is pointless word play. Philosophy is now a dead language.
to Luc:
You don’t like ““there exists an x such that x exists”, so it was presumably MY use of it (didn’t see it elsewhere, but thread is getting messy!) I suspect you didn’t read my clarification immediately afterwards: Exists is used in different ways here, so I should have been more detailed initially. That it cannot really be used as a predicate is beside the point here. The point is that Descartes’ argument, to the extent that it can be regarded as purely logical in a 20th century (late 19th even) sense of logic, is a perfectly correct logical argument, not incorrect, as the person I answered was claiming.
Luc & Kevin:
I don’t follow the clock analogy. By invoking the cogito we are neither trying to determine something as specific as what time it is, nor are we imagining anything. As Ben pointed out above, a thought/experience is an empirical phenomenon. No imagination necessary. The simple conclusion is that a thought implies a thinker and an experience implies an experiencer. And as I originally admitted, this is the extent of what can be concluded from the cogito. I know it won’t yield conclusions like “and I am Andrew Hackett, a 33 year-old caucasian organist with blonde hair and it’s 6pm.” Just as a theist’s “experience” is not evidence for a specific god – but IS evidence that people can have religious experiences.
Thoughts existing without a thinker is something right out of Sophisticated Theology, i. e., disembodied mind.
Kevin:
Noting the similarity of your stance on language with Postmodernism is not name-calling.
But surely God *must* exist if he exists in reality! I have no problem with this at all, and wish he would hurry up and show himself already.
What is the problem, anyway? I am NOT the greatest being conceivable and yet I pretty obviously exist in reality. You really can’t miss me – I’m splattered all over the place.
If existence in reality is a measure of the qualities of a conceivable god, then I must be a greater conceivable god than Jesus or Allah or Yahweh. I can make the channels on the TV change with a flick of my thumb. That’s just peanuts for me.
What does it mean to say that something existent must exist?
Nothing existent must exist in the sense that its nonexistence is not non-contradictorily conceivable. So “exists necessarily” cannot mean “exists in all logically possible worlds”. But what does it mean then?
I think that’s exactly what people who believe in this argument mean. The argument doesn’t work otherwise.
Actually, the theologians who accept the objection that nothing can exist logically necessarily have drawn a distinction between logically necessary existence and factually necessary existence:
“God’s necessary existence has been interpreted in two different ways. Some have understood the notion in the sense of logical necessity; others have attempted to delineate a sense of factual necessity.
If God’s necessity is understood as logical necessity, the proposition ‘God exists’ is logically true. A logically necessary being is one that exists in every possible world. The proposition ‘three plus five equals eight’ is necessarily true; it is true in every possible world. Likewise, if God is a logically necessary being, the proposition ‘God exists’ is true in every possible world. To say that something is logically necessary is to claim that it is logically impossible for that thing not to exist. Just as it is logically impossible for a triangle to have four sides, so it is logically impossible for God not to exist.
In recent years, many religious philosophers have given up on the notion of a logically necessary being. For reasons that will be explained shortly, they decided the concept was not only indefensible but even damaging to theism. Consequently, in order to retain a sense of necessity with respect to God, these thinkers explained God’s existence as necessary in a nonlogical sense; God’s existence, they said, is a factual necessity.
A being who is necessary in the factual sense is one about whom three claims can be made. (1) The being is eternal, that is, it had no beginning and its existence will never end. (2) The being is self-caused, which is to say that it does not depend upon anything else for its existence. It is, in a sense already explained, a se. (3) Everything else that exists depends upon the necessary being for its existence. Here is the key difference between the notion of logical and factual necessity: a factually necessary being does not exist in all possible worlds. In the sense of factual necessity, the proposition ‘God does not exist’ is not logically false. A factually necessary being is, in a sense, accidental.”
(Nash, Ronald H. The Concept of God. Grand Rapids, MI: Zondervan, 1983. p. 108)
“x exists factually necessarily.”
=def
“For all possible worlds w, if x exists in w, then x exists eternally and autonomously in w / then x exists uncreatably and indestructibly in w / then x has always existed and will always exist in w.”
This is the only intelligible and tenable definition of “necessary existence” that I know.
Note that something which exists necessarily in this sense doesn’t exist in all logically possible worlds. That is, factually necessary existence is logically contingent/accidental existence!
Eh, even if we granted them this, it still doesn’t get them anywhere.
It is logically necessarily true that the angles in all Euclidean triangles sum to 180°. However, it is also logically necessarily true that you can construct triangles with arbitrary total angular sums in a spherical geometry. Which logical necessity actually holds depends upon the particular situation. Are you laying tile on a floor, or are you performing intercontinental navigation?
As we just saw, this distinction doesn’t exist.
Both cases don’t even rise to the level of special pleading, but merely wishful thinking.
Typical theology. They start with a really bad faery tale, invent some sort of totally incoherent (but sophisticated-sounding!) back-story, and then get so bogged down in arguing over the size of the Warp Coil Transdemogrificator that they never get to the point of looking for evidence that any of it is actually real.
At least Trekkies have the good sense to know that it’s make-believe. And they’ve got better story lines, too.
Cheers,
b&
“…the proposition ‘God exists’ is logically true….”
It’s too bad that Mr. Nash really doesn’t know what he means by the phrase “logically true”. It is a serious mistake for beginners and anybody else to confuse truth with logical validity, or, if you like, to confuse syntax and semantics. It indicates a very fuzzy idea of what logic really is, at least what it is since Frege in the 1800’s, about 100 years before Mr. Nash was fattening his CV. What logic was before Frege is just a confused version of what it is now (pace Aristotle!), and that is what mathematicians have made it since (and including) Frege (not done by philosophers, if one wishes to fuss about designations).
Logical Truth: http://plato.stanford.edu/entries/logical-truth/
Logical Consequence: http://plato.stanford.edu/entries/logical-consequence/
To Myron:
I am not one to completely dismiss philosophy, as has been discussed here recently related to Krauss, the physicist. So don’t take what’s below too generally.
That Stanford Dic… article on “Logical Truth” is pretty long-winded, isn’t it? I certainly didn’t read it all, and I’ll bet you didn’t either. My claim was not that the pair of words had never been defined. In the Stanford article it is defined 783 times, about half by philosophers before Frege, and the remaining half are likely to have more than half of them nonsensical in any sense of logic today. Now my claim was that our theological author did not know what he was talking about when he used the phrase. And if he happened to be thinking of that Stanford source (probably didn’t exist then!), I’d need to insist on my correctness, since 783 distinct definitions is, if anything, worse than no definition at all.
So if you can actually tell me what the phrase means when used by Mr. Nash, I am all ears. Or even tell me what it means based on all that philosophical historical blather in the Stanford article.
That article is probably a perfect example of why I think that to know at least the rudiments of what logic is, a student should stay away from courses in philosophy (except in a few places like MIT some years ago, courses from Boolos, who unfortunately died rather young). Far better to learn logic from a mathematical logician, and get some clarity on a subject which, in another sense, is all about clarity.
Anyway, I’d challenge anyone here to tell me what the author of the Stanford blurb means by “logical truth”. As with much in philosophy, I suspect it would almost be an insult to philosophers to even expect that a question might actually have a solid answer! As far as that use of language goes, using it just confuses matters in my view. There are such things as (1) validity of arguments in propositional logic, (2) validity of arguments in 1st order logic, (3) tautology, etc., all of which are precise and distinct from each other. And in fact, learning those things is a big part of knowing the basics of the subject.
By all means, use the Stanford stuff for loosy-goosy matters like the philosophy of aesthetics, or indeed the philosophy of sex! But not logic.
That basically says, “If God is necessary, then God must exist.” Which is trivially true. But it just assumes necessity, it doesn’t actually establish it.
In other words, a smokescreen of semantic sophistry meant to hide the vacuousness of the argument.
Speaking of the SEP, its editor Ed Zalta has also done interesting work trying to use theorem provers to show what premisses and such do what work in classical arguments. He’s recently (presented in 2012 at AISB/IACA) reformulated his work on the ontological argument in this respect. The matter is extremely technical (I would not want to try to reproduce it here for lack of symbols etc.), but I encourage those who have some decent mathematics backgrounds to take a look. Of course, the run-of-the-mill believer has no such thing either which is why these arguments seem so persuasive to some. No, Zalta hasn’t shown the argument is sound: actually, it is, in the best reconstructed case more or less a very subtle but very clear (once analyzed) begging of the question. The traditional answer (Kant’s and Russell’s) is actually not satisfactory, as there are perfectly legitimate logical theories where existence is a predicate. In fact, using them with a particularizer quantifier is a good way to formalize statements which we atheists would say are false, like “Some Greek gods are angry”, without having to say there exist Greek gods.
Woops, that should be IACAP.
Oh, I don’t think the OA is subtle at all about begging the question. In fact, there are more than one petitio in there.
I think that you can also go the opposite way with this argument and say what is shows is that an inherent quality of ‘existence’ for ‘things in the world’ doesn’t pan out. Otherwise, wouldn’t everything (as mentioned above, islands, pizza, and every ‘thing’ in existence,) have a Most Perfect Form out there in the universe somewhere?
What’s more perfect that god with a pizza? God with a pizza and a 6-pack on my front doorstep.
And on and on. There’s no such thing as something that is infinitely perfect, because you can always, always, always improve upon it.
You know, I actually like this idea a lot and don’t think it requires any kind of a god. The infinite potential for growth – it reminds me of a Jason Silva musing on humans turning into gods. I don’t know that ‘gods’ is the word I’d use (too many connotations, too much baggage) but I like the overall sentiment.
The OA shares with Jello the same basis for their enduring popularity–they are both slippery, sticky, and transparent. Eat a dish of Jello, read the OA; same difference.
“…it’s simply impossible to prove the existence of anything through the power of thought alone.”
“I think, therefore I am.”
????
Godel, no less, did recast the ontological argument as something in modal logic. People may be interested in looking at Volume 3 of his collected works. Despite the enormousness of his contributions, he is one of the last people I would take too seriously on the existence of god. He was a very convinced Platonist, with respect to the existence of mathematical objects, and so am I. I really do not know if he ever expressed himself on religious matters, but doubt that he was at all religious, at least during the times when he was coherent. Max Tegmark would literally identify the physical universe with actually BEING a mathematical system, which leaves little doubt about such systems’ actual existence, if you accept Tegmark’s view.
I believe Gödel considered his ontological proof incomplete, and for excellent reason. It’s not hard to figure out where it goes off the rails.
That Gödel should have thought that this sort of approach might work I find particularly surprising, since the exact same sorts of diagonalization methods that he and Turing were famous for similarly demonstrate the non-existence of the divine.
Take, for example, the popular informal proof of Turing’s Halting Problem — that of writing a spoiler program that incorporates wholesale the hypothesized solver and does the opposite of what the solver does. With just a few character name changes, that same proof demonstrates that it is impossible for any entity to know whether or not it is all-powerful or if there’s some even more powerful yet hidden entity secretly running the show. So, if even Jesus can’t know if he’s all-powerful, of what sense does it make to claim that he’s the all-knowing all-powerful force behind all that ever is, was, or will be?
Einstein established that there are no privileged frames of reference in the physical world. Gödel did the same in math and logic. It’s a shame that Gödel still somehow managed to cling to his childhood superstition.
Cheers,
b&
Just to clarify, not dispute Ben: I didn’t say that Godel had any belief in the existence of ‘spiritual’ beings of any kind, god included, and didn’t intend to imply that. Ben seems to think he did (or do I misunderstand?), and it would be interesting to know of evidence that he did. I just have never had the energy to dig that up, including now. I had thought that his ontological proof was simply an exercise in logical formalism for him, not any attempt to rescue that as producing any new knowledge, again other than a knowledge about these formalisms. But my copy of that stuff seems to be nowhere nearby unfortunately.
Gödel was a theist, though not a believer in any particular religion, other than perhaps his own. As for Ben’s questions, I suspect that the reason may lie in his semi-response to the stuff mentioned. It seems that he put it this way: either there are absolutely unsolvable diophantine equations or we are not machines. He (somewhat privately) held the second. (There’s a fair bit of scholarship on this topic, actually, which I am eliding.)
That, of course, would mean that Church-Turing doesn’t apply…which, in turn, would lead to a violation of conservation.
Then again, what could possibly represent a greater violation of conservation than a god? Indeed, does it even make sense to propose a god that isn’t capable of violating conservation?
b&
Maybe, but what Gödel actually thought about god is not obvious. He thought that the age was too secular, empiricist and materialist to have his views received well, so he largely kept them to himself. Note that the work on the ontological argument was unpublished.
Honestly, I think the reason he didn’t publish it was because he knew it wasn’t up to his own standards. I wouldn’t at all be surprised if he didn’t think of it a work in progress, with the hopes of someday overcoming its obvious problems.
b&
It would be natural for God to not be subjected to any law of conservation unless you believe that God has to be something finite and not beyond space and time. How could he be God if he wasn’t uncreated?
Oh, I see, such a phenomenon can’t exist because our mind can’t figure this..?
If there’s one bit of pseudoscientific bullshit that can unhesitatingly be instantly rejected with extreme prejudice, it’s anything that amounts to a claim of a perpetual motion machine.
Somebody tries to sell you a perpetual motion machine, first secure your wallet; then run for the hills; then report the scam to the proper authorities.
b&
The thing an uncreated conscious process wouldn’t be a machine. You seemed at ease below with the jain’s conclusion that the world can only be uncreated. No?
Ben, you have a very biblical conception of what God should be…
It is worthwhile to keep an eye on Bragg. He is always chasing sentimental ideas. Fortunately, his producer always gets good guests.
Some of us are working on a project in brain research and rapidly coming to the conclusion that natural language is not only not useful to describe stuff but inherently flawed and very misleading since it automatically carries all sorts of social norms and ideological inferences.
For example words like choice, value, reward, emotions carry little information value and much to distract.
Like physics, probably best to stick to calculus.
That’s not good news for philosophy.
Right, or economics, psychology, humanities, etc.
The problem is higher order concepts: HOC. In brain research these include ideas like choice, value, reward, feelings/emotions, self, personality, utility, consciousness, maybe even individual.
HOC’s carry with them implicit notions about behavior > brain. Notions that need to be tested and proved. Using them presumes they exist and matter/have an effect.
What most brain research now consists of is investigators setting out to prove the existence of brain processes/places that correlate with these HOCs.
Maybe it’s a version of the ontological problem in modern dress. Finding the place in the brain that light’s up for tooth-fairy idea and behavior — does not mean it exists.
That is an ontological fallacy.
This “top-down” kind of research is uniformly unproductive. Mainly because physiological processes are radically opportunistic, bottom-up, responsive to the local environment and continuous — as the Darwin truths teach us.
So our brains have evolved to drink a cup of coffee, unconsciously, in milliseconds and engaged in a continuous feedback loop. See > start to reach > adjust > fingers touch > adjust >…….
So HOC’s aren’t needed, don’t appear anywhere, there is no time for them to have an effect, the bring all sorts of ideological baggage, etc.
Chasing HOCs is proving to be a big waste of time.
That’s not a bug it’s a feature.
Natural language is not really about information as it as about sharing brain state. With just a few modulated noises it brings contexts, experience and social structure to bear, sharing states of being and experience very economically.
Of course, the price for this economy is lost precision.
How can ever claim verbal behavior represents brain states!?
Brain states, that direct behavior occur in milliseconds.
The rest of the statement is unprovable but pretty easily falsifiable.
I don’t think it’s even necessary to go as far as Kant and Russell, and assert that “existence” is not part of the definition of any entity. All one has to do is require the person asserting that he can conceive of a “greatest conceivable being” to state whether he considers “existence” to be part of the definition of “greatest conceivable”. If the answer is no, then the ontological argument fails a la Kant. If he answers yes, then the argument is circular.
Another flaw is that it assume that greatness is a total ordering – that is given two entities one can always determine that one is greater than the other.
Yes. “Maximally great” is a uselessly vague criterion.
Actually, not in all forms. This is where Zalta’s computer analysis comes in. That said, the *original* form of the argument may well be suspect in this way.
Maybe we should call it the Gerontological Argument by now.
LOL!
It is important to mention that the ontological argument is unsound even if existence or necessary existence is regarded as a property, because from God’s being definitionally *determined by* the concept “(necessary) existence” it doesn’t follow logically that God *satisfies* this concept and thus has the property of existing (necessarily). So the argument simply begs the question against those who deny that God satisfies the concepts by which he is determined (conceptually defined). In other words, it begs the question against the atheists who deny that God *has* the properties *ascribed to* him, because they think God doesn’t exist—and nonexistent gods do not have any properties whatsoever, including the property of (necessary) existence.
Edward Zalta would put it this way:
From the fact that God encodes (= is determined by) the property of (necessary) existence it doesn’t follow logically that God exemplifies (= satisfies) this property.
See: http://plato.stanford.edu/entries/nonexistent-objects/#DuaCopStr
Right, but I’m not sure we want to invoke all of that just yet …
Jainists are way ahead of the curve:
” Some foolish men declare that creator made the world. The doctrine that the world was created is ill advised and should be rejected.
If God created the world, where was he before the creation? If you say he was transcendent then and needed no support, where is he now?
How could God have made this world without any raw material? If you say that he made this first, and then the world, you are faced with an endless regression.
If you declare that this raw material arose naturally you fall into another fallacy, For the whole universe might thus have been its own creator, and have arisen quite naturally.
If God created the world by an act of his own will, without any raw material, then it is just his will and nothing else — and who will believe this silly nonsense?
If he is ever perfect and complete, how could the will to create have arisen in him? If, on the other hand, he is not perfect, he could no more create the universe than a potter could.
If he is form-less, action-less and all-embracing, how could he have created the world? Such a soul, devoid of all modality, would have no desire to create anything.
If he is perfect, he does not strive for the three aims of man, so what advantage would he gain by creating the universe?
If you say that he created to no purpose because it was his nature to do so, then God is pointless. If he created in some kind of sport, it was the sport of a foolish child, leading to trouble.
If he created because of the karma of embodied beings [acquired in a previous creation] He is not the Almighty Lord, but subordinate to something else
If out of love for living beings and need of them he made the world, why did he not make creation wholly blissful free from misfortune?
If he were transcendent he would not create, for he would be free: Nor if involved in transmigration, for then he would not be almighty. Thus the doctrine that the world was created by God makes no sense at all,
And God commits great sin in slaying the children whom he himself created. If you say that he slays only to destroy evil beings, why did he create such beings in the first place?
Good men should combat the believer in divine creation, maddened by an evil doctrine. Know that the world is uncreated, as time itself is, without beginning or end, and is based on the principles, life and rest. Uncreated and indestructible, it endures under the compulsion of its own nature.”
Acarya Jinasena, Mahapurana
+1
Just in case some newer reader here might mistakenly think otherwise, it seems not a waste of time to point out that, whatever truth value or otherwise this Jainist stuff might have, it bears very little if any relationship to the reasons that reasonable, scientifically-oriented people here are quite sure that the probability of the existence, of some all-powerful being who has ever had any effect on the physical universe, is so small that it might as well be zero.
I certainly do not mean to imply that there is some lock-step mentality here (I hope not), but surely the above is correct. So the curve that Jainists are “way ahead of” is in somebody’s imagination, I think.
I don’t know what you mean: the Jain religion originated in the very theistic milieu of late Vedic age India: an environment where philosophical arguments for the existence of a god were probably even more popular than they were in medieval Christianity. Being adherents of an atheistic belief system (which is what the orthodox Jain religion is), the Jain philosophers would almost have had to come up with flaws in those philosophical arguments: and this is the curve we are talking about here. The “curve” of realizing that there is a flaw in all of these logical and philosophical “proofs” presented for the existence of god.
Also, in response to peter above, I fail to see how this quote bears “little or no resemblance” to many of the modern arguments about the lack of a coherence definition of what is a god or creator.
“…modern arguments about the lack of a coherence definition of what is a god or creator.”
That is not what I said, is it.
I have neither time to, nor interest in, discussing what Jain philosophers said to theist philosophers at that time and in that place.
There is no evidence for, much evidence against, the existence of any all-x being (substitute several things for x), and it’s as simple as that, and very little related to the philosophical disputes referred to above.
At the danger of sounding at least as rude as you, you did seem to have a lot of time to discuss them in your first comment on the thread :D.
But, seriously, I do think it is an interesting historical fact that in roughly the same time period, there existed two different religious cultures: one of which could clearly see the fact even trying to postulating an all-X being was a futile exercise, much less an undertaking that could be later bolstered with physical evidence; while the other found the same postulating and mental gymnastics sophisticated. Personally, I find the history of philosophy (though not what I have seen of modern philosophy) fascinating. As the American idiom goes, your mileage may vary.
Sorry if I seemed rude. There are just too many things to do. That I might have relatively low interest in something says nothing negative about it.
My point was merely that the so-called ‘new atheist movement’ derives its atheism far more from scientific knowledge, especially post-Darwin, than it does from any particular philosophical disputes, involving Jainists or otherwise.
This is the first time I heard of Jainism (had to google it) but the above quotation reminds me of the Epicurians. I wonder if there was an actual influence.
Comedian Bill Santiago tells the story of talking to a woman who believed that Earth is carried on the back of a turtle, and that is what supports the planet. Bill asked her what supported the turtle, if the planet needed to be supported. The woman said the turtle was carried on the back of another turtle, and that turtle was carried on the back of yet another. “It’s turtles all the way down!” she explained. Sometimes logic just doesn’t fit into the equation.
The “turtles all the way down” story is much older than Bill Santiago and goes back at least a century.
It even has its own Wikipedia entry.
Despite having expressed a certain lack of interest, I am a fairly close acquaintance of a very excellent family of Jains. The general principle of non-violence towards all living things is admirable, though it can lead to some questions, given our present knowledge of what life actually is. These are rather academic mostly, and I just don’t get into it with them, but I do wonder how they deal with the business of zipping down the highway in the north, with no end of bugs being squashed on the windshield!
Yes, the militant non-violence of the Jainists is a rather quaint but unique feature: ancient Jain dictats for exampled ban eating after sunset because you would have to light a lamp which might kill some bugs :D. Then there is the insistence on not eating root vegetables (since the plant is “killed” when you take out a root vegetable). As the Indian comic blogger Krish Askok puts it:
I believe Jainism predates the Epicureans (the foundations date back to, I think, c. 500 BCE), and also the era of increased Indo-Greek contact (which was after c. 320 BCE)
Also, as peter points out implicitly, the similarity between the Epicureans and the Jains ends at their atheism: Most Jain sects preach an austere lifestyle (the most “fanatic” of them ban even the use of clothes) and the only other basic dogma of the religion seems to be a militant adherence to non-violence.
Then keep me, personally, in the Epicurean column rather than with the Jains. I likes me a hearty feast, at least every now and again.
I know you’re joking, but I’m still trying to warp my head around the concept of militant non-violence….
b&
We don’t know for sure. As I recall, the traditional dates for the Jain founding is c. 500 bce, during the famous “axial age”. But I do not know the state of the art there. Anyway, the influence could have been Democritus’ supposed visit to India. (Also, and I cannot check this – be careful of translation. This might cloud difference in words for “resonance” reasons.)
The following quote from Wikipedia (I know that’s not a reliable source, but this particular paragraph seems ell cited) that suggests a different chronological sequence for the events:
This is from the Wikipedia page on atom.
I used to know a lot more of the literature (since I did an honours thesis on ancient atomism) but I’ve forgotten some and haven’t kept up in the past >13 years. In any case, “atomos” *originally* means “not to be cut”, where it is a prohibition. As for the time line, we just don’t know if Democritus really met the “naked wise guys” of India or not. I suspect not, but I have no reason for the testimonium them.
Thanks for the responces Ahannāsmi and Keith. I did some searching and according to wikipedia Maharurana was completed in the 9th century CE. So there is plenty of time for influence. The similarities seem (to me at least) too great to be a coincidence.
I would be doubtful. There was a much older tradition of similar atheistic thought in India (predating both the Jains and the Epicureans) referred to variously as the Lokayata or Charvaca, which is much more likely to have influenced the Jainists (whose religion was anyway, atheistic since there founding some 16 centuries before the Mahapurana).
You may be right. Just to clarify I wasn’t talking about atheism in Indian philosophical tradition in general. Simply the arguments in the quotation that started this thread reminded me strongly of the Epicurians—and not only one or two of the arguments, I believe that most (if not all) of them were also made by the Epicurians and this seems too much of a coincidence. For example Lucretius said:
Fuller quotation at Google books: http://xrl.us/bnr8tp
Oops! I forgot to say that I got the above quotation of Lucretius from Stenger’s book God and the folly of faith.
Here is an interesting vid:
Paul Bloom, Professor of Psychology and Cognitive Science at Yale University and contributing author of the 2012 Annual Review of Psychology, talks about his article “Religion, Morality, Evolution.” How did religion evolve? What effect does religion have on our moral beliefs and moral actions? These questions are related, as some scholars propose that religion has evolved to enhance altruistic behavior toward members of one’s group. But, Bloom argues, while religion has powerfully good moral effects and powerfully bad moral effects, these are due to aspects of religion that are shared by other human practices. There is surprisingly little evidence for a moral effect of specifically religious beliefs.
http://www.youtube.com/watch?v=oPr1N6XVYWs&feature=share&list=UU8Y3OT35DqYXRSqqNErwh5Q
It sounds like social factors, not beliefs/words, is what influences behavior. The words must carry some social signaling value.
Oops, wrong video. Let’s see….
Darn! YouTube glitch. The link works right when put in browser. Go figure.
Here’s the link: http://www.annualreviews.org/page/audio Look at second video.
What bothers me though is the recognition that one needs observation to say something about the world, then to immediately repeat and propound the problem by claiming that such a recognition can be done without basing it in observation!
For example, “the older Bertrand Russell totally rejected the argument on the grounds (adduced earlier by Kant), that “existence” is not part of the definition of any entity (i.e., existence is not a “predicate”), but after an entity is defined, then you can go out and see if it does exist.”
I could call that (OA)^2 – the Ontological Argument on the Ontological Argument.
It is enough to make and test the hypothesis that successful hypotheses on the world, whether on data (observations) or based on data (theories), are based on observation.
[If mathematics is pulled out of the hat, it can be noted that models of integers et cetera are based on observations of operations on real entities.
Moreover, Gödel’s theorems would attack the OA directly, since anything of the complexity of addition can’t be based on logic alone. Or there will be gaps, since the structure will be incomplete if consistent.
And surely “the greatest being” must encompass understanding of integers.]
Indeed, considering that Gödel’s own ontological proof starts out by defining God in exactly such an all-encompassing manner, one wonders why he even bothered continuing past said first definition.
b&
“In the end, it’s simply impossible to prove the existence of anything through the power of thought alone. One needs to observe the thing!” – J. Coyne
Mathematical existence proofs (e.g. that the square root of 16 exists) are not based on observation. But, of course, numbers are abstract objects, so your statement should be qualified as follows:
“It’s simply impossible to prove the existence of anything concrete (physical or mental) through the power of thought alone.”
(But what about: “I think, therefore I and my thoughts exist”?)
Your thoughts are evidence of their own existence.
And math is far more empirical than the mathematicians care to admit.
Take sixteen pebbles and lay them out in a four-by-four grid (such as on graph paper). There’s your empirical evidence that four is the square root of sixteen. Rearrange it into a two-by-eight rectangle and there’s your evidence that two and eight are both factors of sixteen.
Add one pebble and attempt to arrange them in a rectangular grid. After you’ve tried every permutation, you’ll discover that the only such grids are seventeen by one and one by seventeen. There’s your empirical evidence that seventeen is prime.
“Abstract” math serves the same purpose as Newtonian Mechanics. Just as you can use Newton to predict the location of a projectile at such-and-such a point in the future, the Archimedean Sieve can be used to predict whether or not a collection of so many pebbles can be neatly arranged in more than one rectangular shape.
Much of math is very far removed from observed reality, yes. But so what? You can use Newtonian Mechanics to predict the motions of planets that aren’t there; does that make physics somehow specially removed from reality?
Cheers,
b&
It all has to do with predictability and subjectivity.
Any animal signaling is abstract. Math is, however, the most reliable and predictive form of verbal signaling. Mainly because it is a non-local language.
The function of most language/signaling/talk seems to be to signal (over and over) loyalty to, and membership in, the local group(s). Have to check songbirds – they are great template for verbal signaling.
So the conflict is between predictive talk vs. in group, self-referential talk. By definition, math/evidence-based talk feels like it attacks in-group cohesion, because itignores local social norms — thus:”war.”
It must be a shock similar to having someone say repeatedly “I’m with you on your side”, over and over and then making a factual statement, thus no longer saying soothing things. Our brains code that as an attack.
Apparently, our brains don’t care about facts so much as social cohesion. The main goal of language/talk/verbal signaling.
It seems like verbal signaling’s main job is continual reassurance in social settings, to oneself and others. Pretty useless, and in fact counter to the discovering of facts
“Getting real existence from pure logic is just too much of a conjuring trick. That sort of hat cannot contain rabbits!”
(Rescher, Nicholas. The Riddle of Existence: An Essay in Idealistic Metaphysics. Lanham, MD: University Press of America, 1984. p. 3)
This discussion reminds me:
Theologians like William L. Craig have quite a surprising amount of their arguments hanging on the Ontological Argument. In fact when you push a whole range of his arguments (and this even includes his a posteriori, evidential arguments) they corner him into appeal to the ontological argument (OA) – e.g. when faced with questions about God’s goodness and the justification for divine command theory – the Euthyphro Dilemma – Craig will appeal to God’s necessary goodness, a la the OA.
This brings about a Euthryphro Dilemma in of itself, because the OA puts “necessity” ahead of “God.” Plantinga (in his version) for instance says a God must posses “maximal excellence” and “maximal greatness.” This posits an external standard, an already existing value standard, which to which a God MUST of necessity be measured. Hence the theist is still stuck on one horn of the Euthyprho (value/goodness are standards independent of a God, which a God must be measured against in order to be “good.”).
Craig tries to avoid even this problem by claiming that, no, God doesn’t have to measure up to external standards because, you see “It is GREATER to be THE standard than to be measured by a standard.” So God is not measured against outside criteria, but IS also the criteria itself for “greatness” in all respects.
Aside from the obvious viscous circularity (it actually undercuts our very justification for even forming the ontological argument itself!)…accepting Craig’s line of defense results in an absolutely fatal epistemological consequence: You have lost your criteria for ever identifying this God!
You say the God of the Bible and a rising Jesus Christ is indicative of being this God?
I say my dog, who is licking his poop, is indicative of being this God!
You want to try to argue that it makes more sense to think the Biblical God is “God?” By what criteria? You’ve abandoned any claim to external criteria by which to judge what would likely constitute “God.” What appears to be my dog is “God,” and since God himself is the standard by which we would judge any “maximally great being,” – well, ANYTHING my dog does is of necessity “God-like” since he is by definition the sole criteria. Sure, the Christian can make the same claims about the Biblical God or Christ…but that’s the point. But that’s the point – by abandoning any external criteria by which to judge a God, as Craig has, they are in no stronger a position than any other claim that X, Y, or Z may be a God.
Vaal
I’ll again note, there’s a basic but subtle mathematical error in Anselm’s Ontological proof, packed in the implicit assumptions of the word “greatest”. This indicates a maximal with the attribute “great” as basis of the (partial) ordering relationship “greater”. This implicitly requires (A) that the set have an upper bound that is itself an element, which in turn requires (B) that there exists at least one element that for all elements is comparable under the relationship. Neither A nor B is a universal property of posets. (Counterexamples: the integers are not bounded by any element therein; a two element set {P,Q} with P≤P, Q≤Q, and P||Q.) Therefore, the postulated entity does not automatically exist, and the proof does not hold in all cases.
To add insult to injury, there also seems to be a major theological error, in that the phrasing requires that humans can accurately have a concept of God, which would seem to contradict the ineffable nature commonly attributed to God by Christianity.
There’s probably also a second mathematical error, implicit in the “being conceivable” qualifier, in that this may require the ordered set be the naive “Universal set”, which is internally inconsistent (aka “WRONG!”). This is without even dissecting the fast one at “in reality”.
Again without wishing to imply that Godel had any spiritual beliefs, or imply the opposite, I doubt that any other than Godel’s version of the ontological argument would be regarded as really mathematical in the last hundred years or so. And I seriously doubt that what Godel wrote was in error at all. If it was, I’d like to see the error(s), if someone thinks he made any. And to repeat in case of misunderstanding, I doubt that he looked on what he wrote as actually an argument for the existence of anything outside the formalisms of modern logic.
Gödel’s religiosity is the second section in his Wikipedia article, and it’s a well-referenced section.
As for the problems with Gödel’s ontological proof…well, have a whack at it, yourself.
http://plato.stanford.edu/entries/ontological-arguments/#GodOntArg
He starts off with a definition of an entity that Gödel himself famously proved is non-existent. Specifically, anything complex enough to do integer arithmetic is either incomplete or inconsistent; one assumes that counting constitutes a “positive property.”
See if you can find more. It’s not hard.
b&
On wiki’s assertions about Godel’s belief in some sort of god and afterlife, thanks. As I said, I was not aware of that. “Religiosity” seems a strong word for it as briefly presented there.
On the ‘correctness’ of his modal form of the ontological argument, it appears that the Stanford article says just about exactly what I (modestly! ha!) claimed, namely that it is LOGICALLY valid—I claimed no more. Then Stanfordian does go on to criticize the argument severely as to whether it establishes anything beyond the correctness of some modal logical formalism. That’s fine and does not contradict what I said.
However, and not having Godel’s article at hand, the ‘religious’ beliefs of Godel that I formerly doubted perhaps mean that the article by him was done with some intention of trying to convince people about some theistic beliefs. His extreme paranoia leading him to starve himself was undoubtedly most manifest much later, if he actually discussed some of these views with Einstein, who died much earlier. So I guess his ‘craziness’ was multi-dimensional.
Then we’re not reading the same Wikipedia article.
http://en.wikipedia.org/wiki/Kurt_Gödel#Religious_views
As I pointed out, it opens with a definition of something that Gödel himself famously proved to be invalid. It then proceeds from there to include circular question-begging — of the exact same type as Anselm and the rest engage in. “God is perfect. Perfect beings exist. Therefore, God exists.” What nonsense!
Cheers,
b&
First, as I alluded earlier the error in Anselm’s is mathematics implicit to the language of the argument, rather than explicit. Nonetheless, there’s still mathematics.
Second, checking Wikipedia’s entry on Gödel’s ontological proof, his Axiom 1 and 2 also run into the difficulty of potential partial orderings. Gödel has the advantage of being more explicit in his Axioms, but it’s trivial to “refute” the proof by rejecting one of the Axioms, on the basis of the philosophical possibility of such partial orderings in “moral aesthetic”. (There may also be a problem of objective definition of that ordering relationship of “moral aesthetic” vis-a-vis Hume’s is-ought problem. The set of ordering relationships over a set of is-options can be shown constructively, but that does not indicate which element is referred to… even leaving aside the headache of whether Zorn’s Lemma is required when the is-options are infinite.)
Third, Gödel’s proof apparently assumes that all properties considered positive are mutually consistent — neglecting that Justice and Mercy may be inconsistent. This sweeps questions like the Epicurus formulation of the Problem of Evil under the rug.
Fourth, looking through the Wikipedia entry on Modal logic, modal logic formally defines the possible worlds in terms of a frame that is part of a model. It appears “easy” (AKA: a tedious but unremarkable process) to construct a frame and model whose possible worlds have no entities in common. That is, there exist models where no entity has the property of necessary existence. Thus, there does not necessarily exist (at the level of choice between models) anything with “necessary existence” (at the world level). This last looks to be the core flaw.
Interesting post here. I just wanted to make a short point in disagreement: that there are a few things you can prove exist through logic or thought alone.
Example:
(1) Suppose that propositions (i.e. the contents of beliefs, the universals that are instantiated by particular sentences, etc.) don’t exist.
(2) Then it is true that propositions don’t exist.
(3) Then there is a proposition (that propositions don’t exist) that is true.
(4) Then a proposition exists.
(5) But this is a contradiction with (1).
(6) Therefore, by reductio ad absurdum, propositions exist.
You could use the same kind of argument to prove that numbers and properties exist.
Of course, proving that universals exist through logic or thought alone is a very far cry from proving that God exists. Indeed, one might say that the only de re metaphysically necessary objects are narrowly logically necessary, and God is not.
“(1) Suppose that propositions (i.e. the contents of beliefs, the universals that are instantiated by particular sentences, etc.) don’t exist.”
To do that, obviously, you’ll first need to state it in non-propositional form.
I’ll wait…
“You could use the same kind of argument to prove that numbers and properties exist.”
What, pray, do you mean by saying numbers “exist”?
At least in mathematics, where I partly come from, “existence” is often meant as a shorthand for “definable in the current logical system while maintaining the consistency of the system” That’s what we mean when we say “there exists a real number whose square is two”. This does not quite seem to be the meaning of “existence” as used in Natural science (or for that matter, in theology).
Now, to get back to mathematics, what is often left unsaid is that all of this “existence” talk is predicated on the original system itself being consistent. However, it is a big open problem whether the most used logical framework for doing mathematics: the Zermelo-Fraenkel set theory with the axiom of choice (ZFC), is consistent. In fact, there is also some kind of infinite-regress involved here: If ZFC is consistent, then this consistency cannot be proved using just the ZFC (this is one of Goedel’s incompleteness theorems).
So, you see, mathematics asks one to be very wary of any logical argument attempting to prove “existence”: in all probability, it is not the kind of “existence” for which the proof was being attempted.
Your last point is an important one.
The most that could even be hypothetically gained by the Ontological Argument is a conclusion that, for example, “the set of all sets” is a coherent concept. (Which it isn’t.)
Or, more concretely, that, if you were to draw a representation of a right triangle with squares that share a side with each of the sides of the triangle, the two squares would have a combined area equal to the other.
The proof, however, says nothing at all about whether anybody’s ever actually gone out and drawn such a figure. And, when you think about it, it becomes obvious that, though we can get some marvelous approximations of that sort of thing, it’s not even theoretically possible to build a perfect realization of it.
Really, the Ontological Argument is nothing more than bad Platonism run backwards.
b&
‘… “the set of all sets” is a coherent concept. (Which it isn’t.)…’
But the class of all sets is coherent in (here we go again—>Godel-Bernays-v. Neumann set theory, is it not? I think it is definability, not coherence, that is the issue anyway.
Not terribly convincing to me is the phraseology of some people here, who blithely dismiss those who suspect some form of platonic existence holds for mathematical objects. That dismissal is of course common, if not convincing, among empirical scientists.
This eternal question has, among serious scholars, many more than just the rather unstable Godel on its side. And they are not all ‘merely’ mathematicians, where one might suspect a subconscious desire to aggrandize their subject.
Penrose is an example with a foot in physics as well. (He did as much as Hawking in the ’60’s to establish theoretically the almost certain existence of black holes, well before they were empirically found, and did lots more since then.)
And no one here has taken my bait to give real reasons (or references to such) why Tegmark, the MIT physicist, is wrong in his ‘ultra-platonism’ (one might say). He proposes that the physical universe, despite its concrete messiness seeming to say it couldn’t possibly actually BE
(not just be representable by) an abstract mathematical system, is in fact just that. Accepting that would of course mean that denying the existence of mathematical objects implies the solipsist position which denies the existence of external physical reality (or perhaps the gradually dying Copenhagen position about microphysics). Besides existence of abstract objects, this proposal also defangs the thorny issue of why math is “unreasonably effective” in fundamental physics.
So, accepting the Tegmark proposal, when Ahannasmi says “…mathematics, where I partly come from…”, he may be truer than true in a sense which he didn’t intend!
I am afraid I cannot imagine many serious mathematicians or physicists doubting that the universe is an abstract mathematical object (or at least is isomorphic to one), so your whole criticism seems to be rather misdirected. After all, the whole enterprise of theoretical physics is based around the idea that the universe can be described by a collection of mathematical laws, just like any other mathematical system (say a group).
I think this might be the root of all the confusion. No one (at least not me, and none of the mathematicians/physicists/computer scientists I have encountered in my professional work) holds the opinion that just because an object (say the universe) can be described by abstract mathematical laws, it follows that the object in question cannot exist. You seem to be conflating the two distinct statements:
1) No abstract objects can exist in physical reality.
2) Not all abstract objects can exist in physical reality.
TL;DR: ~∃P and ∃~p are very different statements.
Sorry, but I think you might misunderstand:
“…the universe is an abstract mathematical object (or at least is isomorphic to one)…”
The whole point is the distinction between
“is” and “is isomorphic to” here.
If these are mushed together, Tegmark’s whole point entirely disappears. What seems to be a trivial distinction is actually rather deep I think. And the assertion that the concrete universe could not possibly be an abstract system sounds a bit like an often in the past uttered assertion that the earth could not possibly be anything but flat!
Now I have completely lost you. “is” and “is isomorphic to” are precisely the same things in mathematics. The difference comes only when you are talking about real manifestations of mathematical objects. I am not sure it is fruitful question to ask whether the ring of integers I construct on my notepad is the same ring of integers that you construct on your notepad: all we can say is that they are isomorphic.
For this reason, this whole idea of trying to distinguishing “is” and “is isomorphic to” for mathematical objects sounds very much to me like the kind of mental gymnastics that is so popular in eastern mysticism. What do you even mean when you say ‘this bottle in front of me is a mathematical object?’, apart from saying that its behaviour and phenomenology is (in principle) completely described by a set of mathematical laws?
If you mean something more than that, then i think you need to be more precise, and also give evidence in support of why that view.
To Ahannasmi just above:
You say:
“Now I have completely lost you. “is” and “is isomorphic to” are precisely the same things in mathematics.”
I am not talking just about mathematics, but rather about the relationship between it and physics. If, as Tegmark proposes (I know of no one earlier to do so), the physical universe is a mathematical object, and if humans actually discovered which one it is (that is the big TOE question in this context; Tegmark’s question is closer to philosophy and its answer wouldn’t get us much closer to a ‘Theory Of Everything’), then theoretical physics becomes simply part of mathematics. When you say earlier “..I cannot imagine…many physicists doubting…..the universe…is isomorphic to one…” (“one” being a mathematical object), you are speaking metaphorically, since most physicists do not accept Tegmark, and since the exact definition of “is isomorphic to” occurs purely in mathematics, and must be a relation between mathematical objects. If the external universe is not a mathematical object, you cannot be speaking literally of that definition, but rather using it perhaps to say ‘the universe is very accurately approximated by a mathematical object’ or something similar. (Of course we are not even close to knowing of any math. object which contains anything even close to a “self-aware system”, as Tegmark calls them, much less the system, if it exists, which is literally the physical universe.)
You say
“The difference comes only when you are talking about real manifestations of mathematical objects. I am not sure it is fruitful question to ask whether the ring of integers I construct on my notepad is the same ring of integers that you construct on your notepad: all we can say is that they are isomorphic.”
You must have a big memory on your notepad to have actually constructed that infinite set inside it<—that's sort of a joke to say that I think the notion of "real manifestations of mathematical objects" is seriously suspect.
You say
"For this reason, this whole idea of trying to distinguishing “is” and “is isomorphic to” for mathematical objects…"
With emphasis on your last few words, I didn't.
You say
"What do you even mean when you say ‘this bottle in front of me is a mathematical object?’.."
To answer that, if I did accept Tegmark, it would likely be necessary to also have discovered TOE, and to have done a huge amount of analysis with it, if you mean by your question "Which mathematical object" But if you mean something much weaker, I merely have to say clearly in general what I mean by the phrase "mathematical object" (personally I think this is the weakest point in Tegmark, in that he is overly confident about mathematicians having answered that question once and for all—but that is in his papers and you should read them), and having done so, I need merely say that your bottle is one of those objects, but don't expect me to know which one.
You say
"…you need to be more precise, and also give evidence in support of why that view."
This Tegmark's theory, not mine. I am interested in what he says, and think it needs serious consideration, but have not strongly advocated it. However I could just parrot his answers to your questions, but maybe you should get on his web page and get the papers, which are all available for free.
Not at all. Two sets can have differences, yet an isomorphic mapping can exist between them which preserves various properties under certain operations, but it’s not the same as saying the sets are identical. The set of points on the parabola (x, x**2) in the real plane is isomorphic to the real numbers via the function y=x**2 and the inverse x = the square root of y. But the x axis is not the same as the parabola.
Imagine a perfect topological map that is a perfect scale representation of a landscape up to some resolution, lets say one pixel per square foot. The map and the landscape are not identical, but you could say there is an isomorphism between each pixel on the map and each square foot of the landscape. One could also probably construct an isomorphic mapping between how we see the world in our mind, and that portion of our environment that is visible to us. Yet the two are quite distinct.
There is also such a difference between any mathematical object and the real world object it represents in any practical application of math. The differential equation representing a weighted spring or pendulum or other simple harmonic oscillator is quite different from the physical system it represents. There is no mathematical object that is identical to any real physical system.
A map identical to the landscape would be the same size as the landscape and thus useless as a map; then you could say the map is the landscape. A mathematical object exactly identical to a physical system would be hopelessly complex and unwieldy and thus similarly useless. This is why there is always an unbridgeable gap between our understanding and reason, and objective reality. That we really truly see our environment or that we truly understand it are illusions we take for granted because we can function well by approximations and schematic representations, but our mental models and understanding always lack, and always will lack.
@Jeff Johnson
That’s not an isomorphism at all: just a bijection. An isomorphism, by definition, needs to preserve the structures being talked about. In this case, the group structure of the real line is not preserved by your map. Not all bijections are isomorphisms.
@अहंनास्मि (Ahannāsmi)
When I studied math, over 30 years ago now, in analysis a function that was 1-1 and onto, i.e. it was invertible, represented an isomorphism between the domain and the range. So my example is an isomorphism, and the wikipedia page seems to back me up on this:
http://en.wikipedia.org/wiki/Isomorphism
I’ve studied less group theory than analysis, so it could be the term is used differently in group theory, but I don’t recall that difference.
I don’t think that two groups that are isomorphic necessarily represent identical sets of elements, though they must have some group properties in common I imagine.
What is important about isomorphism, dredging in my stake memory, is that you can count on operations in one set or group being preserved after transforming via the isomorphic mapping. This allows you to solve a problem by mapping into a different domain, and then inverting to the original problem space. This technique is used in coordinate transformations, linear transformations, fourier transformations, and in differential geometry, as I recall, though I’m fuzzy on details.
More generally, an isomorphism always involves a mapping between sets, and they are not necessarily identical sets.
In any case, there seems to be no justification for saying that Isomorphism between S1 and S2 guarantees that S1 ‘is’ S2, however you want to define ‘is’. Presumably mapping between groups would only be interesting (or useful I suppose) if the group elements represented different entities with different properties.
To Jeff just above:
Just one point. When you say
“There is no mathematical object that is identical to any real physical system.”,
that is certainly something which Tegmark’s theory would emphatically deny. It seems ‘obvious’ you are right and he is wrong, but as I said earlier, it seems obvious the earth is flat. I’d like to see an acceptable reason why you are right. I do not know of one.
It would seem to me that quantum uncertainty should make it clear that, though one can certainly create computer / mathematical models that very closely mimic reality, the only way to claim that the math is the reality is to claim that reality is a giant Matrix-style simulation.
While it’s provable that one can’t rule out the possibility that such is the case, it’s equally provable that the same applies to the computer / whatever running the simulation. And that very infinite regress tells us that, ultimately, reality simply is — just as it tells us that there aren’t any gods at the base of it all.
Occam, of course, suggests that positing a Matrix without supportive evidence isn’t a good way to place your bets, even if we can’t eliminate the possibility.
Cheers,
b&
I’m leaning toward Tegmark on this. If there exists a wave function that completely describes the behavior of, say, an electron, then in what meaningful sense is the “real” electron distinct from its wave function? If there’s some experiment that can tell the difference, all that means is that our theory is incomplete and we’re using the wrong math. But if the math is right and there’s no such experiment, then what’s left to distinguish physical electrons from abstract mathematical ones? Nothing, as far as I can see.
Intuitively we want to think of electrons and such as tiny nuggets of stuff that happen to obey mathematical laws. But I think this is fundamentally misguided. Either the math is successful at fully deconstructing the physical phenomena until there’s nothing there but math, or else our work’s not done and we still have some math left to discover.
The thing is, thanks to Gödel and P=?NP and quantum uncertainty and all the rest, we have overwhelmingly good reasons to believe that no mathematical function, even in theory, could even hypothetically encompass all of reality. Indeed, we know that math can’t even encompass all of itself — so how could it encompass the rest of reality as well?
b&
Perhaps I’m missing something here, but this seems so obvious to me. I would say that no matter how good the mathematical description, the description remains a linguistic construct which must necessarily be different from what it describes, just as the word ‘table’ can never have a tea served on it.
The mathematical description may be so perfect that it contains all the information needed to put another electron into an indistinguishable state at another time or place, it still can’t have the properties and behaviors of an electron.
To me this just seems to follow from the definition of a linguistic description. No matter how hard we stare at an object, the image we see in our mind is never the object itself, it only relates to it by the information we glean from photons striking our retina. At best we are talking about informational messages that may be encoded, stored, retrieved, transmitted, received, and used to reconstruct a facsimile of the object referred to by the description, but it can never be the thing itself.
So what am I missing here?
Ben, if the physical universe is fundamentally mathematical in nature, that needn’t imply that mathematics must fully encompass itself. It need only encompass the set of abstractions that represent physical reality. This set is much smaller than the totality of mathematics, so no paradox of self-description arises. In any case it’s clear that people like Tegmark and Penrose think that mathematics is up to the task of fully representing reality, and I’m inclined to trust their opinions.
Jeff, I think you’ve drawn the distinction between label and object in the wrong place. Mathematical notations are labels; mathematical abstractions are the objects being labeled. Math itself is not just a mental model or a label we put on physical phenomena; in some deep sense math is fundamental to the way the world works. So my question for you would be: what exactly do you imagine “the thing itself” to be, if not its mathematically determined behavior? What is that nugget of stuff made of, if not math?
On word usage just above, I think the phrases “math encompasses” and “math reconstructs” are just too loose and ill-defined here to be able to agree or disagree.
But to go back to Ben’s “…the same applies to the computer / whatever running the simulation. And that very infinite regress tells us…”, there seems to be a misunderstanding, maybe leading to a devaluation, of Tegmark’s idea here.
We undoubtedly disagree on whether a mathematical object has any reality, if it is non-computable in some sense, since you say “computer / mathematical models”. But Tegmark himself has later drawn a line around his notion of mathematical object to include computability. So I’ll go along with that.
But the ‘idea’, not original with the Hollywood writers of course, that humans might be fooled because what we experience as physical reality is a computer simulation, depends on the ‘real’ reality being where the computer lives; but maybe that’s itself a simulation, etc. ad infinitum. This is superficially more subtle, but really less so, than Tegmark’s proposal. And I think the fundamental difference is the need for a computer to do any ‘running’ here. (This is quite apart from their scientific incorrectness coming from computational complexity, explained in detail by Dennett for the ‘brain in a vat’ supposed experiment.)
Here’s my basic objection: Why need there be anything running the (perhaps you would say) ‘software/math model’? If there is none, the idea is quite different than “Matrix”‘s flawed unoriginal idea, and certainly there is no infinite regress. And in any case, I would be loath to apply Occam’s razor to replace an idea which ‘solves’ both the problem of the actual existence of math objects, as well as the problem of the “unreasonable effectiveness of mathematics”, by a non-theory which solves neither of them, because the non-theory is simpler! “God did it” is a pretty simple non-theory.
To put it back to you in a simple form and introduce Tegmark’s extension: If one accepts his proposal that some particular mathematical system is in fact the external universe, and if you are not so solipsistic as to claim no external universe exists, then you have accepted the actual objective existence of at least one mathematical system, and have thereby become very close to being a platonist. He then says that now it would seem unreasonable to not accept the actual objective existence of ‘every’ mathematical object.
Now to go back to Ben’s claim that “the only way to claim that the math is the reality is to claim that reality is a giant Matrix-style simulation” and look at, not some system that might be a bit close to ‘our universe’, but rather at the absolutely simplest system perhaps, which is not completely trivial, namely the so-called cyclic group of order 2.
(For those where that system needs to be defined, the set has just two elements which they may take to be +1 and -1, and there is just a single relation in this system which is a binary operation that they should take to be multiplication of those numbers.)
To do what I ask, he may need to translate this system to his computer software, but there is no worry here, since it is finite so certainly computable (so nothing like the set of all real numbers, where I sometimes wonder about what people think they are doing when they perform some calculus in their everyday lives, which might be something rather sophisticated like landing a vehicle on Mars, yet adopt this very restrictive attitude about what math is really about, which disqualifies the reals from being real! I realize there are ways around this, but do they?)
But let’s not get off the subject: If Ben really maintains what is quoted above, I need to know why there must be also a computer which runs the software which is that tiny system, existing right there with that ‘mini-universe’ of Tegmark’s, in order for that mini-universe to exist? I realize that of course there will be no self-aware-systems in that system, or in any others that we have been able to find so far, to experience that mini-universe as though it had so-called physical existence. But the same question applies to any purported mathematical system, so that is not a way to avoid the question.
Jeff, it’s not my intention to attribute anything mystical to math; quite the opposite.
But it does seem to me that by saying “The ‘thing itself’ is a physical object” and “The laws of physics are not math” you may be attributing something mystical to physics, some ineffable je ne sais quoi that makes physical objects somehow distinct from the math that governs them. You believe there really is a non-mathematical “nugget of stuff” there, even if you can’t know what it’s made of.
I don’t believe that. Historically, nuggets of stuff (rocks, atoms, nuclei, protons, quarks) have always turned out to mask a deeper layer of mathematical structure. So the lesson I take from that is that physics is not complete until all the “stuff” has been dissolved and there’s nothing left but math.
And I don’t agree that this would be “very disappointing” and that “Everything would be drained of the fullness of its reality.” On the contrary, it would mean that we finally understand what “reality” actually means. Unweaving the rainbow doesn’t abolish rainbows, or make them any less beautiful.
I’m not sure if this is the best place to interject this in these convoluted threads, but…
To quote Milton Rothman: “As an illustration of how nature does not care about what humans think, consider that there are at least eleven ways of writing equations describing the motion of a baseball or a planet. (Hamilton’s equations, Lagrange’s equations, Maupertuis’ law of least action, etc.) These equations are all equivalent to Newton’s second law of motion, but each is different in structure from the others. However, there is only one reality that these several equations describe.”
So, which of these several kinds of maths stuff would Tegmark say is “real”?
/@
Ant, the equations are all equally real in the sense of being physical marks on paper. But the Platonic reality that Tegmark talks about is not the various equations or notations, but the underlying mathematical objects they all refer to. That’s how we know they’re the same, because there is a common structure they all transform into (however you choose to write it down).
But that’s just it. They don’t all transform into the same structure.
That’s why I keep using terrestrial geometry as the example.
At a personal scale, Euclidean geometry, non-Euclidean spherical geometry, Newtonian Mechanics, Quantum Mechanics, Relativistic Mechanics, String Theory — hell, even epicycles and the lot — all will, for example, give you the same area for the floor of the room you’re sitting in, to well within the margin of error.
But we also know for a fact that all are radically different models of the universe, and that all of them are profoundly flawed in some irremediable way. Yes, even the latest ones, even though they’re successful and useful beyond the imagination of any previous era.
They’re all equally mathematically valid, they’re all powerfully useful…and, empirically, they’ve all been unequivocally proven to be pure bullshit.
Fantastically useful bullshit, to be sure. But bullshit nonetheless.
b&
Here’s something else for you Platonists to consider.
Today, Quantum Mechanics and Relativistic Mechanics are irreconcilable, and getting the two to play nice with each other is one of the biggest challenge facing physicists.
Imagine that somebody comes up with an experiment in the spirit of Michelson-Morley that conclusively demonstrates that the two absolutely cannot be married together — that no explanation of the small scale can also account for large-scale phenomena and vice-versa.
Would you still insist on Platonism?
What if no such conclusive evidence is found, but the problem still remains unsolved a century from now?
b&
@ Gregory
Well, here’s the thing. How do we know that “the underlying … objects they all refer to” are mathematical objects?
Why is it that the stuff of reality must be “mathematical” stuff rather than “physical” stuff that is amenable to mathematical description in our (imprecise, incomplete) models?
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Ant: As peter keeps pointing out, the fact that our current working models are imprecise and incomplete is considered by most physicists to be a temporary state of affairs. The consensus is that a complete, precise theory is possible, one that fully specifies physical reality in mathematical terms. At that point, the distinction between “mathematical stuff” and “physical stuff that obeys mathematical laws” becomes moot, since there’s no empirical test you could use to tell them apart. So according to Tegmark we may as well apply Occam’s razor and accept that physics at bottom simply is a branch of mathematics, and that the “physical” entities it deals with are in fact mathematical entities, since there’s no longer any meaningful difference between the two.
Yes, it’s weird to think of reality that way, but as Tegmark observes, physics has been getter progressively weirder and more abstract for about a century now, and this idea just pushes that weirdness to its logical extreme in the direction it’s already going.
“The consensus is that a complete, precise theory is possible”
It’s not clear to me that that is actually the case.
“since there’s no longer any meaningful difference between the two”
Hmm… so it’s just stuff then, and meaningless to say it’s mathematical stuff.
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Ant: Here is the kind of stuff we’re talking about. Sure looks like math stuff to me.
It still seems to me like you’re commiting a Bruno and Sylvie error and confusing the map with the territory.
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* committing
The “set of all sets” is not inconsistent per se, problems arise only when it’s combined with some form of unrestricted comprehension axiom. There are set theories in that have a universal set for example Quine’s New Foundations. Last I checked it was still unknown whether NF is consistent but a version of it (NF with urelements) has been proved equiconsistent with ZF.
Self-reference is not inherently contradictory, just pick any of Hofstadter’s books.
You’re obviously not a mathematical platonist. Some people think (oddly – and many working mathematicians are among them) that there really is a number 2, or the set containing thus and so, etc.
I would like to know who these people are :D.
To me, Platonism (at least in its “world of ideas” formulation in which it was introduced to me in one of my undergrad classes) struck as a rather content-less idea. I could never figure out how it is any different from just making the much more humble claim that we have labels for objects. At least in my experience, when a mathematician writes “the set of integers exists”, she is well aware that she is not making any “existential” (in the natural science sense) claim at all.
Quite a few actually. Just off the top of my head, Cantor, Hermite, Godel, Penrose, … A lot of working mathematicians are naive platonists—naive in the same sence as in the phrase “naive set theory”, and platonists in the sence used in the philosophy of mathematics, see below. I have my platonist moments myself.
In the philosophy of mathematics “platonism” refers to the idea that mathematical objects exist independently of the minds of mathematicians in some objective manner.
“In the philosophy of mathematics “platonism” refers to the idea that mathematical objects exist independently of the minds of mathematicians in some objective manner.”
Which, to be blunt, sounds exactly as content-less and rather like the more exotic kinds of eastern mysticism. In one sense it is a trivial statement: given a formal system, all possible provable statements in the system “exist” independently of the minds of the mathematicians, and in another sense completely meaningless: what does “exist” mean again?
What does “exactly” means again? ;0)
There are essential difference between mathematics and theology or eastern or western mysticism. Mathematics is consistent, persistent, and “objective” (or at least inter-subjective). Plus there are all these (more or less) well defined correspondences with the real world (see the discussions bellow about the unreasonable effectiveness of mathematics).
How is one convinced that the real world really exists out there and not inside their heads if not by its consistency, persistence and objectivity? So if I wanted to be blunt too I could say that your position sounds exactly like solipsism.
I wonder where I said that mathematics is the same as theology or eastern or western mysticism. Indeed, I truly agree that it is not, and as I said earlier, this is just because of the reasons you gave: a strive for consistency, and correspondences with the real world. I wouldn’t be doing what is essentially mathematics as my day job otherwise.
On the other hand, I fail to see how the same applies to platonism, which does sound very much like eastern mysticism in its insistence on making meaningless claims. What is “existence” independent of the minds of mathematicians? As I said earlier, and I see nothing in your comments contradicting that view, I can think of only two interpretations: one of which is trivial (and I believe) the common one in mathematics: that given a formal system, all provable statements in the system “exist” in the sense of being possible to generate by a Turing machine, or the mystical meaningless one which hangs on what the word “exist” in the statement is supposed to mean.
In that light, I find it hard to believe you would accuse me of solipsism: when it is exactly the opposite I argued for :D.
Also, I think I should just add a note to avoid further accusations of solipsism: when I say “What does “existence” independent of the minds of the mathematicians?”, I mean it only in relation to mathematical facts: a mathematical fact like “a bounded entire function is constant” does not “exist” independent of the minds of the mathematician in a way, say the sun does. It does “exist” in the sense that there is a formal system in which it is provable, but I fail to see how that is the same kind “existence” as that talked about in the natural sciences.
Without that last caveat spelled out, I see why Nikos Apostolakis might accuse me of solipsism.
This is getting rather long (we already reached the “threadness” limit) so let me clear possible missunderstandings and perhaps call it a day.
I didn’t actually accuse you of solipsism. I was trying to make a point of misusing the word “exactly” the same way that you did when you equated “mathematical platonism” with “eastern mysticism”. I don’t actually think that one who is not convinced of the independent existence of mathematical entities is exactly like a solipsist. That would be calling myself solipsist (at least the days that I don’t feel particular platonic).
The point about the contrast between theology and mysticism vs mathematics is that due to their essential differences it is not unreasonable to expect that their objects of study have different ontological status. Furthermore, mathematical “entitities” share some of the properties of real objects* that are essential in justifying their external existence. So IMO, mathematical platonism is not obviously absurd or contentless.
* or to be clear our perceptions of mathematical entities share some properties with our perceptions of real objects.
Am I right if I say that Tegmark’s theory implies that self-awareness is a basic property of the universe?
@Tom:
Your argument is unsound because 2 doesn’t follow from 1. If propositions (or other truth-apt representations) didn’t exist, it would not be true that propositions don’t exist. For truths are true propositions, and if there are no propositions, there are no truths either. That is, a propositionless world is a truthless world.
The Ontological Argument was covered in a Jesus and Mo cartoon. Jesus and Mo explain the argument to the barmaid and then order two more pints of beer. The barmaid replies by suggesting that they define the beers into existence.
Jerry beat you to the citation:
http://whyevolutionistrue.wordpress.com/2011/02/23/jesus-n-mo-tackle-the-ontological-argument/
Chers,
b&
I am not sure you even need to get that far, as uder g2-d34147f3f4e571d41cd1577a51e70a35 pointed out. You first need to define propositions, and I don’t see how could you come up with a reasonable definition for which 1 is not a proposition.
Oops, that was supposed to go in reply to Myron’s comment above. Sorry about this.
That J&M cartoon wasn’t the one. They hit the barmaid with the ontological argument and then ordered two more pints. The barmaid the challenged them to define two pints into existence.
Ah…perhaps this one, then?
http://www.jesusandmo.net/2006/09/11/pints/
b&
I listened to the original broadcast with some hesitation because anything with Prof. Haldane (unctuous Catholic apologist) in it is unlikely to offer anything interesting or original (and Haldane did not disappoint on this score).
While half-listening a thought occurred to me which, in my ignorance, I do not recall having heard before. So here it goes.
The premise of the onthological argument is that God must be perfect and therefore must exist because existence cannot be absent from the definition of perfection.
But what about “quantum” perfection?
A god that is always constrained to exist surely must be less perfect than a god that can choose to alternate between existence and non-existence.
Which opens the door to “quantum physics” arguments whereby attempts to observe/perceive god may lead to failure to detect an existing god, i.e., god may exist only when humans act as if he/she did not, whereas he/she would not exist if humans behaved assuming his/her existence.
Any ideas on this?
Anytime somebody uses the word, “quantum,” to refer to something much bigger than a water molecule, they’re almost guaranteed to be grossly misusing the word.
In particular, “quantum” is not the root password to unlocking the secret mysteries of the mind of the universe. Indeed, there’s damned little practical application of quantum mechanics to the macroscopic world. Probably the biggest are the quantum tunneling effects electrons exhibit on the scale of modern integrated circuits — and, then, it’s basically just a nuisance for the electrical engineers designing the chips. Oh — there’s also radioisotope decay, that sort of thing.
Seriously? Does this even need to be addressed, other than with uproarious laughter?
b&
Actually, the mathematics of quantum mechanics has been and is today quite fruitfully applied to things with event horizons like black holes and the entire universe.
See, e.g. https://en.wikipedia.org/wiki/Quantum_cosmology
Yeah, but when was the last time you saw an event horizon at the local market?
That’s my point — that, basically, the closest people get to quantum anything in their everyday lives is by using an iPhone designed to be resistant to quantum effects.
No doubt, Quantum Mechanics has revolutionized the way we understand the universe. But it might as well not exist at all for all it touches on your day-to-day life.
And I’m making that point in an attempt to knock some sense into the Chopra-esque quantum wooers who inevitably show up.
b&
Lasers. Lasers are an everyday item, in DVD players, laser pointers, internet communication hardware. And lasing is an inherently quantum phenomenon. There is no classical theory of lasing.
.
(Just being pedantic; I know what you mean and agree.)
Alright, fair enough. Apart from the lasers….
http://www.youtube.com/watch?v=ExWfh6sGyso
b&
Love it. Cleese is clearly a Republican.
Q.M. underlies the electronic structure of all atoms and molecules. So I guess Q.M. touches all of chemistry, which means it touches everything, basically.
You mean, aside from the “application” that makes you not fall through the vast empty spaces in your chair? 😀 Also, as the user with the hashed user name (i hope so) pointed out above, QM has been applied to black holes, and getting it to match up with the General Relativity math of black holes is one of the biggest open problems in physics.
Of course, keeping in mind the caveat of the lack of a GUT, everything can be reduced to quantum-scale effects.
Just as you can use Relativity to calculate the trajectory of a softball pitch.
But you don’t need Quantum Mechanics to explain, within any reasonable margin of error, anything at all in your daily life. Nor do you need Relativistic Mechanics to do so. Plain ol’ ordinary Newtonian Mechanics (and Maxwell and the like) is more than enough to account for all the phenomena you’re ever going to personally observe (outside of some very contrived scenarios).
religionenslaves was suggesting the consideration of a quantum Jesus who’s both crucified and resurrected until you eat the cracker. I’m just pointing out the absurdity of such a notion and that it’s a gross mischaracterization of Quantum Mechanics.
b&
Mea maxima culpa. Obviously I attached to my inverted commas far too much explanatory power. The whole comment was supposed to be a (clearly failed) attempt at irony, by stretching the OA into a non-OA by means of an appeal to a “quantum-like” (note the inverted commas, please)argument. The accusation of being a quantum wooer is so far off the person I am that I am left totally untouched. Note to self: irony may not travel well in certain speaces.
Hey, no worries. Not only is there Poe’s law to consider, but my ironing meter may be in need of recalcification.
b&
Where do you get your electricity, Ben?
Photovoltaic panels on your roof, isn’t it?
Yes — giant black boxes that magically turn sunlight into negative utility bills. And not one bit of mechanical quantumitude in sight, nosireebob! It’s 100% pure, quantum-free, honest-to-God magic.
Magic! Magic!
b&
The ontological argument was invented by Anselm of Canterbury in 1078. (Ref Wikipedia “Ontological argument”)
Even Wikipedia’s concise but impartial formulation of the argument appears to have holes in it big enough to drive a Mack truck through. Why is it that Xtian thought involves so much outdated, illogical reasoning by medieval theologians? Hasn’t mankind progressed at least a little ways past such logic chopping and word play?
The very idea that if we can conceive of something it must exist is refuted by any of the vast number of works of fiction on library shelves, particularly works of imaginative fiction (i.e. fantasy and SF).
Even better, this: I can easily conceive of our eminent blogmeister having two dozen felines sharing his abode, but that doesn’t mean they exist.
JAC is doing the world a big service by pointing to theological “argument” and saying “the emperor has no clothes.”
I love how the definition of “greater than” is horse-whipped into carrying the whole load of the OA.
1. No dinosaur born with rocket launchers mounted on his tusks ever existed.
2. A dinosaur born with rocket launchers mounted on his tusks could totally kick the ass of any dinosaur who ever actually existed.
3. A nonexistent dinosaur is “greater than” any once-existent dinosaur.
4. An existent deity is not “surely greater than” any non-existent deity.
QED
I’m not particularly interested in the Ontological Argument as an example of philosophical word salad. However I will suggest that anyone going to the IOT website in search of this programme should go off for a ramble through the archives. “To entertain and inform,” is the mission statement for Auntie Beeb, and with some 80-odd years of practice at it, they’ve become pretty good at it.
I’ve got bedrooms to paint next week ; MP3s of Moby Dick, the Ontological Argument, and probably some ‘Science‘ podcasts should make it bearable.
“… and it remains one of the most discussed problems in philosophy.”
Kind of sad when you think about it.
Scary. Why as these people taking up valuable university funds?
I’m not sure that’s true if one resets the clock, though, and considers contemporary concerns only and restricts further to (say) monographs, journals, etc. I suggest the latter, as it is no doubt talked over in many intro to phil lectures, but that doesn’t seem right to count.
I’m still going with the Robert Green Ingersoll argument: “Man created god in his image.”
If you accept that generic ‘greatness’ can be coherently defined, then yes, there is a maximally great being. It’s probably a blue whale, or a sequoia tree. But what does that have to do with a hypothetical God?
Forget Anselm; he plagiarized the idea from Aristotle. This is nothing but Aristotelian ‘natural philosophy’, specifically the bad idea that humans can only imagine perfect objects such as triangles because those perfect objects are present somehow in nature even if we have never seen the perfect object in nature. If wishing things into existence really worked, godzilla would have eaten all the other gods by now and religion would cease to plague humanity.
As far as philosophical arguments for the existence of God I personally prefer Borges’ ornithological argument:
oh! and sub
Wow!!! I hope my failure to understand more than half of the ginormous philosophical and mathematical terms (being in the medical line) won’t totally refute the validity of my comment:
To digress a bit into the tools used to collect the information we digest and analyse and define the existence of an entity. Are they our senses? I guess the scientific method will be satisfied with proving facts based on sight, sound, feel, thought, etc.
(Now, we know that philosophy and logic will make more sense if more practicable/applicable to our living.)
So, for the purpose of practicality, can we draw valid conclusions when our senses experience events that point to the existence of another realm?
And, please, let whoever replies attempt to use simple terms as I am a non-philosophy-major who is just fascinated by the discussion.
Science uses a vast array of tools and instruments that can detect and measure phenomena not available to our senses.
Our senses are notoriously unreliable. For example, in the room you are in, touch a piece of wood or cloth, then touch a piece of metal. Which is warmer? You would be tempted to say the metal is colder, but they are the same temperature, the ambient temperature of the room. Your senses don’t detect temperature per se, they detect heat flow.
So the answer is no, if your sensory experience makes you feel there is another realm you can’t trust that to be a valid indication of something real. Once it was considered true that a crazy person was possessed by demons. Today we know there are biological causes of brain disorders that lead to unusual behaviors. The way we experience the world is very dependent on our brain, and can change radically as a result of injury, disease, or ingested or naturally produced chemicals.
Superman is the greatest superhero ever conceived. Since one of the qualities of greatness is existence, Superman must be real. Now, where’s my Templeton prize?
You just got the NAME wrong! ;^)
I have a non-observable, invisible unicorn in this box: nevertheless, it exists! Actually, my take on it is that the concept of a “God” is a “mental spandrel” that is produced when a dualistically-structured mind attempts to examine (the underlying unity of reality) something that is not dualistic in nature and goes on to try to explain or describe it with a dualistim-based language system. Were a God to “exist”, would that not mean that said God would be subject to all of the ramifications of existence? One might say, “Well, God exists but, being supernatural, is exempt from the effects of being in existence.” More unprovable claptrap. Once a “God” is postulated as an existent “entity”, he falls into the clutches of our dualistic language system, which automatically generates innumerable paradoxes: “Can God create a rock so heavy that he can’t lift it? Does God have free will? How can God be all-good, yet allow evil? Could God stop being God, if he wanted to? Etc., etc., etc…..
Not only that, but She is pink!
b&
Thanks for putting me onto the podcast. No matter how I try, I can never get my head around the ontological argument and just what it is the argument can show. Hopefully this discussion can enlighten me.
I listened to it as I went for my lunchtime walk. I’m still not sure how anyone can think this argument other than wordplay (guess I am way too Humean), but I’m thankful for the philosophers doing so well in explaining the contentions that the argument rests around.
Troll Physics: The Ontological Taco.
I haven’t taken the time to read through the long list of comments, so some one has likely already noted this:
“Theologians, of course, then come back and say that God is the only entity for which existence must be a predicate. That’s hilarious!”
Similarly, I have seen the Cosmological agrument distilled to:
1. Everything that exists has a cause
2. Except this one thing that I’ll define as my God.
3. The universe exists and therefore had to be caused
4. Since I defined God as not needing a cause in (2), therefore God is required to exist to cause the universe.
Same fallacy sleight of hand: OK, I’ll just define my God to be whatever I need it to be.
Sheesh! And that’s supposed to be ‘fisticated? (“My dear … you’re SO ‘fisticated!”)
I have proposed an Ontological Argument against the existence of Yahweh.
1. For sake of this argument, we will accept the Ontological Argument as true.
2. The Greatest Concievable Being (GCB) would not allow such an unstable monster as the Biblical god Yahweh to exist. This is because Yahweh is evil, and the GCB is good.
3. The GCB would be all-powerful, and thus would prevent Yahweh from ever existing.
Conclusion: Therefore Yahweh doesn’t exist.
A couple of steps further put us into the Problem of Evil, as the GCB should be able to stop ANY evil (not just Yahweh), and yet evil exists. Therefore, even if one cannot determine WHY the Ontological Argument fails, one can see that it does indeed fail.
Or, alternatively, I just don’t know what ‘greatness’ is. In which case, the GCB is a mystery entity, and I gain no knowledge from the Ontological Argument, as I apparently do not know what constitutes ‘greatness’.
I can’t encounter the OA without thinking of another great proof, learned in my school days:
1. Nothing is better than God
2. A ham sandwich is better than nothing
3. Therefore, a ham sandwich is better than God
And so I have always found it to be.
In reply to this post:
No, I haven’t. Associating a label with an object is representation, where you use the label to represent the object. It is the nature of representation that what represents contains less information than what is represented. That is exactly why representation is useful.
You are correct that notation, and the words we speak when reading or talking about the notations, are labels representing mathematical objects. But the mathematical object, when applied to model some physical system, is also just a representation of that system; it is a more sophisticated label than a simple word or set of glyphs because the abstract mathematical object actually mimics or simulates certain properties and behaviors of the physical system being modeled. A mathematical object is still just a tool we grasp in our minds. Mathematical objects describe much more about a phenomenon than a mere label, just as a poem describes more about an object than its name, yet both the poem and the mathematical object fall short of being what they describe. If they did not, either we could no longer grasp them in our minds, or we would no longer need them because we could fully grasp the real system in its entirety. Mathematical objects are just stick figure models of reality that are convenient abstract short cuts for our brain, just as a globe is a convenient abstraction of the earth. Simply the word ‘abstract’ means the abstraction is different from that which it is abstracted from.
I don’t agree that math is fundamental to the way the world works. I’d rather say that the way the world works is fundamental to that math which is useful in modeling physical reality. The peculiar effectiveness of math isn’t magic. It seems you are attributing something mystical to math. Because we have the word ‘stone’ in our language we don’t marvel, when we travel to Mars, that our language anticipated the existence of Martian stones, or that our language is deeply fundamental to martian “geology”. Our language was invented to describe nature with mental tools our mind can use, and we shouldn’t be surprised when the linguistic tool we create applies in some other location beyond the original domain of application. It just means our tool successfully captured an aspect of reality that is a pattern repeated elsewhere. Yes this is a beautiful thing, and cause for much joy when we discover a pattern that is widely applicable, but to attribute mystical powers to math is going too far. I’m imagining a story like that of Midas, but the foolish king is enamored of math rather than gold. Life would become very disappointing if everything you touched turned to math. Everything would be drained of the fullness of its reality.
To answer your question, if I haven’t already, the “thing itself” is not a mathematical object nor is its behavior determined by math. The “thing itself” is a physical object and its behavior is determined by the laws of physics. The laws of physics are not math. Physicists write mathematics that describes the laws of physics in ways useful to physicists. A meteor falling toward earth is not the parabola we use to model it’s trajectory, and gravity is not the math we use to model its behavior. An electron is not a particle, nor is it a wave, nor is it the wave function we use to model it. It is what it is, and we can not ‘think’ it. We can only think about it using stick figure mathematical objects that represent limited aspects of it. What is “the nugget of stuff” made of? I can’t know it, but I know it’s not math. Math is a creation of the human mind. The human mind can think about things in terms of math, but the human mind can’t think electrons, think mountains, think planets, or think stars.
“I don’t agree that math is fundamental to the way the world works.”
“The peculiar effectiveness of math isn’t magic.”
“Physicists write mathematics that describes the laws of physics in ways useful to physicists.”
Can you give a single example of a general law of physics formulated in a way which is not mathematical (such an example’s existence seems to be implied by that last quote)? Wigner would seem to disagree with you. Well after he coined that “effectiveness” phrase, one had accuracy to something like 12 digits for an experiment checking quantum field theory, so that theory might be a good place to start in answering the question.
Ah, this is evidence that physics rests on maths – not of anything special about maths. There’s lots and lots and lots of maths which is not useful in physics.
When I studied engineering about (oh Dawkins) 24 years ago, our lecturer explained to us that we learn maths and physics because they are useful to engineering, and that if the plays of Shakespeare turned out to be useful in predicting whether a bridge would fall down, we’d be doing half our courses in the arts faculty.
You’re putting the cart before the horse. Maths seems unreasonably effective because physics rests on it, but that doesn’t make maths special in terms of thought affecting the universe or making mathematical objects real in the same sense as the physical universe.
But that is exactly the problem, why does physics (and thus the actual world it describes) “rests” on maths and how is that not something special about maths? Do you really believe that in some possible world physics could rest in the works of Shakespeare?
We are so used to the effectiveness of mathematics that we take it for granted and it seems trivial, but I don’t think it is. Why should I be able to calculate the probabiliy that a tossed coin will come up heads and then that calculation to be pretty closse to the frequency of heads in a large number of actuall coin tosses most of the times? And why should we be actually be able to calculate pretty accurately what “most of the times” means?
This was just an example off the top of my head there are of course countless examples of the effectiveness of mathematics in describing and predicting the world. Doesn’t that say that there is something “mathematical” about the way the world works? I think this “mathematicness” of the world is what makes physics possible, in a non-mathematical world physics, or any science really, would be impossible.
The answer is because you’ve chosen to study areas where that sort of mathematics works really well. (Cart before horse.) Or you can define all non-confused thought as “mathematics”, which would pull in any rigorous reasoning (e.g. well-reasoned history) which doesn’t violate Bayes’ theorem. (Arguing by definition of “mathematics”.)
So how do you define mathematics?
I’m not making the assertion, you are. I’m saying that you can only claim what you’re claiming by either placing the cart before the horse or playing games with definitions; asking me to play with definitions for you is demanding that I prove your assertion for you.
Oh, sorry that was a genuine question. You said
which sounded like a rough first approximation of how I actually define “mathematics”, but the context of your comment seemed to imply that’s not your definition of it so I would like to know what it is. Perhaps our dissagreement comes from understanding different things by the same word.
And I’m not really try to prove any point, I don’t have a horse (or a cart) in this race.
If you define mathematics as encompassing all coherent thought, then of course that’s going to be the same as science, the process of coherent thought with which we understand the world. That’s an identity. It would only be remarkable if they started as different things.
Well I said it’s a “rough first approximation”. A better approximation would be something like “provably correct thought”. AFAIK there is not much of that outside mathematics; it’s actually harder than it may sound. Most science deals with evidence not proof, again AFAIK, everything that is trully “proved” in science is proved through mathematics.
But really what’s your definition of mathematics?
“…unreasonable effectiveness…”, as Wigner puts it, is not that it describes billiard balls so well, but that this expands enormously far up and down in orders of magnitude, far beyond anything humans would have evolved to deal with. This is especially peculiar surely to those who would maintain that mathematics exists only dependent on humans existing, and would have no existence otherwise.
Indeed. I think though that even the “plain” effectiveness (not only the “unreasonable”) says something about the nature of the world.
“…evidence that physics rests on maths – not of anything special about maths…”
That the fundamental study of the entire physical universe rests (as you say) on math says nothing special. Speak for yourself!
“…There’s lots and lots and lots of maths which is not useful in physics..” And never will be? That is an aspect, that pursuing something purely for intellectual interest has time and time again turned out later to be basic in fundamental physics, which goes along with its applicability to very non-human orders of magnitude, in causing a physicist, Wigner, to marvel at why it has this effectiveness. Hilbert space is probably as good an example as any, maybe Kahler manifolds if you want something more recent, or non-commutative geometry.
“…that doesn’t make …. mathematical objects real in the same sense as the physical universe..” Tegmark would seem to strongly disagree. (I hope my ….’s don’t change your meaning here—don’t think so.)
Conservation of energy and momentum, Newton’s laws, the special theory of relativity can all be stated in english. To do actual calculations you need to translate these ideas into mathematical form, of course.
Here’s a thought that bothers me: in math we want to minimize the usage of axioms. The less assumed and given without derivation the better.
Planck’s constant wasn’t mathematically derived. The ultraviolet catastrophe had the energy of black body radiation increasing infinitely with frequency, using classical mathematics for harmonic oscillators. So Planck made the simplest possible assumption, relating energy and frequency with a proportionality constant and it fit observations. There was no mathematical derivation involved, just a wild guess and some empirical measurement.
Likewise the postulate that the speed of light was fixed in all inertial frames; this is a very peculiar fact. I don’t know if Einstein had some great intuitive insight into this, or if he simply looked at Michelson-Morley and said that if c = x/t seems not to vary as we move through space, then it must be x and t that vary, and he simply had the courage to follow this confounding hypothesis through, while most would have dismissed it as absurd on it’s face. Still it bothers me that this relation between light, space, and time isn’t derived from other known facts, as far as I know. This behavior of light doesn’t arise naturally from the math of Maxwell’s equations or Newtonian mechanics, which is math that gives pretty good approximations of physical nature at a macroscopic level. And I don’t think it can be derived from any quantum mechanical principles, but I’d be interested to know if it can.
So there is a kind of discontinuity, something like a phase transition perhaps, between the mathematics of classical and modern physics. This seems natural to me if math is a conceptual language that humans try to fit as best we can to physical reality, which is something separate and different from the math. At some point our math is too approximate, and it breaks, so we refine it. But if you take Tegmark’s view, and it is all just math, wouldn’t we expect nature to be in some way smoother, more continuous, less arbitrary?
I realize that’s mostly vague gut level feeling. But Mathematics is a language that prizes unlimited variability, and our universe has so many seemingly arbitrary constants. That fact feels fundamentally non-mathematical to me.
I can admit that this sense that our universe is a specific instance of something more general seems consistent with the idea that some underlying mathematical system is generating these instances. Yet I’m still uncomfortable. We still don’t know that these constants aren’t really natural consequences of some underlying as of now still unknown physical properties.
To accept that the wave function is a real entity, as opposed to a mathematical convenience, is hard for me. I suppose if the wave function really is a physical object, there could be something to Tegmark’s idea.
Still I can’t get past the notion that math is a linguistic modeling tool that intentionally uses much less information than the object it is modeling for practical purposes of representational convenience. If your mathematics approaches the object it is modeling in complexity and information content, it kind of becomes useless. So in some sense to say that physical objects really are mathematical objects is meaningless; it obliterates any sense of what a mathematical object actually is, which is necessarily an abstraction of something with mass, energy, and spatial extent. On the other hand, as we drill further and further down in to physical reality, it is conceivable that a point could be arrived at where math and physical reality merge at some ultimately primitive level. I don’t know if there are any good reasons to assume that the wave function is that ultimately primitive level.
And it’s still confusing to me as to what it means to equate a physical object and a mathematical object; it seems to me like equating a poem with the object it refers to. At some level this claim about math sounds as absurd to me as saying a poet could write a poem about a tea cup, or an artist could draw a tea cup, so perfectly that you could pour tea into it and drink it.
Again, I think a lot of the Neoplatonists are missing a few key points.
First, as effective as math is at describing nature, it’s even more effective at describing the unnatural. Euclidean geometry is an excellent tool for regional-scale navigation, but there isn’t even a theoretical possibility of a real two-dimensional “Flatland.” Spherical non-Euclidean geometry is great for intercontinental navigation, but the actual surface of the Earth is an ever-changing non-continuous irregular quasi-fractal. There really isn’t any equation you could ever come up with to describe the surface of the Earth. Your best bet would be to create a digital model with the resolution of Planck length…and, at that point, saying that the math is the map is the same as the territory becomes pretty silly. After all, you could flip just one bit of your model and you’ve now got an equally-valid mathematical description that’s not real. Flip any other bit and you’re in the same boat. The number of valid-but-worng mathematical models vastly outnumber the number of “real” mathematical models; claiming that that one-and-only “perfect” model really is the reality is obviously way off the mark.
Next, even the best mathematical model isn’t going to tell you when a particular radionuclide is going to decay. It’ll give you odds that a certain number of a given sample of radionuclides will decay in a particular period of time, but no math will ever describe that one particular atom. Similar examples abound at the quantum scale; no equation is ever going to be the same as any real-world quantum entity. Similar, yes, but never the same, never even close to the same.
Last…I’ve made this point before, but it apparently needs to be made again. Math can’t even encompass itself. Claiming that math is more real than a reality that it is a subset of is absurd.
Don’t get me worng: math is a wonderful tool. But it’s a descriptive tool, not a proscriptive one.
Cheers,
b&
Where do you get the idea that math is a subset of physical reality? You yourself just argued in this same comment that unphysical mathematical entities vastly outnumber physical ones. You can’t have it both ways.
Regarding radioactive decay: the Schrödinger wave function of a nucleus does indeed predict all the possible decay times of that nucleus, and gives the probability of each. That is the complete specification of that nucleus and all of its superposed histories. Your error seems to be in thinking that any particular history with a definite decay time is somehow privileged and in need of additional explanation. That Copenhagen has to resort to non-mathematical handwaving to single out such a privileged history is, to my mind, a fatal flaw in Copenhagen and a clear sign that it should not be taken seriously as a guide to what’s real.
And obviously nobody claims that the Earth literally is a Platonic sphere, or any other geometrical function, so I’m not sure what you’re on about there. The Earth (like the Universe and everything in it) is a system of particles and therefore corresponds to a (ridiculously complex) wave function that fully specifies its behavior. That’s the math that Tegmark and others regard as the underlying reality of quantum physics.
You’re still looking at this from your Neoplatonist perspective.
The stories that I can tell in the English language vastly outnumber the actual story of human history on Earth. But of what sense does it make to say that the one is a subset of the other? They’re two different things.
There’s another Neoplatonist failing going on here. I used to think that there exists some sort of abstract form of information…but there isn’t. All there is in the real world is communication and computation. Those thoughts going through your mind? They’re nothing more than changing electrochemical patterns encoded in your brain. We know this, as conclusively as we know anything about the universe, thanks mostly to the work of Claude Shannon.
For example, there is no information in a book. The author physically encoded a signal in the book, and the transmission of that signal is completed when your brain interprets the signal as transmitted through reflected light patterns. All this takes energy, and we can calculate the minimum energy requirements for the communication to take place.
But, it is privileged. It’s the one we’re experiencing. There’s obviously something distinguishing this history from any other hypothetical history: we’re the ones here observing it. Any explanation that fails to account for the fact of our observation is less than complete. That there may be an infinitude of other selves that may be experiencing variations on the themes I’m experiencing is irrelevant to me and to any attempt to describe me, unless there’s some way to pick me out of the lineup.
Don’t you see that the second half of that paragraph is doing exactly what the first half is ridiculing?
Science is nothing but a very long history of ever-improving approximations that provide ever-better models that fit observations.
Euclidean geometry is a superlative model, but with well-known errors.
Newtonian Mechanics incorporates Euclidean geometry and vastly improves upon it, enough that it’s almost all most of us ever need, but it still falls short.
And, while Quantum Mechanics is yet another huge improvement over Newtonian Mechanics, we know for a fact that it’s not the whole story. You can’t even explain gravity with Quantum Mechanics, for crying out loud!
Yet, here you are, insisting that there’s a very complex wave function that’s so perfectly congruent with the Earth that it’s the function that’s “really” real, not the Earth itself. But your wave function can’t even account for that apple that hit Newton on the noggin!
If we truly had a provably-complete grand unified theory, I’d be willing to entertain the hypothesis that there might be some merit to your Neoplatonic conclusions, but not only is that not the case, but it’s all but guaranteed that it’ll never be the case. There’s Gödel and Turing for starters, and the practical fact that P probably NP but that, if it does, we probably can’t prove it to be the case.
Hell, I might as well cut to the chase, for that matter.
If there were a mathematical function to the universe, then you could solve the Halting Problem. But we know that the Halting Problem cannot be solved; ergo, there’s no universal mathematical function.
Gotta run….
b&
Sorry, you lost me. I thought you were the one claiming that math is a subset of physics, and therefore unable to encompass the physical world.
And all your myriad counterparts in those other histories think the same thing, that they’re the privileged one. So in what sense is any of them privileged?
There’s no requirement that the wave function generate a unique outcome. It generates all the outcomes, and that’s sufficient to account for our observations of decay times in any given history.
Sorry if I gave the impression that I think quantum theory is complete. Obviously it isn’t, but I think we can be confident that the final theory will involve wave functions of some sort that fully specify particle behavior, even if we don’t yet know the exact form of those functions.
As for being realer than the Earth itself, I’ll ask you the same question I asked Jeff: what do you suppose the Earth itself actually is? When you follow the physics all the way down and peel back all the layers, what do you find at the bottom, if not wave functions obeying mathematical laws?
The only sense in which I’d agree that math is a subset of physics is the same one that English is a subset of physics. They’re both something that goes on in your brain…but that’s not exactly the most helpful of observations.
Yes, and any such counterparts, should they exist, must be able to account for their own privilege. But how they do so is their problem, not mine.
An “explanation” that explains everything explains nothing.
Why did little Suzie die? Because God willed it. Because that’s how the wave function collapsed. Both answers are bullshit.
She died because some idiot was yakking on a cellphone while driving an SUV.
What on Earth makes you so confident that there will ever be a “final theory”?
If you’re asking me what I think the ultimate nature of reality is, then I’ll honestly tell you: I haven’t a clue.
And neither do you.
It’s entirely possible that we could be living in a Matrix-style simulation, or that Lau Tzu’s butterfly is dreaming of Alice’s Red King who, in turn, is dreaming of us. If the simulation and dreams are sufficiently sophisticated, it’s logically impossible for us to ever know that that’s what’s going on.
The butterfly, of course, has no way of knowing that it isn’t a pawn in a game of Sim City being played between the Invisible Pink Unicorn (MPBUHHH) and the Flying Spaghetti Monster.
Occam, of course, suggests that it’s pointless to worry about such stuff and to simply accept that it is what it appears to be — at least, until there’s some reason to suspect otherwise. So that’s what I do.
I think it’s pretty safe to say that there’s a bit more going on than wave function, just as it’s pretty safe to say that there’s more to Mercury than its relativistic orbital calculation.
One thing’s for certain, though: we’ll never be able to know if we’ve ever ultimately described reality, or if we’ve merely reached the resolution and horizon of our observations.
Cheers,
b&
“I think a lot of the Neoplatonists are missing a few key points.”
I’m sure all of us are. In that spirit, I assume you now accept that your earlier view, that Tegmark’s proposal is at all the same as
the ‘Matrix’s entertaining, but clearly wrongheaded, notion of our visible universe being a simulation, is completely off base, since you’ve provided no response to my quite concrete question up above about the needed existence of a ‘computer’.
“…as effective as math is at describing nature,
it’s even more effective at describing the unnatural…”
This is beside the point, even if you could be at all clear about what you mean by “unnatural” in the context of the universe. (Actually a purported Ben Goren precisely identical to you, name and all, with the exception of being a convinced mathematical platonist, plus an ‘earth’ which is precisely identical in every other respect to our earth, would surely be among your unnatural things. But such a thing must necessarily exist out there in ‘our’, but probably not the visible, universe, as a logical consequence of serious proposals for cosmological models. You’ll find this put forward in all seriousness by cosmologists including Tegmark, partly following from extraordinary largeness, infinite in some versions.) And see the immediately below as well, to do with misconceptions of what Tegmark proposes.
“…claiming that that one-and-only “perfect” model really is the reality is obviously way off the mark.”
This is another thorough misconception of Tegmark’s suggestion. He would give reality to every mathematical system, not ‘merely’ the one we happen to inhabit, as I’ve tried to explain in that earlier reply to you. Some of them would contain self-aware subsystems (none of these has yet been even nearly found by mathematicians it seems clear). And many systems would not contain self-aware subsystems.
“you could flip just one bit of your model and you’ve now got an equally-valid mathematical description that’s not real.”
Quite apart from the vagueness of “flipping a bit”, this is the same misconception as above. And he is not saying that any mathematical model that we presently use to describe some rather mundane subset of the universe
(such as the ones you trotted out here—by the way, my efforts to work out who uses in what sense your word “quasi-fractal” produced only suspect self-promotion by certain academics who are not terribly likely to recognize a valid mathematical definition when they see one- that includes the online slides by several from the Berkeley E.E.C.S.–but after all, despite Berkeley’s high reputation in mathematics, that’s the institute where a little academic empire was built by the Deepak-esque self-promoter Zadeh. Computer science has a lot to answer for!)
is literally exactly correct there (but is ‘correct’ as a mini-universe ‘out there’ on its own of course), i.e. is the appropriate subsystem of the purported TOE for our own ‘bit’ of the universe (not just the visible-to-us smaller bit). That is another naive misconception of Tegmark’s proposal.
“even the best mathematical model isn’t going to tell you when a particular radionuclide is going to decay”
That seems so far to be true, and has no bearing on his proposal, nor on whether the reality of mathematics is independent of humans. Additionally related to this but lots else:
“…never the same, never even close…”
That word “never” has been common in the promulgation of mistaken predictions about progress in science (or more often, protestations to the masses!),the most germane one in this blog (sorry Jerry, whatever you prefer to call it) might be the typical attitude before Darwin to explaining the origin and variety of biological species.
“…no equation is ever going to be the same as any real-world quantum entity…”
A system, not an equation—please don’t mis-say it to attempt to be more convincing. And you seem to be certain that no theory
will ever supersede quantum theory—perhaps you meant micro-physical entity, and if so, ignore me there. But it would be clearer if people did not verbally confuse present-day theoretical concepts with stuff that seems to actually be there in the physical universe.
“Math can’t even encompass itself”
That has many meanings, so is impossible to evaluate. We have too many loosy-goosy verbs like “encompass” and “deconstruct” around here.
I’d prefer brass tacks, if you’ll pardon the old-fashioned expression.
“Claiming that math is more real than a reality that it is a subset of is absurd.”
A confusion, typical not just with you, between the mathematics presently known to humans, and mathematics itself as ‘conceived’ by a platonist.
And again, it should be clear that right now I myself would be cheering for Tegmark’s proposal. But I think it is more likely wrong,
though not for any reasons given in this lengthy exchange. He has in fact proposed observations which would falsify it, so it’s not just a bunch of semi-vacuous philosophy. I hope others will read his easily obtained semi-popular articles, on that proposal. But
also on the logical consequence of presently accepted cosmologies, mentioned above, which has us all being repeated in every detail
(and another one of course being the ‘earth’ where that’s almost true, perhaps 10 to the 10 to the 100 metres from here, except that Romney actually got elected there—take that as a joke please!)
Congratulations. You’ve just ontologically defined into existence not only Flatland, but Never-Never Land as well.
That would be the problem with the Neoplatonists, as with all metaphysical philosophers, especially including the religious ones: mistakingly thinking that poorly-defined impressive-sounding conceptions are more true than reality.
Try applying a healthy does of empiricism and see if that doesn’t help clear up the condition.
Cheers,
b&
” ‘He would give reality to every mathematical system….’
Congratulations. You’ve just ontologically defined into existence not only Flatland, but Never-Never Land as well.”
That’s not exactly a thoughtful reply, as I myself can hardly take credit for originating any of this. By sort of sneering at pretty much every mathematical platonist, I don’t think you get any closer to convincing them that the existence of mathematics began and will cease with the existence of humans. You would presumably say the same of theoretical physics, perhaps even natural selection as a law. That is possible, but I think unlikely. It applied to dinosaurs, despite not existing?
“That would be the problem with the Neoplatonists, as with all metaphysical philosophers, especially including the religious ones…”
It is certainly true that accepting the actual existence of any abstract (non-material) object, such as a mathematical system, could bring some people closer to accepting the existence of some kind of abstract ‘god’. Witness Godel here apparently, and maybe even Einstein, though he made it very clear how different from any normal religious belief his was, if you can even say he had any at all.
But guilt by association is hardly the normal way for the scientific-minded to make convincing arguments. It is pretty clear that your anti-neo-platonism is much stronger than my pro-the same. And also the history of such pairs of people, mostly a lot brighter than us I’m sure, makes it unlikely we’ll convince each other to change at all, whether by off-cuff, somewhat emotional, remarks, or by asking for examples/details when it seems that someone has completely misunderstood (or at least misrepresented) Tegmark’s proposal.
As to the latter, at least there is the possibility of showing its falsity by empirical observation and statistical calculation, as he spends several pages explaining. Perhaps you can contribute in that way to its falsification, instead of trying to do so by accusing him of being a “…metaphysical philosopher…”.
I’m sorry, but the full weight of empiricism is against Platonism. At best, Platonism can only be a deepity.
I really don’t see what there is to be gained by attempting to disproof the phlogiston-of-the-week. Let the Platonists offer reproducible empirical evidence to substantiate their claims; until then, this is all just so much metaphysical philosophical masturbation.
Cheers,
b&
Your “…empirical evidence…” in the sense of the largely discredited positivists, is just too simplistic, though it may suffice for biology. Is not 12-digit accuracy in quantum field theory some kind of empirical evidence? (I am admittedly slightly conflating the two questions of existence and effectiveness here; but they are related.)
The “…phlogiston of the…” previous 2500 years perhaps; I assume the “..week..” you speak of is not the metaphorical one of some theologians found in Genesis.
Maybe a week for the present audience (or you anyway) when restricting to Tegmark’s writing on this. But it has been out for a decade and a half, at least.
Surely “..masturbation..” had been changed by the scientific-minded to have a +-sign next to it in the absence of ‘the real thing’; but I suppose the adjective “..philosophical..” qualifying it changes things!
This LJ comment summarises the problem with Platonism: (a) it is a large claim with absolutely no evidence (b) we have insight into the cognitive psychology that biases humans to see the world in terms of forms. That some mathematicians are attempting to revive Platonism is, IMO, mostly evidence that they are humans with human cognitive biases.
Not in the slightest — at least, not of Platonism.
We have all sorts of mathematical models that make all kinds of wonderfully precise predictions. But we also know for a fact that each and every one of them falls hugely short when push comes to shove.
For the longest time, simple Euclidean geometry was all you needed for anything you might do in the entire Mediterranean, if not all of Eurasia — including navigate from one corner to the other.
Our models have vastly improved, but each has represented not only a significant refinement over the predictive properties of the previous one but also a radical shift in the understanding of what’s going on.
So, not only do we have overwhelming empirical evidence that the next model (should we discover one) will represent yet another earth-shattering revolution in understanding, we also know (thanks to Gödel and Turing and the like) that it isn’t even theoretically possible for any sort of a universal explanation to exist.
Since we know for an absolute fact that there isn’t any universally-applicable theory of anything, and since we already know that our current models are inherently flawed, it’s utterly beyond me how anybody can posit Platonism in this day and age with a straight face.
b&
David has it spot on.
Platonism is no different from religion. We know that the claims of the religious are founded not on empirical evidence but on psychology. There’s just as much evidence in favor of Platonism as for any religious claim; there’s just as much evidence Platonism’s core principles as there are against any fundamental religious belief; and we can have just as strong a confidence that the true origins of Platonism lie in cognitive deficiencies as do the origins of religious belief.
To their credit, at least the Platonists aren’t trying to force their discredited theories into the schools, and they’re not leveraging their political power into deleterious sweeping sociopolitical repression.
Cheers,
b&
Re David’s and both of Ben’s:
David’s “comment” reference is an incoherent response to a supposed book review which would seem to have virtually nothing to do with what we are talking about—“I just spent three hundred pages reading about Aristotle and scholasticism” is what the ‘reviewer’ said, along with otherwise an almost entirely self-congratulatory load of pap. If David cannot give us at least the courtesy of explaining a bit how it, or its response, relates at all to what we are talking about, then I must file it with all the others of the form ‘I’m right. This internet reference proves it: xxxxx . I have now emptied my head of anything more to say.’
It is true David then repeats a bit more of what has already been said here, which needs no response, but which also has nothing to do with the apparently worthless click he gave us. Have a click on me, and see for yourself. I assume Ben didn’t even bother to click, which goes along with his apparently willful ignorance of anything Tegmark actually wrote in those easily obtained papers of his.
So his response which says David has it “spot on” would be little worth responding to, except for one bit of unintentional humour in it, to which I cannot resist pointing:
“Platonism is no different from religion.”—by his psychoanalysis at a distance of Plato, Penrose and Tegmark, among several thousand others—“…the true origins of Platonism lie in cognitive deficiencies as do the origins of religious belief.”
As to his reply just before the one re David, it repeats what is earlier from him, so I need not repeat my replies, but for one exception, which is again to ask him to get explicit, this time on something he has earlier also blurted—sorry, but that’s the correct verb, however impolite, for someone blowing smoke. Here are his words, which do sound rather learned:
“…we also know (thanks to Gödel and Turing and the like) that it isn’t even theoretically possible for any sort of a universal explanation to exist.”
I assume readers here have a reasonable grasp of what the incompleteness theorems of Godel say, and what Turing’s solution to the Entscheidungsproblem said—for those interested, Church was a bit earlier on the latter, but Turing was independent and more fertile with his Turing machines, though I wouldn’t defecate on the lambda-calculus either!
Possibly Ben thinks readers don’t have that grasp, since he seems to think he can get away with another bit of off-the-cuff, but learned-sounding, B.S. That B.S., so far as I can see, would imply that a very large number of present day theoretical physicists, Weinberg, Penrose, Tegmark, and tons of others, (and earlier Dirac and Feymann) don’t really know what they are doing when they seek a “final theory”, to quote the first of these. And this somehow follows from pure mathematical results dating from 1930-35.
So all I ask of him is to provide some explicit justification, either by way of explanation himself or a quite detailed reference. It really seems quite extraordinary that all these physicists have laboured so ignorantly for about 80 years, doesn’t it? Notice that I didn’t say he was claiming they wasted their time, just that they did not know what they were attempting all this time. So please don’t change the point again, Ben, and please this time, try to answer the specific question I have put to you. Of course I would never dream of saying you did not know what you were talking about in opposing so-called neo-platonism among modern scientists, just because you didn’t know what you were talking about in trying to enlist Godel and Turing. After all, it seems very unlikely those former questions will ever really be answered, however strongly various people feel about them. All one can say right now is at least Tegmark’s particularly strong form of neo-platonism could be proved wrong by empirical observation.
I’ll be quite shocked, and even finally become somewhat more humble, if it turns out to be some other stuff by Godel and Turing, that I’m unaware of, which you might have been referring to. But I doubt it. Far more likely it is another instance of name-dropping in the hopes of achieving what mathematicians refer to as proof by intimidation.
I think WEIT gets a lot of quite thoughtful readers, though how many read through responses is hard to say. Otherwise, taking this amount of time over responses would be a waste of time. ‘Winning’ an argument, especially when nobody’s mind is really likely to change except maybe about who is worth reading, is more for one’s years of immaturity. And to change your mind about mathematical platonism happens about as frequently as detecting a neutrino.
If Weinberg is or Feynman was a Platonist, I’ll eat my hat.
If any physicist working on a Grand Unified Theory thinks that said theory has anything more to do with the work of Gödel and Turing than anything else in physics, I’ll eat my hat.
Of course, I’m not claiming that Incompleteness means that attempts to unify Quantum and Relativistic mechanics are doomed to failure. How absurd!
I’m pointing out the futility of thinking that any purely mathematical system could encompass all of the Cosmos. Never mind that Shannon shattered any hopes that information is non-physical; even if we were to grant a godlike perspective, even that wouldn’t do the trick.
But the modern physics that Weinberg et. al. are working on is so far from the types of limits that Gödel was contemplating that I’m wondering why you’d try to muddy the waters by suggesting that I think that Gödel is what’s getting in the way of understanding quantum gravity.
Cheers,
b&
Unfortunately Ben’s reply consists entirely of avoiding my request, misrepresenting what I said, and introducing a few additional vague claims (or perhaps the same claim in even more non-specific fashion).
Here are the details.
(1) “If Weinberg is or Feynman was a Platonist, I’ll eat my hat.”
To whom are you replying here? I have no idea of their views in this respect. It is irrelevant, I think. To argue by authority will hardly impress people here. Their names came up as examples of people who worked a great deal on fundamental stuff, in the hopes of an all-encompassing theory. And Ben claims to know how Godel/Turing somehow makes some version of that impossible. But we still have no idea what version (nor do any of the cosmologists or particle theorists who work on this, I imagine).
(2) The 2nd hat-eating drama had him doubting that any physicist would think ‘Godel’ had any connection to his fundamental physics work. That doubting by Ben occurred after he himself introduced exactly that: “…thanks to Gödel and Turing …. it isn’t even theoretically possible for any sort of a universal explanation to exist”
(3) Perhaps not surprising, but Ben has misrepresented what I said in exactly the way I had asked him not to to do that (and he spent much of his reply doing that). After I asked:
“Notice that I didn’t say he was claiming they wasted their time, just that they did not know what they were attempting all this time. So please don’t change the point again..”,
from Ben we got
“I’m not claiming that Incompleteness means that attempts to unify Quantum and Relativistic mechanics are doomed to failure.”
and
“you’d try to muddy the waters by suggesting that I think that Gödel is what’s getting in the way of understanding quantum gravity.”
Doing something “doomed to failure” and “(Godel) getting in the way of understanding quantum gravity” would certainly imply wasting one’s time, exactly what I asked him not to misrepresent me as saying he claimed. So don’t try, Ben, to avoid being specific about your claimed ‘reasons’ that “it isn’t even theoretically possible for any sort of a universal explanation to exist”.
(4) And don’t pretend to be responding specifically by saying
“I’m pointing out the futility of thinking that any purely mathematical system could encompass all of the Cosmos.”
For the third time, I ask that the verb “encompass”, with subject “system”, not be used without making clear what you mean. So maybe on a 4th try, you might be kind enough to say what you mean, if by chance you actually have a clear idea what you mean. This is quite apart from that statement appearing to be right along the lines of my asserting that you are claiming “they do not know what they were attempting” For example, if we look at Weinberg’s book “Dreams of a Final Theory”, we notice him saying “…the search for the final laws of nature..” in the first sentence of the book (For $5 apiece, I can find you many more by him and others I mentioned. And note that “god” does, but “godel” does not, appear in his index). So it will be important that your expected newfound clarity about the verb “encompass” does not imply just about exactly what Weinberg says.
(Perhaps I should add that there is no onus on me to be more precise about the general nature of a fundamental physics theory. That theory is likely far off, I think, if ever, and I surely cannot do it. It is the person claiming the non-existence of something who needs to do so in order to have a chance to show non-existence. A related example, which ties into this in a different way, is Turing’s fundamental work, in which the general notion of computability needed to be defined (via Turing machine was his way) in order to prove that an algorithm for ‘doing all mathematics’ was impossible, that Entscheidungsproblem earlier. There had been 3,000 years or more of specific algorithms for different things before that, with no need for a general definition. There are many similar things in modern mathematics. And I am not asserting that such a fundamental physics theory definitely does exist, just trying to get Ben to explain why he thinks it doesn’t.)
(5) And now we get some additional apparent obfuscation:
“Never mind that Shannon shattered any hopes that information is non-physical; even if we were to grant a godlike perspective, even that wouldn’t do the trick.”
Do tell us just what Shannon’s theorem says, particularly how it puts any real limit on what could possibly be a fundamental theory of the universe (that is, once you have done the same for Godel and for Turing).
(6) And just how does
“the types of limits that Gödel was contemplating that I’m wondering why you’d try to muddy the waters by suggesting that I think that Gödel is what’s getting in the way of understanding quantum gravity”
relate to you saying
“…thanks to Gödel …. it isn’t even theoretically possible for any sort of a universal explanation to exist”?
There must be some kind of line you are drawing for physicists, with quantum gravity on the okay side, but whatever you mean by a “universal explanation” and ” the encompassing of the cosmos” on the naughty side. It might be nice for us to know more clearly just where that line is, and how you can use these theorems in mathematics to get it. Probably it would be even more important for many theoretical physicists to hear this news, and constrain themselves accordingly.
I waited a bit before sending this, hoping Ben would get time to really explain his confident, but vague, claims with something besides the above avoidance and misrepresentation. After another reasonable wait, if we still haven’t got that, I will try to coach him with more detail, not too long I hope, about incompleteness, so he can tie into that and explain himself with less effort and no wild, undefined generalities. But it would be nice if he could lay it out specifically without any coaching, so we realize the nature of his understanding of incompleteness and its supposed relation to Weinberg’s “final theory”.
Again, please excuse the length of this, but surely one has to be interested in something as fundamental as the relation of incompleteness to that purported final theory.
“I’m sorry, but the full weight of empiricism is against Platonism. At best, Platonism can only be a deepity.”
Not if our senses aren’t absolute censors (and so would be our intellect) and that we miss some basic informations about the universe.
As I wrote. The full weight of empiricism is against any claims to the contrary.
That doesn’t mean it’s an absolute, of course. It is entirely possible, after all, that our empirical understanding of gravity is fundamentally flawed, and that the next time you step off a cliff that you won’t fall at an accelerating rate of about ten meters per second per second.
But, if you wish to challenge the validity of empiricism, I’d suggest you start with exactly that sort of a test.
The rest of the claims of empiricism are based on a similar foundation. While there aren’t any guarantees, the bets are as safe as that the Sun will rise tomorrow.
Cheers,
b&
I’m not talking about challenging the validity of empiricism, about talking about questioning empiricism as an absolute way of knowing.
(above) …I’m talking about questioning empiricism as an absolute way of knowing.
An unspecified “other way of knowing” is not ruled out. However, empiricism is the best a bounded rationalist starting from birth and instinct can manage. (And instinct can also usefully be viewed as empirical knowledge encoded in the genes.) Unless you have a specific non-empirical way of knowing in mind.
There are no guarantees, no absolutes.
Empiricism works. Mysticism doesn’t.
How do we know this?
Empiricism builds civilizations. Mysticism fuels scams.
Mysticism is fantastic for parasites, and the parasites have done a superlative job at convincing their hosts of the value of being parasitized. But mysticism would die without its hosts, and its hosts would die without empiricism.
That’s all there is to it, really.
b&
This subject is really where I see the definition of Gnu Atheism playing out. I read the OA and go “Well, that’s dumb, there’s no need to analyze that at all. Moving on.”
I’m interested in seeing the logical debate, but for the most part it’s like watching a chess game. It’s a battle of wits with a set of defined rules, but it’s not really accomplishing anything external to the game. The OA is just self-evidently useless, immediately, at first glance. I appreciate the intellectual effort that goes into beating it so in its own terms, but I’m just flipping over the chessboard on this one.
The OA also relies on a simple trick of equivocation. “Greatness”, unless clearly defined, is essentially a meaningless concept. Sometimes we apply the term to specific criteria, or think we do (“Michael Jordan is the greatest basketball player”), but generally we don’t use it to make literally factual statements (“I have the greatest wife”). The trick of the OA is that we start with a generally meaningless phrase, “God is the greatest being conceivable”, which we tend to go along with without thinking too much about it, only to be then told that we apparently agreed to a more specific definition, “greatness entails existence.” So even if you were to accept that existence is somehow an essential quality of greatness, the argument is still circular. Written differently it would be, “God is the greatest being that exists, therefore he exists.” The OA pulls the same switcheroo as a credit card company that gets you to agree to conditions you never meant to agree to simply because they got you to ignore the fine print.
Even if someone were to fast for twelve days in a pitch-black, silent cavern, to the point where their scambled brain could accept these ontological arguments as valid, all they would have to show for this derangement is the idea that some kind of god exists.
But which god? Or which gods? And what is the relationship between these gods and the world? What are the moral implications of that existence? How often should we pray, and how, and to whom? Are deeds more important than grace? And just when does it become okay to lie and cheat and kill for the sake of these gods?
In short, these ontological arguments offer nothing to religious people, because they already accept the existence of god(s), and such arguments have nothing to say about the *implications* of that existence in the everyday lives of human beings.
And these arguments offer nothing to anyone else, because the logic makes no sense and can be perverted into even greater absurdities. (“God is the greatest purple unicorn conceivable….”)
So really, what’s the point of debating these dusty old relics? They’re dead and rotten, like angels impaled on pins.