A new report at ABC News, “Computer scientists ‘prove’ God exists”, says that two German scientists using a MacBook have proven the existence of God. That’s the bad news. The good news is that it appears to be old news: that is, they have somehow mathematically formalized the ontological proof of God, which has always been known to be wrong, as channeled through Kurt Gödel, who had his own modal-logic proof of God resting on similar arguments.
In case you’ve forgotten this old chestnut, the ontological argument, first formulated by St. Anselm, runs like this (I give Wikipedia‘s characterization of Anselm’s argument, which resembles all the succeeding ones):
- Our understanding of God is a being than which no greater can be conceived.
- The idea of God exists in the mind.
- A being which exists both in the mind and in reality is greater than a being that exists only in the mind.
- If God only exists in the mind, then we can conceive of a greater being—that which exists in reality.
- We cannot be imagining something that is greater than God.
- Therefore, God exists.
The problem with this is that “existence” is not a quality of an object like beauty or size. There may be a most beautiful existing horse, if you define your notion of horse beauty in advance, but you can’t do the same thing for God, for, as the philosophers say, “existence is not a predicate.” Finding the most beautiful horse (“the God horse”) takes as a given that horses exist. Having an idea of something says absolutely nothing about whether it exists or not.
Using such arguments, one could “prove” the existence of many nonexistent things, like unicorns, fairies, or Santa (“a unicorn that exists in reality is greater than one that exists only in the mind.”
I was only dimly aware that Kurt Gödel had constructed a logical proof for the existence of God (read about it here), but that’s been criticized as well, though I don’t understand modal logic. All I know is that you simply can’t prove that something exists by logic alone.
But the two Germans seem to claim otherwise. As the ABC report notes:
When Gödel died in 1978, he left behind a tantalizing theory based on principles of modal logic — that a higher being must exist. The details of the mathematics involved in Gödel’s ontological proof are complicated, but in essence the Austrian was arguing that, by definition, God is that for which no greater can be conceived. And while God exists in the understanding of the concept, we could conceive of him as greater if he existed in reality. Therefore, he must exist.
Even at the time, the argument was not exactly a new one. For centuries, many have tried to use this kind of abstract reasoning to prove the possibility or necessity of the existence of God. But the mathematical model composed by Gödel proposed a proof of the idea. Its theorems and axioms — assumptions which cannot be proven — can be expressed as mathematical equations. And that means they can be proven.
That is where Christoph Benzmüller of Berlin’s Free University and his colleague, Bruno Woltzenlogel Paleo of the Technical University in Vienna, come in. Using an ordinary MacBook computer, they have shown that Gödel’s proof was correct — at least on a mathematical level — by way of higher modal logic. Their initial submission on the arXiv.org research article server is called “Formalization, Mechanization and Automation of Gödel’s Proof of God’s Existence.”
The fact that formalizing such complicated theorems can be left to computers opens up all kinds of possibilities, Benzmüller told SPIEGEL ONLINE. “It’s totally amazing that from this argument led by Gödel, all this stuff can be proven automatically in a few seconds or even less on a standard notebook,” he said.
Yes, it is amazing, and it surely must be wrong. (As always, I suspend judgment on God until the data are in, but that data cannot be purely logical). I kindly request some math-minded reader to find the arXiv paper and provide us with a brief analysis. The ABC article ends as follows:
Ultimately, the formalization of Gödel’s ontological proof is unlikely to win over many atheists, nor is it likely to comfort true believers, who might argue the idea of a higher power is one that defies logic by definition. For mathematicians looking for ways to break new ground, however, the news could represent an answer to their prayers.
I don’t get the last sentence at all. Why is this kind of mathematical trickery “breaking new ground”?
h/t: Karl
I think that what happened is that they have (they claim) a computer assisted proof of an open problem in mathematical logic.
Saying that “existence” is not a property seems arbitrary to me, which makes that objection not compelling.
I’d say that premise #3 is the most glaring flaw.
I disagree. An object must first exist before it can have properties. Properties are tied to existence itself. How can any object have any properties if it does not exist first?
This objection kills the whole argument stone dead.
I don’t think we want to define “property” in such a way that suddenly it’s impossible to say Tom Saywer is smart or Harry Potter wears glasses. Just to defeat the ontological argument? That’s throwing the baby out with the bathwater.
Far better to say that, yeah, we can speak rationally about fictional things having properties…and the ontological agument is still unsound.
That doesn’t make sense to me. We can pretend that the things we pretend exist also have properties. It is pretend. That is just not on when you are supposedly talking about reality. I see no contradictions, no throwing babies.
You have now reduced the question to a much simpler question: who wins in a fist fight: Captain Picard or Captain Kirk?
That’s easy, Kirk because that dude can take a shit kicking. He always gets his ass kicked but just by sheer endurance I think he would win. He fought the gorn and won. Sssssssss
But in a very real sense, there are certain properties that a fictional person cannot have. For example, saying Sherlock Holmes lived on Baker st cannot mean the same thing as someone who actually lived on Baker st. No matter how hard you try, you’ll never find Sherlock Holmes in the historical records, so “Sherlock Holmes lived on Baker st” cannot mean the same thing as “Dustry Springfield lived on Baker st”. In other words, there are certain properties that require existence in order to have those properties.
Fictional things have properties, agreed, but fictional properties can be very different thing from their existing analogue. A real person can wear glasses, and a fictional wizard can wear glasses, but it would be an act of equivocation to say they are the same property. We must go to pains to point out this distinction because our language doesn’t easily accommodate such a distinction without the need for further clarification.
“An object must first exist before it can have properties. ”
So you say. I could easily say that it must have the property of existence before it can have other properties.
Imaginary things can only have imaginary properties.
Only real things have real properties.
If existence was a real property, then non-existence would also have to be a real property.
But imaginary things only have imaginary properties.
Therefore existence/non-existence cannot be a property.
This is why some (Bunge, for example) point out that existence certainly is a property, and there are now many logics with an existence predicate, too. What the problem usually is assuming somehow some sort of ordering somewhere in the proof. Or, in the case of Goedel’s, he talks about “positive properties” but in most logics predicates are dual: A := -B is perfectly legitimate as a definition. Moreover, confusing properties and predicates is pretty endemic, too. One has to show that properties are compossible in some appropriate way, and that needs a theory of factual properties, which is not well developed. It would also tend to beg the question to assume some of the triomni properties are commpossible.
I agree, I’ve never liked that rebuttal. I’d argue that (4) should be:
(4) If it is only the *idea* of God that exists (in the mind), and if God himself doesn’t exist, then we can conceive of a being (God), which is greater than the idea of God.
Then (5) becomes:
(5) We can indeed be imagining something (God) that is greater than the *idea* of God.
At which point the argument stops right there.
Valid. Off the top of my head:
God is the greatest of all conceivable beings. Conceivable beings are logically possible beings. Logically possible beings do not necessarily exist.
“Greatest of all conceivable beings” is still incoherent. Thanks to the Halting Problem and / or Incompleteness Theorem, we know that even the greatest being we could conceive wouldn’t be able to rule out the possibility that it was the subject of a being even greater than it could conceive of.
Plus, if we’re discussing “conceivable”…well, such conception must, of necessity, be done in the imagination. And the imagination is a finite property of a finite being. Constructing a being with a larger-but-still-finite imagination able to conceive of something even more is left as an exercise for the reader.
Cheers,
b&
There are other ways of expressing this argument that bypasses this semantic issue, i.e. use “maximally great being” (ala Plantiga) rather than Anselm’s words, to make the God-assertion independent of human limitation.
Sorry, but that’s exactly as incoherent. And, worse, trivially demonstrated to not be the case. Why doesn’t this maximally great being ever call 9-1-1 when he sees that a priest is about to bugger another child? Another child with a cell phone would call 9-1-1 if he was in a position to see what was going on, so it’s not like anything even remotely approaching maximal greatness would be required to accomplish the task.
Cheers,
b&
You can deal with that by requiring the proposer of the ontological evidence to specify whether “existence” is an attribute of the purported greatest being or not. If the answer is “no” then the argument fails immediately. If the answer is “yes”, then the argument is circular.
The inability of a non-existent thing to have properties is how vampires can suddenly have sparkly skin in the sunlight, instead of going up in flames as they traditionally did. Because they don’t actually exist you can make them be whatever you want, just like god really.
That would be because gods are literary devices; they are miracle workers, and miracles are also literary devices. Miracles are an opportunity to play “What if?” games…and the whole point of a miracle is that it must really be impossible. If it’s possible, it’s not a miracle, even if it’s impressive. Jesus rising into the sky in a hot-air balloon like the Wizard of Oz would not be a miracle. Jesus impossibly rising into the sky by sheer force of will is. But, if just anybody could rise into the sky by sheer force of will, Jesus doing so would just be walking down the road and again not a miracle.
Either that, or you need a white horse….
Cheers,
b&
deus ex machina
Yeah, I’d say P3 and P5 are equally problematic, primarily because the word “greatest” (or “greater”) does no work in this context. It’s meaningless without a specific definition. And there is no definition of “greater” that is universally applicable. To everything.
Which is greater: a couch or a hamburger? Which one is closer to being god?
Pffft…
Depends on whether you’re tired, or hungry.
“Which is greater: a couch or a hamburger?”
A cat.
“Which one is closer to being god?”
A couch.
Depends. Is the hamburger made of sacred cow?
b&
Black is that for which no darker colour can be conceived. And while Black exists in the understanding of the concept, we could conceive of it as darker if if it existed in reality.
Therefore, it must exist.
None more black.
A classic.
D-minor is saddest key.
(http://www.youtube.com/watch?v=TDIipofjBQg)
“(…holding forth about the beauty and complexity of the song, listing high-brow influences…)”
“What’s it called?”
“Lick My Lovepump”
Oh, Nigel.
I also love most of the other improvisatory Christopher Guest movies. “For Your Consideration” left me cold.
And then there’s pitch black.
Aah, but black (just like white) is the abscense of visible colours. Hence, no none-existing darker colour than black can not exist…
I concur. It is therefore safe to conclude that black is in fact white although white also is black and both are non-existent.
Ergo gawd is like totally logically real.
Just be careful at zebra crossings….
b&
Also remember not to panic.
Oh, shit — where’s my towel? My towel! Where’s my goddamned fucking towel!?
Oh…right there.
Nevermind. Cancel red alert. “We apologize for the inconvenience.”
b&
Except, of course, for the minor little detail that anything with a temperature above absolute zero emits black body radiation and is therefore not absolutely black. This includes even empty space and black holes, and nothing can actually be cooled to absolute zero (though you can get damned close). And that’s even before we get into reflective properties.
So, once again, there can always be something blacker….
b&
Hits the nail square on – best analogy I’ve come across.
This reminds me of a hilarious argument I once had with a theist wingnut. He claimed that one of the qualities of God was that he was necessary. Therefore if he can be conceived of, he must exist. I got really excited about this, although the million quid in my bank account that I arbitrarily assigned necessity to, sadly wasn’t actually there when I checked my balance the next day.
Having listened to Presuppositionalists, their understanding and twisting of the word ‘Necessary Being’ is actually kinda interesting.
The short version is that they claim god is necessary in the same sense that the ratios of a circles diameter to it’s circumference is Pi. Namely, that it wouldn’t make sense for god to not exists.
They then smoothly transition from that ‘foundational’ sense of necessary to the more ‘traditional’ one, which is that god is necessary for the world to exist in the way it does currently.
It’s actually a brilliantly clever ploy, as it can be REALLY hard to find the cracks in practice. It’s good mental exercise to try to take them apart.
Of course the argument is still crap, has probably never converted anyone, and exists primarily for ‘winning points’ against atheists, at least in the minds of the theists who use it.
“No, d-g isn’t necessary.” That which can be asserted without evidence is just as easily dismissed without evidence. Not hard to find the crack at all.
Bummer, dude.
Try it again. If it works this time, let me know, and I’ll see if I can’t replicate the experiment.
I’d also say that the definition in premise #1 is nonsensical.
I don’t know about nonsensical, but I can conceive of beings greater than god. Lots of beings actually.
Like, I can conceive of a being that is capable of lifting a stone that god can’t lift, and I can conceive it such that this being is not god.
But none of the gods in the great chain of gods can beat me in tic-tac-toe.
“Like, I can conceive of a being that is capable of lifting a stone that god can’t lift, and I can conceive it such that this being is not god.”
Ah, that’s sneaky.
Premise 1 conveniently uses the passive voice. I want to know who is doing the conceiving here.
Presumably, gods have greater powers of conception than I have. Does this mean that a god conceived by my conceived god would be greater still? And are two gods greater than one god? Inquiring minds want to know.
The conceptive powers of gods is defined by birth control usage, I should think.
b&
Turtles all the way up.
My favorite variation of the argument takes a slightly different flavor.
1. Our understanding of pizza is a dish than which no greater can be conceived.
2. The idea of pizza exists in the mind.
3. A pizza which exists both in the mind and in reality is greater than a pizza that exists only in the mind.
4. If pizza only exists in the mind, then we can conceive of a greater pizza — that which exists in reality.
5. We cannot be imagining something that is greater than pizza.
6. Therefore, I am, right this very instant, eating a perfect slice of pizza.
The Ontological argument is as silly and childish as they come. I’m pretty sure Gödel realized this, which is why he never actually published his proof and considered it incomplete.
What might be confusing the Germans in this article is the fact that you can never exclude the possibility that there’s something even more; that’s the heart of both Gödel’s Incompleteness Theorem and Turing’s Halting Problem. But what they’re missing is that that obstacle applies equally to anything that actually does exist that’s something more than us; it, too, can’t know that there’s not something even more yet.
That is, even if the Big Bang is somehow the intelligent work of a personal creator of some sort, said creator may or may not itself be the creation of some super-creator and is as powerless to rule out that possibility as we are to rule out its own existence.
Cheers,
b&
I have more than once heard it claimed that Gödel’s proof was tongue-in-cheek, but I don’t know whether there is any evidence for this. He doesn’t seem to be known for having a sense of humour.
I don’t think it was a joke; I think it was a serious attempt that he never finished. Remember, he was a lifelong devoted Christian….
b&
Of his own particular denomination of 1 person, no less.
Somewhere it is reported that Dana Scott was desperately phoned by KG in an attempt to ensure his proof survived at one point … I think it is in vol III of his collected works.
Turtles all the way up I say.
Turtle pizza? Not my cup of tea….
b&
Several glaring flaws can be pointed out in the ontological argument (as you yourself ointed out), but none of them have anything whatsoever to do with the Incompleteness Theorem or the undecidability of the Halting problem. Both those statements essentially say that any logical “proof system”, that is expressive enough that some “interesting enough” statements can be written in it, will also be able to express statements that are true, but nevertheless not provable within the system.
The actual proofs of these theorem take some work, but the basic idea is very simple. You show that if a “proof system” is expressive enough, then you can express in that system (let’s call it S) a statement (let’s call it T) of the form “This statement is not provable in S”. This self-reference is crucial, and almost completes the proof, in the following way:
Suppose T was true, then just by what T says, there is no proof of T in S, so there exists a statement T which is true, which can be expressed in S, and which is not provable in S.
Now could T be false? Suppose that this was possible. But, then, since S is a prof system, we should not be able to prove false statements in it, and hence there cannot be a proof of T in S. But this is saying that T is true (again because of the way in which T refers to its own properties), and that is a contradiction, since we assumed T is false. Thus, T cannot be false.
Of course, the interesting part of the proof is showing that T can be “expressed” in S, which is what most of the work is about.
For the similar proof of the undecidability of the Halting problem, I can do no better than refer to Geoff Pullum’s amazing proof in verse. Both these proofs are examples of the wonderful and deceptively simple trick of Diagonalization.
No, the Ontological Argument is a variation on the same thing, and even takes a similar form. It says, imagine something great. Now imagine something greater. Now, imagine something even greater still. Now, imagine something so great that it surpasses all other possible greatness in its own greatness. That’s exactly the same process that Cantor showed is logically incoherent with his diagonalization proofs; the diagonal is greater than anything you could count, and there’re more such diagonals than can be counted.
As for poetry…Pullum’s verse is good. But mine’s much shorter:
All but God can prove this sentence true.
Cheers,
b&
I am sorry, but I thought your original claim was that the ontological argument was invalidated somehow by the incompleteness theorem. You now seem to be saying something different: that it is similar in structure to diagonalization proofs.
Now I have some experience with mathematical logic (though it is not really what I do everyday, so I am not really an expert) and I don’t see any similarities, unless I am missing gsomething. The core of all diagonalization proofs is an explicit construction of an object (sometimes, as in the case of the Halting problem, based on a negation of the hypothesis being proved), that is then shown to not lie in the set it was supposed to be in. In Cantor’s argument for the uncountability of reals this is a real number that disagrees with every number in a countable list “on the diagonal”*. In the proof of the undecidability of the Halting problem, this object is the program “Q” in Pullum’s poem, and in Godel’s proof it is the statement T. On the other hand, the ontological argument tries to do something quite the opposite: it tries to implicitly claim that an object, that is the “greatest” in some ordering, exists.
What you might say is that in several cases, the existence of such a “greatest” element can be refuted by giving a procedure which for every element produces a greater one. For example, I can say that there is no largest positive real number by saying that I can always consider twice of any purported candidate. I can see why that might remind someone of Turing’s proof (though maybe not of Godel’s proof), but to me that comparison seems somewhat like comparing a handgun with a Death Star.
* Incidentally, I also don’t quite get your remark about the “diagonal (in Cantor’s argument) being greater than anything you can count”. The way Cantor’s argument goes is to construct an element that always “disagrees with the diagonal of the list”, so to say, and hence cannot be in the list.
I think the point that I’m trying to make is that the Ontological Argument is trying to demonstrate the existence of a singular countable entity that is bigger than all other countable entities, and completely ignores the fact that he phenomenon in question isn’t even countable in the first place — let alone the silliness of trying to equate something allegedly infinite with a countable number.
Perhaps it’s best to just note that theists are hopelessly confused and leave it at that….
b&
Patrick Grim has written about this specifically, and has pointed out some interesting and more formal ways to the same conclusion. For exsample, there’s no set (collection, etc. – you don’t need a set theory in the technical sense) of all truths. If god knows every truth, then god is self-contradictorially described and hence nothing exists as so described.
Oh, I used to come up with a new variation on that theme regularly back in the USENET days.
“All but God can prove this sentence true.”
“Tell me, God, ‘Yes,’ or ‘No,’ will you answer, ‘No’?”
Jesus decides it’s time to test Satan to see if he’s reformed, but he can’t risk catastrophe. So he sets up a model universe of some kind, just like our own, but private for Jesus. And Jesus makes Satan omnipotent in said universe to see what he does. Either Satan’s omnipotence lets him instantly discover the ruse, that he’s in a fake universe and under observation (thus invalidating the test), or Satan’s omnipotence is incomplete, again invalidating the test. Thus, we know that even Jesus himself has no way of ruling out the possibility that he’s merely a fragment of Alice’s Red King’s Dream.
…and so on….
Cheers,
b&
In the actual article, the authors state:
“The critical discussion of the underlying concepts, definitions andaxioms remains a human responsibility, but the computer can assist in building and checking rigorously
correct logical arguments. In case of logico-philosophical disputes, the computer can check the disputing arguments and partially fulfill Leibniz’ dictum: Calculemus — Let us calculate!”
which seems to be a much more modest conclusion than the headline suggests.
Exactly. Remember that the media is in business to increase circulation.
Or more generally, and paraphrasing Dickens in Bleak House,
The business of Business is to make more business for Business.
(Dickens said it about The Law)
Not all evolutionists are atheists. Many evolution scientists believe in God.
The difference is the churches or synagogues, they are members of, are non-fundamentalist or non-orthodox. Evolutionists who believe in God are not fundamentalist or orthodox, and do not take the bible literally.
In other words, evolutionists who accept the scientific truth of evolution, believe that God
used evolution as part of the process of how he made everything.
Two words: Occam’s Razor.
I’m sold. The best part about the ontological proof of God is that he can be whatever we think he is.
(1) My understanding of God is a being than which nothing more annoying can be conceived.
(2) The idea of God exists in the mind.
(3) A being which exists both in the mind and in reality is more annoying than a being that exists only in the mind. (After all, how much can a purely hypothetical being annoy you?)
(4) If God only exists in the mind, then we can conceive of a more annoying being that which exists in reality.
(5) We cannot be imagining something that is more annoying than God.
Therefore, God exists.
How about this one:
(1) My understanding of God is a being than which nothing more fictional can be conceived.
(2) The idea of God exists in the mind.
(3) A being which exists both in the mind and in reality is less fictional than a being that exists only in the mind.
(4) If God only exists in the mind, then we cannot conceive of a more fictional being that which exists in reality.
(5) We cannot be imagining something that is more fictional than God.
Therefore, God doesn’t exist.
Points 3 and 4 make much more sense in your formulation than in Anselm’s.
I can conceive of a perfect circle, but in order for it to be truly perfect, it must also exist? Therefore I can be assured that it exists somewhere in the Universe?
I can conceive of a perfect cup of coffee, but again, it’s not really perfect unless it exists. So it must exist.
Is THIS the argument?
It cannot be the whole story, as only a dimwit would conclude that my perfect circle or cup of coffee must exist somewhere based on the fact that I can conceive it. Clearly, a conception of a perfect circle is consistent with one not existing in reality.
Either theologians are the intellectual dregs of academe, or they are great at fooling themselves and others by embellishing what are very weak arguments. Probably a bit of both.
Ah, but that is the whole story. The power of delusion is strong.
Actually, it’s worse. If you want to get this ‘greatest being’ ANY of the the personal traits of a deity, you must assign to it a mind. This leads to subjective definitions of ‘greatness’.
Which means that you can conclude that the greatest cup of coffee not only exists, but MUST be in your hand, ready to drink, whenever you want it there.
Exactly! What good is my greatest cup of coffee if it is sitting in a cafe in Roma somewhere, or in a parallel universe?
Going even further, perfect circles can only exist in the abstract. Any circle existing in reality must be imperfect, if only slightly.
Perfection would seem to preclude existence. Only imperfect things can exist. A perfect god, therefore, can only exist in the realm of the imaginary.
I just realized that this scene from Elf pokes fun at the ontological argument.
this should be good
If you start by making up anything you want, everything becomes true.
Reminds me of this lovely bit of logic.
All elephants are pink, Nellie is an elephant, therefore Nellie is pink.
“Doctor Who: Destiny of the Daleks: Episode Four” (1979)
Bingo.
Nellie must first exist before she can have any form of pinkness as a property! 🙂
You know what a human would say to that argument?
“Elephants AREN’T pink.”
This argument, like all the logical proofs for god, are just as trivially dismissible. Only Davros and Theologians are so warped up in their own delusions that they can’t see it.
Usually.
And some well-scrubbed elephants will often have pinkish bits of skin here and there, too.
Cheers,
b&
Well, duh! Everyone knows that it is invisible unicorns that are pink.
heh heh
There may have been a misunderstanding: I think they proved the existence of Jobs.
I hear Republican politicians all the time singing the praises of job-creators. I guess this means that Steve wasn’t God.
They have managed to prove Godel’s mathematical model to be true, it makes sense mathematically and now it can be checked with a small computer in a short time. That doesn’t mean the axioms and definitions are true. It’s still just The Ontological Argument.
“That doesn’t mean the axioms and definitions are true. ”
So it is still just an unproved, unprovable god. Now with added math.
Given that math is cool, this means that they have improved the argument, in the sense that it’s more enjoyable to go over if you are a huge nerd.
I realy don’t get it?!
Do you guys?!
Dan Rau
There’s nothing to get. It’s word-salad.
With cross dressing.
Okay. Who was the wise guy to go and get the dressing upset? Now we’ll never be able to shove it up the turkey’s butt!
b&
It’s cross because it knows how others of its kind have been shoved up butts.
And who was it who told it? Hmmm?
People, please! How many times do I have to say this? No talking in front of the dressing!
b&
Note that an argument is not “just logic”. If an argument is valid and sound, the former being logical and the latter being shown through non-logical means, then you have proved your conclusion true. Validity merely says that if the premises are logically entailed (i.e., logically true), then the conclusion is also true. If the premises are sound, then the premises are true of the world, as it were.
So, to say they “proved” that god exists, there merely showed the validity of the argument, not that it is sound.
I meant to say “to say that they “proved” that god exists is in a narrow sense; they merely showed the validity of the argument, not that it is sound.”
Right.
“I kindly request some math-minded reader to find the arXiv paper and provide us with a brief analysis.”
Executive summary: garbage in, garbage out.
Validity is trivial. “God exists, therefore god exists.” is a valid argument in most logics. Useless, of course, since it is blatantly circular.
The issue with proofs like this is that they take presumptions and frame them in language (never a perfect match anyhow) then use that language to create new rules, which, due to the elastic nature of language and the original mismatch, are not really valid derivations. This often comes up when new ‘legal theories ‘are derived from the language of existing laws. The results can be miles away from original meaning or intent.
Here’s the thing: Let’s assume that it is possible to prove the existence of a supreme creature as a logical necessity. So, what? Religions are based on the supreme being communicating thoughts, desires, commandments, minutia, etc. to us and there’s no freaking way to logically prove that anyone has ever gotten a message about which headgear is appropriate and which is not.
Theists that are convinced a supreme being exist may be silly but certainly not as dangerous as religionists who have direct contact and know with transcendental certainly which life edicts to follow. The existence of a supreme being is a matter of indifference to me as long as it remains a vague notion. Once it speaks to an influential assclown, I get scared.
They typically get around that by applying the same argument to all the properties they want. So, a real ‘kind god’ is more perfect than a kind god which only exists in the mind. A real communicating god is more perfect than a communicative god which only exsits in the mind. And so on.
I would also add that using a computer to run a proof is nothing new or interesting. Many many proofs CANNOT be proved by humans as the number of steps are just too numerous, so computers run them.
So they are ambiguous on what the argument shows and using a computer is a big fat yawn. Nothing to see there.
http://www.jesusandmo.net/2011/02/23/close/
Most excellent!
The notion that existence is not a predicate comes I believe from Immanuel Kant.
But Wikipedia informs us that even Anselm’s contemporary Gaunilo of Marmoutiers thought this argument ridiculous, and parodied it. David Hume thought the idea of proving anything existed by logic alone was ridiculous.
That’s correct, though unfortunately Kant was wrong.
Here is the very short paper which is really just a report of what they did using automatic theorem provers
http://arxiv.org/pdf/1308.4526v4
Note that they don’t claim that they proved the existence of god, they just proved that goedel’s argument is formally correct. The last paragraph of the paper reads (my emphasis):
I meant the breathless author of the piece, not the researchers themselves. I assume they know what a formal proof is 🙂
Also states: “He does not extensively discuss what positive properties are, but instead he states a few reasonable (but debatable) axioms that they should satisfy.” If the axioms themselves are debatable then the entire proof is debatable. I would joke with undergrads that if I could get them to buy into a simple logical fallacy that seems, at first glance, reasonable, I can prove that I have a million dollars in my bank account (as a graduate student, I assure you I didn’t).
From a mathematical standpoint, this could lead to interesting work when established axioms (like those in mathematics, including the axiom of choice, despite its criticism) are used… Millennium Problems, anybody? 😀
For anyone interested in an example:
If I can get you to not look twice at $1 = 10cents * 10cents, then:
$1 = $(1/10) * $(1/10)
$1 = $(1/100)
$1 = $0.01
10cents * 10cents makes absolutely no sense in the first place (pun somewhat intended)… it’s actually 10*10cents, but I can’t prove anything fun if I stick to the rules.
Similar mathematical puzzles include division by 0. If you set up your entire proof on something that itself is faulty, the conclusions can be pretty fun.
In other words, 10cents * 10cents = 100cents^2 =/= $1
Benzmüller and Woltzenlogen-Paleo admit: “Without the first conjunct φ(x) in D2 the set of axioms and definitions would be inconsistent.”
So they give definitions D2, D3 and theorem T2 using Dana Scott’s version:
Substitution yields:
Necessary existence of an individual is the necessary exemplification of all its property possessed by it and necessarily implying any of its properties.
and
Being God-like is a property possessed by God and necessarily implying any of its properties of any God-like being.
All nice and circular.
“All I know is that you simply can’t prove that something exists by logic alone.”
How does one prove irrational numbers exist if not by logic alone? How does one prove infinitely many prime numbers exist if not by logic alone? How does one prove there exist non-trisectable angles if not by logic alone?
Kurt Godel may have been an obsessive and insane theist, but please don’t treat formal mathematics so callously.
Sure, and Pi is infinte decimals.
Our neurons sometimes have a funny way of proving themselves.
It’s important to note that numbers do not exist in the same way that god does.
Numbers are concepts, existing solely in the mind. The world outside may be explained in terms of these numbers. You may find ‘one rock’ out in the world, but you will never find ‘one’.
The concept of God is not what people are arguing for here, but the objective existence of god. And that objective existence of god is primarily outside the mind. You can’t just reason THAT into existence from an armchair, no matter how well you define the concept.
“… that God does”?!!!
/@
*sigh*
“It’s important to note that numbers do not exist in the same way that god is claimed to exist.”
Happy?
That is the whole point, how do you prove that a notion map to an actual physical existence?
We know that observation is both “necessary and sufficient”.
Famously, you _can’t_ build an arithmetic (with + and *) by logic alone. You need to insert notions of number behavior.
I have the funny feeling that it was precisely Gödel that proved that, but I’m not going to waste time looking it up.
And as I always point out at this point, proofs are (mostly, proof theory has made some advances, see above) still heuristics, based on commonly agreeable definitions and methods. Meaning there is logic, but not “logic alone”.
Anyway, it makes the plea “please don’t treat formal mathematics so callously” the ironic statement of today.
Exactly. In the headline, “Computer scientists ‘prove’ God exists”, it is reality that is being callously treated.
I’m reasonably sure no one who commented here actually knows anything about higher math but here goes.
When I say “by logic alone”, I of course mean you can prove irrational numbers exist and that there exist infinitely many primes while sitting in your armchair at home. You don’t need to be out collecting data and performing regressions and getting eaten by polar bears. And more importantly, that’s the *only* way you can learn about those things. There’s no viable empirical method.
As for whether or not numbers actually exist, there’s no reason to get into that here. I’m just defending the results that can come out of rigorous reasoning absent empiricism.
Without disagreeing with you, I’d also like to point out that math is much more empirical than is commonly let on.
For example, I can guarantee you that the original formulation of the Pythagorean Theorem, which had to do with comparing the areas of squares drawn on the sides of a right triangle, was most emphatically an empirical discovery and not something dreamt up in an armchair.
And many famous proofs are themselves empirical in nature. Take diagonalization, for example; by writing out the various numbers in a grid, you can see the diagonal and observe how there’s no way it could appear in a row or column. I’m sure many (if not most or even all) proofs are similar: an exploration is made leading to a discovery, often guided by intuition. That the observations are of the interactions of obtuse symbology as opposed to fruit flies or subatomic particles or distant stars doesn’t seem particularly relevant. Plus, just look at all the mathematical arcana that’s later proven useful to describe real-world phenomenon — such as imaginary numbers and electrical fields. Or, the other way ’round, such as when Newton invented the Calculus to describe planetary motions.
Don’t get me worng; math is definitely highly abstract, pretty much as abstract as it gets. But its feet are still planted in the ground, even if its head is waaaaaay above the atmosphere.
Cheers,
b&
Numbers are mathematical constructs, they don’t actually exist in reality. Otherwise infinity would exist in reality rather than as a mathematical construct. And we know the hare can cross the finish line in a single leap.
“If numbers exist then infinity must exist” is a non sequitur. One can, and in fact must, construct objects. like the natural numbers without invoking any concept of the infinite.
Also, many serious mathematicians would disagree with the statement that numbers don’t exist in reality. One can argue both sides, but don’t pretend it’s a closed debate.
All sets of numbers have an existence axiom in their definition or construction. No matter how clever you are and how deep you go, you’ll hit the need for one. For example:
The irrationals can be constructed from the rationals (limit point closure of the rationals).
The rationals can be constructed from that integers (ordered pairs of numerator and denominator).
The integers can be constructed from the Natural numbers {0, 1, 2, …}.
The natural numbers can be constructed from any infinite, inductive set.
The axiom of infinity is an existence axiom that asserts that an infinite, inductive set exists. One can, with careful wording, make this the only existence axiom in set theory, but there’s no escaping the need for this one if you want to work with any of the types of numbers listed above.
So, mathematicians do not assert the existence of anything from pure logic as the ontological claims to.
Yes, ZFC axioms need to be relied on, but no reasonable person is going to challenge them.
Well, given that we live in a finite universe (multi-verse theories aside) assuming the axiom of infinity is a big deal in the history and philosophy of mathematics. But it leads to such useful results that no one can blame mathematicians for accepting it and soldiering on. The philosophical issues remain.
However, the real point is that the ZFC axioms are exactly that, axioms taken to be true and not proven. And the fact that ZFC includes existence axiom(s) is even more on point.
Theologians want to use the ontological argument to avoid stating their God axiom. Because then that opens up the questions we ask about proposed axioms (questions that the ZFC axioms have generally stood up to quite well).
Is it useful? Is it simple and intuitive? Is it redundant with other axioms? Does it lead to results that conflict with other statements generally held to be true?
I submit that any sufficiently clear God axiom would have tremendous problems with these routine axiom tests.
Regardless of the topic, trying to solve mathematical logic problems in a computer sounds interesting.
They obviously used a “topic” that would stir interest ( be headline fodder) because a normal mathematical topic would only stay locked away in academia.
Regarding your blog post, this manner of thinking(the logic) leads to possible existence, or a possible path to take.For example, since my mind can conjure up Unicorn Pizza delivery service, then in some physical form it is a possibility,assuming of course that our mind is less than the physical world, but not necessarily exist already.Hence, we use scientists and engineers to make it happen.
I liked Greenspan’s recent interview on Charlie Rose, where he stated he learned that things that cannot be measured, atleast currently, can hold meaning.
It seems that for the time being humanity is throwing math and everything else at different situations to see what sticks, either out of greed, curiosity or desperation.
I have some familiarity with the topic as my Computer Science Master’s degree concentrated on automated theorem provers.
Automated theorem provers (such as Coq and Isabelle) simplify the development and verification of mathematical proofs. They work quite well for simple and straightforward mathematical statements, especially those statements the authors had a prior interest in investigating. The domain of natural numbers is well represented; support for the domain of abstract supernatural deities is limited or non-existent.
It appears the authors used Coq and Isabelle to show that traditional, informal proofs can be integrated into an automated theorem prover, then and made some interesting observations about how “powerful” the logic needs to be for Godel’s ontological proof to go through.
To be honest, I think they were just showing off their embedding of modal logic into Coq’s logic of higher-order types.
The author’s code is available on Github: https://github.com/FormalTheology/GoedelGod
The actual formalization of the proof is here: https://github.com/FormalTheology/GoedelGod/blob/master/Formalizations/Coq/GoedelGod.v
It’s actually quite well structured; I’ll try running it at home tonight 🙂
At precisely this point in time, is anyone else thinking of Arthur C. Clarke’s story, “The Nine Billion Names of God”?
Which I’m not having any luck finding on the interwebs…
You’re welcome.
b&
Vous êtes l’homme.
Well, the stars are going out…but it’s just the smog.
The problem here is pretty big.
Lets assume ‘existence’ is a property that must be great for this entity. That’s the fatal flaw, but we’ll give it to them, and still prove there is no “God” in any traditional sense of the term.
You see, there is a greatest things that does exist. It has all power. It has all knowledge. It exists everywhere, at all times. It is Reality itself.
Congratulations, your ontological proof for the existence of god gets you no further than Pantheism, which is basically a more poetically viewed atheism.
The only way you can escape pantheism, and get to a personal, interactive god, is to start saying things like “morality” and “desires” are things which you can define as things for which there is a maximal greatness that must be achieved.
Except I define the most moral entity as being one that would never allow Hell to exist, and would never allow any entity that would create Hell to exist. Therefore, the argument works to disprove Yahweh.
It’s not a very good disproof of Yahweh, of course, as you have to get past two very fatal flaws. Namely, ‘existence’ being an attribute that can be ‘great’, and making claims about objective reality based on a subjective interpretation of greatness.
Now if you’ll excuse me, I’m hungry. Fortunately, this isn’t a problem, as I can imagine the most perfect taco. And naturally, the most perfect taco would exist in my hand right now, with me eating it. After all, whats so maximally great about a taco I can’t eat?
You’re basically debating the starting points of the proof, when the topic is that, if the starting points are true, so and so statements must be true. And then you’re delving into a specific branch of religion,probably out of bias, whose details you used can be debated.
———–
In any case, if I can imagine something greater than reality, then by the Ontological argument,(I’m not saying I buy it or don’t, just for logical fun) then there must be or, the possibility exists of something greater than reality.This would shoot down your starting assumption by the Ontological argument.
————–
Logic and empirical evidence? We know the universe exists, and yet we look for evidence of a multiverse and more dimensions, of Higgs-Bosons that were found first mentally then found empirically. Logic is just one way the mind can see.
———————–
First off, I point out that the argument fails right out the gate. Sure, the computer experiment ignores the failure of the premises, but that wasn’t the point of JERRYs reposting of the article.
Second, I only delve into a particular branch of religion after explaining why the argument fails in a general sense, so that I can demonstrate that even if you ignore that problem with the first premise, the argument still fails to get you to a theistic god. I could make similar arguments against Brahma and Hinusim as well.
Next, I cannot imagine something greater than reality existing. This is not due to a limitation on my part, it is due to the definition of reality. Reality is ALL THINGS. In order for something to exist, it must be a part of reality. Therefore, it can never be greater than reality, as reality contains it. This is why the ontological argument can only really get you to a Pantheistic god.
You can crow all you want about ‘necessary beings’, but any being would need to exist in reality. They are dependent on that reality, on the very idea that existence can even happen.
Also, I have no idea what section 3 is referring to. The most I can say is that the Higgs Boson wasn’t “found” mentally. It was concieved of as a possible explanation. Then we went and checked.
If I hear a loud bang, I can concieve of multiple explanations, such as that something in my closet fell off the shelf, or that the Human Torch is fighting Doctor Doom. I didn’t “Find” superheroes in my mind, I thought of them. And when I went and checked, I found I had a lack of superheroes, but an excess supply of broken lamps.
If God is real, then God would be included in Reality.
This screws everything up for them. Even a God which is conceived of as being greater than reality would be included in reality if it’s real.
Plus, it just looks bad for them to be arguing against Reality, no matter what tactic they try.
Yes, exactly. The exact same faulty reasoning is at play in the various arguments for creator gods. The god creates everything — but, wait. Isn’t the god something? If the god isn’t something, how did it create anything? If the god is something, then there wasn’t nothing; there was the god. The most common tactic is to define the god as somehow outside of existence…which is just a fancy way of stating that it doesn’t exist. Except that they then insist that it does exist, even though it’s not part of existence.
Theists are generally not very good at set theory.
Cheers,
b&
Yes, many arguments which purport to demonstrate or prove God do a sly little bait ‘n switch between “God” and concepts like “Reality,” “Existence,” “Being,” and so forth, thus reducing tautologies like “reality is real” or “existence exists” or “being is” to profound insights into the necessity and greatness of God with just a little bit of vagueness and a heap of equivocation.
Yeah, there are so many things wrong with the Ontological Argument that it’s hard to pick out what’s most wrong with it. You do mention a good one, though: confusing it with ‘reality.’
Another doozy is all the complicated nonsense involved in the casual use of “the Greatest Being Conceivable,” as if a fuzzy, ambiguous abstraction like “greatness” is going to take on the same form in everyone’s mind, and is easily measured. It sure as hell doesn’t and isn’t.
Is a God which is Perfectly Good (‘perfection’ — there’s another one!) better or worse than a God which contains All Things, Good and Evil, and is so high that it is indifferent to which is which? Western and Eastern people can disagree … and one would assume that this one is a gimmee. But no.
Is a God which is totally Other, Infinite, Mysterious, Transcendent and incapable of being grasped by the human mind greater or lesser than a personal God who talks to you and cares about you and helps you find your glasses when you lose them? Depends on who you ask and their mood at the time, I think.
Math is a language without any ambiguity. Using it on sloppy, ill-defined, ill-conceived units and thinking you’re going to discover something about the universe is just dumb.
“Now if you’ll excuse me, I’m hungry. Fortunately, this isn’t a problem, as I can imagine the most perfect taco.”
LOL. I love the fact that food is usually used as the substitute to show how dumb this argument is.
Now if you excuse me, I’m off to mess around with the perfect girlfriend, which has the property of not being inflatable.
Your perfect girlfriend just further highlights the subjective nature of ‘most perfect’.
This is THE INTERNET. What constitutes the perfect girlfriend is going to vary in ways that I think Jerry would prefer I not go into in any further details 😀
Well, the most important part of your perfect girlfriend would need to be inflatable unless you’ve had your most important part removed by the last girl you told wasn’t perfect.
Premise 1: What is greatness? Is there an objective standard for what constitutes greatness? The ontological argument is really a non-starter unless there is a clear, indisputable, objective definition for greatness.
Premises 3&4: Isn’t a god that only exists in the mind and still manages to do wonderful things far greater than one that actually exists? The god that exists only in the mind has a far bigger handicap to overcome than would one that actually existed.
What being could be greater than a being which manages to create and sustain the entire universe and all of existence without actually existing?
I am unimpressed by a god that created the universe while having the huge advantage of actually existing.
Premise 5:
I can always imagine a being greater and more powerful than one that exists.
If God existed, anyone can imagine a greater being over which that god has no power.
Right now, I am imagining a being more powerful than the god of the ontological argument and the god of the cosmological argument combined.
The very fact that I can imagine a being greater than any of the gods recognized by any religion past or present tells me that not one of the gods ever recognized by any religion are the greatest possible being, ergo none are God.
Dawkins used the “the greatest handicap to overcome is nonexistence” approach in the chapter on proofs in The God Delusion. Always got a kick out of it.
I’m a bit surprised that everybody’s latched onto “existence” and that nobody’s noticed the other biggest flaw of “nothing greater.” That’s just like the “name the biggest number” game you might have played as a child — the one that went through a million to a billion to nine billion nine hundred…and so on, that took a pause at “infinity,” and then picked right up again with infinity plus one, and infinity times infinity plus an infinity of infinities.
Point is, “nothing greater” is incoherent. It’s attempting to describe the infinite as a countable number. Purest nonsense.
Cheers,
b&
+1
I did basically touch on that (somewhat indirectly) in the Premise 5 section of my comment.
Actually, that’s not the real problem with ‘greater’. It’s the subjective value of what ‘greater’ actually constitutes.
That being said, you could still propose a being with the ‘greatest possible’ power. Such an entity would be able to do anything that could conceivably be done. He couldn’t make a circle with three sides, but he could make a perfectly 2-dimensional circle in 3-dimensional space.
This list of powers would not be infinite in the sense that “you can always add one”. Rather they would encompass the entire set of all powers. It might still be infinite in some other sense (this being could create 1g of sand, 1.1g, 1.11g, 1.111g, etc…), but it would still be a full and complete list. There would be nothing that could be done, that this entity couldn’t do.
Could it make a mistake?
There are multiple problems with such an argument.
First, physics is nothing more than geometry with the dimension of time added in — Einsteinian physics especially. Presumably, if one may claim omnipotence despite an inability to draw a triangle on the kitchen table with more than 180° in interior angles, then one may similarly be excused for one’s inability to exceed the speed of light. But…well, that means that all physical limitations are logical restrictions based on the multi-dimensional geometry of the universe. And, so, because I lack the requisite potential energy and what-not to run a one-minute mile, I may still claim omnipotence despite said deficiency, exactly the same as my inability to draw a super-Euclidean triangle on the kitchen table can’t be held against me. And the fact that I can get in my car and drive a mile in one minute, or that a cheetah can run a one-minute mile, is no more relevant than the fact that I can dig a globe out of a closet and draw a 360° triangle on its surface.
Second…your proposed hypothetical super-being would still be unable to do all sorts of trivial things. For example, it couldn’t relinquish its power or commit suicide or designate an heir or enter a power-sharing agreement or the like — all things not at all remarkable for an human (and some of them noble and others tragic).
I’ll leave you with a bit of iambic pentameter that illustrates this; it’s a poetic distillation of a popular proof of Gödel’s Incompleteness Theorem. “All but God can prove this sentence true.” You can, of course, substitute any entity you like for “God,” but the point remains: that (and an infinite number of variations on the theme) is something any rational individual can do with ease but that God can never do.
Cheers,
b&
I understand where you’re going with the first part and the ending. But while true in one sense, it ignores a “practical” definition of “all-powerful”, in favor of a solely “philosophical” definition.
An entity that could instantly create an infinite number of universes, over which it has absolute control of every aspect may not be philosophically all-powerful, but it could still create a world wherein everyone is always happy and fulfilled. It would be all powerful for all practical purposes. If anyone in that universes pointed out gods inability to create four-sided triangles, nobody would care. It’d be like pointing out that no matter how rich Bill Gates is, he’ll never have THIS particular quarter.
The second part, though, I fail to understand. Why couldn’t an all powerful being choose to kill itself? All power would include the ability to strip itself of it’s powers. It could also designate an heir of it’s powers. There’s nothing to the idea of being all-powerful that says you have to ALWAYS be all-powerful. It could be all-powerful and then proceed to strip itself of that power, at which point it would no longer be all-powerful.
You answer your question with your last sentence.
Right now, I have the ability to walk over to the windowsill where Baihu is sunning himself and rub his ears. If I killed myself tonight, I wouldn’t even have the power to get out of bed in the morning.
Similarly, an allegedly omnipotent god who decided to share power with me would have trouble the first time we had a disagreement. Jesus thinks every sperm is sacred; I think it should take a conscious decision by a woman to make herself fertile. If Jesus made me omnipotent, he’d either be no longer omnipotent himself, or he’d demonstrate that he can’t make me omnipotent and retain his own omnipotence.
Similar examples are legion. For a parallel of a popular proof of the Halting Problem, imagine what would happen if Jesus decided to test Satan by making Satan omnipotent, but to do so in a safe way such that Satan was really in some kind of simulation and thus couldn’t do any real harm. Either Jesus gives Satan full omnipotence, including the power to detect such trickery — in which case the test will instantly fail as Satan uses that ability to discover Jesus’s deceit — or Jesus doesn’t give Satan said power, in which case the simulation isn’t complete. Therefore, no such ability can exist, and even Jesus can’t rule out the possibility that he himself is but a small part of Alice’s Red King’s dream.
Cheers,
b&
Another point is, “existence” of defined god is arbitrary…there are an infinite number of definitions what people mean by god. Also purest nonsense.
The number of definitions of “god” isn’t infinite, I don’t think. There’re only so many theists, after all.
If I had to take a wild guess, I’d multiply the number of theists, alive and / or dead, by several dozen to come to a first-order approximation of the number of definitions there are. That’s an unwieldily huge number, sure, but not infinite.
Cheers,
b&
Well, could we write a computer program to generate a countable infinity of “definitions of god”? Sure:
i = 0;
while (true)
output (“God is “, i)
increment i
end while
Idealized, this generates aleph null instances of definitions of god. Of course, it takes aleph null time and space to do so.
😉
Hmmm…that would certainly work…but would anybody recognize those as valid definitions?
You could, of course, go with the old standby of adding NOOPs to an accepted definition. “God is the Ultimate Poopyhead, and he knows that 1 + 1 = 2.”
Even still…well, the universe — and humans especially — are assuredly finite. That would offer you a way to generate god-definitions on demand, but the actual number of real, extant god-definitions is still limited.
Unsurprisingly, Arthur C. Clarke offers an interesting take on the subject:
http://downlode.org/Etext/nine_billion_names_of_god.html
If you haven’t already read it, it’s short and fun.
Cheers,
b&
I am a follower of Peano when it comes to definitions: they are just sign-sign correspondences, so yes, they are suitable definitions in that sense.
I could have phrased that better.
As definitions qua definitions, yes, of course, they’re valid.
But would anybody recognize those valid definitions as definitions of something deserving of the identification with the divine?
I could certainly offer a definition of, “God,” as, “That stuff that accumulates in toilet bowls if you don’t keep them clean.” And that definition is certainly valid. But what Christian would recognize it?
That’s why I suggested the NOOPs. They’re still valid, plus they’re recognizable.
…but, even though there’s no limit on how many could in principle be generated, only a finite number every have been or ever will be….
Cheers,
b&
Ah math. It can be tricksy.
Godel’s Definition 1 is:
1. Definition 1: x is God-like if and only if x has as essential properties those and only those properties which are positive
I assert that:
2. The God of the Bible is a jealous God (he says it himself in Exodus 20:5 “I the Lord your God am a jealous God”, and elsewhere).
3. Jealousy is not a positive attribute.
From which it follows that if Godel is correct:
Theorem 1: The God of the Bible is not God-like.
I’m not attacking your religious or lack of religious views.
3.Jealousy is not a positive attribute
So, being jealous over what’s rightfully yours is bad? So if you published a paper, and received no credit for it, it’s not right to be jealous for what’s rightfully yours?
Maybe I should have completed the quote:
You shall not bow down to them or serve them, for I the Lord your God am a jealous God, visiting the iniquity of the fathers on the children to the third and the fourth generation of those who hate me
That doesn’t sound positive to me. Guilt by association is usually frowned on.
Yes, even “god” himself condemns it (Ezekiel 18.1-20); and yet he does it all the time (“In Adam’s fall, we sinned all” as well as the second commandment [Exodus 20.5]). Which goes to show that yahweh does not live up to his own moral law; which in turn goes far towards explaining his own coziness with genocide and slavery.
I think it might help if he read Harris’ The Moral Landscape or Pinker’s The Better Angels of Our Nature or Grayling’s Meditations for the Humanist: Ethics for a Secular Age.
The more pressing question about god is not whether he exists, but whether he wrote a book.
Not really. If God didn’t write a book then you’re still left with God directly revealing sacred truths to individuals and now you’ve got Holy Mouthpieces and their followers — plus everyone a potential Prophet, guru, saint, shaman, visionary, or humble enlightened flame of the divine spark. The problem might even get worse.
A sacred scripture actually reigns them in slightly. Very slightly, to be sure.
One could play this game, as you suggest, with the finest possible unicorn as effectively as with the greatest possible being.
It was Russell who came up with “Existence is not a predicate.” I think this argument for God also runs up against his theory of types, since we conceive the set of all properties that make him great, and then assess the total for greatness with and without the “property” of existence, which means having moved up a level.
But if the premises are in fact self-contradictory, it is easy to show that anything at all, and its contrary, follows from them by valid reasoning.
Don’t forget – any mathematical equation for god must be multiplied by zero.
Ah, multiplication by zero. The true ‘greatest power’ in all of mathematics. Nothing can survive being multiplied by zero. All will be subsumed into zero, no matter it’s value.
Hence, Zero is the pantheistic god.
Makes just as much sense as the ontological argument…
…and any mathematical equation for god involving infinities must be renormalised.
The Importance of the ‘Unicorn Sieve’
There seems to me to be a very much easier way of dismissing the argument right from the first words. The trick in any kind of theological ‘logic” is to disguise the conclusions and to conceal them in the premises. And there are the conclusions disguised as a premise… ‘Beings’ and ‘Greater Beings’
A ‘being’ is a theological construction with no parallel in the real world. So I have to stop you theologians there and declare that the beginning of your reasoning contains an illegal concept, ‘Being’. THERE IS NO SUCH THING!
Because the syllogism can conjure-up unicorns, Craig Lane and Plantinga have invented a ‘Unicorn Sieve’. Again it is a curious piece of monkey-trickery called ‘necessity’. Sadly for the chuckle-brothers who promote such nonsense, their unicorn sieve called ‘necessity’ reveals a terrible truth about themselves. It reveals that, for them, their gods exist by necessity. Probably in order to give them emotional sanity in an indifferent world.
You have to give it to Lane Craig. He keeps on dishing-up this rubbish to new audiences as if he has no knowledge of the amusement is causes.
But if god wanted us to believe in him, surely he would have existed!
Linda Smith.
I don’t think that there can be a god so powerful that he could tell the gullible where their ‘seed-money’ goes when they send it to Mike Murdock!
Dumbest argument for god ever. Perfectly illustrated in this cartoon:
http://www.smbc-comics.com/?id=3066#comic
Are you insinuating Anselm was in dire need of a decent lay?
1 – My understanding of god is a fantasy of which there can be a greater one conceived.
2 – The idea of a fantasy exists in the mind.
3 – A fantasy which exists both in the mind and in reality, is greater than a fantasy that exists only in the mind.
4 – If a fantasy only exists in the mind then we can conceive of a greater fantasy.
5 – We can be imagining something that is greater than a fantasy, but it cannot exist in reality
6 – Therefore, fantasy exists …in the mind not in reality.
The argument may be logically valid, but is it sound? i.e. are all the axioms rational to accept?
Was it important that it was a Macbook used?
Steve Jobs is God?
A computer programmer dies and goes to Heavan.
St Peter welcomes him with open arms. “Come in, come in, you have led a blamless life”
Programmer, trying to adjust to having just died and gone to the Pearly gates asks St Peter ” Steve Jobs ins’t here is he?”
No says St Peter. “We wouldn’t let him in here”
A moment later the clouds part, an intense light shoots forward in well defined shafts. Then appears a heavenly chariot pulled by angels with iPads and iPhones.
Progammer says to St Petere…”hey, I thought you said that Steve Jobs wasn’t here”
St Peter leans forward and whispers…” No, No, That’s God, he just thinks he’s Steve Jobs!”
Reminds me of the same joke, with conductor Herbert von Karajan taking the place of Jobs.
b&
I normally tell that joke about Ridley Scott the film director, because that’s the world I move in.
First heard it with Joe Namath…
That was the first thought I had. OF COURSE a MacBook would think a God exists and his name is Jobs.
Run the same program on a Windows box and it will no doubt prove the Devil…
The cliff notes version of Godel would be Divine Command Theory. The fact that the logic of these “proofs” or “theories” work equally well for pizza, Russell’s teapot, or the Flying Spaghetti Monster is pretty much a QED for Mathematical Theology.
I’d say the weak point is #1: “Our understanding of God is a being than which no greater can be conceived.”
What do we mean with greater? The theist will include omnibenevolence and omnipotence.
But we easily can substitute good with evil: “Our understanding of the Devil is a being than which no greater (including omnimalevolence and omnipotence) can be conceived.”
The we apply the same algorhythm. In the end we are saddled with two omnipotent supernatural entities and that’s a contradiction. I don’t see how a mathematical version can remedy this.
I find this way more convincing that all the parodies, which by definition don’t contain much information.
I can think of a god that is greater than the christian god: A god that created this world without evil. Therefore, what christians worship, is not god.
I can think of a god that is still greater as the god that created the universe: A super-god that created god.
And, I can think of a god that is still greater as the super-god that created the god: A super-super-god that created super-god.
And so on. This is really like “there is a number which we can’t think of a bigger number”. There is no such number, therefore, there is no such god. This, really, disproves god (the god of the definition, of course: “God is a being than which no greater can be conceived” – it cannot exist).
A more humorous way:
I can think of Eric, the super-penguin, who eats gods. Clearly, if he can eat (and destroy) god, he is greater than god. Therefore, Eric exists – and your god does not. I usually use Eric to blow that nonsense “but you can’t disprove god” out of the water. Because, you see, you can’t disprove the existence of Eric.
A bit of googling showed up a couple of posts on Gödel’s modal ontological argument (which is what’s formalized in this paper). Check out http://skepticsplay.blogspot.com/2009/04/godels-modal-ontological-argument.html for at least one blatant problem with this formalization, and http://skepticsplay.blogspot.com/2009/06/godels-ontological-argument-step-by.html for a step-by-step explanation of the proof.
Here’s an argument against the proof to use against believers: it seems to be inconsistent with the Trinity. If there are any properties that God-the-father has and Jesus doesn’t, or vice versa, then at most one of them can be considered God, according to the definition in the proof.
Your argument wouldn’t work against most Christians. For the Trinitarians, Papa, Junior, and the Holy Shit are three manifestations of the same spook — kinda like Cerberus’s three heads. And for the non-Trinitarians, Jesus is just the messenger.
Of course, it’s all faery-tale fantasy with a hell of a lot of special pleading; the real point is moot. I’m just suggesting that you won’t convince many Christians with it, as that’s the sort of thing they’re taught in Sunday School how to “defend” against.
Cheers,
b&
IMHO trying to prove the existence of any ‘god’ is worthless work, but I am a bit hung up on the “reality” of a god, i.e. how do we describe things that only exist in the mind? Although there is not one iota of evidence for any gods’ physical existence, one could argue that anything that exists in a person’s mind is ‘real’ regardless of whether or not such a thing exists beyond one person’s mind. Maybe this is just semantics, but perhaps we need to be more clear on the use of existence and reality.
Well, the reality is that there are things that exist only in the mind and there are things that exist both in the mind and physically. No problem.
For a completely different reason, I tracked this down this morning. It’s a nice summary of the Ontological Argument (in several variants) and 3 other major classes of such arguments: http://www.patheos.com/blogs/daylightatheism/essays/unmoved-mover/
For Jerry—this will undoubtedly be vetted, given our previous disagreement about ‘political correctness’, so no desire on my part for it to appear in the blog. So block it if convenient (no problem either way!), but the following may interest you personally.
“I kindly request some math-minded reader to find the arXiv paper and provide us with a brief analysis. ”
No one else seems to have done that (as of my latest glance through responses), so here are just a few things.
First of all, Godel’s formal derivation (or proof, if you like) is of course perfectly correct. That is entirely different from claiming he has proved anything substantive, and no one much really accepts that he has. I certainly do not think he has moved humanity even the tiniest bit closer to accepting the possible existence of any sort of god (nor did Anselm of course).
The article at issue is not even worth reading; a very short straightforward derivation in formal logic such as Godel’s, whether modal or not, is the last thing in need of even more formalization as a computer-checked derivation. No one has any doubts about Godel’s formal correctness. The article itself may or may not be correct, but there is little doubt that it is trivial, and no contribution at all to logic or anything else of substance, including to computational software related to proof-checking.
Godel’s derivation has some formal cleverness
(he uses 3rd order, no less, modal logic, for anyone familiar with that sort of technicality). There have been several similar things done subsequently to add to that literature, even a claimed argument supposedly doing Anselm’s argument with formal logic in the classical sense, i.e. non-modal. This latter was done by a pair, one of whom is so august as to be the prime mover of the Stanford Encyclopedia of Philosophy, no less! It turns out that all it basically showed was that one can formally deduce the conclusion ‘god exists’ from the formal assumption ‘1=1 implies that god exists’, though they published 3 papers on it in supposedly serious philosophy journals over 20 years without ever realizing that (i.e. that one of their assumptions had the form ‘logically valid formula implies god exists’) until it was pointed out to them.
But this other literature on formal fiddling related to Godel’s derivation is not entirely a waste of time. We have learned a few new wrinkles related to formal modal logic. But I think it is pretty far down there in importance, even in the context just of mathematical logic, a pursuit which I value more highly than most people who respond to your blogs seem to. Perhaps actually studying the papers and popular articles of someone like George Boolos would change their minds. But that does involve doing some real work, and I don’t know how you (Jerry) can manage to do even half of what you already accomplish!
Peter Hoffman
“no contribution at all to … computational software related to proof-checking” seems a bit harsh. Formalizing modal logic within other forms of logic, and doing it so that the automation tools work with modal logic proofs, seems challenging and interesting.
From about 1910 when Lewis invented it, till almost 1960 with the genius Kripke finally saw how to do semantics, modal logic had been nothing else but purely formal, and still mostly is, so I don’t understand “…Formalizing modal logic within other forms of logic..”, or at least any need for that. And already formalized logic is not much of a target for automation tools. Surely it is more informal mathematics.
The formal version of Godel’s argument, written nearly in all detail by Dana Scott, would come in detail to easily less than 30 lines, IIRC.
But perhaps I am missing something here.
The code snippets at github.com/FormalTheology/GoedelGod are indeed rather succinct.
The technical dexterity is evident; so is the sleight of hand.
John Rushby presented last August, simultaneously with Benzmüller and Woltzenlogel-Paleo, a rather more intuitive formal proof in PVS at the aptly named CAV workshop Fun With Formal Methods.
Rushby concludes:
Zalta’s computer aided proof is quite interesting, and I’ve heard him talk about it twice over the years, as he’s refined it a few times. The problem you mention has been removed. Zalta still does not think it should turn one into a theist, though.
“Zalta’s … problem you mention has been removed. ”
This is pretty well impossible, so it’s surely a mix-up to think this ‘removal’ exists. Is it published?
Why impossible?
For two reasons, the first pretty decisive:
1) The papers are not in error, at least on this point; they simply go round in circles to produce finally a triviality, as was realized once more than one serious mathematical logician took the trouble to produce the brief verification that one of the premises had the form ‘logical validity –> conclusion’. You cannot remove such a problem; maybe come up with something different.
But that is unlikely as follows.
2) I corresponded with Zalta and Oppenheimer separately about the problem, quite recently, and no such removal was indicated then, so this supposed removal would be exceedingly recent. And nothing more recent has come to me from either author. They didn’t even seem to realize then that the Polish logician Garbacz had pointed this trivialness out (II, page 587, Vol 90, Australasian J. Phil.). And neither did I till the Australian philosopher Oppy told me after I sent him my short paper saying the same. Is it really the case that philosophical logicians do not realize that writing down something like ‘1=1 –> god exists’ and using it to deduce at great length the formula for ‘god exists’ might be unimpressive?
To summarize (see Garbacz for references), many years ago Z. and O. went to great lengths to claim that a correct translation of the original Anselm into formal logic would be non-modal. And more importantly, it would have three premises, unaware as above that one of these had the form ‘a logically valid formula implies god exists’. Indeed, a second paper was written some years later trumpeting a great triumph, achieved by means of mechanization of the proof, which showed them that their other two premises were unnecessary. Yet a third paper was published on it by them. Then Garbacz finally pointed out the fact above, though he curiously didn’t make much of it, but emphasized other criticisms, ones which actually weren’t that strong (I and III, ref above).
Sorry to spell this out rather pedantically. But I really find it hard to accept that such a ‘removal’ of the problem occurred, yet neither of the authors informed at least one of the persons closely involved with pointing out how either Anselm formulated what is trivial and unconvincing (if they are correct in their formalization of it), or else their formalization is something other than Anselm’s argument, and they’ve produced a silly but formally correct logical argument whose conclusion is the formula they translate as ‘god exists’.
Anselm was of course unconvincing, but perhaps for other reasons.
Some heavy duty discussion going on here that would take me days to sort through.
But methinks LOVE is the answer.
I never really understand how this hackneyed argument doesn’t simply reduce to, “anything that can be dreamt up must exist.” And who would ever buy into anything as ludicrous as that?
Would you argue with Euler’s proof of the existence of God, aka Euler’s Identity, which he came up with at the court of the Empress Catherine the Great in Saint Petersburg to counter Diderot’s preaching of atheism? 😉
Lifted from YouTube watch?v=mIMFgTW23Ho :
. . . Descartes – Euler Theorem . . .
“The most remarkable formula in mathematics”. Richard Feynman
“Euler’s equation reaches down into the very depths of existence.” Keith Devlin
What makes this array of symbols and numbers so beautiful? Firstly, it contains the three basic arithmetic operations exactly once each: addition, multiplication and exponentiation It also connects five fundamental mathematical constants with nothing other than themselves and the arithmetic operations.
Some people describe mathematics as a distinct language in itself. Not only that, but mathematics is considered the universal language as it is both universal and ubiquitous. If that is the case, than Euler’s identity can be considered an extremely pithy literary masterpiece.
0 is the additive identity, as adding it to another number results in the original number.
1 is the multiplicative identity for the same reason as 0.
Pi(π) is one of the most important mathematical constants in the history of mathematics that is ubiquitous in Euclidean geometry and trigonometry.
Euler’s number(e) is the base of natural logarithms and is used widely in mathematical and scientific analysis.
i(√-1) is the imaginary unit of complex numbers, a field of imaginary numbers that are not “real”, allowing for the calculation of all roots of polynomials. Euler’s identity neatly sums up the relation between these five numbers that are so crucial in the field of mathematics. It is also interesting to note that these five numbers were discovered at different points in history spanning over 3000 years.
Euler’s Formula (aka Euler’s Identity) is traditionally regarded as the most beautiful equation in all of mathematics. Yet it’s so much more than that. It’s the equation that governs the whole universe and even defines the human soul!
“God” the cosmic mathematical mind — gazed upon an infinite collection of dimensionless points, each modelled by the number zero. An infinity of zeros is nothing. God did indeed make the world out of “nothing”, but a very special type of nothing.
Euler’s Formula is. eix = cos(x) + i*sin(x)
In the specific case where x = π, eiπ + 1 = 0
The Most Elegant, Magnificent and Divine Equation.
Euler’s Formula is the perfect complement for Leibniz’s Monadology. Together, they form the most powerful intellectual combination in history, capable of explaining the whole of science and establishing a true grand unified theory of everything, embracing mathematics, science, philosophy, religion and psychology. It can even provide an entirely rational explanation of near-death and out-of-body experiences, and homeopathy. It also overturns Einstein’s sacred principle of relativity and provides exactly the same mathematical results via an absolute framework that restores the “reality principle”.
Provide a complete solution of the Cartesian mind-body problem via the Fourier transform – which has the Euler Formula as its engine. We present the Riemann sphere, which works in perfect harmony with the Euler Formula, as the ideal working model of the human soul. And we give the first ever technical explanation of the process of reincarnation.
The Euler equation is everything you thought it was – and more. It’s truly divine, It is the God Equation.
. . . Descartes – Euler Theorem . . .
“The most remarkable formula in mathematics”. Richard Feynman
“Euler’s equation reaches down into the very depths of existence.” Keith Devlin
What makes this array of symbols and numbers so beautiful? Firstly, it contains the three basic arithmetic operations exactly once each: addition, multiplication and exponentiation It also connects five fundamental mathematical constants with nothing other than themselves and the arithmetic operations.
Some people describe mathematics as a distinct language in itself. Not only that, but mathematics is considered the universal language as it is both universal and ubiquitous. If that is the case, than Euler’s identity can be considered an extremely pithy literary masterpiece.
0 is the additive identity, as adding it to another number results in the original number.
1 is the multiplicative identity for the same reason as 0.
Pi(π) is one of the most important mathematical constants in the history of mathematics that is ubiquitous in Euclidean geometry and trigonometry.
Euler’s number(e) is the base of natural logarithms and is used widely in mathematical and scientific analysis.
i(√-1) is the imaginary unit of complex numbers, a field of imaginary numbers that are not “real”, allowing for the calculation of all roots of polynomials. Euler’s identity neatly sums up the relation between these five numbers that are so crucial in the field of mathematics. It is also interesting to note that these five numbers were discovered at different points in history spanning over 3000 years.
Euler’s Formula (aka Euler’s Identity) is traditionally regarded as the most beautiful equation in all of mathematics. Yet it’s so much more than that. It’s the equation that governs the whole universe and even defines the human soul!
“God” the cosmic mathematical mind — gazed upon an infinite collection of dimensionless points, each modelled by the number zero. An infinity of zeros is nothing. God did indeed make the world out of “nothing”, but a very special type of nothing.
Euler’s Formula is. eix = cos(x) + i*sin(x)
In the specific case where x = π, eiπ + 1 = 0
The Most Elegant, Magnificent and Divine Equation.
Euler’s Formula is the perfect complement for Leibniz’s Monadology. Together, they form the most powerful intellectual combination in history, capable of explaining the whole of science and establishing a true grand unified theory of everything, embracing mathematics, science, philosophy, religion and psychology. It can even provide an entirely rational explanation of near-death and out-of-body experiences, and homeopathy. It also overturns Einstein’s sacred principle of relativity and provides exactly the same mathematical results via an absolute framework that restores the “reality principle”.
Provide a complete solution of the Cartesian mind-body problem via the Fourier transform – which has the Euler Formula as its engine. We present the Riemann sphere, which works in perfect harmony with the Euler Formula, as the ideal working model of the human soul. And we give the first ever technical explanation of the process of reincarnation.
The Euler equation is everything you thought it was – and more. It’s truly divine, It is the God Equation.
(aparently taken from http://tinyurl.com/q6x7paq)
See also YouTube watch?v=zApx1UlkpNs
(Please note that all this calculus and algebra business is waaaay beyond my ken and above my paygrade!)
Ooops, sorry about the repeat, it had apparently vanished from my notepad so I copy pasted it again, and then when copying it from my notepad, it reappeared so it is there twice.
Blushing with embarrassment… 🙁
Why does God have to be perfect?
If god was not perfect, he wouldn’t be fine-tuned and therefore the universe would be greater than god.
Hmmm.
Why does a creator have to be omnipotent? This universe may not be the only one, and so fine-tuning does not apply. The universe may be greater than God, whatever that means – men create lots of things which are bigger than themselves, and will last a lot longer than they will individually, or as a group.
The attributes of omnipotence, omnipresence and omnibenevolence are always trotted out for God as if they are inevitably true. I don’t see that needs to be the case.
In logic people say that something is provable when, all too roughly, it can be deduced from certain other statements using certain rules. Here’s where this usage diverges from everyday usage: it doesn’t require that provable statements or the statements from which they are deduced be true.
For myself, I see no hint of the everyday sense of ‘proves’ in Benzmüller and Woltzenlogel’s paper. For example, when they say that KB (a logic) is sufficient to prove T3 or that T1 is a theorem of K (another logic), they don’t mean to convey that T1 or T3 is true. (T3 formalizes ‘Necessarily, God exists’). Benzmüller or Woltzenlogel may personally believe T1 and T3. But their truth is not something either of them claims to have shown, even with the help of a computer.
Three things…
It is so interesting in reading through the posts upon WEIT concerning The Two Germans with a Laptop…’ There seems to be several ways, and many variations of those ways, whereby to refute the Ontological Argument. And that each poster seizes upon, and appreciates a certain kind of response. All the refutations are probably the same; -circular arguments; dodgy premises; symbolic logic; wishful thinking, -and so forth. My own refutation, (above) is not a popular one! It seems to suggest that in matters concerning reasoning, smart people often respond quite differently but succeed in reaching agreement upon the truth or falsehood of the proposition, (that gods can be conjured out of wishful thinking) Curious that we have need of variations around the same logical objections. Such is the human mind.
Secondly, the Ontological Argument offers rich insights into the religious personality-type in that they are all in such agreement that their gods exist that any kind of preposterous and punctured argument stands, for them, as irrefutable! In other words, religious folk are so utterly convinced in the existence of their gods that any trivial half-hearted attempt at reasoning seems to be all that is needed. Their eyes seem to glaze over the refutations. And shortly, Lane Craig or another Apologist will launch the rotten ship upon public waters once again. It is a matter of urgency that we try to understand that feature of Christian Apologetics, that they seem so smugly satisfied with shallow logical devices.
Several people have, like myself, compiled a list of Christian rhetorical deceits; forms of lies, half-truths and most importantly, clever verbal trickery used by Apologists. My list runs to 113. Everyone different! The last, number 113, is called,
“Killing the Aberrant Twin”
And I am grateful to former priest Mark Vernon for displaying the trick in public for all to see. His trick in his Guardian piece concerning Dawkins, was to equate Science myths (sic) with religious myths, and so draw comparisons between the ‘two ways of knowing!!!’ And then to state that Newton is no longer read today, and that the bible continues to surprise and delight people with its ‘truths!’. Therefore, (he surmises) religion is the better explanations for the world and its processes!!
I like my characterisation of the Vernon trick… “Killing the Aberrant Twin”
There will come a time when ever a theologian makes public mischief with his arguments, we simply call out the number and the title of the fraud and encourage him to look it up himself. Perhaps with the Ontological Argument, next time they use it we all should shout together, ‘Number 57, and don’t forget a sieve for all the unicorns you create!’
Math(s) is an essential tool for science, above all, for physics. But to be of use, every constant and variable at the start of a mathematical process must have a demonstrable connection with reality. Claims to knowledge of nature derived from mathematics (or from computer simulations) are worthless without such a connection.
My favourite syllogism:
1st premise
Half a loaf is better than nothing.
2nd premise
Nothing is better than god.
Conclusion
Half a loaf is better than god.
In a similar vein…if God is love, and love is blind, and Stevie Wonder is blind…does that mean that Stevie Wonder is God?
b&
I think that the principal argument is that in this formalism, analized by computers, the “possible necessity” is actual. And it is, the formalism is correct. But the term possible is used ambiguously. When we say that something is possible, we don’t understand that that something actually exist. We don’t know, in fact, we only have a more or less a vague idea. Only in perfect knowledge the possibility is actual.
In perfect knowledge, something possible is actual. In case of perfect knowledge, a possible God (or cat) is an actual God (or cat). In the real world, those who say that God is possible, in fact don’t have the slightest ideea if it’s possible, they just guess.
The problem with the original premise is, in my opinion, common to a large number of religious arguments.
“If God only exists in the mind, then we can conceive of a greater being—that which exists in reality.
We cannot be imagining something that is greater than God.
Therefore, God exists.”
It assumes that because we, (human beings who are the center of the universe and from whom all that is of any importance springs,) can conceive of something, it has to exist. How narrow and self-centered that vision is! Do we dare to believe that we are really that important? This is, I suppose, one of the devices religions use to coax us to their viewpoint- the idea that we are SO VERY important that we can even create a REAL all powerful being just by conceiving of him, which, in essence, the argument is suggesting.
Our egos (aided by endless generations of natural selection) have become so big that most of us just cannot accept the idea that we are just as important in this universe as the lowest amoeba, and that when our life cycle is over, we will close our eyes, our brains will shut down, and all that we felt and remembered, physically and emotionally, will end in one fell swoop as we fall into endlees non-existence.
From another list:
Oh, I LIKE! 🙂
Superb, Diane. I often relate that I am a “Potterite” and believe that the books of Potter are actually truth and that J.K.Rowling was inspired by the great Got H. Potter to write these factual chronicles. For proof,of this, simply refer to the books of Harry Potter! If it’s written there, it must be true!
I’ve always said that the ontological arguments boils down to just two points:
1) Define god as existing;
2) Claim god exists by definition.
The rest is obfuscation.
114) Bait-N-Switch Battlefield Arguments
There are interesting limitations in any intellectual dismissal of theological propositions. Many theologians sense that they may best promote supernatural explanations for the world, its contents and its processes, by getting any detractors to answer in only one mode; that is to get detractors to challenge the logic, rather than the premises upon which the logic is operated.
We now know from this book that the whole of theological belief is based upon logic drawn upon false assumptions concerning the nature of reality. The religious premises are nonsense, but the logic, which leads to a belief that gods made and are operating the universe, – imay seem to be sound. In other words, garbage premises will always lead to garbage conclusions, even if ‘logic’ connects the two. Aquinas famously insisted that religion was logical. He is right. But he is wrong about the results of his logical analysis, which are not true. They are based upon inner connvictions, and not upon universally agreed understandings of the world around us.
Ontological Argument Again!
The Bait-n-Switch arguments concerning the ancient Ontological Proof of the existance of the gods work to oblige detractors to address the logic, rather than the premises. And yet even a cursory glance at the premises reveals the beginnings of a preposterous argument. Great contemporary Apologists for Christianity know very well that their beliefs survive upon flimsy or non-existant evidence, and so the have an instinctive drive to force detractors to address the logic of the arguments, and not the dodgy premises.
The dodgy premises are that there are such things as ‘Beings’ and ‘Maximal Great beings’. ‘Beings’ is a word of a high level of generality, and contains such things as Ghosts; Goblins; those who fly saucers; Santa; Tooth Fairy; witches; unicorns; gods past and present; and the large rabbit whom Alice in Wonderland followed down a hole. ‘Beings’ exist only in the mind. Any logic drawn upon the supposed existance of ‘beings’ must be nonsense.
How Logicians Mistakenly Accept the Existance of ‘Beings’
But those adept in logic miss the obvious objections to the Ontological Argument, and accept the religious demand to do battle upon the battlefield of their choosing, which is logic!
“…garbage premises will always lead to garbage conclusions,…”
As long as it is logic we’re discussing, it ought to be pointed out that this is false. For example, with the garbage premise ‘1=2’, logic allows me to multiply by 0 and logically correctly come to the non-garbage conclusion that ‘0=0’.
That falsity can lead logically to both truth and to falsity is rather basic and long known.
Perhaps it was a typo where ‘always’ was meant to be ‘sometimes’. Quantifiers do give all of us difficulties at times. For example, most USians would agree with the false statement ‘All ballplayers are not pitchers’, thinking they are saying the true statement ‘Not all ballplayers are pitchers’.
One trouble with logic is that everybody has ideas about it, quite naturally, and many have something to say about it, sometimes without having spent much time thinking about it.
Thank you for your interesting observation. But in this context the premises were toward demonstrating an obvious falsehood. I doubt whether any theologian would thank you for pointing-out that multiplying his premises by zero equals zero. It is irrelevant to the context. And since the Ontological Argument is towards demonstrating the certainty of the existence of gods, pizza, Canadian girlfriends, a million dollars in the bank, or unicorns, I feel that your observation may be technical correct but only in another context whereby you seek to extend knowledge of logical possibilities without specific direction.
I tend to feel that most theological arguments are couched as metaphysics because of the peculiarity of the abstraction ‘scales’ whereby the more abstract the statement, the less truth-falsehood content within that statement. At high levels of abstraction there is no truth/falsehood content.
The bottom line for me, and I have held it for a long time, is that theological assertions have been designed by usage to oblige the interlocutor to address only the logical reasoning part of the theology, -which is usually quite good since it invoked the higher reaches of abstraction, (the gods are everything!!!) and so ignore the glaring childish ‘howlers’ which are the major part of religious ideas. And a useful way of understanding just why so many theological claims are rarefied, bizarre and hallucinatory, is that reasoning based upon garbage assumptions are subject to ‘exponential error dispersion’ I have in mind Noah and his sons setting off for the Spitsbergen Islands near the artic circle with a donkey-cart to pick-up a pair of polar bears.
Sorry if you interpreted what I said as criticizing anything else, other than what I quoted of what you said; or if you thought I was in any way regarding Anselm’s or any subsequent version, including Godel’s, as in any way convincing theologically. Several times here, including after this essay by Jerry, I have clearly stated that I did not.
Surely you cannot object to one pointing out a logical error (such as “…garbage premises will always lead to garbage conclusions,…”) in paragraphs which are supposedly about logic! Accepting what you wrote would lead one to reject absolutely everything, a bit like solipsism. Also formal logic itself has nothing to do with your “context”.
Further, you have misinterpreted the ‘multiplication by 0’, just a single example, as having some additional significance to me or to some theologian.
To clear up the latter, take any statement S you wish, not necessarily false. Below is a description of a rather trivial formal deduction of it from the false premise ‘1=2’. And so we then would see a semi-general example, of deriving anything at all from falsity, not just falsity. I hope the example is now general enough for it not to have its details themselves misinterpreted.
First write a few lines to deduce ‘1 not= 2’. (So the bottom line so far is exactly the one just quoted. This is not one of the major theorems of mathematics, so season it to your own taste.)
Now as the next line write the premise ‘1=2’.
Next line will be ‘(1=2) and (1 not= 2)’. (This just combines the previous two lines.)
Now write the line ‘[(1=2) and (1 not= 2)]–>S’. (Here the symbol “–>” is material implication, so read it “implies”. Since ‘[F and notF]–>G’is always a tautology, no matter what “F” and “G” are, this line is acceptable logically.)
Finally write the line ‘S’. (And so we are done. This is completely standard in any decent logic course. The last line comes from the fact that derivation line ‘F’ followed by a line ‘F–>G’ can always then be followed by the line ‘G’. To be even more pedantic, this rule is known as “modus ponens”.)
But I think my original specific example ought to have been quite sufficient, had its method of multiplying by 0 not been misunderstood as implying something more significant.
Thank you for your interesting observations. Your displays of logical possibility are quite difficult to understand as you probably know. I think that we are talking somewhat at cross-purposes. I see this thread as about theological howlers, and not about refuting logic with logic. And the thought of multiplying a theological premise by zero was a little joke.
What about the grand observation that theology takes awful assumptions concerning the nature of reality, and turns them into propositions such as the existence of gods who speak through a burning bush, or who allows some holy men to do impressive feats of magic that defy the ‘laws’ of nature? Theological reasoning (based upon rubbish premises) is quite good, and as with the Social Sciences, it allows great and melting historic Ice-Palaces of speculation wherein there is hardly a drop of truth.
“..Your displays of logical possibility are quite difficult to understand..”
perhaps because logic, as it has come to be understood in the 135 years since Frege, is not quite as obvious and trivial as flippant remarks sometimes seem to imply, responses which probably do more harm than good in a campaign to persuade thoughtful but undecided young people that atheism is the only sensible option.
‘Trivial and flippant’ Hmmm. It’s possible that you feel logic to be the basis of everything, whereas I feel that close observation is the basis of comprehension. Most people seem to live with very little logic in their lives. And most people even go against what logic should inform them. But I’m afraid that you may not have too much success in getting people to value logic as you do. For me, in most cases, bad premises lead to bad conclusions, even if you insist that logically, it is not necessarily so. But I am puzzled why you will not engage with my suggestion that the Ontological Agument is not really about logic; it is about the assertion of crackpot premises, and the pretence that the reasoning that follows those premises somehow make the case water-tight.
This just in… Lane Craig and Plantinga talk of ‘beings’, and of ‘maximally great beings’ -theological concepts. But on another thread adjacent ‘Atlantic: Study More Theology’ we are directed by ‘Don’ letter 32, towards a website by Robert Barron, founder of ‘Word on Fire’ who discusses why atheists like Dawkins just don’t get god. It is (he says) because they keep defining god as a ‘being’.
It is not a new idea; to move their gods around, hiding them here and there to keep their gods out of common criticism. But it does put paid to the Ontological Argument is its basic premises are denied by other theologians. It is the old story of the abstraction scales whereby the more abstract the less truth/falsehood content.
Hiding Their Gods
“….To a person, the new atheists hold that God is some being in the world, the maximum instance, if you want, of the category of “being.” But this is precisely what Aquinas and serious thinkers in all of the great theistic traditions hold that God is not. Thomas explicitly states that God is not in any genus, including that most generic genus of all, namely being. He is not one thing or individual — however supreme — among many. Rather, God is, in Aquinas’s pithy Latin phrase, esse ipsum subsistens, the sheer act of being itself….”
Robert Barron
And so Lane Craig’s ‘Beings’ become ‘the act of being’. It its deliberate obfuscation and sheer verbal deception, Barron’s claim destroys religion’s ‘best’ argument, that you can define anything into existance. Once again I sense the ‘Exponential Error Dispersion’ that occurs whenever you try to unpack any religious assertion. Religious clap-trap has a natural escape velocity in which any further attempt at explaining supernatural mysteries takes you to the land of lunacy. And how did those kangaroos on the Ark hop back to Australia, taking their ancestor’s bones back with them? I’m sure that Woodmorappe, ‘Noah’s Ark; A Feasibility Study’ will invent an answer. I’m sensing that it might involve dinosaurs pulling Jaganaths, gold, cords tied to pyramids, big boats, and a little magic.
“…I am puzzled why you will not engage with my suggestion that the Ontological Agument is not really about logic; it is about the assertion of crackpot premises…”
Disagreement with the truth of Godel’s premises I have already stated several times, so perhaps a lack of engagement would have been more appropriate as a self-criticism. I would be interested to hear in detail which of those premises you disagree with and why, to at least see that you have actually engaged with considering Godel’s premises. Further up, I even gave in quite explicit detail the ‘unfortunate’ premise in a different version of formalizing Anselmism, rather than merely fulminating with the ‘adjectivified-noun’ “crackpot”!
I don’t think ‘formalising Anselmism’ is likely to win many converts from the religions. That, after all, is the purpose of the discussion. And entering into discussions of logical possibility is not for me. After all, the bible and theological exegeses are all forms of pursuing logical possibility based upon dodgy premises. Sorry.
As well thought out as these comments are, at the end of the day it still seems no well respected scientist(s) has earned any headlines with math and computers agreeing in their computational results that the existence of a creator God is NOT likely.
I feel like highschool will never end. If we all have no purpose then why must we be? Trying to decide if Gods real is not a feasable job. Screw u for judging me
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