Proofs of Non-existence

[trish]

Some folks say you can’t prove a negative, but that’s simply not true. There are many examples in science and mathematics of what are sometimes called negative propositions. There are no perpetual motion machines. There is no complete planar map of the Earth that doesn’t have disconnections, rips or tears. Proving a negative requires having a precise characterization of at least one attribute of the thing that doesn’t exist. The total entropy of a perpetual motion machine and its environment would have to be constant contrary to the second law of thermodynamics. For there to be a complete, continuous, one-to-one, planar depiction of the Earth the homotopy group of a plane would have to be that of a sphere, which is not the case.

I’ve heard it argued that one can’t prove the non-existence of gods because one cannot prove a negative. Of course, that’s not why there are no universally accepted proofs of the non-existence of gods. The reason there are no such proofs is that there is no universally accepted definition of godhood and no universally accepted attributes that all gods must share. Baring a universally accepted notion of what gods are and what they all can do, we will never have a proof of their non-existence.

However, some cults, religions and philosophies propose gods having rather well specified histories and powers. Often one can show that these gods don’t exist. For example: one attribute of the Greek gods is that they lived in temples on Mt. Olympus at around 1100BC. One of the occupants was known as Zeus and he turned into a swan in order to have his way with a woman named Leda, who evidently had a thing for swans. I leave it to the reader to construct her (or his) own proof that the Greek gods never existed.

I thought it might be interesting to have a thread in which we collected proposed proofs that specific gods did not exist; e.g. that Zeus could not have existed, or the Old Man in the Sky version of Abraham’s god. I’m not looking for proofs that certain gods are immoral. We know that. That would be an interesting topic for another thread. But here I want proofs that various sorts of gods don’t exist. This might strike you as a rather negative endeavor. But in the end, the complement of our list will show us what sorts of gods we actually might have to look out for!

(Why not a thread collecting proofs that certain sorts of gods DO exist? That would be a good topic for another thread. Along with such a proof, one might also want to argue why creatures with the purported attributes should be regarded as gods.)

[manbearpig]

As far as God and religion is concerned; man evolved into religious belief and it is mans destiny to evolve past the need for it. One could argue that it's happening now in full force. Maybe you can't disprove God though, there are certain events that could disprove Him(or Her?). Alien contact, for instance.

But, on the reverse side of the argument, alien contact could also be proof of Gods existence. It would be a name to the face of the illustrious "Watchers"...Angels, if you will.

Yea, I've been watching too much discovery science...

[hippifried]

The total entropy of a perpetual motion machine and its environment would have to be constant contrary to the second law of thermodynamics.
I believe the gravity powered pump, which has been in use for hundreds if not thousands of years, will continue to run until something breaks or sticks, as long as it stays submerged.

Never was one for obeying the law. :twisted:

I know that's not perpetual motion in the purest sense of the term, butteye don't care because there's always a loophole.

You can rule something out as improbable or unlikely, but you can't prove a negative. To prove that something is impossible, you have to make it positive. "This IS..." The same holds true in Math.


So... Is there proof that "God" doesn't, didn't, or couldn't exist? Of course not. Is that proof that "God" exists? Of course not. Can I prove my answer? Of course not.

[trish]

Of course you can prove a negative. For example, in Euclidean plane geometry triangles don't have four angles, otherwise they wouldn't satisfy the definition of being triangles. There are less trivial examples of course. In the field of real numbers, there is no general solution by radicals of the class of fifth degree polynomials. Such proof can be obtained by showing the proposition is equivalent to a positively expressed law, but the more likely way of proving a negative is to show that it's negation leads to a contradiction.

This thread doesn't ask for proofs that god doesn't exist. It asks instead for proofs that certain specific kinds of gods can't exist. Of course there's no prove that god can't exist, because the concept of god is ill-defined. Once someone proposes a definition of god, then one can hope to prove or disprove the existence of a being that meets the proposed definition.

[hippifried]

Such proof can be obtained by showing the proposition is equivalent to a positively expressed law
Exactly. Or nearly exact. You need to create a positive statement in order to prove it. "This is..., & here's why..."

but the more likely way of proving a negative is to show that it's negation leads to a contradiction.
Contradictions only prove that there's a contradiction & therefore no proof. Lack of proof isn't proof of anything, other than you're begging for an argument.

I don't know how anyone could possibly "prove" that any god or demigod "can't exist". We're human beings. You know, as in NOT omnicient. I'm not so sure we can even prove what we think we do know. If we could really "prove" the "laws" of physics, there wouldn't be this scramble to invent string theory. Although I've never seen any actual evidence of the existence of any god, it's still not proof of non-existence.

Now by default, all monotheists worship the same god, whether they want to admit it or not. If there's only one, it only makes sense that it's the same one. Butif you want to keep the discussion pagan, that's cool. Personally, I kind of like the Hindu version that this is all just Brahma's dream & we better not wake him up or it's all over. Don't think so? Prove it. I think it'd be funny to watch the faces of Christians as they cross over & run into Zeus saying: "What the hell were you thinking?"

[mofungo]

For everything you hold true, the exact opposite is also true. Don't fool yourself, you know nothing and will always know nothing.

[trish]

Theorem: The axioms of Peano arithmetic imply there is NO largest prime number.

Proof: Assume there is a largest prime, call it P. Let M be the product of all the primes (the axioms of arithmetic allow us to multiply together all the members of any finite set of numbers). Consider M+1 (one of the axioms of Peano arithmetic is that every number has a successor). Since both 2, 3 and P are distinct factors of M, P < 3P < M < M+1. Since P is the largest prime and P is smaller than M+1, M+1 isn’t prime. Hence there is a prime number that divides M+1. Let q be the smallest prime that divides M+1. Since M is the product of ALL primes, q divides M. But if q divides M then the ratio (M+1)/q exceeds the integer M/q by a non-zero amount, namely 1/q, which is smaller than one. In other words, q doesn’t divide M+1 contrary to our very choice of q as the least prime divisor of M+1. This is a contradiction. The conclusion reached by every mathematician since Euclid is the negative assertion: THERE IS NO LARGEST PRIME NUMBER.
QED

There are hundreds of thousands of proofs that follow this same general format. Mathematics is littered with theorems and propositions making negative assertions. Here’s one: There is no computable algorithm which can scan any other program P and correctly predict whether or not P will halt in finitely many steps. Here’s another: There’s no general way to trisect a given angle in Euclidean plane geometry with just an unmarked ruler and a compass. And another: There’s no planar map which requires more than four colors if no two countries sharing a length of boundary are allowed to have the same color. Etc.

Now if we assume there’s a god who has powers X, Y and Z and these assumptions alone lead to a contradiction, I think we can safely say there is no god who has all three powers X, Y and Z. If you want to call this a positive statement because it can be put into the form: “if a being has powers X and Y, then it can’t have power Z,” (which is the form of the theorem above) then our disagreement is just semantic. By either classification the argument would still show that such gods can’t exist.

By the way, if you know nothing, then you cannot say "i know nothing" and know it to be true.

[qeuqheeg222]

not that i'm complaining,but do we need a linguistics/mathematics section on HA?this is really good stuff and please keep it up...i havent thought bout geometric proofs and euclidean space in years..thx

[hippifried]

THERE IS NO LARGEST PRIME NUMBER.
Sorry my dearest darling with the huge brain & all that book learnin', but that's an assumption. Allow me to rephrase that for ya.

It is assumed that THERE IS NO LARGEST PRIME NUMBER because to date, human beings have been unable to find evidence of such.

That's a positive statement, & with some research (which my laziness makes me loathe to delve into), it can probably be proven.

Now don't get me wrong. I believe that "THERE IS NO LARGEST PRIME NUMBER", but I have no proof & neither do you or anyone else as far as I know. Especially since mathematics are a human abstract.


Now back to G(g)od/s:

If we assume (maybe this thread should be renamed "evidential assumptions") that any god is omnipotent, wouldn't we also have to assume that such a critter would be immune to paradox?

Where are we going with this anyway? Jesus Quetzalcoatl Aten Odin Vishnu I'm confused. Personally, I'm an idolater. I worship the monolith growing between the boulders downhill from the mountains & above the hills containing the cave of the all-seeing eye.
Aaauuuuuuuuummmmmmmm!!!

[trish]

It is assumed that THERE IS NO LARGEST PRIME NUMBER because to date, human beings have been unable to find evidence of such.

That's a positive statement, & with some research (which my laziness makes me loathe to delve into), it can probably be proven.

Too bad, because I’m waiting with bated breathe. What could this proof be? Who was the first to discover it? Where has it been published? Who’s doing the assuming in the open phrase, “It is assumed.”? How does one accumulate evidence for the logical consequences of an axiomatic system? Why isn’t the proof given above (one that is accepted by all mathematicians) not a proof? Why can’t an human abstraction (the axioms of number theory) prove an abstract proposition (formulated within that very abstraction)?


If we assume (maybe this thread should be renamed "evidential assumptions") that any god is omnipotent, wouldn't we also have to assume that such a critter would be immune to paradox?

That’s not the usual definition of omnipotent (as evidenced by the fact the theologians have been incessantly preoccupied with the paradoxes of omnipotence), but you can expand the definition as you wish. So suppose there was a being who was “immune to paradox.” What would that mean? Would he be green and at the same time, colorless? Would he be both omnipotent and not omnipotent at the same time? Would he exist and not exist simultaneously? If so, then of course he provably doesn’t exist (after all, it’s a consequence of both existing and not existing). QED.


Where are we going with this anyway?

I started this thread for people who want to explore the logical contradictions inherent in certain collections of superpowers…perhaps in the hope (for those who need hope) of finding a suitable set of mutually compatible powers. Human beings are not omniscient. But we don't need to be stupid.

[hippifried]

Human beings are not omniscient. But we don't need to be stupid.
Yeah, but it can be fun from time to time. Besides, periodically it's good to just clear one's mind of all the clutter & nonsense that's needed for us to pretend we're smart.

OMNIPOTENT:
All powerful
Unlimited
I would add - Completely unrestricted - & that would have to include any contradictions that us mere mortals could dream up.

Nice work if you can get it. I'm working on my resume right now for the gig when the next hostile takeover happens. Shhhh... Don't tell anybody.

I'm a big fan of mythology. The one contradiction I've found runs throughout all of it that I've seen. That is the human foibles that have been part of the makeup of all the gods & demigods, & even the omnipotent god of the monotheists. Actually when you look hard enough, they're all pretty much monotheist. Even the various pagans have some uber-creator, whether it's named, unnamed, or unmentionable. The Abramists take the prize for putting the most human foibles on the uber-god. Doesn't make a lot of sense, but it makes for great stories.

Since the dawn of permanent settlement, those that have been too lazy to produce have tried to convince others to support them by claiming they understand the force/s behind nature. Hence the worship of abstracts. All the philosophy, theology, & even the sciences are merely lame attempts to explain what's already there & what we already know. The power is in the byline. Put your name on the idea & everybody thinks it's yours. It's all terribly confusing because none of it's ever really complete. We're not omnicient, but every day we make more extremely complex calculations than all the rocket science that put a man on the moon. We don't even know we're doing it or how. What's the difference which set of abstracts we worship? Ever thought about all the math involved in walking & chewing gum at the same time?

[trish]

OMNIPOTENT:
All powerful
Unlimited
I would add - Completely unrestricted - & that would have to include any contradictions that us mere mortals could dream up.

But what about the contradictions the omnipotent being herself could dream up??? Can she limit herself or not? Is an omnipotent god just a god out of control? That would explain quite a bit.

You haven’t yet explained what it means to be “immune from paradox.” Is it like diplomatic immunity? Does it mean that if god breaks the “laws” of logic he doesn’t have to pay the fine? What is the fine by the way?

You haven’t yet explained why the argument that there is no greatest prime isn’t a proof. Where does it go wrong? In what sense is it an assumption? All proofs, of course begin with a set of premises. Is that all you mean? If so, it should be noted that the premises of number theory are not assumptions about numbers. Rather they, together with the formal rules for the derivation of propositions, constitute the mathematical definition of axiomatic number theory.

You haven’t yet given any support of your assertion that one cannot prove a negative? Let’s call this proposition P. So P asserts “those negative propositions which are not logically equivalent to a positive assertion are unprovable.” What about the proposition P itself. It’s clearly a negative assertion. It has no positive reformulation. Hence P implies “P is unprovable.” In other words P is not some grand law of metaphysics to which we all must bow. P, by it’s own assertion, is unprovable! Indeed, as I’ve shown by example in prior posts that P is even false. There are hundreds of thousands of negative propositions that have been proven.

You don’t have to throw out mathematics and logic to make room for the gods. When you deny the nature and capabilities of the human mind, perhaps you misunderstand the nature of god.

[Kriss]

Some folks say you can’t prove a negative, but that’s simply not true.

It IS true. You can't PROVE anything

THERE IS NO FINITE ULTIMATE PROOF............. ONLY WHAT IS THE MOST LIKELY HYPOTHESIS

[trish]

theorem: the hypothesis that what kriss says is true, follows from truth table tautologies, modus ponens and the hypothesis that what kriss says is true.
proof: we shall assume that what kriss says is true and using only a truth table tautology and modus ponens we shall prove that what kriss says is true. here we go. assume what kriss says is true. the proposition "what kriss says is true materially implies what kriss says is true" is a truth table tautology. hence by modus ponens, what kriss says it true. QED

i'm not claiming this is an ultimate proof...whatever that is. but it certainly qualifies as a proof in the sense the originator of this thread uses the term.

[BrendaQG]

Wow this is a really interesting thread. :-)

In the last couple of weeks, for a course I am taking, I have been brushing up on formal (Boolean) logic. Using this I can prove that negative statements really are proven all the time. Here is what I know.

There are three basic operations in boolean logic. AND OR and NOT. AND and OR combine two propositions. NOT reverses the truth values of propositions.

Theorems are often stated as implications (==>)

So you have a theorem.

If Zeus throws thunderbolts with his hand; Then Zeus is a god.

This is an example of an and statement with a implication. Zeus throws thunderbolts. Literally with his hand implies zeus is a god.

The Negation of this would be to say: Zeus does not throw thunderbolts. Zeus does not throw them with his hand. Therefore zeus is not a god.

The above negative is easily proven. Just open a book about weather and you see that lighting is just static. Therefore Zeus does not throw lighting therefore Zeus is not a god.

QED

[BrendaQG]

Aw :-( Come on we were talking about truth tables and tautologies.... Don't stop.

So ok How about this. Try and disprove this negative.

Given that god (Allah, Yehova, holy trinity) exist, and is omnipotent and omni present with prefect knowledge of the past and future.

There can be no free will.

Scholars have spent centuries trying to figure that out. I think I have the answer I just wonder if anyone here thinks like I do about it.

[trish]

Hi BrendaG. I always find your posts interesting and well worth the read.

I’m gonna disagree with you on what the Boolean negation of “If Zeus throws thunderbolts with his hand, then Zeus is a god” is. The sentence in question is of the form “p->q” which is the Boolean equivalent of “~p or q”. The negation is “~(~p or q)” which, by De Morgan’s Law is equivalent to “p & ~q”. This means the negation of “If Zeus throws thunderbolts with his hand, then Zeus is a god” is “Zeus throws thunderbolts with his hands, yet he isn’t a god.”

Nevertheless, I do think you’re on to something. Let’s instead start with the premise that “Zeus is a god who can throw thunderbolts with his hands.” Let’s also accept the premise that thunderbolts are electric currents conducted via water vapor in the atmosphere. It makes about as much sense to throw an electric current as to throw the Jet Stream or the Mississippi River; i.e. no sense at all. Since thunderbolts are just not the sort of thing that can be thrown, there is no god, or anything else, that throws them. Consequently Zeus doesn’t exist.

For those who like to obsess over vacuous notions like absolute and ultimate proof I include a caution, namely: we only proved Zeus doesn’t exist from the “definition” that Zeus is the god whose throws thunderbolts together with the premise that lightning is an electric current. One could still maintain Zeus’s existence, but one would either have to modify the above definition of Zeus, or the definition of throwing thunderbolts, or (as an act of crazed desperation) modify the premise that thunderbolts are electric currents.

I like your "free will" challenge, BrendaG. I'll have to work on it. :)

[trish]

So ok How about this. Try and disprove this negative.

Given that god (Allah, Yehova, holy trinity) exist, and is omnipotent and omni present with prefect knowledge of the past and future.

There can be no free will.

Scholars have spent centuries trying to figure that out. I think I have the answer …

I’m not sure if I believe in free-will or not, or even if I know exactly what it is. But I don’t think complete knowledge of what will happen negates the possibility of free will. Here’s why.

The phrase “what will be, will be” is tautologically true. Being a mere tautology it can’t entail the non-existence of free will unless the notion of free will itself is already a logically contradictory notion. The notion of free will seems (to me) to be a synthetic notion as opposed to analytic or something that can be known a’ priori; i.e. I don’t think the concept of free will by itself is logically inconsistent. If “what will be, will be” doesn’t contradict the notion of free will, how could mere knowledge of what will be entail a contradiction? I realize this isn’t a proof. I merely offer it as a response to your query,
…I just wonder if anyone here thinks like I do about it. I’m anxious to hear your take.

[mofungo]

No one has 'the answer'. Trish, myself, and everyone else are equally unable to provide a 'solution' to life's little problems. Perhaps Trish is less able because she is trapped in her philosophy. When one endorses a philosophy, one becomes a bigot.

[trish]

have i claimed to have "the answer"? have i even claimed to be in pursuit of "the answer"? i don't even know what "the question" is to which you refer.

i've made my aims in this thread quite explicit and quite modest: to see what assumptions about god lead to nonsense. what's so alarming about that? does this pursuit make me a bigot?!! or is the bigot the one who needs to put a limit on just how far this sort of questioning is allowed to go?

perhaps mofungo could tell us what philosophy i endorse. i don't recall doing any ads, and i certainly didn't get paid for any.

[BrendaQG]

That's all very good I take it that in what you typed ~ means not.

The issue you raised about negation came up in a lecture. You transformed a implication into a or statement. This mistunderstanding is totally my fault. What I should have said is.

Zeus is a god if and only if zeus throws thunderbolts

Let's see if that works in general. Consider this truth table.

P Q P<==>Q ~P OR Q
T T T T
T F F F
F T F T As you see in this last line the double implication and ~P OR Q. Do not match. It is totally my fault for not using the correct symbol though.

As for the free will question. I see that I should add one other piece.

Given that god created the universe.

If god is omnipresent, omnipotent, with perfect knowledge of the past and perfect knowledge of the future; Then there is no free will.

The propositions are. God is omnipresent, omnipotent, and knows everything that has happened or could ever happen. There could not be free will because if god created everything and knows what will happen because god predestined everything.

Here is what I think the answer is.

In quantum mechanics one thing we learn about is the entanglements of different systems. Especially if those systems are interacting, but even if they are not. In relavitiy we learn that systems evolve from past to future along a path never going backwards but depending on past history. One effect enforces a time line the other allows something that happens to effect a quantum state elsewhere with no speed limit (hence past future and present entangle up into one big mess).

From those two things I can explain what I think.

God does in fact know all the possibilities, everything that could have happened, everything that does happen, and every thing that could happen in the future. However GOD being omnipotent means god takes actions to change that future, Which means that god exercises free will. Since god can exercise free will, through omnipotence, then free will must exist. By changing the future god disturbs the pure perfect state that he had established and by creating other possibilities, free will is born.

Man can change the future by his/her deeds but only god has 20/20 foresight

As sallam-ul-lakium

[Quinn]

Great thread. I'm really enjoying this.

-Quinn

[BrendaQG]

Trish.

When you wrote ~PandQ did you mean (NOT P) AND Q or NOT (P AND Q)?

Quinn.

Tell me about it.

[trish]

just checking in for a moment.

i agree, we're having fun.

yes, i did mean ((not p) and q).

i think your revised Zeus argument works fine. i'll have to get back to you on the free will argument.

[trish]

A very thoughtful post; thanks BrendaG.

For the moment, let’s accept your premises:

There’s a unique god that created the universe, is omnipotent, omnipresent and omniscient concerning future and past events. Also we’ll accept as premises the current understanding of relativity and quantum theory.

Your claim is that these premises do not prevent that god from exercising free will. If I understand the argument it goes like this. Even though god knows event E will occur, his omnipotence allows him, should he wish, to exercise free will and change the future so that event E won’t occur. I think you’re implying that this isn’t a contradiction because what happens instead of E is a superposition S of pure states that include E. (Perhaps you’re even implying that his decision to change E recreates the past so that now his prediction was S and not E. If this is part of your argument please let us know).

My own take on this is that S isn’t E and is physically distinct from E. If S occurs instead of E then I think god’s omniscience is compromised. But that’s just my humble interpretation of this difficult puzzle. On the other hand I may have just totally misunderstood your argument, and if that’s the case please try again.

I’ll suggest a modification of your argument I could be comfortable with. God knows E is going to occur. He exercised his free will during the design phase of the universe.

Another modification I could live with: God knows ahead of time what he will choose to do, but he still ruminates, reasons, deliberates and chooses. You know you’re going to choose to brush your teeth in the morning, right? But you still choose to do it each morning. What this shows, I think, is that knowledge of a future decision doesn’t conflict with free will.

At this point I should be honest and confess that I don’t think omnipotence is a consistent characteristic that a god can have…unless one defines it very carefully (“the rock so heavy…” paradox comes to mind for example). I’m also suspicious about omniscience but presently I’ve no argument to offer against the possibility of omniscience.

[Rogers]

Gotta love cats! IF only we really knew why they do the things they do. :?: :?: :?: :!: :!: :!:

[trish]

hi rogers,

ya got me...i just can't seem to avoid those "if's".

[Rogers]

Seems I've killed your thread, trish, and spoiled the fun. That was not my intention. :(

[trish]

I originally meant the thread to explore which combinations of "if's" lead to a contradictory notion of god. I was just going to sit back and let intelligent people (BrendaG, Quinn, qeuqheeg etc.) contribute. This is an exercise that should be of interest to believers and non-believers alike (most people here know that I belong to the latter). I didn’t think I have to explain so often what a proof was, that proofs were possible and axiomatic systems are known to entail negative propositions. Oh well, live and learn. I don’t think you killed the thread, Rogers…though I blame you for introducing the first cat.

[Idgaf]

But has anyone read either God The Failed Hypothesis
http://www.amazon.com/God-Failed-Hypothesis-Science-Shows/dp/1591024811/ref=pd_bbs_3/104-8200763-0857526?ie=UTF8&s=books&qid=1191889128&sr=8-3

or The God Delusion by Richard Dawkins
http://www.amazon.com/God-Delusion-Richard-Dawkins/dp/0618680004/ref=pd_sim_b_1/104-8200763-0857526

[Rogers]

I didn’t think I have to explain so often what a proof was, that proofs were possible and axiomatic systems are known to entail negative propositions. Oh well, live and learn. I don’t think you killed the thread, Rogers…though I blame you for introducing the first cat.
I think I've got you now, trish. I think the closest approximation to what you're after in my vocabulary may be, model scenarios. I never realized just how little I knew about mathematics, and just how different the scientific and mathematical methods were... seriously! :oops: I've always thought that mathematicians were a strange breed... one guy I used to work with only ever had a single pencil and a single sheet of paper on his big desk, and that was it. :) I think I better put this pic up again and stick to being an agnostic. I far prefer to test the observable.

[hippifried]

But has anyone read either God The Failed Hypothesis
or The God Delusion by Richard Dawkins
Nah. Why bother? I already know what I think about the subject, & at my age, I don't have time to worry about what some obscure would-be philosopher going for another degree thinks about anything. Well... Not enough to strain my eyes on some tome anyway. Is it out on DVD yet?

So I forgot, & I'm too lazy to backtrack. Are we trying to prove there is or is not a God? WHY??? I'm staring at my calculator, & can't for the life of me figure out how to work this question into a math equasion. I know that 3 apples plus 2 oranges equals 5 fruits, but that doesn't tell me how many kiwis to put on top of a banana cream pie. Oh well... I can play God by adding some walnuts & celery, & turning the whole thing into one of my imfamous waldorf salads. Trust me... It's Heaven. It really does exist.

[trish]

So I forgot, & I'm too lazy to backtrack. Are we trying to prove there is or is not a God?

No, we aren't. Our goal in this thread is to refine the our picture of god to avoid contradictory attributes.

[hippifried]

Oh... :shock:

Ok...

[hippifried]

Oh... :shock:

Ok...