Nevermind the future. Prove to me empirically that an apple has never before fallen up. And if you want to evoke the can’t-prove-a-negative nonsense, then prove to me empirically that an apple must fall down. When you’ve finally given up this silly line of attack, you will realize that your best proof is not empirical at all, but rather is a mathematical formula that is derived from and follows strict rules of first order logic.
A person who believes that it’s even possible for gravity to have ever ceased working is the one who’s being silly, not me. But I’ll forge ahead anyway.
Fossils demonstrate that the law of gravity has always been in force on the planet Earth. If stuff didn’t always fall down, then how did those bones get into the mud to become fossils? If the law of gravity has always been in force, then everything (which includes apples) has always fallen down.
The existence of the Earth itself demonstrates that Gravity has always existed. If gravity has ever failed in the past, then its orbit around the Sun would have changed and there would be evidence of it. There is none. If gravity did not exist, the Earth would not be spherical in shape (though not a perfect one), the Moon would not orbit it, meteorites and other objects would not have impacted its surface.
Experiments by physicists have demonstrated that gravity is an inherent characteristic of mass. IOW, you can’t have one without the other; if there is mass there will be gravity. Gravity works only in one direction, towards the center of mass. So, for as long as there have been apples, apples have fallen down, towards the center of the mass of the Earth, stopped only by the Earth’s own surface.
Now who’s being silly?
Lib:
Your definition of possible worlds does not adequately explain what they are. You tell me a property of possible worlds (they contain one true propostion) but not what they are. Luckily there are clearer definitions out there:
“David Lewis thinks that all possible ways that the universe could be is a way that some concretely existing universe really is. Moreover, cosmoi and universes are the same for him. Thus, worlds are concrete universes. A world represents some cosmos if it is that cosmos. The actual world is the world we inhabit.”
“A propositional Ersatzist may take a world to be a maximal collection of compossible propositions.”
“Leibniz, on the other hand, thinks that worlds are maximally consistent ideas in the mind of God. The actual world is the idea that God has chosen to actualize.”
Yes, there are many different ideas on what a possible world is. Lewis believes possible worlds are other ways our world could have been, and that they actually exist. Others believe a possible world is simply a maximal collection of compossible propositions. Leibniz believes possible worlds are maximally consistent ideas in the mind of god. You may agree with one of these. I have been unable to determine your actual belief about what possible worlds are.
The point I am making is that, whichever of these views of possible worlds you take, possible worlds are completely irrelevant to god’s existence. Any proof that uses possible worlds can in no way be used to prove god’s existence. Why? Well, you already seem to be on the right track:
This is a misleading statement. Putting aside possible worlds and the proof for a moment, our world does not have to have been created by god. Now lets put possible worlds in again. Now the proof shows that god did create our world. So, we proved it, right?
Wrong. For a very simple reason: possible worlds can not exist without god. Any proof that uses possible worlds is presupposing the existence of god.
Think about it; if there is not a god, then everything is necessary because there is nothing that could change anything. All circumstances follow inevitably from other circumstances. In other words, if god does not exist, there can be no possible worlds. Whatever exists in our world is necessary.
Leibniz and Lewis seem to understand this, and I have no idea why you still don’t see it. Possible worlds are other ways in which the world could have been. But what could possibly cause these worlds to be different? The ONLY answer is god. Only god exists without a cause. Nothing else could cause a world to be different.
You are making the false assumption that modal logic can be applied to god. If you accept that modal logic can be applied to god, then the proof is valid. The problem is that modal logic requires the premise that god is possible. The problem is modal logic itself, and its use of possible worlds. Possible worlds can not exist without god. By its very nature, modal logic presupposes god’s existence. Therefore a proof using modal logic to prove god is meaningless. Modal logic can be useful in many things, but it can not be used to prove god because it already presupposes god. Possible worlds = god. There is no way around it. Do you not see that you can’t use a form of logic that presupposes god in order to prove god?
I haven’t said what I believe about the matter.
No compelling evidence so far. From what you’ve said, we have no way to know whether any fossils didn’t just float up into space. Have you counted them all and compared them to the known number of fossils that have formed?
Actually, the earth’s orbit is eccentric, varying between 0 and 0.06 every 100 000 years, but nevermind that. At least you’re making progress by using one of those dreaded logic devices, the Law of the Excluded Middle. By positing the opposite (“if gravity did not exist”) of what you wish to prove (gravity does exist), you may prove its opposite false, and thereby prove the original assertion true. That works because of another device of contemptible logic, the Law of Noncontradiction, which states that either A or Not A is true. If A is true, then Not A is false; and if Not A is true, then A is false.
Even despite the deficiencies in your descriptions, let’s give you that you proved soundly that the earth, the moon, and some meteors are driven by gravity. You haven’t shown that this is mere coincidence. Why must these bodies do these things?
I think it might be more precise to say that gravity is the mutual attraction between two objects that have mass. Given how we define gravity, we should be able to derive a general formula and show why apples must fall down.
Let’s posit two bodies, A and B, with mass. If gravity depends on mass, as per the definition, then that dependency can be represented as a product of the masses: m[sub]A[/sub]m[sub]B[/sub], the mass of A multiplied by the mass of B.
Because gravity is a relation between two bodies with mass, we may posit that the distance between them is a factor of consideration. Attraction implies that there is some distance between the bodies of somewhere between 0 and [symbol]¥[/symbol]. Because we’re dealing with distance, we can discard negative numbers.
As the distance between two bodies increases, we can assume that the attraction diminishes, since remoteness implies a diminished influence. Let’s call the distance between the objects r, measuring from the center of one body to the center of the other. The relation in distance may be expressed as 1 / r[sup]2[/sup]. We square r because the attraction, as defined, is mutual; thus, the distance for each body from the other must be a factor of consideration, so r * r.
Multiplying m[sub]A[/sub]m[sub]B[/sub] * 1 / r[sup]2[/sup], we get m[sub]A[/sub]m[sub]B[/sub] / r[sup]2[/sup]. So far, we have accounted for the relation of gravity in terms of mass and distance. All we need now to describe the magnitude of its force (c.f., Newton’s Third Law) is to account for its strength. The strength increases as the masses increase but diminishes as the distances increase; therefore, it should be multiplied by the masses and divided by the distances.
Let’s call the factor of strength, G. We can now state the entire dependency relation of the magnitude of gravity’s force:
F[sub]g[/sub] = Gm[sub]A[/sub]m[sub]B[/sub] / r[sup]2[/sup]
The apple must fall unless it is one hellaciously large apple, in which case, according to the formula, it will pull the earth up.
[…shrug…]
That should have been Newton’s Second Law.
Night
Well, I can’t claim it as my definition. It is the standard definition from modal logic and is derived from the definition of possible itself: <>A = ~~A.
David Lewis is engaging in Doxastic Logic.
But that is a world, not a possible world.
Again, I don’t see a reference to modal logic’s possible worlds.
Your ecclectic listing notwithstanding, it might behoove us, when dealing with a modal tableau, to stick consistently with principles and definitions from modal logic, no?
I can see why — after all, I haven’t said it forty times yet. Let me strive toward that goal: A possible world is a world with at least one true proposition. With patience, you’ll soon be able to determine my “actual belief” about what possible worlds are.
You will recall that in this proof, God’s existence is, by definition, not merely possible, but necessary. Your heartfelt yearnings notwithstanding, all that is required to prove His existence is to show that He exists in all possible worlds, thereby proving that the defined being exists.
Well, I suppose we might as well put them aside; certainly, you have. At any rate, if there were no truth, there could be no possible worlds. In case you’re not clear on what a possible world is in this context, it is a world with at least one true proposition. Thus, truth is a prerequisite to possibility.
I’m getting dizzy.
Right.
Oh, drat.
I thought you said that that is misleading.
Nope. Possibility is not enough. A cow is a bovine, but a bovine is not necessarily a cow. The worlds could have come from God (and, as I said before, it is a trivial proof to show that they must come from God), but God could not have come from the worlds. God, as defined, must exist necessarily (in all possible worlds).
There’s so much wrong with that that I hardly know where to begin.
First, I see no reason to equivocate with the term “necessary”. It doesn’t mean things change; it means truth in all possible worlds. Second, it can be shown that, in our actual world, there is much uncertainly (Heisenberg) about circumstance. And finally, if you assert that “whatever exists in our world is necessary”, then you assert that nothing in our world is false. Therefore, “I am the best looking man on earth” is true. In fact, with one fell swoop, you’ve knocked the Law of Noncontradiction on its ass, because you, too, are the best looking man on earth. So is Jab. And don’t forget Vorlon.
I’m just dull, I guess.
Are we leaving modal logic again?
I’m sorry, Night, but as you’ve clearly demonstrated, I’m too slow witted to keep up with this roller coaster. I have a very difficult time flipping my brain inside out repeatedly in order to change subjects five times in one paragraph. I don’t know what more to say. Except maybe this: a possible world is a world with at least one true proposition. 
Night
That deserves separate consideration, especially given Jab’s come-lately resurrection of the topic of logic’s tautological nature.
That fact is that what you’ve said in the quote is true, and applicable much more generally than you might like. All closed epistemic systems (including logic) are inherently either contradictory or always true. You can know nothing for a certainty because you always assume the validity of the system itself.
You not only cannot prove God’s existence, you cannot prove your own. Why? Because before you can do anything at all, including prove your existence, you must first exist. That makes your existence axiomatic. Because your conclusion — that you exist — is the same as your axiom — that you exist — you cannot escape arguing in a circle. Thus, reason is fried by its own law of Circulus in Demonstrandum.
Certain knowledge requires immediation from an open epistemic system where truth is absolute. In doing our little logic exercises and our little science experiments and so on, we are constantly appealing to an open epistemic system. This is called “faith”.
Lib:
Is that forty already? I admit I am having trouble understanding this definition, though not because I am ignoring it. It seems to me that if a possible world is simply a world with one true proposition, then you are already assuming that there is some absolute truth that you can apply to this world. On the other hand, it is possible to imagine a world in which propositions are true because they are internally consistent with that world at a given moment, rather than with absolute truth. I do not know which “true” you mean. Also the definition does not state whether possible worlds exist or not, and it does not state whether possible worlds are other ways our world could have been or not. There are three possibilites:
A. Possible worlds are other ways our world could have been.
This presupposes god. If a world is a way our world could have been, and that world contains truth, and yet it is not our world, there must be some power greater than the world, and there must be some truth that can be applied to the world.
B. Possible worlds are not other way our world could have been.
This means that possible worlds are irrelevant to us, so there is no point talking about them.
C. Some possible worlds are other ways our world could have been, some are not.
Look at each world, and throw it into either A or B.
In any case, possible worlds can not be used to prove god, because they are irrelevant to god. If anything, you could use god to prove possible worlds, but not the other way around.
- If god exists, he exists in all possible worlds.
This is technically true, IF you are using a standard of absolute truth (god) to judge the truth of the one true proposition that constitutes a possible world. If possible worlds only need be internally consistent, then you could just imagine a world without god to disprove him, so you must be referring to absolute truth. While it might be technically true, this premise is misleading because it makes possible worlds seem more important to god than they are. A more accurate premise would be:
- If god exists, he existed before all possible worlds, and in all possible worlds.
Existing apart from possible worlds is important, because the first premise allows us to treat god as though he is limited by possible worlds.
- God exists in at least one possible world.
This is clearly a bad premise. You have already admitted that it is impossible for god to exist in only one possible world, and yet you defended this premise by saying it is unavoidable. If something is clearly wrong, is calling it unavoidable really a defense? Perhaps if wrongness is unavoidable in a certain proof, the proof should be discarded? The reason this premise fails is that possible worlds are irrelevant to god. They are dependant on him, he is not dependant on them. Therefore “in at least one possible world” is irrelevant, because possible worlds have no power over god. A more accurate premise would be:
- God exists.
It seems to me that it is impossible to prove god, because god will always be more fundamental than whatever logic you attempt to prove him with. In fact, as you have said, whatever logic you try to prove him with will be dependant on him, and therefore you will be arguing in a circle.
I agree. This proof relies on faith. And I guess it proves that believing in god is logical, because assuming you have faith, you will reach a noncontradictory conclusion. In other words, faith does not contradict logic.
I will also agree with you that science, as far as it requires absolute truth, is appealing to faith. But this is where we may part. Logic and science may assume absolute truth, and in doing so may be appealing to faith, but their conclusions do not rely on faith to be useful! I have already said that if you treated the proof like we treat science (black holes, for example) that the proof would show that god is a useful idea for explaining things. It just can’t be used to definitively prove god’s actual existence. The reason we have science is not to definitively prove things, it is to come up with explanatory and useful theories, which we may accept as absolute truth, but which do not have to be absolute truth to be useful. Perhaps our world is the only world, and perhaps there is no absolute truth, but our world only need be internally consistent at any given time, and perhaps not even that. Logic and science may require faith as part of their process, but their results are useful even in a world in which we do not know if there is absolute truth.
Night
I can’t follow your discussion about truth. Rather than taint it with my own misunderstandings, I’ll leave it alone as an internal dialog between you and yourself and just offer general philosophical treatments of truth as I understand them. The main schools I’m familiar with are Coherence, Identity, Correspondence, Deflationary, and Revision.
Basically, the Coherence Theories hold that the truth of any proposition is contingent on its coherence (i.e., “systematic or logical connection or consistency”) with specific sets of propositions. Identity Theories (probably the most controversial) maintain that for every true proposition, there is an agent of truth called a “truth maker” (also known as a “fact”). Correspondence Theories have morphed lately from their original view that truth is correspondent (i.e., conforming) with fact to a newer interpretation via Russell and Moore that reality relations comprise truth. Deflationary Theories (also called Redundancy, Disquotational, and even No-Truth) do not view truth as a product of epistemological inquiry, but rather as mere statements that are assertions; for them, basically, truth is something that isn’t there.
One of the most recent schools consists of the Revision Theories, developed by Gupta and Herzberger in the late 20th century to deal with paradoxes. It is a rather weird theory set (the Quantum Mechanics of Logic, some call it) wherein truth is defined as a “Tarski biconditional”: S is true if and only if P, where S is the name of the sentence and P is the sentence of the language. Consider the assertion, “This statement is false.” Once considered not a proposition at all, the assertion is a proposition in the Revision school and — here’s the weird part — it is true if and only if it is false. We could deal with it further here, but sources are available online if you wish to pursue them.
At this point in the discussion, after you and I have gone round and round, it might be a good place to shake hands, agree to disagree on many matters, and satisfy ourselves with having found common ground on at least one matter: “faith does not contradict logic”. Well said, Night.
Really? If all the mass in the universe were represented by a single body, that body would have no gravity field?
All the rest of that was nice and looks correct, but if you already knew that, why did you ask me to explain it?
I wanted to illustrate that logic has an important role in epistemic systems, including science. Empirical evidence is only a part of the picture. An important part, but certainly no more important than reason and experience.
Lib, do you or do you not believe that empirical evidence is necessary to establish the existence of God?
Faith does not contradict logic, and logic cannot replace faith.
We can see objects seemingly being pulled towards something in space, and we accept this as evidence. We have a concept of black holes, and since the evidence (apparent strong gravity) fits the concept (extremely dense object) we can believe the evidence supports the concept.
We can see that we exist, and the universe exists, and we accept this as evidence. We have a concept of god, and since the evidence (existence) fits the concept (creator) we can believe the evidence supports the concept.
There is no way to prove god, simply because he is more fundamental than anything we could use to prove him. Nothing is adequate to prove god, because he outclasses everything. He depends on nothing. However, the problem is not that there is no evidence of god. The problem is that either everything is evidence of god, or nothing is evidence of god, and we can’t know which.
It was for me.
A careful and limited definition of God is needed to be able to argue about the existence of God.
The prevalent argument here defines God in terms of aseity. That’s the must-be-ness of God, described way at the top like so:
q -> Nq.
Or, as the burning bush allegedly said to Moses, “I am that I am” (thatIamthatIamthatIamthatIam…)
Either there’s some first cause that has aseity, or there’s not. This first cause need not be omnipotent… in fact, it’s not, because God cannot become non-existant. It also need not be intelligent… perhaps it is a probability function, canonized along with:
if there are things
and two things are added to two things
you have four things.
or
if there are circles
then the circumference of the circle divided by its diameter is a precise number that’s a little bit more than 3.
Note that aseity doesn’t have anything to do with finding a perfect, or omnipotent, or loving being. I don’t think the latter question is logically debatable.
On another note: if it is proven that the universe will not end in a big crunch, followed by another big bang, does this mean that scientists have failed once again to disprove the existence of God?
- This universe was not spawned by another identical universe
-because no universe identical to this one can spawn another universe. - Either God is the first cause of the universe, or a different, un-like universe is responsible for this whole shebang.
- If there is a chain of different universes (larger or whatever), either the chain goes back forever (an end but no beginning), or the chain does ultimately go back to a first cause (i.e. God).
Engywook
Welcome to Straight Dope Great Debates.
Why not? God becoming nonexistent would simply mean that all true statements would become false. All worlds would cease to exist, not because God is all worlds, but because all worlds would become not possible.
I can’t find any question (let alone a latter one) preceding that assertion. At any rate, aseity merely means “from the self” (Latin a: from, se: self). You may say that n [symbol]®[/symbol]n implies aseity, but that is tangential to the argument and is not biconditional.
Now you’re equivocating. God, as necessary existence, has been proved to exist. But God, as aseistic existence has not. God need not have “caused” worlds to be; rather, they exist simply because He does.
A difference only a philosopher could perceive.
Tris
“You can tell whether a man is clever by his answers. You can tell whether a man is wise by his questions.” ~ Mahfouz Naguib ~
— “A Philosopher on Wonder and Beauty”, Jesus the Son of Man, Kahlil Gibran
Lib, here is a link which you may truly enjoy reading on the subject. It seems very comprehensive and deliberately open-ended.
http://www.stats.uwaterloo.ca/~cgsmall/ontology.html is a wonderful link as well. It spans several pages, though. Quite involved.