But God has never done an impossible miracle. Sure resurection, water to wine, plagues. etc. are all beyond human ability. But those miraculous events are not contradictory with themselves. A planar circle with area not equal to pi r[SUP]2[/SUP], or a four sided triangle, or a unit value that added to another unit vale equals three unit values, these are things which are self contradictory. Part of the premice of the OP is that such things are imposible even for God, because they are fundamentaly impossible.
You can still say ‘there is nothing God cannot do’, but a four sided triangle is a ‘nothing’.
You’re on the right track, but note that I said above, Keep in mind also that the question is not so much “Is there a God?” but rather, "What, if anything, is what people refer to as God?"
There are powers higher than we–many–but they are subordinate to the fundamental laws of pattern and number.
Actually, I believe in the divine. It is not synonymous with “the universe.” I believe that the Divine is a tendency within the universe. To wit, the furthering of sat-chit-ananda, or being-consciousness-bliss. The universe aims for greater being, greater consciousness, and greater bliss. It does so through life, through sentient/conscious entities, and, eventually, through the afterlife. That which furthers this vector we call “good”; that which inhibits it we call “evil.” The will to further this vector we call “love”; the will to inhibit this vector we call “hatred.”
This also explains how evil is possible in the universe: the divine is a tendency, not an absolute. But this also explains our intuition that “good wins over evil.” The overall direction of the universe is toward the good.
The meaning of life? To further the vector. You can further the vector in an infinite number of ways. Love people. Create beauty. Work. Sleep. Anything that furthers being-consciousness-bliss has meaning, actually adds to the divine, increases it. And I think this matches our intuition that life does, in fact, have meaning.
Your last post (#43) was quite beautiful, Aeschines.
I don’t think it is necessary for us to agree on your explanation of pattern and numbers; spiritually, I really like the way you gave a clear description of a reason why it is possible to have a strong sense of ethics without resorting to the omnipotent creator hypothesis.
Sure, mathematical truths might hold in other possible universes. Assuming, of course, that logic applies to them (frankly, I am not sure it even applies to our own.) Let’s assume they do for now.
Even then, all of the mathematical truths we know may still be true in that world, but rendered meaningless, like if I tried to convince you that “Some xygloxergies are polyspeetronicists” was one of the prime maxims of the universe. A nice toy but utterly meaningless.
Mathematics is nothing special; it is just a tool we use to analyze our reality. Granted, it is a bit more fundamental than science, since it seems to get closer to metaphysics than science, but nonetheless, concepts do not have a meaningful “existence” like the quotes from the OP claim.
**Aeschines ** seem unconcerned with such comments. It looks like he has “faith” that mathematical properties of our universe have an independant existence (whatever the universe and even whether or not there is an existing universe), in the same way some people have “faith” god exists, and he’s unwilling to take into account any comment to the contrary.
I can understand why someone would think at first glance that this ratio is necessarily equal to pi, since it’s a property of the universe we’re living in, and it’s essentially impossible to “grasp” an universe with different properties, but since he has (assumedly) put a lot of thoughts in this issue, he should at some point have understood that what appears to be “common sense” isn’t necessarily true, especially when refering specifically to an alternate universe.
These comments are pretty much word for word what you said before. To repeat, you are gratuitously asserting that a different mathematics is possible in an alternate universe. You need to prove that. I am asserting otherwise. It is not “faith,” it is an appeal to our power of understanding, pure and simple. 2 + 2 = 4. IT COULD NOT BE OTHERWISE. Anywhere. Either you perceive this or you don’t. Can it be proved? Absolutely not. But without the facts of mathematics being taken for granted, absolutely nothing coherent about this or any other universe can be stated.
So, how are you dismissing ** MC ** statement to the effect that the ratio between a circle’s circumference and diameter isnt necessarily equal to pi in a non-euclidian space?
Non euclidian mathematics precisely use basic assumptions which are different from the euclidian mathematics we are used to but still are internally coherent, which is the only thing which matters.
You stated yourself that in an alternate universe where pi wouldn’t be equal to 3,14…, one could conceive an euclidian universe where it would be true. It seems to me akin to admitting that indeed, one can conceive universes where pi takes various values, hence that this value isn’t some sort of “meta-universal” and eternal truth, but a specific property of a given universe.
You’ve pretty much supplied the argument for me, except for the last sentence. “Pi” as 3.14… is NOT a property of “our universe.” There is no such thing as a perfect circle in our universe, and it is likely that space itself is curved to some extent in any location. Please see my point again about mathematics NOT depending on the physics of any particular universe.
Pi, rather, IS a property of a circle in a two-dimensional space. You keep cherry-picking arguments here (and are, in effect, turning this into an argument about pi, which has been dealt with elsewhere–did you see the link someone posted?) but have yet to answer my question, Could our universe be the same except with 2 + 2 = 5? No, and God can’t change it.
I didn’t adress this question because I’m not convinced it makes any sense.
First, asking if something would be the same if it was different would be what we call a “Lapalissade”, here, after a guy who was told to be still alive until he was dead. IOW it doesn’t make sense.
Second, I’m not convinced that saying 2+2 = 4 is anything else than a tautology, or stated otherwise a different way to define exactly the same thing, rather than a mathematical relation. We would need a mathematician to chime in, but I strongly suspect that saying 2+2=4 is exactly the same thing that saying 4=4. In other word, your asking whether something can be what it is not.
Finally, and more importantly, I fail to see in what way it’s relevant to your OP. Asking whether our universe would be the same given different conditions don’t adress at all the issue of alternate universes , which, by definition, wouldn’t be our nor the same.
I would add too that you’re assuming that the concept of “two dimensional space”, for instance, would actually have sense, or could be conceived in these alternate universes. I see no reason to assume that, either. We can’t know anything about these universes. It still falls down to your assumption that there are some universal concepts, mathematical or otherwise, which would hold true in any universe, or even more arbitrary, in the absence of any universe. It’s akin to state that space, for instance would exist, at least as a concept, if there wasn’t any universe (hence any space).
I see no difference between the belief in an everlasting god and in an everlasting “pi” (or whatever else) . And you failed to give evidences for a mathematical concept to exist in the absence of anything else. As far as I can tell, if nothing exists, then mathematicalc concepts don’t exist, either.
I would like to add that perhaps space doesn’t exist in our universe in the popular sense anyway. Space is a human conception developed upon our perception of light in relation to our other perceptions such as time and mass. Three dimensional (or four dimensional, or two dimensional) space is construct that we use in order to deal with the perceptions which we experience but we can’t be sure that those dimensions exist in any way apart from our conciousness. Thus the geometrical maxims that the OP refers to are merely tools which we use to understand a construct of our own creation. It is like saying that a centimeter is ten milimeters no matter what, which is true, but that doesn’t really say anything of absolute truth since both centimeters and millimeters are human constructions created to help us understand our perceptions of space (which is also a human construction).
I would like to add that perhaps space doesn’t exist in our universe in the popular sense anyway. Space is a human conception developed upon our perception of light in relation to our other perceptions such as time and mass. Three dimensional (or four dimensional, or two dimensional) space is construct that we use in order to deal with the perceptions which we experience but we can’t be sure that those dimensions exist in any way apart from our conciousness. Thus the geometrical maxims that the OP refers to are merely tools which we use to understand a construct of our own creation. It is like saying that a centimeter is ten milimeters no matter what, which is true, but that doesn’t really say anything of absolute truth since both centimeters and millimeters are human constructions that have no value other than that which we have given them.
factually incorrect. You are either lying or, more likely, are merely ignorant. mathematically principles are a method of taking assumptions about reality and based in logically coterminus originas and endings (so its congruent to reality). It makes no assumptions that other existences could or could not be possible.
In other words, we believe 2 +2=4 because we have seen that 2+2=4. Hhis is not neccessarily an objective fact. It is the product of our perceptions, and appears to be accurate. But we could be wrong.
That is also possible. In fact, unless we experimented in all possible places and times in this universe, we could not actually prove that 2+2=4 everywhere in this universe.
Yes, God could make a universe where 2+2=5. Or where Pi=3.00… More to the point, there is probably nothing special about our particular mathematical constructs, which likely apply to the universe as a whole, barring black holes and other spacial phenomena. it might be that 2+2=4 everywhere in every universe. maybe God likes math. Maybe not. If you’d like, when I die, I’ll ask God about it.
According to some branches of physics, the universe’s rules and physical laws are really nothing more than the product of chance, formed when the quagma (maybe) erupted into existence. At that “time”, natural law was undefined.
Now, I think it probably that certain concepts, such as 2+2=4, are essentially the easiest way to go and most likely for a universe, but that’s just a personal opinion.
Not “factually incorrect”–since it’s not a matter of empirical fact. It’s a philosophical matter, and, as I’ve recognized elsewhere in this thread, philosophers DO disagree with each other on this. Your tone is rather insulting. But let’s move on.
No, we can’t be wrong. As I have stated elsewhere, there are NO experiments being performed to determine whether 2 + 2 = 4. No such experiments are possible.
As no such “proof” or experiment is possible, there would be no way to test to see if this is true in all times and places. Since there is no way to test for it here, there is no way to test for it ANYwhere. That’s what I meant by 2 + 2 = 4 holding true in all possible universes. And it certainly would hold true.
You’re right that there’s nothing “special” about our mathematics; it’s true, it’s universally true, and that’s all that’s required of it.
Absolutely. These “laws” or properties could be otherwise. But the truths of mathematics could not.
Easiest to do WHAT?
That’s precisely right. And one truth of logic is that something cannot be what it is not. God can’t change this; nothing nor anyone can. But this is not the only truth of logic. These truths are can be recognized and built upon so that we can do nice things like empirical science, etc. These truths are the absolute foundation of That Which Is.
It’s pretty simple. God, as conceived monotheistically, doesn’t have the power to alter the fundamental truths of pattern and number. He is, in effect, subordinate to them.
Second, “alternate” universes as conceived of in modern empiricial science DO NOT assume different principles of pattern and number. Rather, they ASSUME that the same principles hold true. Hence, anyone who would like to attack the OP argument by blithely stating, “Well those rules could be different in an alternate universe,” is positing that such a thing is possible, and the burden of proof is on him or her. My argument says nothing about alternate universes, and I believe that the concept itself is meaningless to the argument I have presented. (If I speak of “different worlds” in this or other posts, I am not speaking of “alternate universes.” For example, the afterlife is a world different from our own, but information may pass both ways between here and there, albeit with some difficulty.)
But here is my quick take on the matter. First, according to the common conception, some kind of barrier is required between universes for them to be called alternate. That is, we do not refer to distant galaxies as “alternate universes” simply because they are distant. Why? Because we receive information from them in the form of light, and, conceivably we could travel to them, given enough time or the proper technology. Hence, an alternate universe is one to and from which no matter, energy, or information may be transmitted-- at least not without great limitations (e.g., there might be only one wormhole connecting two universes, etc.).
If indeed no matter, energy, or information whasoever can travel between one universe and another, then, from the perspective of either, the other universe simply does not exist. Hence, any speculation as to what rules may or may not apply in such a completely disconnected world are irrelevent. By definition, proof of the claim is impossible.
If, however, matter, energy, or information can travel between the other universe and our own, then in what sense is it “alternate”? Is it “alternate” simply because we feel it or deem it to be so? This the point of my argument about the other side of the room: should I deem it to be an alternate universe? Why or why not?
Suppose that two “universes” are connected by a wormhole, like two sides of an hourglass. Is there any reason not to consider this a single universe with a particular topology? Further, it is reasonable to suppose that in one side of the hourglass 2 + 2 = 4, but on the other 2 + 2 = 5? How is this any less arbitrary than supposing that the other side of the room might be mathematically different?
To sum up: If we define an alternate universe as a place completely disconnected from our own, than said place is, from our perspective, non-existent and any suppositions about its qualities are completely gratuitous. If, however, the other univese and our own are connected to some degree, then to suppose that 2 + 2 = 5 in that universe is logically equivalent to assuming that 2 + 2 = 5 in some other part of our own universe.
The monotheist is faced with one further difficulty: since God is defined as omnicient, he has knowledge of every universe in existence. Hence, every universe is connected through him and information could pass between them if he so willed.
I do. The main reason being that 2D space doesn’t exist even in our OWN universe. It is 100% abstraction, although we use physical objects such as paper as modeling material.
In that case they are equivalent to non-entities and are hardly appropriate material on which to build a counterargument. In other words, I am saying that the set of universe in which 2 + 2 = 5 is the EMPTY SET, and your counter is that I am wrong because this might be true of a universe IN the empty set.
Ah, but our arguments are completely different. Remember that my original argument was NOT that mathematical truths hold true in any universe (yes, an assumption in the original argument), but that God is subordinate to them inasmuch as they could not be otherwise and thus could be willed by him into existence. OTHERS came in with the CLAIM that there could be “alternate universes” in which the same rules of pattern and number did not hold true. This is a different argument, one that I am willing to argue, but I’d like people to understand that the CLAIM that different rules of pattern and number could hold true in “alternate universes” is their CLAIM and they need to prove it! I never introduced the concept of “alternate universes,” and I don’t even wish to validate such a concept.
Further, I would claim that a complete nullity is impossible, since the rules of pattern and number are sufficient to constitute a universe in their own right.
It depends on how you define “concept.”
It depends on what you mean by “concept.” Further, I believe that existence is not an action but rather a modality.
Aeschines:
I think you’re really close to something here. But, imagine 5 distinct universes, each with no connection whatsoever with the others. This could be so*, even if we (in Universe 1) have no way of knowing of, or travelling to, or veiwing any of the other 4. Not even a wormhole. These 4 other universes may as well NOT exist as far as we are concerned, yet they do (in this hypothetical construct).
It is similar to what theists say about God. That it is outside of our universe–outside of our laws of physics. They say this, yet maintain that we can be touched by or know of its existence. This is of course impossible because if it can act on us, or we upon it, then there is some sort of connection between God and our universe-- and you can’t have it both ways.
That is why I believe there are only 3 choices about God: either 1) there is no God; or 2) there is a God but it is unknowable therefore the EXACT same (to us)as non-existent; or 3) God is everthing (pantheism).
*But only in a manner of speaking. If the “5 Unconnected Universes” (para. 1) DID exist and proposition 3 (para. 3) is true, then it would take all 5 to make up God (everything) even though we can only have knowlege of “Universe 1” and no others. In this case however, I believe that the “5 Unconnected Universes” become just 1 Universe, as I consider “Universe” to be the same as “all that exists”-- whether it is all connected or not.
By the way, I don’t know what the plural of universe is. By my reckoning however, we don’t need a plural because there can be only One. (which, if true, would make Pantheism actually Monotheistic in a way, but not in the way most monotheists on our planet believe).
Yes, Kant had space as one of his “categories.”
I am not in complete disagreement here, although I think it’s an error to consider our consciousness as existing outside of Nature. Our perceptions are themselves natural phenomena.
The word “merely” is problematic here. They can be used as tools, it is true, but the principles of mathematics are also true in themselves.
But it does say a little tiny something about absolute truth, or implies certain principles which must always hold.
I know what you mean, but I can’t agree. First, we must note the simple fact that we are not omnicient and there are many things about which we know nothing. However, it is an internal contradiction to define, for example, Entity A as something about which we never can know anything. For we would have to know enough about Entity A to know that we could know nothing about it.
Hence, if we are a bird looking down on 5 universes and can tell somehow that they could never come into contact with each other, that’s one thing. But to define another universe (an “alternate universe”) as one whose content is unknowable to us, then there is absolutely no logical difference between that entity and the empty set.
Yes, you are hitting on another argument against monotheism. Namely, there is no “test” for omnipotence or omnicience or any other supposed characteristic of this being. Again, qualities that cannot possibly be proved belong to the empty set!
Yes, this is it. A sufficiently powerful being would be able to bully us and claim to be the One God, but said being could never prove this to us. My belief is that what people refer to as God is really that great Tendency in That Which Is toward being-consciousness-bliss. This tendency arises from the fundamental principles of pattern and number.
Yes, but this is just semantic. If people wish to use the term “alternate universe,” we need to approach their arguments with an understanding of what they mean by the term. In most cases, I think they mean something logically inconsistent by the term.
We may not be able to define the above-mentioned “Entity A”, but that does not mean that it doesn’t exist. As you pointed out, we are not omnicient.
Again-- we may not be able to define that entity, but we can hypothesize that entities exist that we have can not possibly have any knowlege of. We can even name the hypothetical entity "God’ if we wish. But this does not show an existence of the traditional monotheistic God or even allow that one exists in any way that is meaningful to us.
Do you believe there can be more than one universe? Or do you define universe as I do (i.e. All That Exists (including that which we can never know))? I realize this is essentially a semantic question, but I am curious about how you define “universe”.
Sure. But you certainly can’t use such an entity as grist for an argument, as some are trying to do here. I repeat: such an entity can NOT be included in any set other than “the set of things about which we can have no knowledge,” which is equivalent to the empty set. Do you see what I mean? If someone says “there is a universe in which 2 + 2 = 5 but about which we can have no knowledge,” that’s a contradiction. If we know that 2 + 2 = 5 is an element of that universe, then we know something about it. But if then the person concedes that we can have knowledge of this place, I would ask, What then makes it an “alternate universe?” Back to square zero.
Full agreement here.
I avoid using the term, except in the sense of our universe of stars and galaxies. The meaning here is pretty clear. When I wish to use a term that encompasses all, I use the ad hoc term That Which Is. The trouble is that if you use the term “universe” to mean That Which Is, then it becomes conflated with the meaning “all galaxies, all physical space” and gives credence to the notion that only the physical universe exists–which I deny.