8

Consider the following proof:

(1) Let the Universe be defined as the set of all things.

(2) It is impossible for a thing to come from itself. (You can't be your own parent)

(3) 2 implies a set of things cannot contain its own source.

(4) For all things X:

   (5) Assume the Universe came from X.

       (6) 1 implies X is a member of the Universe

       (7) 3 implies X cannot be the source of the Universe

   (8) 5 and 7 contradict - therefore 5 must be false.

   (9) 8 implies the Universe did not come from X.

(10) 4 implies For all X, the Universe did not come from X

(11) 10 implies the Universe Came From Nothing.

How would you characterize this reasoning? Does the reasoning hold? What is a counterargument? How does this reasoning relate to historical positions in philosophy and logic?

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    The discussion in @philosodad's answer made me notice something else: (1) defines the universe as the set of all things and in (3) you conclude a set cannot contain its own source. But for that you have to assume the universe is also a thing, which would make the universe a member of itself. But in ZFC (current common set theory), a set cannot be a member of itself. See en.wikipedia.org/wiki/Axiom_of_regularity . So your proof will have to be much more rigorous (including logic and set axioms) to work. – Koeng Sep 13 '12 at 18:22
  • I do not think math is involved here. – mick Sep 14 '12 at 22:02
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    @user1131467 What I mean is that in order for your proof to be really consistent, since you are talking about borderline complex cases (universe, thing/non-thing, causation outside time, etc), you'd have to be really rigorous, including dealing with axiomatic issues of logic (and set theory). You could simply specify a so called "naive set theory", but you would end up with other paradoxes. It doesn't seem to me as a proper proof on the beginning of the universe if you simply state "I'll just use these axioms, because then my proof works", without really tackling the foundational problems. – Koeng Sep 15 '12 at 5:31
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    @mick I'm not sure if you are refering to my comment, but in any case: logic and math are not completely separate things, specially because the former sets the foundations of the latter, including set theory. When you use propositions like "a set of all things" and syllogisms, you are talking about things that are closely related to math (even though we didn't directly cite math). On the edge of reasoning (as is in this case), it is very hard not to stumble of those related matters. – Koeng Sep 15 '12 at 5:42
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    @smartcaveman Again, not my point (but I'm willing to discuss those in a chat, if the case). My point is that if we are going to talk about things in the limit cases of logic and ultimate ontological affirmations, we have to deal with the details of foundations. Otherwise, as I said, it's just an interesting thought, without a strict rigorous base. You are exactly right that "We have to try to do a little better than this". – Koeng Sep 21 '12 at 18:40

11 Answers 11

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If you make the supposition that no thing inside the universe could generate the universe and that every thing that exists is inside the universe than the direct conclusion is that the universe was not generated by a thing, which is similar to saying that it was generated by nothing.

The difficulty here is that you have to ask yourself what you mean by "thing" and "nothing" and whether "nothing" means the same thing as "not thing". The field of philosophy has historically been very interested in questions of this nature.

There are several places that this argument can be attacked. The first would be to attack the premise, and argue that there might be entities outside of the space time continuum. Platonic forms would be an example of proposed entities that exist but are not "things" inside the universe.

We could also attack the application of cause--saying that the universe "came from" something implies rules of cause and effect that only exist inside the universe itself. The universe didn't "come from" nothing, because the words "come from" have no meaning outside of the universe. That would be the scientific position... that you can't use concepts relating to time and space outside of time and space.

Based on the former point, you can't assume that a universe can't create itself. Since time, space, and the laws of cause and effect don't apply outside the universe, some form of cosmic event could be occurring inside the universe that somehow reaches outside the universe and in fact is what creates the universe. So premise 2 could be invalid.

Edit

There is another flaw in this proof, which is that it defines the universe--that is, the space time continuum itself--as a thing bounded by the same rules as every other thing in the universe. However, there are properties of the universe which are not properties of any thing within the universe, for example, the universe itself can expand (that is, generate additional space and time) without apparently getting that space and time "from" anywhere. So it isn't clear that the universe is a "thing" in the sense that a particle is a "thing". It all comes down to definitions.

Further Edit

Based on comments, you seem to believe that we cannot reject 11 without rejecting 2. That isn't true. As I've pointed out, we can reject 1 or 2. Most people reject 1, that is, the majority of humans believe that there is more to reality than the universe of things, and given the nature of the universe, 2 is not supportable when applied to the universe since cause and effect are only valid within the universe. We could point out that since anti-matter exists and moves backwards in time, 2 is invalid even within the universe.

Further, we could accept 1 and 2 and still reject your argument by questioning whether the universe is itself a "thing". This is a major unstated premise of your argument, and without it your argument does not hold at all. In fact, it would be just as valid to use your reasoning to show that the universe is not a thing! If you insist that the universe is a thing, we could point out the difficulty of having a set contain itself, since this leads to Russel's paradox, and question what version of set theory you are using and attack that.

The fact is, it's difficult to prove things about the origin of the universe. That's why there is a field of cosmology at all, and why the field of philosophy continues to have new ideas despite having thousands of years of literature to draw on.

  • Good answer, +1. Besides, we have the transposition from logical to ontological. That kind of argument requires the universe existence to obey the laws of logic, which may not be the case. – Koeng Sep 12 '12 at 19:18
  • @Koeng: What is an example of something that does not obey the laws of logic? I thought everything obeyed the laws of logic by definition. – Andrew Tomazos Sep 12 '12 at 19:32
  • @user1131467 I have just answered something related: philosophy.stackexchange.com/questions/3637/… . We don't know really what is the relation between logic and the universe. Logic works very well, but that doesn't mean we can assume the universe has to obey it. Gödel incompleteness theorem, for example, is based on a variation of the statement "This affirmation is false", which indicates some limit of logic. – Koeng Sep 12 '12 at 19:46
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    @philosodad: Statement 1 is a definition, not a premise - as such I assert you cannot assign it true or false, you can only argue that you don't understand what it means. All 1 says is that you can replace occurences of the word "universe" with "all things" or "everything" in the body of the proof - without changing the semantics of the original proof. I assert my proof is independent of the definition of thing. Whatever your definition of thing is the proof works, even in the narrowest or broadest sense. (provided everything and nothing are literally derived fromyour definition of thing). – Andrew Tomazos Sep 15 '12 at 1:14
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    let us continue this discussion in chat – philosodad Sep 15 '12 at 3:05
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I would characterize it as an empty sequence of syllogisms that only superficially resembles something that anyone calls a proof. The relation "comes from" is vague, and it is used in ordinary speech to refer to links between objects we observe--- so a donkey comes from it's parents because we observe donkeys and parents.

When applying this relation symbol to the universe, one is making an error, in that the different things that the universe could come from cannot be distinguished observationally from one another. So there is no meaning one can assign to this argument, it is a meaningless sequence of words.

This is the position of the physicists and the logical positivists. It is not the position of philosophers, which is why one can ignore almost everything in the whole field of philosophy.

I should point out that it is ridiculous to phrase arguments of this form in logical proof form, as all the deduction going on is of the trivial Aristotelian variety. The nontrivial aspects of logic involve quantification, and this is not included in any non-mathematical logical system, which makes those systems a hinderance rather than a help. Aristotle didn't develop anything even remotely close to something which one should call a real logic.

  • By your reasoning the question "Where did the universe come from?" is a meaningless sequence of words, because you cannot "apply the relation symbol to the universe". – Andrew Tomazos Sep 12 '12 at 18:20
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    @user1131467: I mean, stop using words which pretend to have meaning. Give me a procedure to make sense impressions which will tell me where the universe came from, or else stop wasting people's time. – Ron Maimon Sep 13 '12 at 8:01
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    @user1131467: I can't, there isn't any such universe, so "where did the universe come from" is a nonsense question, it makes no sense, I never ask it, nor do I consider it meaningful to talk about, and stop wasting people's time – Ron Maimon Sep 13 '12 at 16:27
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    @NieldeBeaudrap: I just mean the relation "come from" doesn't mean anything at all when applied to the universe and something else. It's nonsense, and there is nothing to consider. – Ron Maimon Sep 13 '12 at 16:38
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    @user1131467: I don't think all of philosophy is a waste of time, just this question and related questions. When the "majority of people" come to understand this, the field will make some progress, so I just tell them, and wait. – Ron Maimon Sep 13 '12 at 18:33
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I think your argument is essentially correct, but that you have to take care in how you describe the universe. Do you mean everything that is, or everything that ever was? Or, bearing relativity in mind, are you interested not in matter but in the collection of events which have happened throughout space-time?

Consider a simplified account of the universe as just "everything that ever was". Then you potentially have a problem of double-counting. I am made up of many particles. I have not always existed, nor will I always exist; nor am I identical to the particles that make me up at any given point in time. I am rather a pattern of information in those particles, and furthermore a dynamical system supported on them, like the crest of a wave on the ocean. But nevertheless, we're interested in the particles that make me up, most of which have been around for a very long time. Does it make sense to distinguish between the particles that make me up now, as they are now, from the way they were two hundred years ago? Of course, particles aren't really distinguishable, so it doesn't make a lot of sense to talk about individual particles except to the extent that they are accidentally localised and trackable as crests in the particle field. And the gloss of "two hundred years ago" ignores the relativity of simultaneity. So in fact you have to be careful about what you mean by "the universe" and "ever was".

I think the most careful approach to talking about the Universe, or anything that might be 'caused', is to talk about "all dynamics". What do I mean by 'dynamics' in this case? I'm going to be evasive but inclusive; whenever anything which causes another thing to happen, that happening is 'dynamics'. We might refer to that happening as an 'event', as would be typical in relativity theory; matter, antimatter, energy, and so forth correspond to relationships between events. That is to say, any causation corresponds to an event; and the Universe is the set of all events and relationships between them.

A category theorist would describe the events in the universe as objects, and the relations between them as arrows — assuming simple two-place relations between events, that is. Anything which took part in causing the universe would have to be an arrow pointing into the Universe "from nowhere"; and it's not clear what the point of entertaining such things would be other than to give the Universe a "cause" just for its own sake. It's not very strongly motivated. Perhaps if one insists on complicated many-place relationships between events a more sophisticated argument than this would be necessary, but ultimately I think that a "relationship between events" in which some events are "missing", in order to allow these relationships to "cause the Universe", is contrived.

Now your reasoning applies directly. The Universe U is the set of all events and relationships between them. If something else E were to cause the Universe, this would seem to mean that the 'causing of the Universe' is an event which E relates to. But if E is a relationship on events, it seems that it should be part of the universe. If you suppose (as you've postulated) that no part of the Universe can have caused itself (along with the rest of the universe), it then follows that nothing can have caused the Universe.

The weakest parts of this argument are your postulate that nothing can be its own cause, and the notion that I've used that "the causation of the Universe" is an event. It is possible that the Universe is something sufficiently complicated that it doesn't make sense to talk about a singular event as "the creation of the Universe". But then it doesn't necessarily make sense to talk about a singular cause. Perhaps we should consider instead a collection of 'initial' events for the Universe, which taken together constitute the creation of the Universe; but then anything which caused them would fall subject to the same argument.

3

6 is broken.

You cannot derive from the definition of the Universe as the set of all things, that the Universe is itself a thing.

It's easy to see why one might make this mistake. After all, if the Universe isn't a thing, then what is it? The problem is that what you are actually saying in premise 1 is that the term "Universe" is used to refer to the set of all things. This does not entail that there is such a thing as a Universe, any more than a mention of unicorn entails that there is such a thing as a unicorn.

The inference of 11 from 10 is also broken. Since you are talking about things in terms of sets, "Nothing" would by convention refer to the empty set. While there are acknowledged problems with the concept of a "universal set", every axiomatic set theory will account for an "Empty Set". Therefore, any Universe or "universal set" will necessarily contain the empty set. By saying that the Universe came from the Empty set, you are refuting the very logic that you used to draw your conclusion.

A more elegant formulation of the idea that I believe you are getting at is known as Russell's antimony. Different branches of logic and set theory propose different solutions to the apparent paradox. Most involve some form of distinction between a "set" and a "class" or a very particular definition of a universe (such as a Grothendieck Universe). If you google any of these terms you will find plenty of information that you can use to twist your brain into deeper circles.

  • The main complaints here are definitional, not structural. Specifically I can define the universe as the collective every thing, the universe as a thing, and "nothing" as synonymous with "no thing", "not a thing" - and to "come from nothing" is synonymous to "not come from a thing". You are making up and imposing your own definitions, rather than using the authors. – Andrew Tomazos Sep 21 '12 at 8:47
  • @user1131467, I am using the definitions that are implied by the language in the "proof". When one speaks of the "set of all things", I think it is safe to assume that the common definition of a "set" is valid within the context of our discussion. When every single formal set theory equates the concept of "nothing" to the "empty set", I believe it is fair to make that further jump as well. Unless you are prepared to redefine every word in your post, you have to accept that readers will rely on their commonly accepted academic definitions in order to proceed with a discussion. – smartcaveman Sep 21 '12 at 8:54
  • In general, I believe that if you took the time to express the "proof" in formal first order logic, it would become clear that there its current formulation involves unresolved blend of first-order logic and unquantified predicate calculus. – smartcaveman Sep 21 '12 at 8:57
  • @user1131467, You have the right to define anything however you'd like. The problem is that the philosophical community recognizes predefined meanings for the terms you are using and there has been extensive study on the relations between these meanings. If your objective is to declare your cleverness, then congratulations.. However, if you are actually interested in finding out more about how people much smarter than either of us have addressed the same problems over the past 200 years, you will be get a lot further by starting from their established interpretations. – smartcaveman Sep 21 '12 at 9:01
  • Your implication is that my definitions are somehow unusual, which I refute. The synonyms listed above are fair and uncontroversial. Once you say the "empty set" (which you did, not me) you have to define it, and you also have to define whether or not it is a thing. If you say it is a thing, than it cannot be nothing - and visa versa. So long as you pick one the proof remains intact. And either way, whether the universe came from the empty set and/or nothing is practically equivalent and the distinction is uninteresting. – Andrew Tomazos Sep 21 '12 at 9:18
1

First of all, about your primary assumption: "Let the Universe be defined as the set of all things." it is your assumption which is not necessarily true in reality. I personally don't agree with you (and have reasons for that but examining it will be a book), as I think of the whole universe of ours as the set (or class) of all possible things --w.r.t. a background set of logics this universe being based upon-- which come to be possible (in different forms, with an eye open to evolution in the course of time) following the causality. Based on this viewpoint we can easily have universes instead of a single universe, and the number of these universes can be infinitely large, equal in number to the number of all sets of background logics upon which a self-consistent universe can be based. This is why the first assumption is misleading to me, it can at most trivially say "Let the Universe be defined as the set of all things in that universe", and although of course only the trivial expressions are the absolute truths, but such a trivial assumption would make the rest of proof all lame. You say this universe comes not from inside itself, trivially true, but there is still a possibility that it comes from a group of elements of another universe! Note that according to the definition of universe above, not all distinct universes would be contradictory w.r.t. each other. (Mention that causality needs a starting point and one set of background logics can yield different universes according to different starting points for their causality chain. Although not all consistent universes are required to have exactly a same set of background logics, one universe may be able to exist as a sub-universe to the other although it can exist on its own as well. Also there may exist universes which are just partly contradictory.)

However, you can then talk about the class of all universes and bring again a similar proof that the class of all universes would have come to existence from nothingness. It is just this point that believers in God introduce God as the source of all sources, the cause for all causes, the reason for all reasons, the creator of all possible sets of logics, the organizer of all the possible sets of initial conditions, the originator of causality, and the creator of all the infinity of universes including ours. For this to be able to be true but the believers in God need to introduce him as something out from the set of all universes already defined, so he would be for example a single perfect existence whose existence is not confined to time (all the universe had time as they had causality), so no start and no end, and this solves your problem since you will no longer need to find a parent for him! That he creates the universe from nothingness but is somewhat the same as what you have proved, there in your proof all the universe(s) should have come to existence from nothingness spontaneously and this idea of the believers in God introduce a cause for that "coming to existence", the will of God! There would of course arise then many questions on hows and whys, but this answer was only to address your question and nothing more.

  • Statement 1 is a definition, not a premise. You can't "disagree" with it as such, you can simply say you don't understand the meaning of it. I am simply stating that when I say the word "universe" in the proof I mean the set of all things. Everything. This includes at least the physical universe, and at least every other thing that exists, at minimum. So when you say there could be other universes, this is by the definition I am using, impossible. (Clearly the set of all things must be unique.) – Andrew Tomazos Sep 15 '12 at 1:23
  • (In the same way that for example the set of all cows must be unique) – Andrew Tomazos Sep 15 '12 at 1:37
  • Ok, got it! maybe my comment could be regarded as a help to complete your answer, only, as you are giving a statement about the real world and when you say "let the universe be defined ..." one may see if it is ok to be defined such, in math everything is up to you how to define and how to assume but in reality things are different slightly! Anyway, that was only one suggestion and the proof was nice on its own, thanks – owari Sep 15 '12 at 17:49
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By (1), Universe contains all causes, all sources, i.e., there is no cause, no source, indeed, nothing, that stands apart from, independent of, Universe.

But the proper conclusion to draw from this is not that Universe came from Nothing but rather that Universe simply is. The premise that Universe must have a "source", indeed that it is even meaningful to speak of the source of all sources, is what must be rejected.

That there is something rather than nothing is self-evident, thus Universe exists, Universe is eternal.

  • What does it mean for something to "simply is"? By my definition things that "simply are" are eternal and don't come from anything, in other words there is nothing that they come from, or they come from nothing. This is all synonymous by my definitions. – Andrew Tomazos Sep 21 '12 at 16:38
  • @user1131467: ex nihilo nihil fit. I think the phrase "the Universe Came From Nothing" means something other than what you intend it to. – Alfred Centauri Sep 21 '12 at 16:44
  • Well it means whatever I define it to mean in the context of my proof - you can argue my definitions are unusual, but I assert they are not. – Andrew Tomazos Sep 21 '12 at 20:59
  • @user1131467, your arbitrary assertion is irrelevant and renders your "proof" meaningless except, perhaps, to yourself. – Alfred Centauri Sep 23 '12 at 1:34
  • Well as I have now made clear my intended definitions, my proof is now meaningful to you too, as it was already to everyone else with an ounce of common sense. Doesn't come from anything is a perfectly valid synonym for comes from nothing. – Andrew Tomazos Sep 23 '12 at 4:42
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This question is essentially asking: "does the set of all sets contain itself".

(1) Let the Universe be defined as the set of all things.

premise accepted

(2) It is impossible for a thing to come from itself. (You can't be your own parent)

premise debatable but accepted for the sake of arguing

(3) 2 implies a set of things cannot contain its own source.

You are arguing that the universe cannot come from itself by (2), because it's a thing. But by definition (1), universe contains all things, so it must contain itself. This contradicts with (2), thus the proof is self-contradictory

  • I don't see the contradiction sorry. The universe is a thing. Something cannot come from itself. The universe cannot come from itself. I fail to see how whether or not "the universe contains itself" is relevant. I think you are conflating "contain" with "comes from". – Andrew Tomazos Aug 11 '14 at 22:26
  • You are saying the universe is a thing, and the universe is the set of all things, you have implicitly stated that the universe can "come from" itself, which contradicts with (2). – what is sleep Aug 12 '14 at 15:31
  • I'm sorry, but you are not making sense. Where did I implicitly state the universe can come from itself? I don't think X can come from X (that's a premise), as that is contrary to the very definition of "coming from". – Andrew Tomazos Aug 12 '14 at 17:41
  • According to your definition (2) and (3), A contains B implies B comes from A. Since the Universe contains itself, then it must come from itself, by your definition. – what is sleep Aug 12 '14 at 19:18
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You have proven that the argument did not come from a thing - not that it came from nothing. The other alternative reading of "did not come from a thing" is that it has always existed (which as you are making it the set of all things ever, is the more reasonable reading)

Sorry for the brief answer, late for work!

  • Where did an eternal thing come from? It came from nothing. This seems a satisfactory answer based solely on the definition of eternal. – Andrew Tomazos Sep 21 '12 at 11:29
  • No, an eternal thing did not "come from" at all. It always was. This is different from "came from nothing". Of course, this (in combination with the other comments on answers here) is reading like "I define the universe as coming from nothing, therefore it comes from nothing" - even when your definition of "coming from nothing" doesn't fit. – Ryno Sep 21 '12 at 13:14
  • Based on my definitions of words "not coming from anything" is synonymous with "coming from nothing". Further the proof has more substance than you give it credit for with your characterization of it as a definitional tautology. – Andrew Tomazos Sep 21 '12 at 13:16
  • Based on your definition of words, you can prove anything you like. The rest of us have a shared definition that we like to use however. Good luck with your theories. – Ryno Sep 21 '12 at 14:07
  • Your implication that my definitions are somehow uncommon is incorrect. – Andrew Tomazos Sep 21 '12 at 16:34
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You start with 'the set of all things'. This already involves a contradiction. See Russells Set Paradox. From a contradiction anything can be proved...

  • The set of all things does not contain a contradiction. Whether the set of all sets that do not contain themselves contains itself - is a self-referencing contradiction (in that if it does than it must not, or if it does than it doesn't). This is the same as "this statement is false". You wouldn't suggest I can't use the word statement and false because of this, in the same way Russells Paradox has no bearing on the proof. – Andrew Tomazos Sep 21 '12 at 11:21
  • Yes you're right I've misquoted Russell. However the point still stands. In Set Theory, formalised by ZFC you cannot form the set of all Sets. Its disallowed because of a line of reasoning that starts from Russells Paradox. This forced set theorists to invent larger set theoretic universes, like NBG where the set of all sets form a class and not a set, and grothendieck universes. Naively put, I'd say we cannot conceive of everything, whenever we try, there remains stuff outside our conceptualisation. – Mozibur Ullah Sep 21 '12 at 17:49
  • Sorry I don't accept your reasoning. The proof does not rely on ZFC set theory axioms. – Andrew Tomazos Sep 21 '12 at 21:01
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(1) Let the Universe be defined as the set of all things.

Are we to assume naturalism then? Deities may very well be a thing that is both a thing and by general consensus transcending the physical universe. Seems like that first premise just needs some further clarification.

Now there does seem to be a ambiguity on what we are discussing here. Are we trying to prove creation ex nihilo or is coming from nothing an accidental euphemism for coming into existence uncaused.

  • Say a deity created the physical universe. The Universe in (1) includes at least both the deity and the physical universe. So where did the deity come from? The proof just shows (derived from some reasonable axioms) that there has to be something that came from nothing, and that the Universe as a whole (deity included or not) came from nothing. Whether the physical universe came from nothing, or a deity that came from nothing created it, or a deity created it that came from something else that came from nothing, etc - it doesn't say. – Andrew Tomazos Jul 17 '14 at 11:13
  • As for "coming into existence uncaused", I consider that a synonym for both "coming from nothing" and likewise "being eternal". – Andrew Tomazos Jul 17 '14 at 11:15
  • @AndrewTomazos I think your conclusion should be rephrased, then - "came from nothing" and "had no beginning" do not mean at all the same thing to me. ("is eternal" implies "had no beginning", but it also implies no end, which I don't think you want to address here.) – Brilliand Jul 17 '14 at 19:07
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Your point (2): is any god a "thing"? Because no religious person is worried with the question "where did God/some god came from?" For them, the gods may have always existed.

Is the Universe a "thing" in the same sense as us?

If the gods may have always existed, why can't the Universe?

  • Yes, if a god exists, it is a thing under my definition of thing. I don't see the relevance to the proof of what questions a religious person worries about. If an eternal god created the physical universe, then that god came from nothing so collectively the universe came from nothing. Yes the Universe is both a thing and a collection of things, as is a person a thing and also a collection of things. My proof shows that something must have come from nothing, it doesn't comment on whether that was a god or a big bang or whatever else. – Andrew Tomazos Jul 18 '14 at 21:00
  • I think you're stumbled upon the term "came from". Why do it have to "came"? Universe is not an animal, a cloud, a planet. These things come, these things go. Not the universe, I guess. – Rodrigo Jul 19 '14 at 2:33
  • It can it just is not. That is if we are to believe what the cosmologists have to say. – Neil Meyer Jul 19 '14 at 17:34
  • nobody knows the final truth of the cosmologic and of the microscopic, both may be infinite, who knows they meet each other again, on the other way around? We have to believe nothing. – Rodrigo Jul 19 '14 at 23:52

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