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Theists often claim that it is impossible that the universe just randomly

Theists often claim that it is impossible that the universe just randomly "sprang into existence" out of nothing, for no reason. M-theory posits a cosmological world-view in which an infinite number of universes are continually coming into and going out of existence within the framework of an eternal multiverse. If correct, does this disprove the theist argument?

I would have thought that the obvious theistic response would be that it is the existence of the eternal multiverse that is at issue. I.e., why are there any universes rather than none? From what I've read of Hawking's response to this, it does not seem to me to be very impressive. As usual with these things, it fails to take the motivations of its opponent at all seriously.

None of that is of course to say that the theistic argument referenced is any good.

If causality is a category of perception as Kant claims why are so many

If causality is a category of perception as Kant claims why are so many scientists unfazed intellectually by the claim that the Big Bang theory must be an incomplete theory of the universe because the existence of the big bang must have been caused by something prior to the big bang? Personally I side against the scientists in my firm belief that they are defying commonsense in their rejection of the idea that the existence of the universe at the time of the big bang must have had a prior cause. So scientists seem to be rejecting the idea that all occurrences have a cause.

According to Kant, causality is among the organizing concepts through which our mind unifies its experience. Like space and time, causality as well is then not objective (i.e. wholly independent of our mind), but still "empirically" objective in the sense that we cannot help but structure and anticipate the world of our experience as causally ordered.

This sort of account explains your "firm belief" that an uncaused cause defies commonsense. But it also cautions us against claiming any knowledge of what the world might really be like, apart from how our mental faculties are organizing it for us.

The very strength of our conviction that nothing like an uncaused Big Bang could possibly have happened -- the strong feeling that we know this "a priori" -- would suggest to Kant that this belief discloses something about ourselves (about our way of organizing and unifying experience) rather about the world we inhabit.

And so physicists could actually appeal to Kant in rejecting your belief as a constraint on their theorizing much like they might appeal to Kant when they set aside the constraint that their theorizing must present space as Euklidean.

Are physical and logical truths distinct and, if so, how are they related? Is

Are physical and logical truths distinct and, if so, how are they related? Is one more fundamental than the other? By ‘physical truth’ I mean something true in virtue of the laws of physics, such as ‘masses attract other masses’ (gravity) and by ‘logical truth’ I mean something true in virtue of logical or mathematical principles, like ‘2 + 2 = 4’. Could there be a world where some of the physical truths of our world were false but all of the logical truths of our world were true? That is, a world where masses always repelled other masses but 2 + 2 = 4? Conversely, could there be a world where some of the logical truths of our world were false but all of the physical truths of our world remained true? That is, a world where 2 + 2 = 5 but where, as in our world, masses attract other masses? [We’ve been discussing this hours and feel in desperate need of professional guidance - please help!]

One of the things usually taken to be distinctive of mathematical and logical truth is that such truths are in some very strong sense necessary, i.e., they could not have been false. Assuming that it is in fact true that 2 + 2 = 4, how could that have failed to be true? (Or, to take a logical example: How could it fail to be true that, if Goldbach's conjecture is true and the twin prime conjuecture is also true, then Goldbach's conjecture is true?) Presumably, the answer to this question depends upon what, precisely, one thinks "2 + 2 = 4" means, but it is hard to see how one could accept the statement that 2 + 2 = 4 as both meaningful and true and think that it might not have been true. It's important to be clear that this statement does not say anything about how actual objects behave, e.g., that if you put two oranges on a table with two apples and no other pieces of fruit, then you'll have four pieces of fruit. Weird things might happen in some worlds, but that would not make it false in that world that 2 + 2 = 4. It might make it uninteresting or irrelevant, but that is all. It's also important to be clear that we are not talking about whether the sentence "2 + 2 = 4" might have been false. Of course it could have been false, since "4" could have meant what "5" means, and then "2 + 2 = 4" would have meant what "2 + 2 = 5" does mean and so would have been false.

Precisely what makes the statement that 2 + 2 = 4 true is not a question I'm prepared to answer here, however. (I'm not sure I'm prepared to answer it anywhere.)

The question about physical law is less clear. Some people have entertained the view that the most fundamental physical laws are, like mathematical laws, necessary, i.e., that there could not have been a world in which they were false. Sometimes this view seems to be tied up with some idea of the form: The laws are what tell us what mass, force, etc, are, and so if those laws did not hold, there wouldn't be masses, forces, etc. (Thomas Kuhn held a view of this sort at some times.) But most people seem not to care for this view and so regard the laws of physics as contingent, i.e., not necessary. That is just to say that the laws might have been otherwise. As has been noted by Hawking, among many others, universes in which the laws were different probably would not support life, or even be very stable. Our universe seems to be "just right", as Goldilocks famously said. But that does not mean there could not have been such universes, and some physicists, like Hawking, again, actually think there are all those other universes. (For what it's worth, however, and while we're on the topic, I think Hawking's recent remarks on the relevance of all of this to the question whether there is a divine being are not worthy of a man of his intelligence.)

By the way, you will sometimes see people talk about something called "physical necessity". This is a "relative" form of necessity, and it means: necessary, given the laws of physics. But what is physically necessary need not be necessary in some stronger sense: what could not have been otherwise, period, and not relative to anything else.

So, what do we have? Logical and mathematical truths are necessary. Physical truths are not (assuming we do not take the other view). So the laws of physics could have been otherwise, whereas the laws of logic and mathematics could not.

Do you really believe that the entire universe was made by a "big bang?" Doesn

Do you really believe that the entire universe was made by a "big bang?" Doesn't it seem like there must be some type of higher being something? It just doesn't seem like all the pieces of the puzzle come together from a few dust particles...

I believe that your question is a good one, and that there is a further one that it suggests. The further question is where the dust particles might have come from. Or if we mean by "the universe" absolutely everything, including dust particles, then the universe did not come from a few dust particles or anything else, as, if it did, then the universe came from a part of itself, which is clearly impossible.

Can something really be divided into an infinite number of parts? It seems like

Can something really be divided into an infinite number of parts? It seems like it's theoretically possible to infinitely continue dividing something, but that is in no way the same thing as saying that something can be infinitely divided at any point in temporality, since an infinite period of time must be reached before something has been infinitely divided (which is not even a theoretical possibility). It seems like vast claims and supposed paradoxes in physics and mathematics are founded on this dubious assumption that an object or shape can be theoretically divided into an infinite number of parts.

It may help to say that we only need "infinite divisibility"--we don't need the division to have actually taken place, only to be possible in principle.

Also, what is your model of "dividing" here? Do you imagine scissors and paper and a lot of cutting? Perhaps there are other ways of conceptualizing infinite division that don't require time.

We're told that all matter in the universe is "expanding", presumably due to

We're told that all matter in the universe is "expanding", presumably due to residual energy release created by the "big bang". But what (or perhaps more importantly "where") is the universe expanding into? I'm not approaching this from an astrophysical perspective, but from an ontological one. Namely, if all matter in the universe is expanding into the vacuous nothingness, and the universe is surrounded by nowhere, then how can something (the universe) exist in nothing and nowhere?


Greetings, I've been pissing off my scientist friends and delighting creationists with the notion that both contemporary cosmology and Christianity share a fundamental ontology - first there was nothing and then there was everything. The Big Bang is a story of miraculous creation. Therefore, both have equivalent epistemological status - either both are the Truth, or both are just good stories. I am particularly interested in arguments against. Cheers, Chris Alexander, NC

What fun!

But there are disanalogies -- the Christian view doesn't quite hold there ever was nothing, for there always was God -- and also I don't think it's exactly accurate to describe the Big Bang as 'first there was nothing then there was something' (it's rather: everything in the universe can be traced backwards to a singularity/explosion but nothing can be said about what if anything preceded that moment) -- but more importantly I would take issue with your claim that they have equivalent 'epistemological status' (if you m ean that in any technical sense): for scientists believe in the Big Bang as a result of a tremendous amount of empirical evidence while religious belief in divine creation is based on no such thing. So even IF both were versions of 'first nothing, then something,' the reasons for believing in them are extremely, profoundly, and fundamentally different -- hence they differ in epistemological status.

hope that's useful --


Andrew Pessin

Is it conceivable that something finite can become infinite? Isn't there an

Is it conceivable that something finite can become infinite? Isn't there an inherent conceptual problem in a transition from finiteness to infinity? (My question comes from science, but the scientists don't seem to bother to explain this, such as in the case of gravity within a black hole -- a massive star collapses into a black hole and gravity in it rises to infinity? The more interesting example to me is the notion that the universe may well be infinite, but the main view in cosmology is that it began as finite and even had a definable size early on in its expansion. How could an expanding universe at some point cross over to have infinite dimensions?)

A few comments on Hilbert's Hotel (since Charles Taliaferro has brought that up) and "actual infinities":

  1. If you want a standard presentation of the usual Hilbert's Hotel "paradox", which has nothing to do with money, then check out Wikipedia's good entry. The "paradox" just dramatizes the basic fact that an infinite set can be put in one-one correspondence with a proper subset of itself. There is nothing paradoxical about that: on the contrary, it is tantamount to a definition of what it is for a set to be (Dedekind) infinite.
  2. Can there be "actual infinities" in the sense of realizations of Dedekind infinite sets in the actual world? Well, money won't do, to be sure (but that's just a fact about money, not about the general impossibility of "actual infinities"). Suppose you think that there are space-time points, and that actual space-time is dense -- i.e. between any two points there is another one. Then the points in a space-time interval will be Dedekind infinite. [Proof: label the end points 0, A. By the denseness hypothesis there is a point between, label it 1. By the denseness hypothesis again there is a point between 0 and 1, label it 2. By the denseness hypothesis again there is a point between 0 and 2, label it 3. Keep on going. That gives you a sequence of points 0, 1, 2, 3 ... in the interval. And by the Hilbert's Hotel shift, mapping the point labelled n to the point labelled n+ 1, it is Dedekind infinite (for that maps the labelled set of points one-one into a proper subset of itself).] But there isn't anything in the least paradoxical about holding that there are space-time points, and they are dense.
  3. Not all Dedekind infinite sets can be put into one-one correspondence with each other, by Cantor's diagonal argument. That means there not all infinite sets are the "same size" and we can talk about smaller and larger infinities. But this hasn't anything to do with the Hilbert's Hotel "paradox" (if you are muddled about that, in its original form a "paradox" about the smallest kind of infinite set, you certainly can't unmuddle yourself by talking about larger, uncountable, infinities). We might, however, raise questions about whether sufficiently large higher infinities can be realized in a physical world at all like ours

Are symmetry principles laws of nature, or meta-laws of nature? The intuition is

Are symmetry principles laws of nature, or meta-laws of nature? The intuition is that laws of nature are contingent. That is, it could be different in different logically possible worlds. Does this hold true for symmetry principles? Could there be some symmetric principles that had to hold in all possible worlds?

My view (which I defended in my recent book, "Laws and Lawmakers" from Oxford University Press) is that symmetry principles in physics are widely regarded as meta-laws. For instance, the principle that all first-order laws must be invariant under arbitrary displacement in time or space explains why all first-order laws have this feature (and, in a Hamiltonian framework, ultimately explains why various physical quantities are conserved). The symmetry principles function as constraints upon what first-order laws there could have been. Had there been an additional force, for instance, then the laws governing its operation would have obeyed these symmetry principles, since these symmetry principles are meta-laws. Eugene Wigner and others have suggested that the relation of symmetry principles to the first-order laws they govern is like the relation of those first-order laws to the particular events they govern.

I see no reason why symmetry principles would differ from first-order laws by holding in all possible worlds. It is easy to construct a set of first-order laws that violates any of the classical symmetry principles (e.g., that treats some spatiotemporal locations differently from others). So the symmetry principles seem to be contingent, just as the first-order laws are. However, the symmetry principles could still be more robust under counterfactual antecedents than the first-order laws are. As I said, had there been an additional force law, then it would still have accorded with the classical symmetry principles.