I'm pretty sure that mathematicians and physicists would both reject the way you've described them. Mathematics not only accepts the concept of infinity but has a great deal to say about it. To take just one example: Cantor proved in the 19th century that not all infinite sets are of the same size. In particular, he showed that whereas the counting numbers and the rational numbers can be paired up one-for-one, there's no such pairing between the counting numbers and the full set of real numbers. Thus, he proved that in a well-defined sense, there are more real numbers than integers, even though in that same sense there are not more rational numbers than integers. Now of course, we sometimes talk about certain functions going to infinity in a certain limit. For example: as x goes to 0, 1/x goes to infinity, even though there is no value of x for which the value of 1/x is infinity. Rather, we say that at 0, the function is not defined. There are good reasons why we say that, though this isn't the...

I guess I'd have to disagree with the idea that "all of philosophy and logic point to a reason or cause for everything." There's certainly no argument from logic as such; it's perfectly consistent to say that some events are genuinely random. Some philosophers have held that there's a reason (not necessarily a cause in the physical sense, BTW) for everything, but the arguments are not very good. On the other hand... quantum mechanics is a remarkably well-confirmed physical theory that, at least as standardly interpreted, gives us excellent reason to think that some things happen one way rather than another with no reason or cause for which way they turned out. An example: suppose we send a photon (a quantum of light) through a polarizing filter pointed in the vertical direction. We let the photon travel to a second polarizing filter, oriented at 45 degrees to the vertical. Quantum theory as usually understood says that there's a 50% chance that the photon will pass this filter and a 50% chance that it...

I think it's a bit optimistic to say that physicists are close to proving the existence of a multiverse, but we can set that aside. There are different ideas of a multiverse in physical theory, but none of the ones that cosmologists take seriously call for showing that literally every possible "universe" exists. Rather, what's at stake is the idea that the totality of the Universe writ large contains relatively isolated sub-parts that have many of the characteristics of the physical universe as we usually think of it. In particular, the values of various physical "constants" would vary across the different sub-universes. But the important point for your question is that this is entirely about physics and has nothing to do with God. God, as usually understood, is not a physical being at all, but a being who (among other things) underwrites the existence of physical things. God doesn't exist within this or any other physical universe on the usual theological view. Put it another way: if the God...

Not quite correct. Cyclic theories still posit a Big Bang, but they also posit a cycle of expansions and collapses. This is not something I know much about but you can read a bit more here If we suppose that the non-cyclic Big Bang model is correct, then in at least one sense, the universe isn't a case of getting something from nothing: it's not an example of matter appearing uncaused in a universe where there are earlier times with no matter. Of course, that's consistent with there being no explanation of why there's matter/energy at all. That may not quite amount to getting something from nothing, but it's an idea that doesn't sit well with everyone. Some versions of the Cosmological Argument are meant to explain why contingent things (like the physical things we're familiar with) exist. The explanations typically appeal to the existence of a Necessary Being—one who's very nature requires that it exist. If there's no such being, then it might be that there's no explanation for why contingent...

The best word to look up is univocal , which is roughly the opposite of equivocal . It means, more or less, unambiguous, or having one meaning. Without the whole sentence, it's a bit hard to be sure what the author meant, but the idea of complementarity, in part, is that we can't bring pairs of concepts such as position and momentum both to bear in a single experiment; we must choose. In classical physics, we can. There is, as it were, a univocal point of view that we can take on a physical system classically, whereas in applying quantum theory we must choose between incompatible experimental arrangements and "complementary" physical concepts.

If I understand your question correctly, it's whether there really could be more than three dimensions in physical space. The best answer, I should think, is yes. One reason is that there are serious physical theories that assume the existence of more than three spatial dimensions: string theory is the example I have in mind. More generally, though, it's not clear why we should doubt that this is possible. The fact that we can't represent it to ourselves imaginatively doesn't seem like a very good reason. We can't represent curved space-time to ourselves imaginatively, but if general relativity is right, space-time does curve. We have a notoriously hard time representing quantum mechanical objects to ourselves imaginatively, and yet quantum mechanics is the cornerstone of much of our physics. We can even say things about what it would be like to live in a world with more than three spatial dimensions. Consider: think of a plane in 3-space, and imagine a walled square in that plane. An object can...

Let's use a phrase from the philosopher David Lewis: concrete worlds . Let it mean complete, concrete universes. Lewis thought that there are concrete worlds other than our own, and that there is at least one for each way our world could be. Lewis also characterizes these words in the way you do: they aren't in our space-time, so they're not at any spatial or temporal distance from our concrete world, and they don't interact causally with our world. As Lewis understand things, they wouldn't be other worlds if these conditions didn't hold. Lewis thought there were such things. He thought that making sense of ordinary truths about what's possible calls for them. My admittedly unpopular view is that this is the wrong way to think about possibility. Even if such worlds do exist, there may be (would be, I'd say) non-trivial modal truths about them. Any particular such world might not have existed, for example. Far as I can see,here's no home in Lewis's account of modality for these sorts of...

I don't quite recognize relativity in what you're saying. Relativity tells us that an experiment in one inertial (non-accelerating) frame will look the same in any other inertial frame (that part also applies to Newtonian physics) and that the speed of light (in a vacuum) is the same in all inertial frames. (That part is a departure form Newtonian physics.) Relativity also tells us how to translate velocities, times, etc. between different inertial frames, and it gives an answer that's different from the Newtonian one. But the evidence for relativity has nothing to do with picking some one observer and giving that observer special status. On the contrary: that would go completely against the point of relativity. Further, there's no question of drawing experimental conclusions of whatever sort based on just one observer. Rather, what relativity says is that whichever observer performs an experiment, his/her state of inertial motion won't affect the physics. Whether the evidence from the observer's...

It is indeed an interesting question, and in fact it's more than one question. To begin with, my colleague is correct: in special relativity, length is like velocity in classical mechanics: it's a "frame-dependent" quantity. However, the theory of relativity is also a theory of absolutes; between any two points in space-time there is a quantity called the interval , and it is not frame-dependent. To put it in the jargon of relativity, the space-time of special relativity has a metric -- a generalized "distance function" -- and that metric delivers an unequivocal answer to the question of whether the interval between w and x is equal to the interval between y and z. But now we have a new question: suppose that relativity says that the interval between w and x is, in fact, the same as the interval between y and z. What kind of fact is that? Suppose that the two intervals have no overlap. Doing business as usual, so to speak, we come up with the answer that the intervals are equal, but we ...

I'd say that you don't have the Big Bang theory down correctly if by the Big Bang Theory you mean what physicists mean. Whether a physicist accepts some version of the Big Bang account as a piece of physical cosmology and whether the physicist believes that nothing is real except for the physical are two different questions. Some physicist (perhaps even most for all I can say) believe that there's nothing outside the physical, but that's not a claim within physics. It's a metaphysical claim that the Big Bang hypothesis doesn't settle. But suppose we're physicalists (i.e, suppose we think only the physical is real.) Is the combination of physicalism and the Big Bang inconsistent? I don't see why. You say that to speak of a beginning implies an occurrence within time. Let's concede that; it's logically harmless. The first moment, if there was one, was, of course, a moment in time. If time began, it began with the beginning; we can agree that this is circular (or better: a tautology.) But ...