Take the case of a box sitting on a table. In an introductory physics course, we

Take the case of a box sitting on a table. In an introductory physics course, we'd say that there are two forces acting on the box: the force of gravity, pulling it down; and a normal force of precisely equal magnitude, pushing it up. Is there any real difference, though, between saying that there is no net force acting on a body, and saying that no forces are acting on it at all?

Sure there's a real difference. The first account implies that the box is being compressed vertically because gravity acts on all its parts (molecules) whereas the opposing force is acting on its bottom surface (where it touches the table). The second account implies that there is no such compression, that the box, even if it is somewhat elastic, has the same height when it is sitting on the table as when it is floating in outer space. The first account -- correctly -- implies the opposite: that the (not perfectly rigid) box is slightly less tall when it is sitting on the table than when it is floating in space.

The first account is also more elegant in this sense. Suppose the table is forcefully kicked out from under the box so that the box starts falling. The first account can easily explain this by pointing out that, with the table out of the way, the gravitational force now acts unopposed. The second account has to say -- oddly -- that the kicking away of the table somehow brings a gravitational force into existence.

Sure there's a real difference. The first account implies that the box is being compressed vertically because gravity acts on all its parts (molecules) whereas the opposing force is acting on its bottom surface (where it touches the table). The second account implies that there is no such compression, that the box, even if it is somewhat elastic, has the same height when it is sitting on the table as when it is floating in outer space. The first account -- correctly -- implies the opposite: that the (not perfectly rigid) box is slightly less tall when it is sitting on the table than when it is floating in space. The first account is also more elegant in this sense. Suppose the table is forcefully kicked out from under the box so that the box starts falling. The first account can easily explain this by pointing out that, with the table out of the way, the gravitational force now acts unopposed. The second account has to say -- oddly -- that the kicking away of the table somehow brings a gravitational...

Could there (is it conceivable/possible) be an alternate reality/universe (a

Could there (is it conceivable/possible) be an alternate reality/universe (a rich complex universe) which was such that mathematics could not provide any (or say very little) description of it?

Why not? We can conceive a nice large space filled with moving matter, all as in our universe, except that the laws of nature vary randomly in space and time -- which is really to say that there are no laws of nature. You could still use geometry to describe the trajectories of objects, but you could not simplify these descriptions with general formulas that cover, say, the force that objects exert on one another. Nor of course could you project any descriptions into the future (predict what will happen) nor even describe with any accuracy what is happening elsewhere or what was happening in the past (because you would have no firm ground for reasoning backward from the data you have to their origins).

So it seems that we can conceive such a world. But whether a cognitive subject could have experience of such a world, could hold it together in one mind, that's another question, one that is very interestingly examined in Kant's Critique of Pure Reason.

Why not? We can conceive a nice large space filled with moving matter, all as in our universe, except that the laws of nature vary randomly in space and time -- which is really to say that there are no laws of nature. You could still use geometry to describe the trajectories of objects, but you could not simplify these descriptions with general formulas that cover, say, the force that objects exert on one another. Nor of course could you project any descriptions into the future (predict what will happen) nor even describe with any accuracy what is happening elsewhere or what was happening in the past (because you would have no firm ground for reasoning backward from the data you have to their origins). So it seems that we can conceive such a world. But whether a cognitive subject could have experience of such a world, could hold it together in one mind, that's another question, one that is very interestingly examined in Kant's Critique of Pure Reason .

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.

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...

It seems that most astronomers and theoretical physicists believe that time only

It seems that most astronomers and theoretical physicists believe that time only began at the formation of the universe with the "big bang". Assuming that this is correct, is it possible for time to end (to no longer exist)? If so, what conditions would be necessary for this to occur? JW (Australia)

The easiest way to think of this may be in terms of some regular relation between time and the size of the universe. Expressing this regular relation as some mathematical formula, it may turn out that, going back from the present in accordance with this formula, we get to a past point of time at which the size of the universe is zero. We would have reason to postulate such a starting point as the origin of the universe if all we know about the universe supports or is at least consistent with our backward extrapolation. Big bang theorists believe that this is (by and large) the case.

The same mathematical formula may be such that, going forward from the present, we get to a future point of time at which the size of the universe is zero once more. We would have reason to postulate such an end point of the universe if all we know about the universe supports or is at least consistent with our forward extrapolation.

There are other conceivable end-of-time scenarios. The amount of stuff in the universe might be declining in accordance with some regular formula which predicts that there will be no stuff left at some future point in time. Or the amount of motion in the universe might be declining in accordance with some regular formula which predicts that all motion will cease at some future point in time. Again, if all we know about the universe supported or were at least consistent with such a forward extrapolation, we might have reason to postulate such an end of time.

To sum up. The passage of time presupposes that something is happening. Something happening in turn presupposes stuff moving in space (or some analogues, on which see Peter Strawson's book Individuals). Time can end by any of these three presuppositions ceasing to hold. We cannot experience such cessation. But we can have reason to postulate it by forward extrapolation -- just as we can have reason to postulate a beginning of time (big bang) by backward extrapolation.

Such extrapolation raises further philosophical issues: What can support our assumption that any mathematical formula (any laws of nature) supported by the evidence we have near the present will continue to hold? And likewise backwards: What supports a big-bang theorist's assumption that the laws of nature she relies on did not evolve but rather held all the way back in time so as to sustain her extrapolation?

The easiest way to think of this may be in terms of some regular relation between time and the size of the universe. Expressing this regular relation as some mathematical formula, it may turn out that, going back from the present in accordance with this formula, we get to a past point of time at which the size of the universe is zero. We would have reason to postulate such a starting point as the origin of the universe if all we know about the universe supports or is at least consistent with our backward extrapolation. Big bang theorists believe that this is (by and large) the case. The same mathematical formula may be such that, going forward from the present, we get to a future point of time at which the size of the universe is zero once more. We would have reason to postulate such an end point of the universe if all we know about the universe supports or is at least consistent with our forward extrapolation. There are other conceivable end-of-time scenarios. The amount of stuff in the...