If time machines have been invented, then no-one can change that. If you were to step into a time machine, travel back in time and try to prevent the invention time machines, you would fail.

That's a lot of difficult questions! First: I think we can do wrong to people who don't yet exist. It seems unfair to be less respectful of someone who will be born in, say, 2020 than someone who was born in, say, 1995. Second: it is not obvious that your second question makes much sense. You can't do wrong to a being who doesn't exist, never has existed and never will exist, simply because there are no such beings! A future being isn't yet around to be harmed, but will be later. But non-existent beings aren't there to be harmed.

You go on to consider a conditional: 'if ... it isn't wrong to cause them never to exist ...' where 'them' is supposed to refer to future people. But if we cause there to be no future people then 'them' doesn't refer and there is no issue about harming them.

Still one might want to argue that we have a duty not to make the planet uninhabitable because we have a duty to our species. I am not sure how to justify that, but the thought seems to have some intuitive appeal.

I take it that by "bivalence", you mean the principle that every proposition is either true or false. And if we take that principle in unrestricted form---we really do mean every proposition---then, well, it's hard to see how it could fail to imply that the proposition expressed by "There will be a riot in London on 13 January 2076" is either true or false.

If you don't like that conclusion, then you have to abandon bivalence---or, perhaps, the claim that the sentence in question expresses a proposition, though that seems rather worse. But note that you do not have to abandon bivalence, so to speak, across the board. You might still think that every mathematical proposition is either true or false, or that every proposition about the past is either true or false, or.... Perhaps there is something special about the future here.

As you probably know, Michael Dummett argued that one way to understand debates over "realism" takes them to turn upon our attitude towards bivalence regarding propositions about the subject matter in question: So a view that gave up bivalence for statements about the future would be a form of "anti-realism" about the future.

Others may have things to add, but one obvious way is that many of our beliefs about the past are caused by things that happened in the past and produced traces, either directly or indirectly, in our brains. But on the usual view about how the universe is wired up, our beliefs about the future aren't caused by future events.

This doesn't make knowledge claims about the past uniformly more secure than knowledge claims about the future. Some facts about the past may be well nigh inaccessible; their traces may be faint or non-existent, and there may be no good general grounds for inferring. (For example: I'd guess that there's almost no hope that anyone will ever know exactly how many people were on the swath of ground now marked out by the University of Maryland campus at noon on April 3, 1808. But -- skeptical worries aside -- we can reasonably claim to know that the earth will rotate on its axis over the next 24 hours.

Still, knowledge of the past has a certain priority. Our knowledge that the earth will rotate on its axis over the next 24 hours is based on things we know about the past and generalizations that this knowledge supports. Something like this is true in general: knowledge of future events is grounded in knowledge of the past, but not vice-versa.

You've raised lots of issues, but I wanted to single out one in particular. You seemed particularly worried by the possibility that there might be some sort of influence from present to past. The worry seemed to be that if someone did the wrong sort of monkeying around now or in the future, your past might be wiped out. That's a disturbing thought, but fortunately we needn't read Gödel et al that way. The trick is to distinguish between influencing the past and changing the past. Think of it this way: reality (or physical reality, anyway) just consists of the eternally-existing set of all events. On this picture, there's no question of a sort of "moving present" with events becoming present and then slipping into the past. There's just the set of events with all their many relations. You might find it useful to read what my fellow panelists Peter Smith and Jasper Reid had to say in response to question 2032 . Among the various relations are space-time relations, but there are also causal relations. It's just that we can't think of causing in the way that the "moving present" picture suggests as a sort of bringing-into-being.

On our usual way of thinking about things, causes are always unambiguously earlier than their effects. The speculations you're considering suggest that this may not be so -- that sometimes the direction of causation isn't the same as the direction of time. But the important point is this: the total set of events just is what it is, so to speak. If someone in the future exerts an influence on what I'm typing here, it's not a matter of their changing what I type; it's a matter of certain events in the future of my typing standing in a particular relation to all the events that make up my typing this reply.

This may be a little easier to grasp if we forget about changing the past and think about affecting the future. If my typing this "now" causes something to happen in the future, that doesn't mean I'm changing the future -- that somehow the future was one thing until I decided to type what I'm typing. Rather, it's that there's a cause and effect relation between events that come after my typing and the typing itself.

This picture seems odd when you first encounter it, but I dare say that it's the one most philosophers end up settling on. And if we accept it, then your past is safe; it simply is what it is, for better or for worse. Meanwhile, if you want to read an already-classic account of what it might mean to affect but not change the past, I recommend David Lewis's article "The Paradoxes of Time Travel." It first appeared in the American Philosophical Quarterly 13:145-52 (1976), and it's reprinted in his Philosophical Papers, Volume 2 (Oxford University Press, 1986). But in any case, I don't recommend eating Weltanschauungen. It tends to produce intellectual indigestion.

I think the difficulty here lies primarily in understanding God's knowledge and power as sort of "supersized" versions of our own knowledge and power. God's attributes are analogical at best. But the key to breaking through this kind of puzzle has to do more with the concept of time than of either omniscience or omnipotence. It's a commonplace of theology and phil of religion that God is "outside time." In other words, God's experience is not sequential, like ours is, but is eternally and universally present. So it makes no sense to talk about what God may or may not do "in the future" and what he knew "beforehand." Of course, what it means to be outside time is just as much, if not more, of a puzzle than the one you originally set out, but it seems to be closer to the target of inquiry than concerns about whether God's knowing or acting "comes first."

I'd go along with Peter Smith's answer, but I figured I'd just take the occasion to point you in the direction of a couple of classic discussions in this area, which you might be interested in following up. First, your question is startlingly close to a problem raised by Saint Augustine at the end of the fourth century AD -- you're in good company! If you're not already familiar with Augustine's discussion, it's in his Confessions, book 11, paragraphs 17 to 38, pages 168 to 174 in this edition. I don't know how much his own solution to the problem would actually appeal to you, which is effectively to say that time only really exists in the mind, the past in memory, the present in sight or consideration, and the future in expectation. But another way around the problem is suggested by J.E. McTaggart's article, 'The Unreality of Time', first published in the journal Mind in 1908 and available online here. McTaggart lays out various alternative ways of thinking about time, and it's up to you to decide which you'd prefer to adopt: but, if you adopt what he calls the 'B-series' view, then the temptation to deny the reality of the past and future will fizzle out altogether. On this view, the present moment, "now", is no more real than other temporal moments, past or future, in precisely the same way as the present location, "here", is no more real than other spatial locations, in front or behind -- and that's an analogy I'd invite you to ponder.

Take the sentence "Verdi died over a hundred years ago." That's true. It isn't made true by something happening now. The event whose occurrence makes that sentence true is something that happened in the past, in the 1901. (And this isn't a case like the founding of Rome by Romulus and Remus, a mythical event. Verdi was a real person. His death is an event that actually took place.)

I wonder just what is being said, then, by "there is effectively no actual past". Is it being claimed that really was no such actual event as Verdi's death after all (just as there was no actual event of the founding of Rome by Romulus and Remus)? The past is a blank and all history is a myth? That's absurd. Or is it being claimed that Verdi's death isn't now actual, i.e. isn't now happening. But that is trivial -- no one disputes that! So it is not immediately clear what sensible but interesting view can be expressed by "there is effectively no actual past". More needs to be said.

Another point: it is too quick to say that "it is commonly accepted that which cannot be measured cannot physically exist". For example, what about extensionless spatial points? Many would say that spatial points (or space-time points) exist, even though they have no size to be measured. The present could be like that. Sure, we can measure the distance between different spatial locations -- use a ruler! But equally, we can measure the distance betweeen different "temporal locations" -- use a clock. Thus, the kitchen clock tells me that eight minutes have passed between the past moment when I started writing this response and the present moment as I finish writing this paragraph now.

So some problematic assumptions underlie the question as put. Still, I certainly don't want to suggest that there are no deep and interesting questions in the philosophy of time, including questions about the ontological status of the past and future. One good place to start, if you want to explore these matters, is Robin Le Poidevin's engaging book Travels in Four Dimensions.

I shall begin with a 'philosophical' kind of answer, the kind of answer that philosophers ever since Aristotle's time might have given. (Indeed, it is closely related to the answers that Aristotle himself gave to Zeno's paradoxes of motion. Perhaps you're already familiar with those paradoxes: but, if not, then I'd invite you to look them up, for you might enjoy pondering them). I think the flaw in your question lies in that phrase "the next moment". In the case of space, you seem to be treating it as continuous in the sense that, between any two points, no matter how close they might be, there will still be further spatial points between them -- so that to jump straight from one to the other to be would have to involve some sort of teleportation, bypassing all those intervening points. And yet (as a philosopher might tell you) time itself is equally continuous, and in exactly the same way. At any given moment of time, there is simply no such thing as the next moment. The continuous nature of time means that, between any two moments, let's call them t₀ and t₁, there must be an intervening moment, call it t_0.5. And, between t₀ and t_0.5, a further moment, t_0.25. And then also t_0.125, t_0.0625, t_0.03125, etc., all standing between you and the moment you initially took to be the 'next' one. In a certain sense (and I don't intend this as an account of how motion works physically; just how it could work, logically), the mistake is to try to build up a big motion out of lots of little ones. The big motion ought to be the starting point. (It is said that Diogenes' response, when he heard Zeno spouting off about his 'proof' that motion was impossible, was simply to walk across the room!). Once you have the entire motion, between A and B, only then should you start to break it down and contemplate its component parts: getting half way between them by t_0.5, getting a quarter of the way by t_0.25, etc. The fact that there is no mathematical end to this process of breaking the motion down -- as opposed to trying to build it up from its 'least' parts -- means that there is no moment at which the object has to cross any real distance at all.

That, as I say, is the kind of answer that a 'philosopher' might give: but, particularly when it comes down to the kinds of topics that are nowadays studied by physicists, we philosophers ought to accept that we can't do everything on our own. (I've mentioned Aristotle already in this reply. Of course, in his day, there was no distinction to be drawn between a philosopher and a physicist -- but that's no longer the case). Now, I am not a physicist, and so here I cannot even pretend to approach the full story. But, for a start, quantum mechanists seem quite comfortable with the notion that an object might indeed just dematerialise from one place and materialise in another. Indeed, according to quantum mechanics, it's not at all clear that an object is ever in any fully determinate place at all. And then the string theorists will go on to tell you that, when you get down to the level of something called the "Planck length" (of the order of 10^-35 metres, about a trillion trillion times smaller than something already as tiny as an atom -- a shorter distance than I suspect your friends could ever even have approached imagining!), alongside something called the "Planck time" (of the order of 10^-44 seconds -- if anything, even more mind-bogglingly tiny!), then everything to do with space and time starts to go a bit haywire. For a start, there are ten dimensions down there! Now, it's not yet clear where all this cutting-edge physical research is going: but, who knows, maybe space and time will turn out not to be quite as continuous as Aristotle suggested after all. Although space and time certainly do still remain fascinating topics for philosophers, and philosophers surely do still have something to offer in this area, Einstein and his ilk taught us that we're not really competent to lay down the law about them on the basis of pure a priori speculation alone.

But, rather like Zeno, I'm tempted just to get up and walk across the room. No one seriously believes that motion doesn't exist: the philosophers will explain how it's possible that there should be such a thing at all, and the physicists will endeavour to find the laws of nature that explain how it actually works in the real world.

Nice question.

Is it not the case, however, that everything you say is compatible with the proposition 'Time is a dimension or framework within which things happen'? If all the atoms stopped moving then time would carry on, so to speak, but nothing would happen.

Similarly, we could suggest that 'time is that which allows the measurement of movement'. If all the atoms stopped moving, there would have to be time for the statement 'they have stopped moving' to make sense.