Originally posted by Mentat
That is pretty much what I'm saying, but I still think it's a valid point, since you cannot change the past from being the past. I'm saying this because:
1) If you could move the "present" back to another point in time, then everyone else would be in the future.
Assuming that the people from the present existed at the time in the past you plan to visit, then their former selves (and even your own former self) would exist where you went. The history of their existence states that they were at a given set of coordinates in space time, assuming you go back to a given temporal offset and close to the same physical coordinates as they existed in 'our' history, then you, as the time traveler would have to see them. With you, the time traveler, in the past and given the general rules of cause and effect, the future would then be somewhat fluid, since any changes you effected by being in the past, ripple through time altering events that followed those points in space-time.
2) If, instead, you move yourself out of the present, and into the past, then you have the same argument that I was using before (you cannot be in the past, because to "be" is to be now).
This is a statement, not an argument. Your initial argument was that time travel was illogical, inherently. This is only a statement that you cannot go into the past because it's in the past.
If you remember, one of the premises of this discussion was that we, hypothetically, have a method to go back into the past. Given that, you need to show the logical inconsistency that this sets up. If it always created a paradox, then that would be something forming a good argument, but just travel into the past doesn't create a true paradox.
BTW, the problem with moving the "present" into the past, with everyone else in the future, is that nothing that they "are doing" (please take note of the "are doing" part, since it's written in the present tense) has happened yet. You effectively destroy everything but yourself, since they have yet to come into existence (they are in the future).
Also, as to representing where something was on a graph, that is no big effort when compared to trying to plot a point where the object, A, exists and then plot a point where all other objects exist.
If time is an a dimension, then we are
required to have all those versions of ourselves in the past. Spacetime describes a set of four coordinates that can locate things in space and time. If 'Sam' existed at x,y,z,t - where t is in the past, then if backwards travel in time is possible, and we were able to travel to t at coordinates very close to x,y,z, then by the definitions of a coordinate system
'Sam' would have to be there. The act of visiting the past could, as mentioned prior, alter events leading to the present, as well as the state of the present.
We do not all exist in the past (unless you subscribe to the idea that we are constantly replicating new versions of ourselves, and that that is what traveling through time really is - in which case, I have some logical and scientific problems with that for you), and so the time traveller is removing himself from the rest of us to...where?
The idea of replicating is not accurate. If I move from place x to x+5. At some point in time I existed along all points between x and x+5 (assuming straight line movement). I didn't replicate myself. If I had been a point, then my motion would have produced a line in space and time. I hadn't replicated myself, I just existed at all those points in space-time. In fact, had my 'point' self had not moved, but existed thru a span of time, it would still form a line. A line orthoganol to all three spatial dimensions, but parrallel to the time access (but I digress). Going back in time is like producing a line (not a geometric line, just a contiguous set of points) that is discontinous in time at the point my 'point' self jumped back in time. It proceeds from a position in the present, jumping (or moving outside of our normal three-dimensional hyperplane) to a position in time previous. The prior self existed back there just as the my 'point' existences motion thru time produced a line
Let's add a dimension.
Let's use an example of two dimensional space with time as a third. We will use a cartoon, where all the cartoons are written like a child would draw them - with no overlap - this will be our bounded two dimensional space, with each frame being an instant in time. If we pick a particular point in the cartoon as 'now', then reverse the film a number of frames, that reverses time. You'll notice that the position in the film corrosponds to time and that there are things back in time. If we take a character from the present of our film, draw him into the past frames (as he looked in the present) then he has traveled to the past (given his past is defined by the positions, on the frames prior, in the film).
Now for a little depth.
Now let's generalize the film, making each frame of our movie, three dimensional. True, the film will take a lot more space

, but still the analogy will hold. Time travel would be going back to a previous frame in the picture. The
only difference between that time travel and the one we speak of is 'cause and effect' - by going back to a point in time previous to now, we start causing/changing things that were not events in our original history. If there is something that was changed that would effect the time traveler or his decision/ability to travel back in time, then we have a paradox.
There is some conjecture that the entire universe is basically the described 4D movie, with each frame being the hypothetical smallest unit of time (the time it takes light to traverse the distance of Planck's length) by the physical dimensions of the universe, and that all the past and future already exists, and only our consciousness is stepping thru the frames. In this scenerio, time travel would be logically impossible.