Again recapitulating what a paradox is. If time travel works at all (the premise) then I can look up a historical event, and send a hand grenade back through time to that event. What then? The response "you obviously can't do that" isn't answering anything. What happens when I do? Deliberately, to defy the argument that it's impossible. What then? That's the whole issue.

Please answer this question: what happens if, today, you decide to not have gone to the store yesterday? What stops you from deciding this?

The way this particular idea of time travel works is like this:

1. A time traveler throws a grenade, killing Joan of Arc.

2. History happens.

3. The time traveler who killed Joan of Arc is born.

4. The time traveler goes back in time and kills Joan of Arc.

5. We hear of this event.

If we are looking at this when at time 5, do we find it surprising that it happened? Do we need any explanation? We can ask "what would have happened if the time traveler had instead killed Chairman Mao?", and we can get into a discussion on the possible future life of Joan of Arc etc. But since the event has already happened, we don't need a fundamental explanation for "why didn't it go differently", "what stopped the time traveler from doing differently" etc.

If you then accept that the future is just like the past - it is already decided - then the same banality happens if we learn of this event at time 3. We can ask "I wonder what would happen if this child wouldn't one day kill Joan of Arc", but it is simple musing about alternative histories, like asking "I wonder what would have happened if Hitler hadn't killed himself". The fact is that Hitler did kill himself, and that the child will kill Joan of Arc.

If you imagine the future as changeable, or if you imagine that beings can choose what they will do, then the paradox arises. But if you consider the future as set in stone, and if you consider that humans can't chose to do one way or another, than there is no paradox: history COULD have been different, but it just isn't. The same thing that stops you from changing the past also stops you from changing the future.

Note: I am not claiming that this view is "correct". Just that, if you accept it, than time travel really doesn't give rise to any paradox.

Answer: I have a time machine. If that means anything, it means I can go back to yesterday and decide not to go to the store. Otherwise what is it? Some kind of television into the past?

It is a loop between the present and the past. You keep talking though about deciding to do things, and in this paradigm, there is no such thing. I am not 'deciding' to write this post, it is simply a consequence of the evolution of the universe and my life so far. I may feel like I am free to write it or not, but that is only an illusion.

Just as much, if you have a time machine, and go to the past, you will do exactly what you had already done in the past. It is not something you have a choice on, it is simply a consequence of the universe so far. The same would be true if you went to the future - all your future actions were decided the moment you were born, the moment the Earth formed, the moment the universe was formed. There is no choice.

Ah. Then I decide to disbelieve in the deterministic model of the universe proposed. And I cannot be faulted for that, because its a consequence of the evolution of the universe. So we're done here.

Agreed! I said from the start - I'm not claiming that this is how reality works. I'm just pointing out that it is self-consistent and that it does solve the paradox.

I myself can't entirely believe this notion of a fully deterministic universe. Especially one that doesn't even involve randomness (though randomness by itself wouldn't bring in any possibility of choice).