happy birthday!

Something occurred to me about the Achilles & the tortoise paradox, but not sure whether it's correct. The conclusion would only be sound if you consider two dots (conceptial dots, with no volume, no size, no shape etc) that are constantly moving at different, but constant speeds. Then yes, the distance between the two dots would become infinitely small but the faster dot would never catch up with the slower dot.
But human being (and tortoise) do not move in a constant motion. We walk/run by taking a step, having a pause, however temporary (or in the case of the tortoise, a really long pause), before taking the next step. So essentially our movement is move, pause, move, pause etc. rather than one smooth movement. So it's perfectly logical for Achilles to catch up and overtake the tortoise, since it is possible for Achilles to move to a point before the tortoise has moved away from it.

Well, that's only if you believe that time exist as, essentially, one line. By that logic you would also be saying that there is no such thing as free will. Because the grandfather paradox is essentially saying that you can't change history because if you did go back in history and changed something, that change would have happened as part of history, so in which case you did not change history (there, another paradox).
But if you think of time as a plane (or maybe as possibility tree-ish thing, where each node is your decision), then you could easily solve that paradox. You could logically go back in time to kill your grandfather and still exist, but the "grandfather" you killed wouldn't be your grandfather anymore, since for you to exist you would have been born to someone else.
Of course, then there is the question of whether you are still "you" if you're not really "you" anymore, since you are technically not the same person as you were. Then you could go on to question what makes "you" "you", but then that would be a philosophical question of identity, which I don' t think anyone has an answer to, and is not really that relevant to the paradox.

I just read about the omnipotence paradox. Here's what I understand for the argument: since the being (say God) is omnipotent, then he has the ability to make himself unable to do something. So yes, he would be able to create a stone that he cannot lift because he makes himself unable to lift it. I guess the idea here is that when normally, we consider the idea of being "unable to do something", it is a passive state that we cannot control, whereas here, inability is an active state, so God actively makes himself unable to life the stone. I guess that sort of makes sense, once you wrap your mind around it.

And I agree with Beon (not completely though) that a lot these paradoxes are just playing on the vagueness of words. For example, "heap" is a subjective idea. If I want to, I can define heap to be "comprising of more than 1 component", and you won't be able to logically argue that I am wrong since there is no definite definition for "heap". Then in this case, 2 grains of sand make a heap, but not 1 grain of sand, and that's when a heap turn into a "non-heap", paradox solved.

For the Buridan’s ass paradox, if the two piles are the same then just start with any pile, or each one bite from one then from another. Why would you starve to death thinking about which one to eat? I mean if you are starving, presumably your aim would be to feed yourself, and not think about "how best" to feed yourself (that's only something you think about when you are not that hungry, and hence is able to think about other things), so it wouldn't matter which pile you eat from, whether they're bigger or smaller etc. as long as it can fill you right? Or maybe I think in too simplistic a manner.

Ouch, I think I just sprained my brain. Nice list though