A number of paradoxes have been attributed to Zeno. One of them is the Paradox of the Runner : in order for a runner to get to the finish line, she needs to cross the first half of the track. Once she's done that, she needs to cross half the distance from the halfway mark to the finish line. Once she's done that, she needs to cross half the distance from that point to the finish line; etc. It seems that there are infinitely many finite intervals that she needs to traverse before she makes it to the finish line. But it's impossible to accomplish in a finite amount of time infinitely many tasks, each of which takes a finite amount of time. Therefore, the racer cannot make it to the finish line. It's common to hear that the solution is to appreciate that the sum of infinitely many finite quantities can be finite. Mathematicians have taught us, we're told, that the infinite sum: 1/2 + 1/4 + 1/8 + 1/16 + ... actually sums to 1. So, if we view the racer as traversing the first...

Assume God knows that Hitler will go to Hell, because God knows all truths and it's true that Hitler will go to Hell. Does it follow that Hitler was "doomed" to that fate, that he had no say in it? I'm not sure that it does. For the reason it's true that Hitler will go to Hell might just be that Hitler freely chose actions that will condemn him to Hell. Some of the truths God knows may well have been made true by free actions on our part. See also Question 7 and Question 579 .

Have you looked at Thomas Nagel's What Does It All Mean? (Oxford)? You might also check out the resources here: http://www.apa.udel.edu/apa/governance/committees/teaching/orc/index.html Don't know how pop you want to go, but you might consult some books here: http://www.amazon.com/exec/obidos/tg/guides/guide-display/-/E6HCUZQ3JZNO/102-8596721-2293711

Because he was amazing. Wonderful writer, deep and original philosophical positions, tantalizing arguments. (Read his Enquiries , for instance.) Also, by all counts, a remarkable person. (Read Mossner's biography.)

It would be natural to describe you as an atheist, yes. You find the proposition that God exists intelligible (because you find the concept of God intelligible), but you believe that proposition is false. You'd be in the position of someone who had a concept of the Loch Ness Monster, who understood what the world would have to be like for there to be such a creature, but who believes that there is no such creature. What would we call someone who believes that the concept of God makes no sense? Perhaps an atheist too. But labels aren't important. Understanding differences is. You and such a person would both refrain from asserting that God exists, but for different reasons: you, because you believe that God does not exist, and he, because he believes that any proposition involving the concept of God is unintelligible.

The obvious answer to your question is Yes. You perceive the real world by opening your eyes, listening, touching, etc. The real world is composed of trees and traffic lights and eagles, and you perceive them using your organs of sense. If you think this is a cop-out, that somehow the world I described isn't "the real world", then you'll have to say more about what "the real world" is and about why you think the world I described isn't really "real".

You might also have a look at some of the other entries in the category: Probability.

I see the laptop on my desk. This seeing entirely depends on some fabulously complicated neural shenanigans in my head. The three-dimensional laptop certainly isn't in my head. But what about my perception of the laptop -- is that in my head? I make a fist. Its existence entirely depends on the operation ofparts of my body. Is the fist inside my body or part of it, as my liver is? Nothing gets "constructed in your brain". This is a loose (if natural) way of speaking that can get you into trouble. If we open your brain, we will find nothing there beyond neural matter -- no images, no portions of visual space. The activity of your brain does make possible your apprehension of the world around you, but it's certainly not to be identified with what's apprehended. The three-dimensional world that I perceive does not exist in my brain, optic nerves, retinas, etc., even though it's true that I could not perceive it without the latter. In fact, I would go on to say that my perception of the...

If everything that exists is finite and God is in some way infinite, then you're right that it follows that God does not exist. Does this prove that God does not exist? Well, the argument establishes this if its assumptions are true. The problem is that most people who believe that God exists will not acknowledge that your first assumption ("Everything that exists is finite") is true. So, in order to convince them, you'll have to give an argument for that assumption. Now that assumption isn't the same claim as the conclusion of your argument ("God does not exist"), but it is close enough that debates about it might well recapitulate debates about the original issue, namely whether God exists. So in sum, the logical form of your argument is great, but it's doubtful that it moves us much closer to settling the central question you raise about God's existence.

Right, the judge did argue that ID wasn't science. But one of his grounds was that there couldn't be evidence for it. So I wonder whether Richard's first paragraph in fact ought to make one pause about at least one of the judge's arguments. Perhaps one way of addressing your question would be to say that the hypothesis about a designer is -- if you insist -- scientific. But if so, it's a lousy scientific hypothesis (like astrology, alchemy, parapsychology, etc.): vague, hard to test, in so far as it can be tested it hasn't been confirmed, and there's a deep, highly confirmed, more parsimonious account that's available as an alternative. Given all this, the insistence on teaching ID in the science classroom must be explained in terms of the School Board's religious motivations. And that's something that we should take to be ruled out by the Establishment Clause of the First Amendment. (The justice in Pennsylvania also ruled in favor of the Plaintiffs on the grounds that the motivation behind...