How is Zeno's paradox solved? Thanks, andrea

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...

If God exists and he knows it all, even the future, then he knew Hitler would go to hell before Hitler was even born. Why would God give someone life, just to send him to hell for all eternity? Is this fair to Hitler and all those doomed to go to hell or is this proof that God doesn't really know it all, not the future at least?

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 .

I read that David Hume is called the "amazing". Why was this? Allan Whatley

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.)

If I believe that God does not exist, but at the same time think that the idea of God is meaningful, am I an atheist? If not, then what position - philosophically - do I take?

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.

Is there a way to perceive the real world? Thanks.

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".

An old device called a stereopticon held two photographs taken from closely related viewpoints, such that on looking into it the observer saw a three-dimensional view of the photographed scene. This proves that we unconsciously construct, in our brains, a three-dimensional space out of two two-dimensional images, one per retina. Also, if you have someone hold up a finger, it is easy to bring your finger down on to its tip, but if you try this with one eye closed it is difficult -- proving that two eyes are necessary for seeing three-dimensional space. But this means that our three-dimensional visual space is inside our heads, whereas we clearly experience it as out side our heads. So which is it?

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...

How can God exist if every thing that exists is finite? If an entity is infinite does that not conclude that it does not exist? My question is, have I even scratched the surface at disproving the existence of God? Descartes said that an infinite essence created all living things, but if this is the case, how can nothingness create existence? A comment would be much obliged. This is driving me crazy. Any opinions?

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.

In relation to the debate raging in the US about evolution and Intelligent Design, I would like to know whether positing the existence and prior activity of an intelligent designer is a scientific or a philosophical question. Is it scientifically conceivable that the existence of a designer and of things having come about purposefully as opposed to randomly could ever be deduced from available or putative evidence?

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...