The Greeks were ace weren't they? The olden days ones, not today's chaps obviously, rotters the lot of them. Forever gabbling away, can't understand a word of it.
One member of this rather spiffing club was a bloke called Zeno who came up with a number of irritating Paradoxes that are both obviously wrong and yet more tricky to actually disprove.
My favourite of many years is that of Achilles and the tortoise where Zeno shows that despite being many times faster than the tortoise and with only a short head start to make up it is still impossible for Achilles to overtake our lumbering quadruped.
As Aristotle puts it "In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead."
I'm not sure that's a clear as it could be though. Allow me to demonstrate.
Let's say Achilles is ten times faster and the tortoise has ten meters head start. In the time it takes Achilles to run to the tortoise's starting point the tortoise has only progressed a meter - the clever money goes on Achilles at this point, surely? No, think of the odds you'll get on the tortoise for a start!
So Achilles runs the next meter but by this time the Tortoise has made it another ten centimeters. Achilles covers this distance but is now short a centimeter - then short ten millimeters - then one millimeter. In fact every time Achilles reaches the point where the Tortoise was the Tortoise has moved on. Forever. In ever decreasing increments.
Now I've raced Tortoises many, many times and this almost never happens in reality, despite not being as fast a runner as Achilles - but where's the flaw in Zeno's logic? Bertrand Russell couldn't work it out and he was a clever bastard.
One blogger makes an ultimately unsatisfactory, but valiant, attempt to solve the quandary here at Spunkyy thoughts
Incidently,I collect philosophers' deaths - everyone has to have a hobby don't they? My sources say Zeno was killed by the "tyrant of Elea" but it's all a touch too vague for me. I'll probably let you in on some of the more exotic ones at some future time - if it's possible to ever reach that point.