A paradox is a statement that on the surface makes no sense at all, yet cannot be disproved. A 'pera-dox' is our sad attempt at wordplay. Paradoxes exist in many academic fields, including physics and mathematics. Here are a few logical paradoxes you can ask Siri (or the Android equivalent) and wait for your special little iPhone to explode.
There is only one barber in a town and he shaves men, and only those men, who do not shave themselves. So who shaves the barber? There are two shaving possibilities for every man in this town. He either shaves himself or the barber shaves him. But the barber cannot shave himself because he only shaves men who do not shave themselves.
Maybe the barber could go on holiday every now and then to get a shave from some exotic location or other. Or, when asked why he's suddenly clean-shaven, could claim a goat ate his beard in his sleep. He ought to be fine so long as the authorities don't look too closely into it.
You can never do anything. Because to do something, you must first complete half that task. Before you complete half that task, you must complete half of your first sub-task. But hold up. Before you can even THINK of half of your first sub-task, you will HAVE to tend to half of half of your first sub-task. So we can see that every task consists of an infinite amount of sub-tasks. Since it is impossible to perform an infinite number of tasks, we can thus demonstrate that it's impossible to do anything at all.
Instead of falling into a severe depression over this, or making philosophical excuses for being a lazy bum, I suggest you do something regardless. Then celebrate your infinite accomplishments, inflating your ego. Maybe even dance on Zeno's grave. You have defeated Infinity; that should do wonders for your self-image. You could, on the other hand, use this knowledge for evil and make excuses whenever your parent, teacher or your editor asks you to do something.
THE IMPOSSIBLE FIGURE PARADOX
The picture below is a paradox because you see it, and it’s there, and seeing is believing. Except you know what you see is not possible. That is, such a figure could not exist in reality. An effect achieved by attempting to view three dimensions using only two. M.C. Escher draws stuff like that, except you can appreciate his works because he isn't trying to explode your mind-head.