Who doesn’t like a good puzzle? Tests of our knowledge and dexterity, word play and numerical problem solving, these are the things that have propelled science to its currently lofty status…a genuine need to solve the puzzles of the universe.
But not all puzzles can be solved. Some are inexorably unsolvable, and the word used to describe such puzzles is paradox.
I would think that most people are familiar, at least with the word and its definition, but for argument’s sake, I’ll lay it out for you. The Encarta English Dictionary (North America), lists the following: something absurd or contradictory; a statement, proposition, or situation that seems to be absurd of contradictory, but in fact may be true. Or self-contradictory statement; a statement or proposition that contradicts itself.
The idea is quite rudimentary though the practical application of the word can be a bit tricky. In some cases, the thought process that leads up to a paradox is akin to mental gymnastics, and to that end I’ve included a few below.
THE GRANDFATHER PARADOX
This is a contradictory situation created by theoretical time travel, it goes as follows:
Suppose a man invents and builds a time machine for the purpose of travelling back in time to kill his biological grandfather before the latter met the traveler’s grandmother. As a result, one of the traveler’s parents (and by extension the traveler himself) would never have been conceived. Of course, had the time traveller not been conceived, no time machine could have been constructed, and no time travelled achieved, thus the grandfather would continue on and eventually produce through his genetic line, the time traveller born anew. This would imply that he could not have traveled back in time after all, which means the grandfather would still be alive, and the traveler would have been conceived allowing him to travel back in time and kill his grandfather. Thus each possibility seems to imply its own negation, a type of logical paradox.
The Grandfather paradox, first put down on paper in 1943 by science fiction writer René Barjavel, is a classical example of a logical paradox, and happens to be one of the more easily understood examples.
We deal with paradoxes in the real world on a regular basis, as is evidenced by the colloquial use of the term Catch-22, which is: being in need of some thing that can only be had by not being in need of it.
THE BARBERSHOP PARADOX
Briefly, the story runs as follows: Uncle Joe and Uncle Jim are walking to the barber shop. There are three barbers who live and work in the shop—Allen, Brown, and Carr—but not all of them are always in the shop. Carr is a good barber, and Uncle Jim is keen to be shaved by him. He knows that the shop is open, so at least one of them must be in. He also knows that Allen is a very nervous man, so that he never leaves the shop without Brown going with him.
Uncle Joe insists that Carr is certain to be in, and then claims that he can prove it logically. Uncle Jim demands the proof. Uncle Joe reasons as follows.
Suppose that Carr is out. If Carr is out, then if Allen is also out Brown would have to be in—since someone must be in the shop for it to be open. However, we know that whenever Allen goes out he takes Brown with him, and thus we know as a general rule that if Allen is out, Brown is out. So if Carr is out then the statements “if Allen is out then Brown is in” and “if Allen is out then Brown is out” would both be true at the same time.
Uncle Joe notes that this seems paradoxical; the hypotheticals seem “incompatible” with each other. So, by contradiction, Carr must logically be in.
There are more complex logical paradoxes as well, some that have a deeper meaning, such as below.
THE GOD PARADOX
The arbitrary suspension of one of more laws of physics, as is prescribed by virtually every Biblical Miracle, requires the progenitor of such an action to be, by definition, omnipotent – all powerful. Conversely, Biblical creator ideology demands that the same entity be omniscient –all knowing. These two concepts are in conflict and create an insurmountable paradox.
An entity that is omniscient possesses complete knowledge of the universe, including knowledge of whatever actions the entity itself will take in the future.
This knowledge of future events rules out free will – the entity will already know the choices it will make in the future and their subsequent effects. Such preordained choices cannot be changed otherwise they will not have been preordained.
Though an all powerful entity –omnipotent- has the ability to do anything, including the ability to make a different choice, however, the will to make a different choice would already have been foreseen –or preordained- and therefore the resulting change would not have been a different choice from that foreseen.
The resulting paradox creates an infinite regress that cannot be overcome.
If one deigns to be a logical person, one cannot deny the contradictory relationship between the two states above, though I suspect that few will acquiesce to the idea that the very existence of a God is by nature a logical paradox.
 This of course notwithstanding the question of why he would want to do such a thing