Russell’s Paradox

While breezing through a comic book, I read a few balloon captions about a mathematician named Gottlob Frege. Frege searched for the unshakable foundation upon which to build all mathematics. It surprised me that a mathematician would search for such a thing because I always figured numbers were already pretty solid, being numbers and all.

There are things, however, according to the comic book, calledparadoxes, which are capable of capsizing venerated mathematical systems easy as pie. Bertrand Russell’s famous paradox did just that to Gottlob Frege’s system, which is based on the idea that one can use a property to define any other group of properties and therefore form setsof properties. Russell’s Paradox is described like so: Consider a set of barbers who shave only those men who do not shave themselves. And here’s the paradox: suppose there is a barber in this set of barbers who does not shave himself. Then, by the definition of the set, he must shave himself. But no barber in the collection can shave himself. (If so, he would be a man who does shave men who shave themselves.) So, in short, if the barber is in the set, he’s not in the set. And if he’s not in the set, he’s in the set.

When he was young, Russell wanted to invent a machine that, using logic, would have the capacity to answer any question put to it with a logically indisputable answer. He was searching for the same thing Frege was searching for. He wanted to know the truth. All truth. And if he was to know all truth, he needed, at first, to know the fundamental truth, the foundation of all math and logic. But he never found it.

He eased up later in life on the whole fundamental truth thing and gave himself over to humanitarian pursuits and witty aphorisms, like the one you often see attributed to Charles Bukowski. “The cause of the trouble,” he said, “is that in the modern world the stupid are cocksure and the intelligent are full of doubt.”

This is the type of meme-worthy paradox I’m comfortable with. And it’s easier to understand than the one that made Bernard Russell famous. And it may even be true. But I have been having dreams at night of trying to repair equipment that refuses to be repaired. Logic doesn’t seem to apply. Nor do the laws of physics. And I find that the absolute truths I have built my career upon, for example, that a vapor expands to fill whatever container it inhabits, are, between the hours of eleven o’clock pm and seven am, useless. And I wake in the morning full of anxiety.

I have been having dreams that I’m running away from someone or something and I approach the mansion. It’s the same mansion as ever, although it looks quite different. Like a jail one night. A university building another night. A boarded-up library. I’m in the basement now. Down with the unrepairable boilers and pumps and pipes wrapped in insulation. It’s dark and I feel at home and I have a flashlight that doesn’t work and I’m crawling through tunnels beneath the first floor and now I’m climbing a ladder and I’m stepping out into a room equipped with a narrow bowling alley where three of my high school friends, Jimmy Walsh, Boot, and Dave Disabito are waiting with grappling hooks and spears. I’ve been here many times and I know that it goes on and on. I’m alone again now, as I’m walking down an abandoned hallway. But, at the same time, I’m with someone. I’m not sure who it is. But I’m always with someone even when I’m alone. And I’m climbing and shimmying. Always trying to get to the roof. Because I know the roof is where I must be. Once I’m on the roof, I might be free. I might understand something that I have been, thus far in my life, unable to comprehend. And I’m waking up the higher I go. I hear water running through pipes. I’m waking up as I try to jimmy the lock. Distant conversation. I’m waking up and I never make it to the roof. And Deb says, how did you sleep? And I say, “I was in the mansion again. And I think I was with you. But I’m not sure.”

And I’m driving my truck eastward on Route 80, the mist still swirling, the world still a maze of misshapen rooms, and from the radio, crisp statistics regarding the Spurs and the Warriors and the Broncos and the Panthers and then, eventually, the mechanical equipment once again, a commercial dishwasher at Prairie Hills Retirement Home, with a bad circuit board, supplied with 24 volts from a transformer which always and without fail follows the rules, and a cup of coffee that the maintenance guy, Randy, offers me and I fool myself into thinking that the world is solid, that I know enough to get by, and I no longer consider the mansion and I don’t wonder who is with me every night in the tunnels and stairwells, and I believe that this waking world is the only world of consequence, that nothing is unknowable. That Salvador Dali was insane. That nothing goes on forever. That Charlie Kaufman is insane. And the concept of infinity is nothing more than a nightmare invented for mathematical theorists. And there is no paradox that need concern me. There is only this. This lamp. This ashtray. This paddle game.

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