On Proof and Logic

I have this half memory of an article about the car guys, Tom and Ray Magliozzi, in which they talked about their experience at MIT. One of them had an assignment to show that something was possible. The answer was intended to be theoretical. Although the professor hadn't been explicit, the assumption was they the students would go fiddle with equations and axioms until they had proved that this particular thing was physically possible. Instead, the Magliozzi who was taking this class went home and built a physical object that performed the action in question.

Problem: Prove that X is possible.

Solution: Build a device that performs X.

Evaluation: But you were asked to prove X is possible.

Response: It's a proof by construction. That thing right in front of you does what you asked. X must be possible or our device couldn't do it.

At the time I just shook my head. How could this not be a convincing argument? Proof is a funny thing, but an existence proof can be satisfied by showing that at least one exists.

Of course, there are other systems of logic. Some of them seem silly to us. We think that we live in a Boolean world. We think we live in a world where a double-negative implies a positive. I scratched my head for days after hearing Atish explain the world he lived in. It was a world in which, as he would say convincingly, "if it is not true that that animal is not a cow, it does not mean that the animal must be a cow."

A dozen years later and I'm still trying to work that one out.

Kim and I are having a great deal of difficulty making sense of things. The usual laws of logic don't seem to apply. Yesterday was three months since Elena died. You'd think things would be getting easier. Some things are. Some things aren't. Kim was cautioned that this is the point where some aspects will get even harder to deal with.

Logic is one of them. You stand so firmly on logic only to find the foundation is shaky. Maybe our world isn't so Boolean. It was not true that Elena was not a healthy child. It seems though that this was not enough for it to be true that she was a healthy child. This excluding the excluded middle seems to be leaving an awful lot out.

We're having a harder time, though, with proof. It just doesn't seem possible for a healthy and happy six year old to die so suddenly. The fact that it happened still doesn't convince us that there is any way in which it could have. The existence proof is unconvincing.

Argument: It can't happen.

Reply: It did happen.

Evaluation: Somehow that doesn't prove that it could happen.

Published in: on May 23, 2006 at 12:01 pm  Comments (4)  

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4 CommentsLeave a comment

  1. It’s hard to be in this beautiful place and not think of Elena. Your logic and proof words today remind me of many of my own thoughts lately. Elena’s death was not logical, regardless of any proof to the alternative. Looking at the ocean here today I can almost sense her – alive, happy, dancing on the beach. This is where I’ve decided to put her for now – roaming these sands with the wild horses that have lived here for generations. There’s a spunky new born foal that’s been hanging around our house with her mom and sister. She’s got a certain gleam in her eye that reminds me of Elena. And she’s driving poor Lou crazy – sound familiar?? I’m thinking of you all.


  2. oh the world isnt boolean, its very analog. Different degrees to everything. Hope you cope better with the loss.


  3. not that this is at all the same level… but when I was surprised by my husband announcing that he wanted a divorce… i went thru this period of why and how did this happen… i kept looking at my “perfectly happy marriage” and trying to figure out where and when it went sour.

    the thing was, I couldn’t do it. I never did find out the why or the how… what i realized was that the logic behind the divorce didn’t matter any more because the reality was… i was divorced.

    I wonder if that might not be the same with such a death as Elenas. There is no logic behind it and looking over the course of the years of her life… it can’t be…. but reality tells you other wise.

    I use to sum that up with… “Sometimes, I really hate reality.”


  4. Oh, don’t let anyone tell you when the hard part should be over. This Sunday will be our son’s 2nd birthday in heaven. The sting of death is still very real. The first year for us was the roughest. I think once you get through that first year, you know you CAN make it – but it’s still hard. Take one day at a time. My thoughts and prayers remain with you.

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