Monday, May 09, 2005

Counter-Intuitive Logic

I was reading through the first chapter of the topology book I got and it was going over basic logic and set notation. I started thinking back to when I took logic in the philosophy dept. and the things that seemed strange to me:

1. The use of "or" mathematically. In everyday language, "or" almost always means A or B and not both. People usually adapt to this one quickly though.

2. The truth values of if-then statements. My favorite illustration of this is the following statement: "Every single congressman I know has killed at least one prostitute in a coke induced stupor and had to have it cleaned up by the mafia." Logically, this is: "for all x, x being a congressman that I know"-> "there exists a prostitute y such that x has killed y in a coke induced stupor and x has had the mafia clean it up." This is a completely true statement, since I don't know any congressmen, but filling in the right name for x would show up on a blog somewhere.

3. The whole necessary vs. sufficient game. I have to say that I don't like when people use this in a non-mathematical or scholarly situation. Grad school websites love to do it when talking about admissions requirements. Although I would like to see it incorporated into Valentines Day advertisements: "Getting your wife a diamond is a necessary condition for the really freaky business, getting her a Tiffany's diamond is sufficient (assuming, of course, that you ask for the freaky business in a piecewise smooth manner!)"

So anyways, I like logic a lot. If there was a market for logicians, I'd be all over it. Though, really, maybe a federal grant could be found to support logical evaluation of the media and politicians... er... probably not.


Anonymous Anonymous said...

They use the HELL out of necessary and sufficient in first year econ grad classes.

Chris Silvey

May 9, 2005 at 10:14 PM  
Blogger Adam M Osman said...

Yeay... by that of course I mean CRAP.

Well, ask me again in two years...

Good to see you posting Andy. I wish my finals were over too...

May 9, 2005 at 11:56 PM  

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