### 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.

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.

## 2 Comments:

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

Chris Silvey

http:www.chrissilvey.com/weblog/

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...

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