September 16, 2008

Laws of Logic Make the Political Scene

...and get completely mangled in the process, unfortunately. In this column about the McCain campaign's desire to have things both ways on every issue (via Yglesias), Jonathan Rauch puts the following words into the mouth of McCain advisor Steve Schmidt:

"You may have heard of the law of the excluded middle. No? It's from philosophy. Logic, to be specific. It says that if X, then not not X. Wait, bear with me. If a statement is true, then the negation of that statement cannot also be true. Otherwise everything could be true at once. You'd have fuzzy logic."

(Schmidt then goes on to say that this law isn't in the Constitution but was written by left-wing academics, so McCain can ignore it.)

But of course that isn't the law of the excluded middle, which says that P or not P. It's the law of double negation introduction. Double negation (as opposed to elimination) is intuitionistically acceptable, and excluded middle isn't. What Schmidt really means to reject is the law of non-contradiction, which says that P and not P is false (and is intimately related to double negation introduction).

Rejecting the law of the excluded middle might show an openness to nuance and rejection of false dichotomies, depending on your logic of vagueness. But I don't think any logic of vagueness will let you get away with rejecting non-contradiction or double-negation introduction. (I could be wrong, though.)

I also note that in asserting that everything could be true if a contradiction were true, Rauch assumes that we are not working with a paraconsistent or relevant logic; his description of these as fuzzy logics seems inapt, but we'll let that slide.

Posted by Matt Weiner at September 16, 2008 06:47 AM

Hi Matt!

Heres a relatively common exchange:

Are you still going to the concert?
I am and Im not.
How so?
Im going, but Im working the gates.

Makes perfect sense.

Heres the relevant sentence, fleshed out:

It is the case that I am going to the concert and it is not the case that I am going to the concert.

In other words: It is the case that P and not P.

Does it violate the law of non-contradiction? I dont know.

Maybe this is just a case of two different uses of the phrase going to the concert. If so, then I have to say: It is the case that P and not R.

Im not sure. What do you think?

Posted by: Joel Schmit at September 16, 2008 02:35 PM

Joel - two different uses of the phrase is, I think the standard explanation of this common phenomenon.

Matt - I think Mark Colyvan and some post-docs are working on a paraconsistent approach to the sorites paradox, so maybe there is a logic of vagueness that lets you reject non-contradiction. Also, I was struck by just how wrong that reference to fuzzy logic is, but it's probably based on the Bush/Gore line about fuzzy math (I really can't remember who accused who of that), together with having heard the phrase "fuzzy logic" somewhere. (Fuzzy logic actually being, of course, another logic of vagueness, except that it's more popular with engineers than philosophers.)

Posted by: Kenny Easwaran at September 17, 2008 10:55 PM

Hi Joel! I'm not sure I would diagnose that case as two different uses of the same phrase (if it's the common phenomenon) -- it seems to me more like using a contradiction to implicate something that's true -- but I don't work on this area, so "two different uses" may be more accurate.

Dialethists, who believe that there are true contradictions, sometimes say that borderline cases of vague predicates yield true contradictions -- that's probably relevant to the Colyvan stuff.

It was definitely Bush who kept accusing Gore of "fuzzy math" whenever Gore pointed out something true that involved numbers. Here's a good explanation of Bush's use of the term, here's Bob Somerby's account of the details of what Bush was doing.

Thanks for reminding me of that. I'm going to stick a fork in my eye now.

Posted by: Matt Weiner at September 25, 2008 06:37 AM