Truth Functional Conditionals, or why we can't accept that it's any given Saturday -- or Thursday

Maybe it's the sweater vest I'm wearing, or my unintentional schadenfreude, but I had a heck of a lot of fun watching the No. 1 USC Trojans get peeled and deveined by a Pac 10 opponent with a losing record and a featured running back that's my height.

Say what you want about Jim Tressel not being able to coach his teams in big games.  Pete Carroll can't handle the little ones.  USC's two-faced troubles are well documented.  In 2006 it was the same carravan to Corvallis that killed the Trojans.  Last year, SoCal was again embarassed by elementary competition -- this time at home.

Columbus can't slay the dragon, Los Angeles can't swat the fly.

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Watch out Pete.  If you thought the Beavers were brutal wait until you see Stanford's new tree.

So, as the rest of the nation privately smirks (a la John McCain) at the thought of a championship race blown wide open and a new dawn in parity, I thought I'd tackle the big question.

Can we learn anything from this?

The answer.  Not really.

If you're an unemployed philosophy B.A. who wasted $100,000 on a useless, but intimately satisfying liberal arts degree you might remember the truth functional conditional.

Like it or not, the concept provides the underpinnings for the rational assumptions we make about everything in life, from dating to football. 

As Wikipedia describes, truth functional conditionals "can be viewed as a subset relation between the extension of (possibly complex) predicates."

What the hell are you talking about Jon?

I'm glad you asked.  I'm considering the logic we use to compare college football teams that haven't played one another.  As I write this Minnesota, Colorado, Alabama, and Oklahoma are all undefeated.  Despite their flawless resumes, there's nary a soul (outside of Tuscaloosa) that wouldn't rank them in the following best to worst order:

1. Oklahoma, 2. Alabama, 3. Colorado, 4. Minnesota

How do we come to this conclusion?  Sure, there are objective statistics: margin of victory, offensive yards accumulated, defensive yards allowed, but these simply aren't the bread and butter of our assumptions system. 

Disagree?  Tell me right now (without looking at an almanac) who has had the better statistical offense in 2008: the unranked Golden Gophers or the No. 8 Crimson Tide? (If you guessed Saban's squad, you'd be wrong -- they rank 57th nationally, compared to Brewster's 45th place mark. See)

But wait, you protest.  It's not that simple.  There are alternative variables, like strength of schedule that dramatically impact a unit's quantitative output.

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No. 5 Ohio State got pretzeled by No. 1 USC, who got overrun by an unranked Oregon State team who was completely outmatched when they played No. 12 Penn State.  If the Buckeyes beat the Nittany Lions when they visit Columbus on October 25th what are we to make of it?

I won't argue that opening against a then top-ten Clemson in the Georgia Dome in primetime is a little different than playing Northern Illinois at home -- and needing a last minute stop to hang onto the win -- but even here reasonable minds can disagree.  Consider this guide, that seeds Minnesota's Big 10 strength of schedule above (as harder than) Alabama's SEC slate.

The point is you can use numbers to say anything.

And that's why we're more likely to rely on subjective intuitions, or loose preconceptions, to determine a team's stock.  Where do we get these preconceptions?  Truth functional conditionals, my friends.

We're talking about the (seemingly logical) connections we make in order to compare a catalog of unrelated subjects.  For example, every fifth-grader (tenth-grader if you're from the South) knows that if A is greater than B and B is greater than C, A must be greater than C.

We don't realize it, but we follow this same logic when we rationalize the strength of a given team in comparison to outstanding competition.

The problem is cold intuition doesn't translate to a live arena like competitive sports.

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No. 5 Michigan was shocked in 2007 by the FCS Appalachian State Mountaineers.  They went on to poach the defending-national champion Florida Gators in the Capital One Bowl.  Could the I-AAs have sacked the SEC?  It depends.

Reputation, tradition, and rankings aside -- performance in the present depends on one thing: the eleven men who take the field. 

Our attempts to acknowledge this simple truth are routinely thwarted by self-proclaimed masterful, and ever so often emotional, past to present models of thought.

Are material assumptions clouding your judgment?  Answer this simple hypothetical:

If flip a coin and it turns up heads fifty times in a row, what's the (percentage) chance it will come down tails on the fifty-first flip?

Reasonable minds can disagree, but it really is any given Saturday...or Thursday.

Now quit thinking so hard, crack open a beer and enjoy today's football.

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