Argument Validity

Once upon a time, by which I mean about a decade ago during the last Pax Americana Prosperous Times That Would Last Forever, I was in a fraternity.  More specifically, I was the social chair of a rapidly growing fraternity.  We had the best average member GPA of any Greek organization on campus, a fact we touted as a pissing contest victory despite (a) none of the other chapters giving a shit and (b) that same GPA clocking in approximately one full standard deviation below median for the campus as a whole.

Fraternities mainly exist as conduits for narcotics distribution. [1]  Sororities, on the other hand, exist mainly to corral all the hot girls of a campus into one place where they can pretend to like each other with minimal transaction costs.

One of the delightfully banal things about the Greek system is that every chapter has a derogatory nickname loosely based on its Greek letter appellation or common accepted moniker.  And thus Delta Sig becomes Delta Fag, Delta Tau Delta becomes Dorks ‘Till Death, Kappa Delta Klansmen’s Daughters, Alpha Phi All For Free, Chi-O Chi-Hos, AXO A Coke Ho, Gamma Phi Beta Jam A Vibrator, Kappa Kappa Gamma Visa Visa Mastercard or Daddy Daddy Please, Delta Phi Epsilon Dogs, Pigs, and Elephants, Tri-Delt the poetic if you can’t get some anywhere else, Tri-Delt or Tri-Delt, everyone else has, et cetera and ad nauseum.  No points for guessing SDT’s unfortunate sobriquet, but what did you expect joining, girls?

Sigma Alpha Epsilon, or SAE, gets one of two nicknames: Somebody, Anybody, Everybody – referring to the fact that SAE is the largest Greek organization on the planet – or Same Assholes Everywhere, referring to the members thereof.  Let’s explore the latter.

What our nickname is trying to tell us is that all SAEs are assholes.  Logically strong, remember?  Essentially, if you know an SAE, he is an asshole.  No half-assing about it.  Let’s call that our premise.

P: All SAEs are assholes.

Now let’s say we have a dude named Jizzypants.  Not what his momma calls him, but a mantle borne of 5 AM Jaegermeister shots, copious vomit, paddles to the bare ass, and one unfortunate incident with a Chi-Ho pledge back in his dorm room. [2]

Jizzypants is an SAE.  Can we conclude anything?

If you said, “well, yeah, he’s an asshole,” you’re right.  If you’re slightly bored and think better of yourself for getting it quickly, well, there’s a reason this post was tagged “The Basics.”  Congratulations, asshole, you’re going to grow up to brag to your third-grader about how simple long division is.   Except you won’t remember how to do it, which will really make you the asshole.  Thanks, Dad.

More importantly, let’s break it down into what should rapidly become our familiar logical form:

P: All SAEs are assholes.
P: Jizzypants is an SAE.
C: Jizzypants is an asshole.

What we have here is a valid argument, and it gets validity from the fact that the truth of the premises guarantee the truth of the conclusion.  If those premises are true, the conclusion must be true solely based on them.

Hold on one second, because we need to take a detour from the real world.  In the real world, we care about truth.  Validity doesn’t.  If we assume the truth of the premises, and the conclusion still has to be true, the argument is valid.  Even if the premises are actually false.  Huh?  Look at it like this:

P: Jenna Jameson is a man.
P: All men have penises.
C: Jenna Jameson has a penis.

The first premise is decidedly untrue, and I used Jenna Jameson as an example because we’ve all seen proof of that ourselves.  Some of you more genderqueer folks are also tut-tutting and scheming about how to educate me re: the second premise being false as well, and that I need to watch my kyriarchically oppressive cisprivilege backpack or some other pleonastic neologism you diddled up on your way to a _____ studies Ph.D.  I’d tell you to put a sock in it, but I’m not sure we’d derive the same meaning from the phrase.

Either way, the argument is valid despite the premises being untrue.  Why?  Because if the premises were true, the conclusion must be.  Note the must.  If a conclusion is possibly true based on premises, it isn’t valid.  Consider the following.

Alpha Phi’s nickname of All For Free is intended as a reference to those sisters’ easy availability for sex.  We have a number of words to describe this, so we’ll use “slut,” even though it’s really a girl-word with the true meaning “girl in my similar social circle or class who’s 10% hotter than I am.”

P: All Alpha Phis are sluts.

See Jane.  See Jane indiscriminately sleep with SAEs.  See Jane attend the Vagina Monologues.  See Jane “take ownership of her sexuality.”  See Jane proudly call herself a slut.

P: All Alpha Phis are sluts.
P: Jane is a slut.
C: Jane is an Alpha Phi.

OK.  Assuming our premises are true, must the conclusion be true?  No.  Could it be?  Yes.  We know that the set of girls who are sluts and the set who are Alpha Phis have some overlap, so Jane could be a member.  But we can’t prove it, so our argument is invalid.  It’s invalid because it could be false.  Not because it is false.  Because it could be.

Of course, Jane is not in the Greek system; she’s a GDI, or God Damn Independent.  Any former Greek will immediately deduce this lack of affiliation: if Jane was in a sorority, her sisters would have talked so much shit behind Jane’s back that she was either shamed into being more discreet in her couplings or turned straight-up to prostitution like a number of Tri-Delts I used to know.

Even though validity and truth are different concepts, and we need to evaluate validity without regard to (actual real world) truth, it’s important to understand both.  We now have two ways to attack an argument we think is flawed.

First, is it valid?  Does the truth of the conclusion follow from the truth of the premises, or is there a missing assumption?  If there’s an assumption, it’s invalid.

Second, if it’s valid, is one or more premise false?  If the argument is facially valid, the only way to discredit it is to knock out a premise.

[1] Our brother chapter several hours to the east had recently lost its charter for supplying an estimated 60% of the cocaine trade of a third-tier metropolis.  We never got caught ourselves.

[2] Yes, it’s a true story.  The nickname and chapter have been changed just enough that anybody who knows Mike in real life will recognize it.


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