A Quick List of Common Fallacies

1.         Ad Hominem

Attacking the speaker instead of the message.  “Senator Pinko’s ideas on crime are wrong, because he’s a Democrat.”

2.         Equivocation

Where words change meaning from premise to conclusion.  You know what equivocation is, because every dirty joke you’ve ever heard uses it.

For instance,

Premise:

 

I want to see your peacock, cock, cock.  Your peacock, cock.

Conclusion: Gee, Katy Perry must really like birds. [1]

3.         Exclusivity

Exclusivity is an option-limiting fallacy, where people falsely believe that either one option or the other must occur, without realizing both can, or some unstated third option.  For instance, young folks often think that if they don’t get in to ______ school, their lives will be ruined.  They don’t realize that both can occur until the loan bill comes due.

4.         Absence of Evidence

I like to call this the Apple Juice argument:

Why do I only drink apple juice in the mornings?  Because OJ will break into your hotel room and rob you of sports memorabilia at gunpoint.

When I’m teaching, I always laugh and forget why I was making fun of OJ Simpson and have to look back at my notes.  The absence of evidence fallacy is “We couldn’t find enough evidence to convict OJ of murder, so he must not have done it.”  Stated more broadly, just because you have no evidence something is true does not mean it’s false.

5.         Composition

Whole to part: The characteristics of the group are falsely assigned to each member of the group.  American colleges now are 60% female, so each American college student is 60% female.  LGBTQIAXRA is going to have to add a couple more letters.

Part to whole: The characteristics of the individual are falsely assigned to the group.

 

The Rock is often concerned with whether people can smell what he’s cooking, so the WWE must be a nasal health organization.  Or a restaurant.

6.         Circular Reasoning

This is a perennial favorite among logic neophytes.  They all love to find circular reasoning in everything.  It’s actually pretty rare, and blatantly obvious when it occurs.  The best examples, like most other real world logic, come from rap music.

 

“I’m hot because I’m fly.”  Mims.

P: I’m attractive.
C: I’m attractive.

7.         Absolute numbers vs. percentages

Any link between absolute numbers and percentages is suspect.  A larger percentage of a smaller number can still be smaller than a smaller percentage of a larger number; 10% of 1000 is larger than 90% of 100.

8.         Statistical fallacies

Biased sampling and control group issues come up from time to time.  Imagine a study that purports to show that most Americans support a full-scale legalization of marijuana that was solely conducted in Northern California and Boulder.   The sample must be representative of the population it claims.

It also can’t contain any loaded questions, or those that force an assumption on the answerer.  The classic example is “have you stopped beating your wife?”  Oooh!  Double bind.

9.         Correlation vs. causation

Correlation does not imply causation.  Hospitals are full of sick people, so if you go to the hospital you will become sick.

10.       Categorical fallacies

The most common of all, categorical fallacies are anything where the scope changes categories.  These will often manifest in either past/present/future time changes – what happened vs. what will happen – or shifts in probability or prescriptive nature, like can happen vs. should happen vs. will happen.

It is currently noon where I am.  I could make a categorical fallacy argument based on that:

P: The sun is currently out where I am.
C: The sun will always continue to be out where I am.

11.       S/N or Transitive Fallacies

Assuming a sufficient condition is necessary, or vice versa, or incorrectly chaining transitive conditionals.

[1] Note this is an identical equivocal conclusion to that we could have reached from “I Kissed A Girl.”


We’re Not Just Sure, We’re Contrapositive

So I lied.  One more basics post.

We’ve dealt so far with how to conceptualize and diagram conditional statements.  Here are two special cases that come up from time to time:

No – The word no is just as logically strong as all and when, and also indicates a form of sufficiency.  Let’s say we take a break from shooting the most expensive music video ever [1] to fight Krist Novoselic backstage [2] and for some reason play a dueling-pianos duet with Sir Elton:

 

Why do we do it?  Because nothing lasts forever, even cold November rain.  More precisely, no thing lasts forever.

How do we deal with a statement like that?  Two steps:

1.  Change the no to an all.

All things last forever, or, if it’s a thing, then it lasts forever.

T –> F

2.  Negate the necessary condition.

If it’s a thing, then it does not last forever.

T –> /F

So, no thing lasts forever becomes

T –> /F.

AND/OR contrapositives

Sometimes, you can get conditionals with conjunctions [ANDs] or disjunctions [ORs] in them.  Like this:

 

What does Gene Simmons do on an average night?  Two things.  He rocks and he rolls.  If it’s night, he’s rocking and rolling. [4]

N –> Rock and Roll

The contrapositive of this needs a slight tweak.  Since we know night is enough to guarantee that we both rock and roll, the absence of one or the other means it can’t be night.  

/Rock or /Roll –> /N

Simple lesson: when taking a contrapositive, just switch and to or and vice versa.

Homework example:

 

So ladies if the butt is round

And you wanna triple-X-throw down

Dial 1-900-MIX-A-LOT.

Kick them nasty thoughts.  Baby got back. [5]

[1] November Rain was the most expensive music video ever shot at the time, mostly due to the rotating helicopter shot of Slash outside the church.  It was eclipsed almost immediately in cost by TLC’s Waterfalls.

[2] Guns N’ Roses got into an infamous backstage scuffle with Nirvana at either the 1991 or 1992 MTV Music Video Awards.  I’m too amazed Slash is relatively sober enough to play the solos on the beat [3] to remember.

[3] Scratch that.  I just heard the outro solo.

[4] We’ll ignore for now how he also parties ev-e-ry day.

[5] Trivia time: the masterful introduction to Baby Got Back was done, in a woefully uncredited role, by Mrs. Mix-A-Lot.


Just Dropped In To See What Condition My Conditional Is In

Start with an affirmation.

 

Not that kind of affirmation.  A conditional statement.  Yeah, it’s actually called an affirmation.  Nobody calls it that.

A fair number of cities in America have bars named Rick’s American Café, after the infamous (and fictional) Rick’s Café Americain in the seminal Bogart film.  Go to Casablanca for real, and you might be excited to attend the real Rick’s, until you learn that it was founded in 2002.  You’d also be shocked at the price of alcohol in a Muslim country.

Anyway, the real Rick’s – the royal Rick’s – the editorial Rick’s – is a stuffy basement shithole in a Midwestern college town.

 

This Midwestern college town most certainly does not lack for shithole bars, either of the sub- or superterranean variety.  Rick’s, however, is Dana Carvey Church Lady meets short bus special: a delightful top-40 punctuated meat market that serves as the final stopping point of a Thursday through Saturday night for just about anybody in town.  Until, of course, The Gambler plays.

So.  Our affirmation.

If you’re at Rick’s, you’re at a bar.

R –> B.

What happens when we take our conditional statement and negate both sides?

/R –> /B?

If we’re not at Ricks, are we not at a bar?

Well, no.  We could not be at Rick’s and still be at a number of other bars, either drinking a man-sized [1] well G&T at the Blue Lep, pissing in the ice trough after a round of Smoker’s Coughs [2] at Brown Jug, struggling through the whale wars at Charleys, [3] mingling with the underaged at Skeeps, [4] or just getting herpes from the jukebox over at the 8-Ball. [5]

The takeaway is that negating both sides of a conditional statement gives us the inverse, which is invalid.

Likewise, what happens when we flip our original conditional?

B –> R

If we’re at a bar, are we automatically at Ricks?  Once again, no – we could be at other bars, wreaking havoc in other parts of town.  We will, of course, end up at Rick’s.  You always do.

Reversing the conditional like this gives us the converse.  Like the inverse, it’s invalid.

Let’s try both.  Flip them AND negate both sides:

/B –> /R

If we’re not at a bar, we’re not at Ricks.  Now we’re getting somewhere – remember that, in our original conditional, being at a bar was necessary for being at Ricks.  If you negate the necessary – which is, if you recall, necessary for the sufficient condition to be able to occur – you just made the sufficient impossible.  In other words, if you’re not at a bar, you’re not at Rick’s, because Rick’s is a bar and it would be impossible to be at Rick’s without being at a bar.  Make sense?

This is valid, and called the contrapositive.  Every conditional statement contains its contrapositive.  Automatically.  Every conditional statement contains its contrapositive.  If you have any conditional statement – any at all, like, say,

 

When the sun shines, we’ll shine together

SS –> ST

You automatically know that its contrapositive is also valid – that if you aren’t shining together, than the sun isn’t shining either.

/ST –> /SS

Transitive Logic

Unlike Django, conditionals can be chained, as long as the sufficient condition of one conditional matches the necessary condition of another.  Back to the bars.

If you’re at Skeeps, you’re 19.  And probably a ten-pounds-overweight Tri-Delt. [6]

S –>19

If you’re 19, you have a fake ID.

19 –> FI.

Note that the sufficient condition of one statement matches the necessary of another.  When this is the case, the two conditionals can be chained: if you’re at Skeeps, you have a fake ID.

S –> FI.

The contrapositive of this also holds: if you don’t have a fake ID, you’re not at Skeeps.

/FI –> /S.

When the sufficient conditions of both statements match, or the necessary conditions match, we can’t validly chain the conditionals.  If, for instance, you’re at the wine bar in Melange, you’re 35.  If you’re at the wine bar in Melange, you’re drinking overpriced wine.

M –> 35
M –> D$$$W

We cannot validly conclude that if you’re 35, you’re drinking overpriced wine. Remember, there’s always that one creepy 35 year old in the corner at Ricks just sort of staring at the dance floor, usually next to Black Guy In A Wheelchair. [7]  He’s drinking Bud Light.  And some of your Sharkbowl when you’re not paying attention.

35 –> D$$$W is invalid.

That’s it for the basics.  Next time we start exploring the really illogical shit that people really think.  For real.

[1] God bless you, Steph, wherever you are.

[2] A shot of Jagermeister with a float of mayonnaise.  I will buy you one if you ever figure out who I am, track me down, come to wherever I live, ask politely, and put out afterwards.

[3] Hit the treadmill.

[4] Unofficial but explicitly stated door policy: “if she’s over a 7, she’s over 21.”

[5] The only bar ever to smell worse after the smoking ban.

[6] See [3], supra.

[7] Seriously, I thought this dude owned the place until I talked to him one night.  He was a dick.


Chateau D’If: A Further Sufficiency/Necessity Primer

One caveat.

Just because the sufficient condition guarantees the necessary does not mean the sufficient condition causes the necessary.  We’ll get into causes like a privileged LUG who just decided dreadlocks represented the real inner struggle of her sophomore year later, but conditionals have no causal meaning.

Take, for instance, Stevie Nicks telling you that thunder [cymbal] only happens when it rains.

She’s telling you that if it’s thundering, then it’s raining.

T –> R

Or, hell, that players only love you when they’re playing.

If they love you, then they’re playing.

LY –>  P

What Ms. Nicks is not telling us is that thunder causes the rain, or that players’ loving you causes them to play.  We know, for instance, that despite thunder occurring concomitantly with rain, the latter is actually caused by condensation, or miracle Cthulhu piss, or something.  Fuck if I know.  I’m a logician, not a paleomythometeorologist.  But the rain is definitely not caused by the thunder.  Likewise, playing is not caused by players loving you – that stems from a volatile admixture of testosterone, boredom, barely-concealed narcissistic injury, and, in the case of Fleetwood Mac, one elephant-assload [1] of cocaine.

Take your silver spoon, dig your grave.  Silent prayer for those of us that missed the 1970s. [2]

The easiest way to determine which of your conditionals is sufficient and which is necessary is to look for indicator words, like we did with conclusions and premises.

Sufficient indicator words tell you that the condition following it guarantees the necessary.  Sufficient indicator words, therefore, must be absolute and tell you something about 100% of the condition they mention:

If, all, every, when, whenever.

When S happens.  Not “sometimes S leads to…,” not “S can mean…”  but whenever S occurs.  Every.  Logically absolute.  Every good boy deserves fudge.  What do we know about a good boy?  If he’s a good boy, then he deserves fudge. [3]

Necessary indicator words will espouse some sentiment of requirement, or, you know, necessity.   They will also be absolute and logically strong.

Then, needs, requires, must have, only*

Only is a tricky one, as it refers to the necessary, or, put another way, the referent of the ‘only’ is the N condition.  For instance, what’s the only way to a man’s heart?  Through his stomach?  Sweet, but anatomically retarded.  The only way to a man’s heart is directly through the sternum, with force.

Look at the only, and at the next word that directs its reference: the is.

The only way to a man’s heart is through the sternum.  Ignore the stuff between them for a second.  The only way is through the sternum.  If you got there, you must have gone through the sternum, as the only way there is through the sternum.

If you’ve reached a man’s heart, you must have gone through the sternum.

MH –> TS.

What heals a broken heart?  Time, right?  In fact, only time will heal that broken heart.  Here only refers to time:

Heart Healed –> Time.

Look at the examples used at the top.  Thunder only happens when it rains.  It may seem like we have two contradictory signals – only indicates necessity and when generally indicates sufficiency – but here the when only exists as the referring word paired with the only.  The pair is really “only when,” indicating necessity.  If it’s still confusing, look at these two side by side:

Thunder happens when it rains; Thunder only happens when it rains.

First: Thunder happens when it rains.  When it rains, then it thunders, or rain guarantees thunder.

R –> T

Second: Thunder only happens when it rains.  When do we get thunder?  Only when it rains.  Thunder guarantees rain, as thunder does not occur if it doesn’t rain.

T –> R

One last special case: unless, until, except, and without.

Most logic books will tell you these indicate a negatively framed necessity.  That’s an acceptable way to understand them, but there’s a much easier method in practice.

Take each of those words when they occur, replace them with “if not” and make the very next thing the S condition.  Whatever else is there becomes the N.

Sweet golden-voiced pudgeball Kelly Clarkson wants you to know that her life would suck without you.

If not you, then life would suck.

/Y –> LWS

The estimable Mr. Broadus [4], in hosting the evening’s festivities, would like to remind us that the bitches ain’t leaving until six in the morning. [5]

If not 6 AM, then the bitches ain’t leaving.

/6 AM –> /BL

What happens at 6 AM?  We don’t know.  What we do know is that if the bitches have left, it must be at least 6 AM.  Smoke an ounce to that and we’ll cover more next time.

[1] Probably literally.  How else did they smuggle it back then?

[2] Like me.  Fuck.

[3] Rule 34 leads me to believe that there must be a music-lesson-themed gay porn out there titled Every Good Boy Deserves Fudgepacking.  You’re on your own finding it.

[4] What’s my motherfucking name?  Snoop Fuck if I know.  Pick an animal and stick to it.

[5] Six in the morn!


Das If: Conditional Logic, Part I

Some logical statements merely contain a preposition: it’s hot in herre, Bo can’t rap, Jizzypants is an asshole, et cetera.

Others contain a hypothetical relationship between two conditions.  Those of you who bothered to read the caption have probably figured out that we call the latter set conditional logic.

The two conditions are the sufficient and necessary.  The next time you get that bourbon feeling enough to do something socially maladroit and some nasty Eichmann librarian type tries to scold you by reminding you of “how unnecessary” your actions were, look her right back in the eye with a smirk and respond “…but yet, not insufficient.”  Do it in a Dr. Evil voice for added mirth.  She’ll shut up nine times out of ten, making the response not technically sufficient, but worthwhile all the same.

So what does this shit mean?

The sufficient condition guarantees the necessary condition will occur.  Every single time the sufficient condition happens, the necessary condition will happen as well.  Sufficiency is the ultimate in logical strength: it’s enough by itself to allow you to validly conclude the necessary will come to fruition.

The necessary condition must occur for the sufficient condition to be able to occur.  The necessary enables the sufficient to happen, but doesn’t mean it will.  The absence of the necessary condition bars the sufficient from coming to pass.

If the sufficient condition happens, then the necessary condition will happen.

If the necessary condition happens, the sufficient can happen.

So far so good?

The relationship between sufficient and necessary conditions is best represented by the if-then statement.  If the sufficient occurs, then the necessary does.  In shorthand, we’ll represent that as:

S –> N

Timewarp time.  Let’s say you’re over in London circa 1995 and happen to find the one girl in the club who doesn’t look like calcified dogshit, which is a lot harder in London than I would have thought.  Even better, she’s not married to that fauxhawked asshole David Beckham yet.  You spit your game, and she retorts:

If you wanna be my lover, you gotta get with my friends.

Let’s assume that what she’s actually saying is that all her lovers have gotten with her friends, or that if you’re her lover, then you’ve gotten with her friends.  On a side note, what perverse sentiment is this song conveying?  Is she suggesting her friends test her potential sexual partners before she deigns to accept them?  Oh, he had a decent-sized Member of Parliament but refused to kiss me on the Union Jack.   Then he suggested we take the Bakerloo line on the first date! [1]  Thumbs down, girlfriend.

Anyway, If you’re her lover, then you’ve gotten with her friends.

Sufficient condition: being her lover.
Necessary condition: got with her friends.

L –> GF.

Are you taking the Bakerloo line to Poundtown? [2]  If so, it is absolutely certain that you have gotten with her friends.

If, on the other hand, you’ve gotten with her friends, will you be her lover?  As any young man stuck in the infamous FriendZoneTM knows, going the castrati route through her parade of nitpicker Czechoslovakian judges – who, after all, have a direct investment in her remaining single – is the most surefire way to remain safely outside her panties forever, but you do have the off chance of catching her drunk and lonely one night where she’ll realize how you were always there for her like some knight in shining baggy pants and maybe this could… yes… before she regrets ruining the friendship in the morning and avoids you forever after.  In other words, getting with her friends does not guarantee the sweet horizontal honeypot mambo you were after in the first place.

GF –> [nothing]

But… it does make it possible.

GF –> [HOPE][4]

What about you renegades that think you can pull this bird without getting with her friends first?  Hell no, I’m not jumping through those wizened hoops.  Well, remember how we said getting with her friends was necessary?  You know, like mandatory or required?  Yeah.  You’re going home with your hand.  And since I assume with no basis whatsoever that you’re in your twenties now, your hand was a prepubescent innocent in 1995.  Pedophile. [5]

If you have not gotten with her friends, you will not be her lover.

/GF –> /L

Extra credit: what’s the conditional logic of Beyonce’s dictum?


[1] This is an elaborate anal sex joke.

[2] Sadly, there is no actual London Underground stop at Poundtown.  The closest is probably Leicester Square. [3]

[3] This is another elaborate anal sex joke.

[4] As Edward Abbey reminds us, this springs eternal in the male gonad.

[5] This is NOT an anal sex joke.


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.