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.

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One Comment on “Just Dropped In To See What Condition My Conditional Is In”

  1. Noah says:

    I’m a bit confused by this:

    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

    Aren’t there conditions where you might shine together, when the sun isn’t necessarily shining? Which would mean the contrapositive is not valid?

    Sent you an email.


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