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!

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