# Finally, the fried chicken proof you’ve been searching for

Rose Woodhouse

Elizabeth Picciuto was born and reared on Long Island, and, as was the custom for the time and place, got a PhD in philosophy. She freelances, mainly about disability, but once in a while about yeti. Mother to three children, one of whom is disabled, two of whom have brown eyes, three of whom are reasonable cute, you do not want to get her started talking about gardening.

### 16 Responses

1. Mike Schilling
Ignored
says:

Hold on.  5 implies that B is reflexive (let x = y), and thus not a strict ordering, so you also need to prove that ~Bkp. This is most simply done with the additional axioms:

(A) Rk
(B) Ok
(C) Sk
(D) Cx -> ~Fx

A, B, and C together with 1 imply Fk, while D together with 16 gives ~Fp. SInce both Rp and Rk,  by 3, ~Bkp.  QED.Report

• Rose Woodhouse in reply to Mike Schilling
Ignored
says:

But “better than” is relational, but not reflexive. That said, I meant to do something like your A through D, and that’s why I had premises 1 and 3, but I totally forgot. Still valid.Report

• Murali in reply to Rose Woodhouse
Ignored
says:

I’m not sure how you get no 3:

`(x) (y) (((Rx & Fx) & (Ry & ~Fy)) –> ~Bxy) `

or are you simply assuming itReport

• Mike Schilling in reply to Rose Woodhouse
Ignored
says:

But “better than” is relational, but not reflexive.

Then 5 has to become something like:

5a (x) (y) ((Rx & Gx) & (~Ry | ~Gy))–> Bxy)

Given the current 5, 13, and 19, you can conclude Bpp.  I.e. B means “at least as good as”, not “better than”.Report

• Rose Woodhouse in reply to Mike Schilling
Ignored
says:

Yeah, you’re right. Sorry about that. But Bpp would mean Popeye’s is better than Popeye’s, no? Not at least as good as. I think the problem can be solved by adding x is not equal to y in premise 5, and adding another premise that ~Gk (to prevent UI of 2 or 4 with KFC), right?Report

• Rose Woodhouse in reply to Rose Woodhouse
Ignored
says:

Wait. You were totally right the first time. Instantiate k as R, O, and S, and make premise 5 that (x) (y) (((Rx & Gx) & (Ry & Fy)) –> Bxy). Which gets more to the heart of the matter anyway.Report

• Mike Schilling in reply to Rose Woodhouse
Ignored
says:

But Bpp would mean Popeye’s is better than Popeye’s, no? Not at least as good as.

Maybe this is a difference between how philosophers use logic and how mathematicians do.  You started with “truths” and expressed them as axioms, to see what consequences you could derive.  I started by viewing the axioms purely as formalisms, and tried to determine what semantics they described (e.g, that since Bxy is reflexive, it must be analogous to >= rather than strict >.)

And programmers use the converse of this: given a real-world problem, find (or, if need be, build) something whose “axioms” generate the right semantics to describe it.   Java, for instance, provides a number of types that represent collections of things:

• a Collection is just a bunch of stuff, with no furthersemantics
• a List is an ordered collection
• some Lists are good at random-access, e.g. give me the fifth one.
• a Set is an unordered collection that, unlike a List, can’t contain duplicates.  (It’s very much like a mathematical set.  The only question you can ask is “Does S contain O?”)
• etc.
• These are all quite abstract, that is, not intended to solve any specific problem.  Using them requires mapping the semantics of the actual problem onto the semantics of the particular collection, e.g.

We’re going to process a collection of vehicle registrations, and we want to discard any duplicates.  We’ll put them in a Set, and throw away any we’ve already done.

And, having done this mapping, we can pick a type of collection and use all of its facilities, knowing that they’re both correct and likely to be useful.Report

• Rose Woodhouse in reply to Mike Schilling
Ignored
says:

I’m actually not sure it’s all that different. We start with premises, not “truths.” Logic is not my main area; a logician may well disagree with me that having stipulated B as the predicate “better than” that Bpp means “Popeye’s is better than Popeye’s.”

Seriously, how awesome is it that you read through and actually checked this? You rock!

• Kyle Cupp
Ignored
says:

I need to go back to school.Report

• BlaiseP
Ignored
says:

Heh.  Nice bit of work, that.   Alas that you have not eaten actual Cajun chicken, which Popeye’s is decidedly not.   The best chicken shacks in Louisiana are run by the Creoles.

It is well understood by all God’s Faithful that Delpit’s Chicken Shack in Baton Rouge is what the angels eat in heaven.Report

• Kazzy
Ignored
says:

No idea what any of this means BUT…

You are correct that Popeyes is better than KFC.  WORLD’S better.

You are wrong in that you have never eaten at Popeyes.  Shame on you.Report

• Mike Dwyer
Ignored
says:

I just stumbled on to this. Obviously I dispute. KFC is on my ‘death row last meal’ list. Wash it down with a tall glass of Big Red and they can send me off to the electric chair a happy man.Report