## Tuesday, May 14, 2013

### On Troikas 2: Glitches

Glitches

The logic of troikas is highly non-Aristotelian. Even though each Stooge is as logical as he can be, the system within which they operate adds error on its own. These systematic errors include: weak and, strong or, weak majority, strong majority, arithmetic glitch, equivalence glitch, implication glitch, modus ponens breakdown, sorites failure, heap glitch, set loops, double-binds, Orlov doubt states, failed reductio, and failed dilemma.

Weak And  is this election:
Moe                 Larry               Curly
Are you an ape?                  no                    yes                   yes
Are you a bozo?                  yes                   no                    yes
Majorities agree to these propositions:
* I am an ape.
* I am a bozo.
* I am not both an ape and a bozo.

Strong Or   is this election:
Moe                 Larry               Curly
Are you an ape?                  yes                   no                    no
Are you a bozo?                  no                    yes                   no
Majorities agree to:
* I am not an ape.
* I am not a bozo.
* I am either an ape or a bozo.

Here is a weak majority:
Moe                 Larry               Curly
Do you like ale?                              yes                   yes                  no
Do you like beer?                            no                   yes                  yes
Do you like cider?                           no                   yes                   no
Majorities agree to:
* I like ale.
* I like beer.
* I don’t like cider.
* I don’t like most of those three.

Here is a strong majority:
Moe                 Larry               Curly
Do you like ale?                              no                     no                  yes
Do you like beer?                            yes                     no                  no
Do you like cider?                           yes                     no                  yes
Majorities agree to:
* I don’t like ale.
* I don’t like beer.
* I do like cider.
* I do like most of those three.

Here is an arithmetic glitch:
Moe                  Larry                    Curly
x          =                        1                        0                      0
y          =                        0                        1                      0
Majorities believe:
*   x  =  0
*   y  =  0
*  x+y =  1

Here is an equivalence glitch:
Moe                 Larry               Curly
Do you love Alice?                         no                    yes                   yes
Do you love Bob?                           no                    no                   yes
Majorities believe:
* I love Alice.
* I love Alice and Bob equally.
* I do not love Bob.

In the above election, this also passes:
* If I love Alice, then I love Bob.
so this is also an implication glitch.

Here’s another implication glitch:
Moe                 Larry               Curly
Are you a bum?                               yes                   yes                  no
Are all bums crooks?                       yes                   no                   no
Majorities believe:
* I am a bum.
* All bums are crooks.
* I am not a crook.

Related to the implication glitch is modus ponens breakdown:
Moe         Larry           Curly
Are all men fools?                           yes            yes              no
Are all fools goons?                        yes             no             yes
Are all men goons?                         yes             no              no
Majorities believe:
* All men are fools.
* All fools are goons.
* Not all men are goons.

I also call this Barbarism because it undermines the validity of that classic Aristotelian syllogism, BARBARA:
All A are B, all B are C, therefore all A are C.