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.