Blogic 6: Syllogistic Unification

Dear all,

In the last posting it was shown that all the 24 Leibniz syllogisms are divided into 4 equivalent classes: Barbara triad, Celarent zodiac, Barbari hexad and Celaront triad.

Because the elements of an equivalent class are equivalent to each other,

if we can prove that Barbaba, Celarent, Barbari and Celaront are equivalent to each other, then all Leibniz 24 syllogisms are forming a big equivalent class. I will try to prove it in this blog.

Barbara is equivalent to Barbari

Proof:

Barbara =

= OOA1                 Brownian coding

= Oyz Oxy Axz          Boethius recoding

= Oyz Oxy [x]z         Brownian expansion of Axz

= Oyz Oxy [x][[z]]     Law of involution

= Oyz Oxy [x][[x][z]]  Law of pervasion

= Oyz Oxy [x] Ixz      Boethius recoding

= [x] Oyz Oxy Ixz      implicit Law of commutation

= AAI1                 Brownian coding

= Barbari              Boethius recoding

Barbari is equivalent to Celarent

Proof:

Barbari =

= AAI1                 Brownian coding

= [x] Oyz  Oxy   Ixz   Boethius recoding

= [x] Oyz [[x]y] Ixz   Brownian expansion of Oxy

= Oyz [x] [[x]y] Ixz   implicit Law of commutation

= Oyz [x] [   y] Ixz   Law of pervasion

= Oyz Exy        Ixz   Boethius recoding

= Ixz Oyz        Exy   implicit Law of commutation

= IOE1                 Brownian coding

= Celarent             Boethius recoding

Celarent is equivalent to Celaront

Proof:

Celarent =

= IOE1                  Brownian coding

= Ixz Oyz Exy           Boethius recoding

= Ixz Oyz [x][y]        Brownian expansion of Exy

= Ixz Oyz [x][[x]y]     Law of pervasion

= [x] Ixz Oyz Oxy       Boethius recoding