On 5/31/2013 10:36 AM, Julio Di Egidio wrote: > "fom" <fomJUNK@nyms.net> wrote in message > news:UY-dnUnFksIIUDrMnZ2dnUVZ_g-dnZ2d@giganews.com... >> On 5/30/2013 11:20 AM, Julio Di Egidio wrote: > <snipped> > >> is there a criterion >> for deciding whether either of the complete connectives should >> be viewed as the canonical complete connective? That is, is >> there an asymmetry in the dyslexia we call truth-functional >> logic? > > Why should there be a canonical one?
After one long answer... a simpler observation.
When mathematicians are confronted with a multiplicity of equivalent forms, they often seek "a principal branch".
The relationship of that view to general equivalence seems to be related to failures of the distributive laws in certain structures. A short time ago I identified this exact aspect in relation to the discussion of the category of pointed sets as described in Lawvere. Lawvere uses that category to examine a category in which the distributive laws fail. But, it is the structure of an equivalence class with a canonical representative.
It certainly manifests itself in logic. The distributive laws become an issue in the logical research of Pavicic and Megill. Their logic is, however, algebraic in nature.
My "story" is in the following link. It also contains a discussion of "principal branches" at the end. This open apology to the few talented professionals who participate in this newsgroup had been motivated by some misunderstandings that had happened. I am the one with non-standard views, so the burden of explanation and smoothing any disagreements falls to me.