SUO: Re: Thirdness
> Yes, transitivity is a property of relations -- i.e., it is
> a metalevel property. It may be considered as a one-word
> abbreviation that a certain axiom applies to a relation:
>
> For any relation R, transitive(R) <=>
>
> (Ax)(Ay)(Az)((xRy & yRz) => xRz).
>
> From one point of view, this statement could be considered
> a second-order proposition, since it has a quantifier over
> relations. But when you perform "hypostatic abstraction",
> you convert relations into "things", which may then be used
> as the arguments of other relations. In that sense, the
> axiom is a metalevel statement about how the relations may
> be applied to other things at the object level.
So, if one tries to follow your talk here, one should realize that the axiom
really involves a quaternary relation - past this hypostatic experience - the
relation is between a relation (hypostatic-abstracted), and the three terms
involved in the above statement. So transitivity-sort-of-seen-as-a-relation is
quaternary, not triadic.
> Peirce's notion of Thirdness is in effect a metametalevel
> property about a entire class of metalevel relations (such as
> transitivity, sign-relation, intentionality, etc.) which obey
> axioms that define how they relate entities at the object level.
The way you use this whole thirdness thing on the SUO really seems to reduce to
a convoluted way of saying that there are ternary relations. Do we really need
to engage in Peirce's exegesis to make that claim?