- Several people have referred recently to the idea that Laws of Form, and particularly Chapter 11 with imaginary logical values, provides an answer to the problems Russell found in Principia Mathematica leading to the Theory of Logical Types, which essentially banned self-referential forms.
I am interested in this and wondered if anyone had done any work on it, or seen any work on it, which actually formulates self-referential forms such as “This sentence if false” into LoF notation?
If so I would be interested to work on it.
The problem with Russell, well, one of the problems with Russell, is not his having or wanting a theory of types but his lacking a theory of signs, a semiotics, which, being afflicted with the isms of logicism, nominalism, syntacticism, and their ilk, the need and utility of which he lacked the sense to know. That is one of the reasons why I take up Spencer Brown’s calculus of indications and his Laws of Form within the sign-theoretic environment of Peirce’s theory of triadic sign relations. I’ve written a few things about how the simpler so-called paradoxes look in that framework so I’ll post a sample of those later.