Category Archives: Logic

Semiotic Transformations Re: Transformations of Logical Graphs • (4) • (5) • (6) Our investigation has brought us to the point of seeing both a transformation group and a triadic sign relation in the duality between entitative and existential interpretations of … Continue reading →

Semiotic Transformations Re: Transformations of Logical Graphs • (4) • (5) Our study of the duality between entitative and existential interpretations of logical graphs has brought to light its fully sign-relational character, casting the interpretive duality as a transformation of … Continue reading →

Semiotic Transformations Re: Transformations of Logical Graphs • 4 “I know what you mean but I say it another way” — it’s a thing I find myself saying often enough, if only under my breath, to rate an acronym for … Continue reading →

Semiotic Transformations Once we bring the dual interpretations of logical graphs to the same Table and relate their parleys to the same objects, it is clear we are dealing with a triadic sign relation of the sort taken up in … Continue reading →

Re: Transformations of Logical Graphs • (1) • (2) We’ve been using the duality between entitative and existential interpretations of logical graphs to get a handle on the mathematical forms pervading logical laws.  A few posts ago we took up … Continue reading →

Re: Transformations of Logical Graphs • 1 Another way of looking at the dual interpretation of logical graphs from a group-theoretic point of view is provided by the following Table.  In this arrangement we have sorted the rows of the … Continue reading →

Re: Interpretive Duality in Logical Graphs • 1 Re: Mathematical Duality in Logical Graphs • 1 Anything called a duality is naturally associated with a transformation group of order 2, say a group acting on a set   Transformation groupies … Continue reading →

Re: Interpretive Duality in Logical Graphs • 1 Re: Mathematical Duality in Logical Graphs • 1 Re: Laws of Form • Lyle Anderson LA: Definition 1.  A group is a set together with a binary operation satisfying the following three … Continue reading →

Re: Mathematical Duality in Logical Graphs • 1 Re: Laws of Form • Lyle Anderson Re: Brading, K., Castellani, E., and Teh, N., (2017), “Symmetry and Symmetry Breaking”, The Stanford Encyclopedia of Philosophy (Winter 2017), Edward N. Zalta (ed.).  Online. … Continue reading →

All other sciences without exception depend upon the principles of mathematics;  and mathematics borrows nothing from them but hints. C.S. Peirce • “Logic of Number” A principal intention of this essay is to separate what are known as algebras of … Continue reading →