Category Archives: C.S. Peirce

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 →

Re: Interpretive Duality in Logical Graphs • 6 The last of our six ways of looking at interpretive duality is arrived at by taking the previous Table of Logical Graphs and Venn Diagrams and sorting it in Orbit Order. Resources … Continue reading →

Re: Interpretive Duality in Logical Graphs • 2 Dualities are symmetries of order two and symmetries bear on complexity by reducing its measure in proportion to their order.  The inverse relationship between symmetry and the usual dissymmetries from dispersion and … Continue reading →

Re: Interpretive Duality in Logical Graphs • 2 A more graphic picture of interpretive duality is given by the next Table, showing how logical graphs map to venn diagrams under entitative and existential interpretations.  Column 1 shows the logical graphs for … Continue reading →

Re: Interpretive Duality in Logical Graphs • 1 Another way of looking at interpretive duality in logical graphs is given by the following Table, showing how logical graphs denote the sixteen boolean functions on two variables under entitative and existential … Continue reading →

Re: Interpretive Duality in Logical Graphs • (1) • (2) • (3) Last time we took up Peirce’s law, and saw how it might be expressed in two different ways, under the entitative and existential interpretations, respectively.  The next thing … Continue reading →

Re: Interpretive Duality in Logical Graphs • (1) • (2) For a sense of how the choice of interpretation bears on cases beyond the bare minimum complexity let us start with the familiar example of Peirce’s law, commonly expressed in … Continue reading →

Re: Interpretive Duality in Logical Graphs • 1 A logical concept represented by a boolean variable has its extension, the cases it covers in a designated universe of discourse, and its comprehension (or intension), the properties it implies in a … Continue reading →

The duality between Entitative and Existential interpretations of logical graphs is a good example of a mathematical symmetry, in this case a symmetry of order two.  Symmetries of this and higher orders give us conceptual handles on excess complexity in … Continue reading →