Category Archives: Model Theory

Re: Animated Logical Graphs • 23 Let’s examine the Formal Operation Table for the third in our series of reflective forms to see if we can elicit the general pattern. Or, thinking in terms of the corresponding cactus graphs, writing for … Continue reading →

Re: Ontolog Forum • Joseph Simpson JS: Today I found an interesting publication that might relate to the current discussion of Animated Logical Graphs (ALG).  Please see: Mathematician Solves Computer Science Conjecture in Two Pages The “sensitivity” conjecture may be … Continue reading →

The following Table will suffice to show how the “streamer‑cross” forms C.S. Peirce used in his essay on “Qualitative Logic” and Spencer Brown used in his Laws of Form, as they are extended through successive steps of controlled reflection, translate into syntactic … Continue reading →

The step of controlled reflection we took with the previous post can be repeated at will, as suggested by the following series of forms. Written inline, we have the series and so on, whose general form is   With this move … Continue reading →

A funny thing just happened.  Let’s see if we can tell where.  We started with the algebraic expression in which the operand suggests the contemplated absence or presence of any arithmetic expression or its value, then we contemplated the absence … Continue reading →

Another tactic I tried by way of porting operator variables into logical graphs and laws of form was to hollow out a leg of Spencer Brown’s crosses, gnomons, markers, whatever you wish to call them, as shown below. The initial idea … Continue reading →

We have encountered the question of how to extend our formal calculus to take account of operator variables. In the days when I scribbled these things on the backs of computer punchcards, the first thing I tried was drawing big … Continue reading →

Last time we contemplated the penultimately simple algebraic expression as a name for a set of arithmetic expressions, namely, taking the equality sign in the appropriate sense. Then we asked the corresponding question about the operator   The above selection … Continue reading →

To get a clearer view of the relation between primary arithmetic and primary algebra consider the following extremely simple algebraic expression. In this expression the variable name appears as an operand name.  In functional terms, is called an argument name, … Continue reading →

In lieu of a field study requirement for my bachelor’s degree I spent two years in various state and university libraries reading everything I could find by and about Peirce, poring most memorably through reels of microfilmed Peirce manuscripts Michigan … Continue reading →