Tag Archives: Theorem Proving

Re: Operator Variables in Logical Graphs • 11 The rules given in the previous post for evaluating cactus graphs were given in purely formal terms, that is, by referring to the mathematical forms of cacti without mentioning their potential for … Continue reading →

Re: Futures Of Logical Graphs • Themes and Variations This post and the next wrap up the Themes and Variations section of my speculation on Futures of Logical Graphs.  I made an effort to “show my work”, reviewing the steps … Continue reading →

Re: Operator Variables in Logical Graphs • 9 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. Alternatively, if we think in terms of the corresponding … 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 →

Re: Operator Variables in Logical Graphs • 7 A trick of discovery I learned by observing Peirce’s working methods, more than anything he wrote outright, might be put in the following words. Take what is constant, Treat it as variable, … Continue reading →

Re: Operator Variables in Logical Graphs • 6 A funny thing just happened.  Let’s see if we can tell where.  We started with the algebraic expression where the operand suggests the contemplated absence or presence of an arbitrary arithmetic expression.  … Continue reading →

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

Re: Operator Variables in Logical Graphs • 4 We have encountered the question of how to extend our formal calculus to take account of operator variables. In the days when I scribbled my logical graphs on the backs of computer … Continue reading →

Re: Operator Variables in Logical Graphs • 3 Last time we contemplated the penultimately simple algebraic expression as a name for a set of arithmetic expressions, specifically, taking the equal sign in the appropriate sense. Then we asked the corresponding … Continue reading →

And if he is told that something is the way it is, then he thinks:  Well, it could probably just as easily be some other way.  So the sense of possibility might be defined outright as the capacity to think … Continue reading →