Re: Logical Graphs • Formal Development
Re: Laws of Form • Lyle Anderson

LA:

What does it mean to assign a label or name to a node of the Logical Graph?

In LoF, the variables of the algebra represent unknown expressions of the arithmetic.  There are two tokens in the expressions for Logical Graphs, the node and the edge.  You assign different symbols to the naked node of the outside and the node representing the inside, since the edge between them represents the boundary of a distinction.  When you put a letter “a” next to the naked node, what does that mean?  If “a” represents another Logical Graph of uncertain arrangement, then how is it attached to the naked node?

Dear Lyle,

By now we’ve seen quite a few ways to represent Peirce’s logical graphs and Spencer Brown’s formal arrangements in various styles of formal languages and concrete media.  A fairly detailed discussion of how to translate among the more common representations we’ve been using, along with those I found useful in computing logical graphs, was given in the post linked below and serialized in the fourteen posts which follow it.

• Logical Graphs • First Impressions

As a general consideration, we need to remember one of the first lessons we learned in geometry, and never confuse the drawing, the representation, with the mathematical object it represents.  Despite their name, “graphs” in the sense of mathematical graph theory are mathematical objects, not to be found on the page, screen, or in the state of any concrete system, whether cognitive or computational.  The same goes for Spencer Brown’s formal arrangements.  Among other things, that is one of the reasons Peirce’s pragmatic semiotics is so critical to understanding logical graphs, laws of form, and logic in general.

Regards.

Jon

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