Logical Graphs, Iconicity, Interpretation • 2

In the first place there are likenesses or copies — such as statues, pictures, emblems, hieroglyphics, and the like.  Such representations stand for their objects only so far as they have an actual resemblance to them — that is agree with them in some characters. The peculiarity of such representations is that they do not determine their objects — they stand for anything more or less;  for they stand for whatever they resemble and they resemble everything more or less.

The second kind of representations are such as are set up by a convention of men or a decree of God.  Such are tallies, proper names, &c.  The peculiarity of these conventional signs is that they represent no character of their objects.  Likenesses denote nothing in particular;  conventional signs connote nothing in particular.

The third and last kind of representations are symbols or general representations.  They connote attributes and so connote them as to determine what they denote.  To this class belong all words and all conceptions.  Most combinations of words are also symbols.  A proposition, an argument, even a whole book may be, and should be, a single symbol.

C.S. Peirce (1866), Lowell Lecture 7, CE 1, 467–468

The Table in the previous post can now be sorted to bring out the “family resemblances”, likenesses, or symmetries among logical graphs and the boolean functions they denote, where the “orbits” or similarity classes are determined by the dual interpretation of logical graphs.  Performing the sort produces the following Table.  As we have seen in previous discussions, there are 10 orbits in all, 4 orbits of 1 point each and 6 orbits of 2 points each.

\text{Boolean Functions and Logical Graphs on Two Variables} \stackrel{_\bullet}{} \text{Orbit Order}

Boolean Functions and Logical Graphs on Two Variables

Resources

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This entry was posted in Amphecks, Animata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Constraint Satisfaction Problems, Deduction, Diagrammatic Reasoning, Duality, Equational Inference, Graph Theory, Laws of Form, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Model Theory, Painted Cacti, Peirce, Proof Theory, Propositional Calculus, Propositional Equation Reasoning Systems, Spencer Brown, Theorem Proving, Visualization and tagged , , , , , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

1 Response to Logical Graphs, Iconicity, Interpretation • 2

  1. Pingback: Survey of Animated Logical Graphs • 4 | Inquiry Into Inquiry

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