Animated Logical Graphs • 81

Re: R.J. Lipton and K.W. ReganA Negative Comment On Negations

Minsky and Papert’s Perceptrons was the work that nudged me over the line from gestalt psychology, psychophysics, relational biology, etc. and made me believe AI could fly.  I later found out a lot of people thought it had thrown cold water on the subject but that was not my sense of it.

The real reason Rosenblatt’s perceptrons short-shrift XOR and EQ among the sixteen boolean functions on two variables is the adoption of a particular role for neurons in the activity of the brain and a particular model of how neurons serve computation, namely, as threshold activation devices.  It is as if we tried to do mathematics using only the inequality \le instead of using equations.  Sure, we can express equations in roundabout ways but why tolerate the resulting inefficiency?  As a final observation, x \le y for boolean variables x, y is equivalent to x \Rightarrow y so this fits right in with the weakness of implicational inference compared to equational inference rules.

But there are other models for the role neurons play in the activity of the brain and the work they do in computation.

Resources

cc: Peirce List (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18)
cc: Category Theory • Cybernetics (1) (2) • Ontolog Forum (1) (2)
cc: Structural Modeling (1) (2) • Systems Science (1) (2)
cc: FB | Logical Graphs • Laws of Form (1) (2)

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.

2 Responses to Animated Logical Graphs • 81

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

  2. Pingback: Semiotics, Semiosis, Sign Relations • Discussion 14 | Inquiry Into Inquiry

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