There were a few extra things I had written for Ed’s Radix Fidem project that I edited out because it seemed to veer a little too much off course. It was regarding the ineffectiveness of the two logics when used outside of their scope.
Have you ever seen network systems diagram, or mobile application workflow, or even those corkboards on crime dramas that demonstrate the relationship between POIs (persons of interest), evidence, dates, etc.*? That those aids are needed is a further clue about the effectiveness of logic only in small, hyper-contextual situations. Those diagrams use sight (sense data) to bypass the need to recall and sort through all the bits of information. A visual representation frees the mind to “sense” relationships without having to actually think through it.
Similarly, consider symbolic logic notation. Logicians use the rules of inference and symbols to reduce the complexity of large logical problems. One could literally “think through” the entire problem—freestyle, if you will—correctly, but symbolizing it allows the logician to perform the proof thinking on a level that requires less mental energy.
* Real-life investigators use software for that sort of thing. Interesting.
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Using the symbolic structures like that is rather like the lower edge of intuition. Yet, I seem to recall that logicians often deny that intuition is that reliable. It’s more like associative logic: seeing patterns that are not obvious. Leaping over linear logical steps that way is critical to the way humans normally operate, but it only works reliably if you do it on purpose.