29 Aug
2023
29 Aug
'23
12:28 a.m.
Alex,
The words 'structure' and 'diagram' have multiple informal meanings in
dictionaries of English. They also have multiple formal meanings in different theories of
engineering, science, architecture, mathematics, ...
Alex> Diagram is just a picture. Rotate it on 180 grads or delete labels, nothing to
think about structure :-)
From ancient times to the present, the angles and sizes of many kinds of diagrams have
been very significant -- but there is usually some fixed ratio of the size of the diagram
to the structure it represents: diagrams in geometry, architectural plans, maps of the
earth, moon, stars, and designs of engineering systems (a car, a pump, or a violin, for
example).
But I agree that some diagrams of linguistics or logic can be moved or rotated without
changing the meaning.
But the beauty of Peirce's existential graphs is that they can be used for multiple
purposes. For representing logic, an EG can be mapped to and from a linear notation
without any change in meaning.
But in 1911, he wanted to generalize his graphs to represent "stereoscopic moving
images" or "moving pictures of thought". For those purposes, he could
generalize EGs to map pictures, even moving pictures, to graphs that have two kinds of
information: abstract logic that has no implicit physical information and representations
of physical structures where the relative positions and angles are significant.
This is a very important reason why Peirce's diagrammatic reasoning is far more
expressive than predicate calculus *and* LLMs. I'm writing another article about
Peirce's Delta Graphs, which appear to be going in that direction (just before Peirce
had a serious accident and left the document incomplete). But he left enough hints and
requirements to indicate the direction he intended. In 2018, I published an article about
generalizing existential graphs (see the references in the PDF I sent).
John
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From: "Alex Shkotin" <alex.shkotin(a)gmail.com>
Ravi, et al.,
For me there is a much more powerful idea and this is the idea of a structure. If a
diagram can help to get or work with structure we use it.
Diagram is just a picture. Rotate it on 180 grads or delete labels, nothing to think about
structure :-)
So "All necessary reasoning without exception is struturematic"
Consider this kind of structure: create a node and draw an arrow from it and at the end of
it create another node, and so on ad infinitum.
Thinking the process is complete we get the structure for the natural numbers.
It can probably be drawn if it helps in its study.
Alex