
Emergent Logic - daly
I just read an essay about Minds, Machines and Godel.
https:&#x2F;&#x2F;pdfs.semanticscholar.org&#x2F;bde3&#x2F;b731bf73ef6052e34c4465e57718c03b13f8.pdf<p>I hold the somewhat rare opinion that Consciousness and
Intelligence in humans are &quot;emergent properties&quot;, similar
to a traffic jam as an emergent property of cars and roads.<p>I am also of the opinion that this &quot;emergent mind&quot; does not
follow any known logic but has its own &quot;emergent logic&quot;.<p>By analogy, cars logically can go from one place to another
without stopping but traffic jams can cause a car to stop
even though the road ahead and behind are still flowing.<p>Emergent rules do not follow from the substrate rules.<p>Emergent properties arise from complexity. I am of the
opinion that the difference between an intelligent animal
such as a monkey and a human is directly related to the
complexity of brain structure. Since intelligence is assumed
to emerge from complexity. The &quot;logic&quot; (bad word) of each
is of &quot;a different order&quot;, somewhat like the difference between
a car traffic jam and a bicycle traffic jam.<p>What this &quot;emergent logic&quot; is, though, I cannot say.<p>The closest I have come is by analogy to chaos theory.
Nonlinear equations can exhibit states that never repeat
from very simple nonlinear equations. Current &quot;logics&quot;
seem &quot;linear&quot; to me and thus cannot be chaotic.
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daly
There is a path to a kind of logic that seems to be well-defined but chaotic.

The connection seems to be thru Homotopy Type Theory (HOTT) If we look at HoTT
we find a mapping between logic to topology.

There is work at CMU by Kristina Sojakova [http://reports-
archive.adm.cs.cmu.edu/anon/2015/CMU-CS-15-10...](http://reports-
archive.adm.cs.cmu.edu/anon/2015/CMU-CS-15-105.pdf) using logic to prove the
equivalence S^1 x S^2 = T^2 (S^1 is a circle, T^2 is a torus)

There is work on the relationship between the torus and Stephen Smale's work
on strange attractors
[https://link.springer.com/content/pdf/10.1007/s00209-014-138...](https://link.springer.com/content/pdf/10.1007/s00209-014-1388-1.pdf)

Strange attractors show a natural fractal character for some initial values,
leading to chaotic behavior on the torus.
[https://en.wikipedia.org/wiki/Attractor](https://en.wikipedia.org/wiki/Attractor)

It should be possible to develop a logic based on a torus that was sound but
leads to chaotic behavior. That would certainly form a basis for "nonlinear
logic".

My claim would be that a "nonlinear logic", aka chaotic logic, would be a
"higher order logic". In that higher order logic we would find "emergent
behavior" which is the kind of behavior that is unpredictable but sound.

Mapping from chaotic functions on a torus to a supporting logic would escape
deductive logic, and likely provide a logic that is not covered by Godel.

The chaotic behavior is sensitive to starting values where values differing by
epsilon could be stable or chaotic, I'm not sure how to capture this notion of
"nearby values" in a logic.

Note that chaotic values don't diverge to infinity but remain "within the
logic" but never achieve what might likely be called a "fixed point".

------
kazinator
> _somewhat rare opinion_

It's rather more common than you might think. E.g. "Ant Fugue" in Gödel,
Escher, Bach.

