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Emergent Logic

2 pointsdaly2 comments

I just read an essay about Minds, Machines and Godel. https://pdfs.semanticscholar.org/bde3/b731bf73ef6052e34c4465e57718c03b13f8.pdf

I hold the somewhat rare opinion that Consciousness and Intelligence in humans are "emergent properties", similar to a traffic jam as an emergent property of cars and roads.

I am also of the opinion that this "emergent mind" does not follow any known logic but has its own "emergent logic".

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.

Emergent rules do not follow from the substrate rules.

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 "logic" (bad word) of each is of "a different order", somewhat like the difference between a car traffic jam and a bicycle traffic jam.

What this "emergent logic" is, though, I cannot say.

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 "logics" seem "linear" to me and thus cannot be chaotic.

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... 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...

Strange attractors show a natural fractal character for some initial values, leading to chaotic behavior on the torus. 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".

> somewhat rare opinion

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

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