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Limits of AI. The Gödelian argument. Complexity Explorers Krakow.


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Is Artificial general Intelligence of human level possible?
Let’s watch and discuss the classic point of view denying current computers as able of reconstructing human-level intelligence.
The base slides gather facts about Gödel's theorems, its link to works of Turing followed by Penrose's examples of human 'insight' that apparently/questionably escapes abilities of any AI.

Published in: Science
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Limits of AI. The Gödelian argument. Complexity Explorers Krakow.

  1. 1. Limits of AI Gödelian Argument Complexity Explorers Kraków Marcin Stępień @marcinstepien Kraków 2018-11-14
  2. 2. src: “Kurt Gödel's achievement in modern logic is singular and monumental – indeed it is more than a monument, it is a landmark which will remain visible far in space and time. ... The subject of logic has certainly completely changed its nature and possibilities with Gödel's achievement.” John von Neumann
  3. 3. src: Photo by Cmichel67 - Own work, CC BY-SA 4.0, Gödel’s theorem “Tells us what we don’t know and can’t know. It sets a fundamental and inescapable limit on knowledge of what is. It pinpoints the boundaries of ignorance - not just human ignorance, but that of any sentient being.” Paul Davies Foreword to “Thinking about Gödel and Turing” by Gregory J Chaitin, 2007
  4. 4. src: “Either mathematics is too big for the human mind or the human mind is more than a machine.” Kurt Gödel
  5. 5. src: “There can be no machine which will distinguish provable formulae of the system from unprovable ... On the other hand if a mathematician is confronted with such a problem he would search around and find new methods of proof.” Alan Turing Lecture to the London Mathematical Society 20 II 1947
  6. 6. Inspired by Epimenides paradox All Cretans are liars - Epimenides from Crete
  7. 7. Gödel's Incompleteness Theorem - Numberphile src:
  8. 8. Gödel's Incompleteness extra 1 - human above machines? src: up to 6:40
  9. 9. Penrose Tiling ❏ Non-periodic tiling generated by an aperiodic set of prototiles. ❏ The aperiodicity of prototiles implies that a shifted copy of a tiling will never match the original. Photo ty Solarflare100 - Own work, CC BY 3.0, By Geometry guy at English Wikipedia, CC BY-SA 3.0, Kite and dart protitiles
  10. 10. By PrzemekMajewski - Own work, CC BY-SA 4.0,
  11. 11. Roger Penrose: Strong A.I. vs. The Euclidean Plane src:
  12. 12. Strong A.I. vs. The Calculation Problem. Commutative property. src:
  13. 13. src: “My incompleteness theorem makes it likely that mind is not mechanical, or else mind cannot understand its own mechanism. If my result is taken together with the rationalistic attitude which Hilbert had and which was not refuted by my results, then [we can infer] the sharp result that mind is not mechanical. This is so, because, if the mind were a machine, there would, contrary to this rationalistic attitude, exist number-theoretic questions undecidable for the human mind. ”
  14. 14. It is not about anti-mechanist view ● Gödel was a convinced dualist * * "The Implications of Gödel's Theorem" J.R. Lucas 1998 ● Penrose calls himself "a very materialistic and physicalist kind of person"
  15. 15. What can be answered What cannot be answered Encoded rules, axioms System (Turing complete computing device + data)
  16. 16. System (Turing complete computing device + data) Human’s insight Encoded rules, axioms Created / learned input What can be answered What cannot be answered
  17. 17. Views classification by Scott Aaronson, further critique 1. Consciousness is reducible to computation (the view of strong-AI proponents) 2. Sure, consciousness can be simulated by a computer, but the simulation couldn't produce "real understanding" (John Searle's view) 3. Consciousness can't even be simulated by computer, but nevertheless has a scientific explanation (Penrose's own view, according to Shadows [Of The Mind]) 4. Consciousness doesn't have a scientific explanation at all (the view of 99% of everyone who ever lived) Scott Aaronson “Quantum Computing since Democritus”