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The Philosophical Computer

Here I use Python to replicate Grim, Mar & St. Denis’ experiments in paradox, fuzzy logic, chaos, and game theory.

To give an idea of the material they cover, here's the table of contents:

  1. Chaos, Fractals, and the Semantics of Paradox
  2. Notes on Epistemic Dynamics
  3. Fractal Images of Formal Systems
  4. The Evolution of Generosity in a Hobbesian Model
  5. Real-Valued Game Theory: Real Life, Cooperative Chaos, and Discrimination
  6. Computation and Undecidability in the Spatialized Prisoner's Dilemma

For each chapter, I'll post a tutorial that explains the code and gives more formal derivations of the results.

Most of the book chapters are also published as papers, listed below.

 

References

  • Grim, P. (1993). “Self-reference and chaos in fuzzy logic.” IEEE Transactions on Fuzzy Systems 1(4), pp. 237-53
  • Grim, P. (1995). “The Greater Generosity of the Spatialized Prisoner's Dilemma.” Journal of Theoretical Biology 173(4), pp. 353-9
  • Grim, P. (1996). “Spatialization & Greater Generosity in the Stochastic Prisoner's Dilemma.” BioSystems 37(1-2), pp. 3-17
  • Grim, P. (1997). “The Undecidability of the Spatialized Prisoner's Dilemma.” Theory and Decision 42(1), pp. 53-80
  • Grim, P. & Mar, G. (1991). “Pattern and Chaos: New Images in the Semantics of Paradox.” Noûs 25(5), pp. 659-93
  • Grim, P. & St. Denis, P. (1997). “Fractal Images of Formal Systems.” Journal of Philosophical Logic 26(2), pp. 181-222
  • Grim, P., Mar, G., St. Denis, P. (1998). The Philosophical Computer: Exploratory Essays in Philosophical Computer Modeling. Cambridge, MA: MIT Press.
  • Grim, P., Mar, G., Neiger, M., St. Denis, P. (1993). “Self-reference and paradox in two and three dimensions.” Computers & Graphics 17(5), pp. 609-12
  • Mar, G. & St. Denis, P. (1994). “Chaos in Cooperation: Continuous-valued Prisoner's Dilemma in Infinite-valued Logic.” International Journal of Bifurcation and Chaos 4(4), pp. 943-58
  • Mar, G. & St. Denis, P. (1996). “Real Life.” International Journal of Bifurcation and Chaos 6(11), pp. 2077-86
  • Mar, G. & St. Denis, P. (1999). “What the Liar Taught Achilles.” Journal of Philosophical Logic 28(1), pp. 29-46
  • Stewart, I. (1993). “A Partly True Story.” Scientific American 268(2), pp. 110-2
  • Stewart, I. (2000). “Logic Quasi-Fractals: A Fractal Guide to Tic-Tac-Toe.” Scientific American 283(2), pp. 86-8