The Philosophical Computer
Exploratory Essays in Philosophical Computer Modeling
Patrick Grim, Gary Mar, and Paul St. Denis
with the Group for Logic & Formal Semantics
forthcoming from MIT Press/Bradford Books
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Chaos, Fractals, and the Semantics of Paradox

From the Bivalent Liar to Dynamical Semantics

The Simple Liar in InfiniteValued Logic

Some QuasiParadoxical Sentences

The Chaotic and Logistic Liars

Chaotic Dualists and Strange Attractors

Fractals in the Semantics of Paradox

The Triplist and ThreeDimensional Attractors

Philosophical and Metalogical Applications

Notes on Epistemic Dynamics

Toward a Simple Model: Some Basic Concepts

SelfReference and Reputation: the Simplest Cases

Epistemic Dynamics with Multiple Inputs

Tangled Reference to Reputation

Conclusion

Fractal Images of Formal Systems

The Example of TictacToe

'Rug' Enumeration Images

Tautology Fractals

A Sierpinski Tautology Map

Value Solids and MultiValued Logics

Cellular Automata in Value Spaces

Conclusion

The Evolution of Generosity in a Hobbesian Model

The Prisoner's Dilemma

Classical Strategies in Iteration

Generosity in an Imperfect World

Spatialization of the Prisoner's Dilemma

A Note on Some Deeper Strategies

Greater Generosity in an Imperfect Spatial World

Conclusion

RealValued Game Theory: Real Life, Cooperative Chaos, and
Discrimination

Real Life

Chaotic Currents in Real Life

RealValued Prisoner's Dilemmas

PAVLOV and Other TwoDimensional Strategies

Cooperative Chaos in InfiniteValued logic

The Problem of Discrimination

Continuity in Cooperation, the Veil of Ignorance,' and Forgiveness

Conclusion

Computation and Undecidability in the Spatialized Prisoner's
Dilemma

Undecidability and the Prisoner's Dilemma

Two Abstract Machines

Computation and Undecidability in Competitive Cellular Automata

Computation and Undecidability in the Spatialized Prisoner's Dilemma
Appendix A: Competitive Strategies
Adequate for a Minsky Register Machine Appendix
B: An Algebraic Treatment for Competitive Strategies
Afterword
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