The Decoy Effect (Asymmetric Dominance) Rational Choice Subversion in Decision Theory
A formal mathematical proof of the Decoy Effect exposing how asymmetric dominance violates the Axiom of Independence of Irrelevant Alternatives.
Deconstructing Paradoxes & Cognitive Logic
Rigorous, step-by-step mathematical proofs, game theory models, and cognitive bias explorations.
The Cognitive Reflection Test System 1 Heuristics vs. System 2 Deliberation
A deep mathematical analysis of Shane Frederick's Cognitive Reflection Test exploring dual-process cognition, algebraic reflexes, and impulse override.
The Wason Selection Task Falsification Failures and Evolution of Confirmation Bias
Analyzing Karl Popper's falsification principle, conditional logic traps, and evolutionary psychology through Peter Wason's classic four-card selection experiment.
The Linda Problem Conjunction Fallacies and Representativeness Heuristics Exposed
A formal mathematical proof of the Linda Problem exposing how the representativeness heuristic violates Kolmogorov's probability axioms and conjunction rules.
Gabriel’s Horn Paradox Infinite Surface Area vs. Finite Volume in Calculus
A rigorous calculus proof of Gabriel's Horn demonstrating how a geometric solid of revolution possesses finite volume but infinite surface…
The St. Petersburg Paradox Infinite Expected Values and Bernoulli’s Expected Utility
A rigorous deconstruction of the St. Petersburg Paradox analyzing infinite mathematical expectation, logarithmic utility, and finite wealth truncation.
The Unexpected Hanging Paradox Gödelian Incompleteness and Retroactive Logic Traps
Dissecting the Unexpected Hanging Paradox through formal backward induction, self-referential epistemic logic, and Gödelian incompleteness.
The Birthday Paradox Combinatorial Probability, Hash Collisions, and Pigeonhole Logic
A formal mathematical proof of the Birthday Paradox exploring combinatorial probability, Taylor series approximations, and cryptographic hash collisions.
The Muddy Children Puzzle Synchronous Epistemology and Iterated Reasoning Proofs
A formal mathematical proof of the classic Muddy Children puzzle examining synchronous communication rounds, epistemic Kripke frames, and iterated elimination.
The Blue Eyes Island Paradox Common Knowledge Induction and the Logic of Silence
A formal mathematical proof of the Blue Eyes Island Paradox dissecting common knowledge, epistemic induction, and the informational value of…