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Latest 100 posts

• The Hypergame Paradox
• ZFC as One of Humankind’s Great Inventions
• Hilbert-type Infinitary Logics
• Forcing and the Independence of CH (Part 2)
• Forcing and the Independence of CH (Part 1)
• The Ultra Series: Guide
• Shorter Proof of Countable Saturation (Ultra 7.5)
• All About Countable Saturation (Ultra Series 7)
• Ultraproducts and Compactness (Ultra Series 6)
• Infinitely Large Primes (Ultra Series 5)
• Ultraproducts and Łoś’s Theorem (Ultra Series 4)
• Hypernaturals in all their glory (Ultra Series 3)
• Hypernaturals Simplified (Ultra Series 2)
• Ultrafilters, Ultraproducts, and Hypernaturals 1: Introduction
• Even Numbers are Tautologies
• Notes on motivation and self-improvement
• First Order Truth Trees
• One nonstandard is worth infinitely many standards
• This post is lying to you
• Some half-baked thoughts on moral arbitrariness
• Asymmetry between the infinite and finite
• PA doesn’t trust its provability predicate
• No more than half of anti-sets are big
• A Dating Puzzle, and Bayesian Experimental Design
• What precedent does the Trump Twitter ban set?
• Divisibility Tricks and Orderly Numbers
• What’s the probability that an election winner leads throughout the entire vote?
• Quantum Chess
• Biblical inerrancy
• Formal Semantics 1: Historical Prelude and Compositionality
• Two more short and sweet proofs of propositional compactness
• The Theory of Knots
• A Compact Proof of the Compactness Theorem
• ZFC, and getting the right answer by accident
• Polish Notation and Garden-Path Sentences
• Defining uncountability
• Who would win in a fight, logic or computation?
• Computing truth values of sentences of arithmetic, or: Math is hard
• How uncomputable are the Busy Beaver numbers?
• The Arithmetic Hierarchy and Computability
• A Self-Interpreting Book
• Epsilon-induction and the cumulative hierarchy
• Nonstandard integers, rationals, and reals
• Transfinite Nim: uncomputable games and games whose winner depends on the Continuum Hypothesis
• A Coloring Problem Equivalent to the Continuum Hypothesis
• No known unknowns in Peano arithmetic
• The subtlety of Gödel’s second incompleteness theorem
• Undecidability results on lambda diagrams
• The Anti-Set Program
• Pictures of some extremely large numbers
• How to draw lambda diagrams
• Fundamentals of Logic: Syntax, Semantics, and Proof
• The Pictorial Mathematics of Klak-Adbmal
• The Rise of Anti-Set Theory
• The Transfinite Factorial
• On Self-Hating Theories of Arithmetic
• Updated Introduction to Mathematical Logic
• Finiteness can’t be captured in a sound, complete, finitary proof system
• The Mindblowing Goodstein Sequences
• Wacky Non-Standard Models of PA
• The Continuum Hypothesis is False
• Kolmogorov Complexity, Undecidability, and Incompleteness
• Constructing the Church-Kleene Ordinal
• What ordinals can be embedded in ℚ and ℝ?
• Visualizing the rationals
• The order type of the rational numbers
• Can you compute all the countable ordinals?
• Immoral or Inconsistent?
• Constructing ordinal numbers in ZFC
• Meaning ain’t in the brain
• On philosophical progress
• Logic on Planet Zorko
• A result on the incompleteness of mathematics
• A Gödelian Logic Puzzle
• Crazy conditionals
• A Dice Puzzle
• Proving the Completeness of Propositional Logic
• Sum and Product Puzzle
• Four Pre-Gödelian Limitations on Mathematics
• A proof of the Compactness Theorem
• A challenge to constructivists
• Describing the world
• The full solution to the dog puzzle
• The Surprise-Response Heuristic
• Three paradoxes of self-reference
• A logic puzzle about dogs
• A suspicious proof of God’s existence
• Fractal Trees
• In defense of collateralized debt obligations (CDOs)
• Six Case Studies in Consequentialist Reasoning
• Will we ever build a Galactic Empire?
• Earning to give or waiting to give
• Diversification is magic
• Paradoxical Precommitment
• Solving the Linear Cournot Model
• Building an analog calculator
• Complex numbers in physics
• The laugh-hospital of constructive mathematics
• Can chess be solved?
• For Loops and Bounded Quantifiers in Lambda Calculus