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Thesis

In my thesis, I propose a naturalistic answer to the classic question 'how is a priori knowledge possible?' in what some have considered its most difficult case - mathematics. My answer involves a relationship between: meta-semantic facts, Quinean theory revision, natural selection and the availability of 'multiple targets' for mathematical knowledge.

Papers In Progress

Philosophy of Math:
• Mechanism and Lob's Theorem
• A Posteriori Mathematics and Malament Hogarth Space-Times
• Kant 's Question and Debates about the Boundaries of Logic
• A Realist Solution to the Access Problem
• Berkeley and the Bridges - what do empirical applications of mathematics commit us to?
• On the Conformity Between Armchair Reasoning and Experience
• Against Michael Potter on Godel and Carnap
[revised ending]
• The Role of Philosophy In Axiom Choice (early draft)
• On Proof and Psychology (early draft)

Epistemology:
• Contra Williamson on Counterfactuals and Thought Experiments
• Fixing Bogossian on Analyticity and Epistemology
• The Problem of a Priori *Analytic* Knowledge
• A Priority, and the Doctoroids
• (Contra) Kim on Belief and Epistemic Normativity
• The Skeptic and the Obvious Proof-Theoretic Fact (warning:0th draft)

Misc:
• Paraphrase, Ontology and the Index Theorem (early draft)
• Massive Suggestiveness: A Neo-Kantian Theory of Beauty (warning:0th draft)
• On Quantification and Reality -Why the World is a Lump
• Three Indeterminacy Arguments Refuted
• The Semantic Skeptic
• Thompson's Violinist

Programming

Truthtabler: I wanted to write things that people could play online, so here's my first javascript program, a little game where you can practice doing truthtables.

Nested Quantifier Game: Mathematicians are always complaining about how it's impossible to really teach calculus to non-majors, because a) most people don't understand statements with nested quantifiers while b) you need to understand statements with nested quantifiers to understand central notions in calculus, like continuity (for every epislon there is a delta, such that, whenever |x-c| is less then delta, the difference between f(x) and f(c) is less than epsilon).

I highly doubt that most people can't understand such expressions, so I think a great research program, would be to do try to figure out how to teach people to understand these statements. a little game, which tries to do this.

Latin Game: In highschool, I convinced my latin teacher that I had a latin specific learning disability. I don't know whether that's true, but what is true, is that I've taken 6 years of latin, and still have to recite endings to myself to try to figure out what case a given word is supposed to be. Here's the demo for a little tetris style-game I wrote to make that process easier .

Motto

Paul Grahm is a programmer-type who also writes great essays, including some about how to write great essays. He says: "I like to find (a) simple solutions (b) to overlooked problems (c) that actually need to be solved, and (d) deliver them as informally as possible, (e) starting with a very crude version 1, then (f) iterating rapidly."

This quote also sums up how I try to approach philosophy.

My CV

Philosophy in Progress

Emerson Hall Problems