Topic Index

Concepts and topics from the lectures, in the lecturers’ own words, with links to the moment each is discussed.

0.9999 repeating

15-year-old self

17th and 18th century

2022 Nobel Prize in Physics

a priori knowledge (2)

a priori synthetic judgments (3)

Achilles and the tortoise

Ackermann function

Action at a Distance

active motion and passive motion

actual infinity (3)

actually infinite (3)

Adam (2)

adjacent spatio-temporal points

Aharonov-Bohm effect

Alan Cobham (2)

Alan Turing (3)

Albert Einstein (2)

algebraic numbers (2)

algebraic real numbers (2)

algorithmic shortcut (10)

all motion is impossible

Allegory of the Cave

alternating harmonic series

alternating series

analytic a priori

analytic judgment

Anatoly Karatsuba

Andrei Kolmogorov (3)

Andrey Kolmogorov

anti-realism (2)

arbitrary set potentialism

Archimedean spiral

arctangent function

Aristophanes (2)

Aristotelian potentialism

Aristotle's wheel

artificial intelligence (2)

associative operation

axiom of choice (5)

axiom of countable choice

axiom of separation

balls in a sack

bang plex stack hierarchy

barista paradox

begging the question

believing is seeing

Bell Inequality

Bell Test Experiments

Bell's Theorem (2)

Berry's paradox

Bertrand Russell (3)

better color box

billiard ball (6)

birth of computer science (2)

black and white TV

Bletchley Park (2)

blind man who's stumbling down the right road

Bloomsbury circle

Bohr (5)

both routes (2)

bounded quantifiers

Brobdingnagians

busy beaver function

canary in a coal mine

Cantor Bendixson derivative

Cantor Bendixson process

Cantor Hume Principle

Cantor pairing function

Cantor Schon principle

Cantor space (2)

Cantor-Schroeder-Bernstein theorem (3)

Cantor–Schröder–Bernstein theorem (3)

Cantor's cruise ship (2)

Cartesian coordinates (2)

Cartesian dualism

Cartesian product

category mistake (3)

cause and effect (4)

characteristic sequence

Charged Particles

chocolatier's game

Church-Turing thesis (3)

clear and distinct perception (2)

Clifford the big red dog

closure properties

Cobham-Edmonds thesis (2)

Cogito ergo sum

collapse of the wave function

color measurements (2)

common concepts

common induction

comparative size principle

complementarity

complexity theorists (2)

computable real numbers

computably undecidable

computation and its limits (2)

Computation transcends technology

computational complexity

computer science's fight for recognition

concepts of the understanding (2)

conceptual framework

conceptual lens

conditionally convergent

configuration space

consequent conjunctions

Conservation of Energy

Conservation of Momentum

constant conjunction (2)

constructible universe

continuous functions

continuum hypothesis

contradiction (2)

convergent form of potentialism

Cook-Levin theorem (3)

corrupting the youth (2)

countable choice (2)

countable infinity (3)

countable union of countable sets

countably additive

countably creative

countably infinite (3)

countably infinite subset

crisis of representation

critical philosophy (2)

Critique of Pure Reason (2)

cross-sectional area

cumulative hierarchy

custom or habit (3)

David Hilbert (5)

Deal with the Devil

decimal notation

decision problem

Dedekind arithmetic

Dedekind finite

Dedekind infinite

definability is not definable

definition by recursion

dependent co-origination

diagonal argument

diagonalization (4)

Dialogue Concerning Two New Sciences

Dialogues Concerning Two New Sciences

diatribes versus dialogues

different species

Dijkstra's algorithm (4)

discrete linear order with endpoints

discretely finite

distinction between the countably infinite and the uncountably infinite

distinction between the potentially infinite and the actually infinite

divisibility of a line segment

dogmatic slumbers

dominion over the animals

double slit experiments

draw the line objection

dream argument (2)

driving directions (3)

Edmonds' conjecture (3)

Edsger Dijkstra (2)

efficient computation (4)

efficient solvability

efficiently verifiable solutions (4)

Einstein, Podolsky, and Rosen (2)

Electric Fields

Electromagnetic Field

Electromagnetic Waves (2)

electron mirror

electrostatic forces

empirical beliefs (2)

empirical beliefs under good conditions

empirical verification (2)

entanglement (2)

Entscheidungsproblem

epiphenomenalist

epistemic issue

epistemological

epistemological nihilism (2)

epistemological quality

epistemological status

epistemology (2)

equinumerous (3)

ethical and political relativism

Euclid's Elements

Euclid's principle (2)

Euclidean geometry (2)

Euclides and Terpsion

evil genius argument

exhaustive search (4)

existence and essence

existence is a perfection

exoteric and esoteric

exponential growth

exponential notation

extended Church-Turing thesis (2)

extended real numbers

fact value distinction

faculties of the mind (2)

faithful to the Earth

false judgment (2)

Fermat's Last Theorem (2)

finite partial sums (2)

finite words (2)

first cause (2)

first meditation (3)

first order logic

force and vivacity

foreign language (2)

form and matter

forms of intuition (2)

foundations of quantum mechanics (4)

frustum of a cone

fundamental physics

fundamental theorem

fundamental theorem of arithmetic

Galileo Galilei

Galileo's paradox (4)

Galileo's wheel

general comprehension principle

General Theory of Relativity

genuine progress

geocentric world

geometric series (2)

George Dantzig (4)

German idealism

Gestalt psychologists

Gettier problem

Ghirardi, Romini, and Weber

Gian-Carlo Rota

Gödel's incompleteness theorem (2)

Google Maps (2)

Graham's number

graph isomorphism

Gravitational Waves

half marathon runners

halting problem (7)

hard electron (2)

hard problems (4)

hardness box (4)

harmonic series

Harvey Friedman

hexagonal wheel

hidden variable tradition

Hidden Variables

Hilbert's bus (2)

Hilbert's Hotel (2)

Hilbert's program

Hilbert's train (2)

history of philosophy (5)

how are a priori synthetic judgments possible (3)

human understanding (2)

Hume (6)

hyperbolic geometry

hyperbolic spiral

I think, therefore I am (3)

idea (3)

immediate impression (2)

immortality of the soul

impossible event

induction scheme

infinite matrix

infinite regress (2)

infinite series (2)

infinite sum (2)

infinitude of primes

injustice as its own punishment

Inquiry Concerning Human Understanding

instrumentalism

instrumentalist (2)

integer programming

intelligibility

interactive dualist

interference effects

interference pattern

interleaving the digits

International Congress of Mathematicians

intrinsic value

Inverse Square Law

irrational numbers (2)

irreducibly chances

Isaac Newton (2)

isolated points

iterated exponentials

Jack Edmonds (3)

Jack the Giant Killer

Jacques Derrida

James Clerk Maxwell

John Conway's Game of Life

John Henry Poynting

John von Neumann (5)

justified true belief

Kant (5)

Karatsuba's method (4)

Karatsuba's multiplication algorithm (3)

Karp's 21 problems

knowledge is perception (5)

knowledge is simply perception

knowledge is the same thing as perception

knowledge is wisdom

Koch snowflake curve

Kolmogorov complexity

Kurt Gödel (3)

Ladner's theorem

lambda calculus (2)

large cardinals

large language models (2)

largest tweetable number

Law Number One (2)

law of identity

law of non-contradiction

laws of logic (2)

laws of nature (3)

least number principle

Lebesgue measure

Leonid Levin (3)

levels of infinity

Lévy-Collot theorem

LIGO Nobel Prize

limitations of computation (2)

linear programming

linear programming duality

linear time algorithm (2)

linearly finite

linearly ordered (2)

Liouville constant

listing the elements

logarithmic spiral

logical empiricists

logical fallacy (2)

logical independence

logically coherent (2)

logicist program

Löwenheim-Skolem theorem

Lucas-Penrose interpretation

macroscopic (2)

magnetic fields (2)

man is the measure of all things (3)

many-worlds interpretation

marital status of the number five (3)

Martin Heidegger

matching problems

Mathematical Foundations of Quantum Mechanics

matrix multiplication

matters of fact (3)

Maxwell's Equations

Maxwellian electrodynamics (2)

measurement problem (3)

Meditations on First Philosophy

memory-free strategy

mental arithmetic

mental geography

metaphysics (3)

methodological doubt (3)

Michael Faraday

Milky Way galaxy (2)

millennium problems (2)

mind-body problem

mind/body dualism

minimal criminal

minimax theorem

modal logic (2)

Modal Model Theory

modal semantics

modified Gabriel's horn

monism and dualism

more committees than people

more fruit salads than fruits

most contested equation in middle school

multiverse view (2)

my perception is true for me

natural log of 2

natural number lattice

natural numbers (6)

natural philosophy

Natural Selection (2)

necessary and universal

necessary properties

nested interval argument

neutron interferometry

never stop growing

new computational paradigms

Newton's Laws of Motion

Newton's Shadow Theory of Gravitation

Newton's Universal Law of Gravitation

Newtonian mechanics (4)

Newtonian physics (2)

non-being is not

non-deterministic polynomial

nonlinear form of potentialism

NP problems (3)

NP-complete (3)

NP-complete problem (3)

NP-completeness (5)

NP-intermediate

number and numeral

numerically finite

omnibenevolence

omniscience, omnipotence, omnibenevolence

On the Mind-Body Problem

one-to-one correspondence (4)

one-to-one function

ontological proof

ontologically light

our essence to be more than any essence

owner's manual for human life

P equal to NP (3)

P not equal to NP (3)

P versus NP (6)

P versus NP question (5)

paint-based theory of surface area

painter's paradox

pairing function

paradox of giants

paradox of supertasks

paradox of the miniature human

paradoxes of infinity

Paradoxes of the Infinite

parallel postulate

partial products (2)

parts and wholes

passive observation

Paul Feyerabend

perfect squares

philosopher kings

picture of the universe

pig and the baboon

pigeonhole principle

pink sunglasses (2)

Plato's Theaetetus (4)

playing the game and making up the rules at the same time

Poincaré conjecture

Poincaré disk model

polar coordinates

polynomial time (3)

polynomial-time algorithm (6)

positional number system

positive rational numbers

post-quantum cryptography

Postulate of Collapse

potential infinity (3)

potentialism (2)

potentialist character

potentialist translation

potentially infinite (3)

potion for wisdom and memory

power of computation

power of pre-processing

power set of the natural numbers (2)

power set of the real numbers

prime factorization (2)

Principle of Locality

probabilistic law (2)

probability claims

probability problem in Many-Worlds

probability zero

problem of induction

process philosophy

programs as data

projective sets

Prolegomena to Any Future Metaphysics

proof by contradiction (2)

public key encryption

purely rational thinking things

putting your judgment into words

quadratic time algorithm (2)

Quadrature of the Parabola

quantum computers (3)

quantum computing (3)

Quantum Entanglement

quantum mechanics (11)

Quantum Mechanics and Experience

quantum mechanics in your face

Quantum Non-locality

quantum theory (2)

Queen Catherine of Sweden

Queen Christina

radical branching

random choice balls in a sack

rational numbers (3)

rationalism (2)

rationalism and empiricism (3)

rationalist (2)

real numbers (6)

recreating his self

recurrence relation

redundant work (4)

reference and intentionality

reflexive order

regulative and not constitutive

regulative self

relations of ideas (3)

relativism of Protagoras

Rene Descartes (2)

replacement axiom

Richard Dedekind

Richard Karp (3)

Riemann hypothesis

Riemann rearrangement theorem

Robertson-Seymour theory

Robinson Crusoe

row of dominoes (2)

running around the hearth

S4.2 (2)

Schrodinger (2)

Schrodinger equation (3)

scientific notation

scientific project (4)

scientific realism (2)

scientific revolution (6)

second meditation

second order assertion

second order logic

secondary qualities

secret doctrine

Secrets of LLM Performance

self-referentiality

self-refutation argument

self-similar fractal

sensory deception (2)

set theoretic pluralism

shortest path (3)

shortest path problem (3)

simplex method (2)

single-cell amoeba

single-celled being

skeptical arguments (2)

Skeptical School

small forcing extensions

Socratic fallacy

Socratic wisdom

source of knowledge

Spacetime Curvature

special theory of relativity

start from scratch (4)

statistical correlations

Stephanus numbers

Stephen Cook (3)

straightedge and compass

Strassen's algorithm

strictly larger (3)

strong double arrow

strong induction

subatomic particles (3)

subgraph isomorphism (2)

subject and a predicate

successor relation

Superposition (5)

supremely perfect being

surface of revolution

surface tension

surprising claim

syntax-semantics dichotomy

synthetic a priori

synthetic empirical

tabula rasa (2)

Tarski's theorem on the non-definability of truth

Ted Baker, John Gill, and Robert Solovay

Thanksgiving turkey

the animal that has no limits

The Apology (2)

the book of nature is written in the language of math

the call is coming from inside the house (2)

The Emergent Multiverse

the enlightenment (2)

the eternal return

the future will resemble the past (2)

the man who can change the appearances for the better

The Meditations (3)

the most controversial equation in middle school

The Phantom Tollbooth

The Republic (3)

the Sophist (3)

the verb to be must be totally abolished

the world in itself (2)

theory of becoming

theory of the forms

thermodynamically irreversible

things in themselves (2)

thinking thing (3)

Thompson's Lamp

Thracian servant girl

three boxes in a row

three bullet-proof beliefs

Tim Maudlin (2)

to be is to be perceived

total of nothing box (2)

transcendental idealism

transcendental illusion (3)

transcendental numbers (2)

traveling salesman problem (3)

traveling salesperson problem (5)

Travis Norsen (2)

triangular number

trivial supertask

true judgment (2)

true judgment plus an account (2)

Turing machine (10)

Turing-complete

TV screen problem

two and two equals four (3)

two paths experiments (2)

Un-American Activities Committee

uncertainty principle (2)

uncertainty relation (2)

uncountable infinity (3)

uncountably additive

uncountably creative

uncountably infinite

undecidable problems (3)

uniform distribution

uniqueness of the prime factorization (2)

unit square (2)

universal problems

universal Turing machine (2)

universality (2)

Velocity of Light

virtuous circle

visible spectrum

Von Neumann (10)

Von Neumann's Rule One (2)

Von Neumann's Rule Two (2)

Voodoo Doll Analogy

wave function (3)

wave-particle duality (2)

wax block model (2)

white electron (3)

winning strategy

Wittgensteinian

You can't step in the same river twice (2)

you know it when you see it (2)

Zeno (3)

Zeno's paradox (2)

Zermelo-Fraenkel set theory (3)

Zermelo–Fraenkel axioms (2)

zigzag path (2)