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C
canary in a coal mine
“of the next two centuries, because he foresaw it. He thought of himself as a canary in a coal mine. It used to be when people would go into mines, there was always the possibility of very poisonous” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 7: Nietzsche's Warning to the Future▶︎ watch 2:05 · read ↗︎
Cantor
“We'll start with Zeno and the classical ideas of Aristotle and Archimedes, but eventually, we'll move through Galileo, and then we'll see Frege, and Dedekind, and Cantor, and the 20th century…” (Joel David Hamkins)
Lectures on Infinity · Intro: Infinity Has a Story to Tell▶︎ watch 0:25 · read ↗︎
Lectures on Infinity · Lecture 5: Potential vs Actual Infinity▶︎ watch 57:27 · read ↗︎
Lectures on Infinity · Lecture 6: Galileo's Paradox of Infinity▶︎ watch 3:39 · read ↗︎
Lectures on Infinity · Lecture 9: Beyond Countable Infinity▶︎ watch 1:35 · read ↗︎
Lectures on Infinity · Lecture 10: Set Theory's Deepest Mystery▶︎ watch 0:46 · read ↗︎
Cantor Bendixson derivative
“by casting out the isolated points, yeah? So cast out the isolated points. So for example, in, with this convergent sequence that I had here, the, this point is isolated, which means” (Joel David Hamkins)
Lectures on Infinity · Lecture 10: Set Theory's Deepest Mystery▶︎ watch 21:40 · read ↗︎
Cantor Bendixson process
“a certain process called the Cantor Bendixsen process, the Cantor Bendixsen derivative, yeah. So we form the next set, C1, by casting out the isolated points, yeah? So cast out the isolated points.” (Joel David Hamkins)
Lectures on Infinity · Lecture 10: Set Theory's Deepest Mystery▶︎ watch 21:30 · read ↗︎
Cantor Hume Principle
“as the number of noses in the classroom. And this brings us to this principle called- that I call the Cantor-Hume Principle, also known as just by Hume's Principle, which says that we want to say…” (Joel David Hamkins)
Lectures on Infinity · Lecture 6: Galileo's Paradox of Infinity▶︎ watch 2:29 · read ↗︎
Cantor pairing function
“So it's a sort of nicer formula. This is called the Cantor pairing function. A pairing function is a function that takes pairs of objects and gives you back individual objects in a way that is a…” (Joel David Hamkins)
Lectures on Infinity · Lecture 8: Hilbert's Hotel Is Always Open▶︎ watch 30:51 · read ↗︎
Cantor Schon principle
Lectures on Infinity · Lecture 7: What Does Finite Really Mean?▶︎ watch 2:24
Cantor space
“So let's consider what's now called Cantor space or the space of infinite binary sequences. So these are the sequences, for example, maybe we have the sequences of zeros and ones. So we have this,…” (Joel David Hamkins)
Lectures on Infinity · Lecture 9: Beyond Countable Infinity▶︎ watch 52:18 · read ↗︎
Lectures on Infinity · Lecture 10: Set Theory's Deepest Mystery▶︎ watch 4:16 · read ↗︎
Cantor-Schroeder-Bernstein theorem
“Okay, I can tell you the answer to this question. It's quite interesting. The answer is yes, and this is known as the Cantor-Schroeder-Bernstein theorem proved at the end of the 19th century. So it's…” (Joel David Hamkins)
Lectures on Infinity · Lecture 6: Galileo's Paradox of Infinity▶︎ watch 31:35 · read ↗︎
Lectures on Infinity · Lecture 9: Beyond Countable Infinity▶︎ watch 1:02:40 · read ↗︎
Lectures on Infinity · Lecture 10: Set Theory's Deepest Mystery▶︎ watch 10:09 · read ↗︎
Cantor–Schröder–Bernstein theorem
“And notice that I'm using here the Cantor-Schroeder-Bernstein theorem about comparison of size, which we discussed in another lecture. Namely, I didn't show directly that the reals have the same size…” (Joel David Hamkins)
Lectures on Infinity · Lecture 9: Beyond Countable Infinity▶︎ watch 1:02:42 · read ↗︎
Lectures on Infinity · Lecture 10: Set Theory's Deepest Mystery▶︎ watch 10:43 · read ↗︎
Lectures on Infinity · Lecture 6: Galileo's Paradox of Infinity▶︎ watch 31:34 · read ↗︎
Cantor's cruise ship
“Okay, so there was an ocean liner, Cantor's Cruise Ship pulls in to the hotel, and Cantor's Cruise Ship is full of guests, full of passengers. Every passenger on Cantor's Cruise Ship” (Joel David Hamkins)
Lectures on Infinity · Lecture 8: Hilbert's Hotel Is Always Open▶︎ watch 50:31 · read ↗︎
Lectures on Infinity · Lecture 9: Beyond Countable Infinity▶︎ watch 1:43 · read ↗︎
Cartesian coordinates
“He created, he took Cartesian coordinates in geometry. Cartesian is just the adjective form of Descartes. He invented those. He invented them, in fact, lying in bed one morning. He hated getting out…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 1: Descartes Reboots Everything▶︎ watch 27:02 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 2: The Birth of Modern Science▶︎ watch 35:39 · read ↗︎
Cartesian dualism
“And this is the idea that everything in the universe can be divided into one of two categories. That's why it's a dualism. It's Cartesian 'cause he came up with it. Everything in the universe, you…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 1: Descartes Reboots Everything▶︎ watch 40:30 · read ↗︎
Cartesian product
“countable, then A cross B is countable. So A cross B means the set of pairs, AB. Where A is in A and B is in B, yeah, so the Cartesian product of two sets is the set of pairs. We could maybe just…” (Joel David Hamkins)
Lectures on Infinity · Lecture 8: Hilbert's Hotel Is Always Open▶︎ watch 38:00 · read ↗︎
categorical
Lectures on Infinity · Lecture 7: What Does Finite Really Mean?▶︎ watch 23:46
categories
“Some philosophers call them categories. Can we come up with a complete list? Why? Is there a system to them? Where do they come from? Maybe they do come from perception, and this is a bogus argument.…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 4: The Soul Behind the Senses▶︎ watch 17:49 · read ↗︎
category mistake
“called a category mistake. Okay? That asking which path it's on is like asking about the marital status of the number five or about the weight in grams of Catholicism or about the political…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 3: Two Laws That Can't Both Be True▶︎ watch 5:16 · read ↗︎
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 5: Three Ways to Save Reality▶︎ watch 27:15 · read ↗︎
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 2: When Physics Stops Making Sense▶︎ watch 8:44 · read ↗︎
causality
“phenomena into causal relationships. So if you wanna understand science, this is what Descartes wanted, you have to understand causality. And of course, for Hume, causality is contingent and imperial.” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 4: Why You Can't Prove Tomorrow▶︎ watch 4:32 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 5: Kant Wakes from His Dogmatic Sleep▶︎ watch 7:21 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 6: How Your Mind Builds Reality▶︎ watch 22:16 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Recap: Making Your Beliefs Your Own▶︎ watch 4:53 · read ↗︎
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 4: The Soul Behind the Senses▶︎ watch 18:09 · read ↗︎
cause and effect
“know matters of fact, MOF, that we do not have immediate, direct impressions to tell us what they are? And his answer to that is- cause and effect, a causal relationship. His example, he gives the…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 4: Why You Can't Prove Tomorrow▶︎ watch 2:08 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 5: Kant Wakes from His Dogmatic Sleep▶︎ watch 7:19 · read ↗︎
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 2: When Every Perception is True▶︎ watch 41:56 · read ↗︎
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 4: Bell's Impossible Proof▶︎ watch 7:19 · read ↗︎
centillion
“I could write one centillion, and a centillion is 10 to the 303. So that's a number that's much bigger than filling the tweet with nines, with the digit nine.” (Joel David Hamkins)
Lectures on Infinity · Lecture 4: The Largest Tweetable Number▶︎ watch 1:13 · read ↗︎
characteristic sequence
“This is called the characteristic sequence of the given set A. So for any set A, I can just write down its in-out pattern for the natural numbers, either zero is in or out, one is in or out, two is…” (Joel David Hamkins)
Lectures on Infinity · Lecture 9: Beyond Countable Infinity▶︎ watch 59:31 · read ↗︎
Charcot
“discipline until the end of the 19th century basically, like Breuer and then Charcot and Freud. Up until then, if you wanna do psychology, you did philosophy. It was part of philosophy. And Hume is…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 4: Why You Can't Prove Tomorrow▶︎ watch 28:03 · read ↗︎
Charged Particles
“charged particles, okay? Unlike gravitation, this force can be either attractive or repulsive. It's repulsive if you have two positive charges or two negative charges. It's attractive if the charges…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 4: Bell's Impossible Proof▶︎ watch 26:19 · read ↗︎
chocolatier
“Okay. So, in the first version of the game, the game has infinitely many rounds, turns. You know, it will go infinitely. And on every round, the chocolatier serves up finitely many new exquisite…” (Joel David Hamkins)
Lectures on Infinity · Lecture 2: Supertasks: Doing Infinitely Many Things▶︎ watch 30:42 · read ↗︎
chocolatier's game
“the chocolatier's game. So the chocolatier's game is a game played with two players. There's the chocolatier, who will be serving up chocolates, exquisite creations on a kind of serving” (Joel David Hamkins)
Lectures on Infinity · Lecture 2: Supertasks: Doing Infinitely Many Things▶︎ watch 30:20 · read ↗︎
Church-Turing thesis
“generality, that belief is something known as the Church-Turing thesis. We will return to that at the end of this episode. Now at first this might seem crazy. You're probably like, "Wait a minute.…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 1: Is There Anything Computers Can't Do?▶︎ watch 16:18 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 3: Easy Problems, Hard Problems▶︎ watch 26:41 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 5: AI, Quantum Computing, and Beyond▶︎ watch 32:08 · read ↗︎
circle
“That's exactly what a circle is. A circle can be thought of," he argued, "as a polygon with infinitely many sides." It's the actualist case because, first of all, we can definitely talk about circles…” (Joel David Hamkins)
Lectures on Infinity · Lecture 5: Potential vs Actual Infinity▶︎ watch 14:27 · read ↗︎
clay
“in 147A and B, clay of the potters, clay of the stove makers, clay of the brick makers. Well, if the person doesn't know what the word clay means, that's not gonna help. Do you think anyone can…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 1: Is Knowledge Just Perception?▶︎ watch 20:52 · read ↗︎
Clay Institute
“amount of scientific progress. And so we'll return to this in a different episode, but in homage to Hilbert's 1900 list of open problems, in 2000, the Clay Institute issued seven millennium problems,…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 1: Is There Anything Computers Can't Do?▶︎ watch 6:42 · read ↗︎
clear and distinct perception
“and distinct perception of them. This is his phrase, and it's become kind of a technical term. It's because he can have a clear and distinct perception of these that he can be sure that they're true,…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 2: The Birth of Modern Science▶︎ watch 1:30 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 3: Hume's Map of the Mind▶︎ watch 25:32 · read ↗︎
Clifford the big red dog
“My son, when he was younger, one time came up to me and asked me, "Daddy, what color is Clifford the big red dog?" And I thought to myself, "We're gonna have to keep him in the house for a long time.…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 5: Kant Wakes from His Dogmatic Sleep▶︎ watch 23:22 · read ↗︎
Clive Wearing
“Rob's point about time that we were discussing. There's a case of a musicologist, Clive Wearing, who had such severe damage to his memory capacity that he basically has a seven-second memory span.…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 5: Defeat as Philosophical Victory▶︎ watch 32:43 · read ↗︎
closed sets
“up to more and more complicated sets. Say he proved it for closed sets of reals. It's also true for open sets of reals and so on, and then he wanted to move to the next level of complexity of sets…” (Joel David Hamkins)
Lectures on Infinity · Lecture 10: Set Theory's Deepest Mystery▶︎ watch 1:43 · read ↗︎
closure properties
“So let's think about the nature of countable sets. What kind of closure properties do countable sets exhibit? If I have a countable set and I add one more element to it, then I claim it's still a…” (Joel David Hamkins)
Lectures on Infinity · Lecture 8: Hilbert's Hotel Is Always Open▶︎ watch 17:40 · read ↗︎
Cobham-Edmonds thesis
“to revisit our definitions, okay? And in particular, basically revisit the Cobham-Edmonds thesis. And so Cobham and Edmonds both advocated identifying efficient computations with polynomial time.…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 5: AI, Quantum Computing, and Beyond▶︎ watch 30:51 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 3: Easy Problems, Hard Problems▶︎ watch 17:21 · read ↗︎
Cogito ergo sum
“comes from, "Cogito ergo sum." "I think, therefore I am." You see, doubting is thinking something. To doubt is to think something might be wrong, right? If I doubt that the sun is shining,” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 1: Descartes Reboots Everything▶︎ watch 34:58 · read ↗︎
Cohen
“known whether it was a theorem or not, you know? Cohen showed that it is not. He showed the analogous result for the negation of the continuum hypothesis. Namely, if the axioms of set theory are…” (Joel David Hamkins)
Lectures on Infinity · Lecture 10: Set Theory's Deepest Mystery▶︎ watch 34:48 · read ↗︎
collapse
“able to show is that that's not the case here, okay? That this phenomenon that people started to call collapse, this business of forcing the system to pick a value, to pick a path,” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 3: Two Laws That Can't Both Be True▶︎ watch 13:55 · read ↗︎
collapse of the wave function
“in which von Neumann's Law Two... Von Neumann's Law Two is sometimes referred to as the law of the collapse of the wave function on measurement. So those physical situations in which von Neumann's…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 5: Three Ways to Save Reality▶︎ watch 3:40 · read ↗︎
color
“measurements we're gonna be talking about here, let's call the color of these electrons. Once again, electrons don't actually have colors. I'm talking about certain components of the intrinsic…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 1: The Experiment That Broke Reality▶︎ watch 2:04 · read ↗︎
color box
“You feed an electron into the input aperture of a color box, it comes out this aperture if it's a black electron, and it comes out that aperture if it's a white electron. Okay.” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 1: The Experiment That Broke Reality▶︎ watch 5:09 · read ↗︎
color measurements
“plug whatever arrangement you've set up. You plug the outcomes of the measurements you did on these particles before you fed them into the hardness box, and you use it to predict the outcomes of…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 2: When Physics Stops Making Sense▶︎ watch 1:04 · read ↗︎
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 1: The Experiment That Broke Reality▶︎ watch 31:44 · read ↗︎
commensurable
“The side of the three-foot square is obviously square root of three. But what does that mean? What is the square root of three? Is it commensurable with one? If it's commensurable, this means that…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 1: Is Knowledge Just Perception?▶︎ watch 24:38 · read ↗︎
common concepts
“what are we gonna do about what Socrates calls the things that are common to more than one sensory domain? Let's take the number two, which he mentions at 185B.” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 4: The Soul Behind the Senses▶︎ watch 9:56 · read ↗︎
common induction
Lectures on Infinity · Lecture 7: What Does Finite Really Mean?▶︎ watch 32:23
comparative size principle
“is about the comparative judgment. And so I wanna introduce what I call the comparative size principle, which is that we wanna say that one set has at least as many elements as another if the other…” (Joel David Hamkins)
Lectures on Infinity · Lecture 6: Galileo's Paradox of Infinity▶︎ watch 26:17 · read ↗︎
complementarity
“He had a shtick that he referred to as complementarity, okay? He said, "Look, here's a little more detail about why it's impossible to tell any story. If you have one of” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 3: Two Laws That Can't Both Be True▶︎ watch 18:44 · read ↗︎
complete
“statements being true, is in fact what he would call complete, meaning that whenever you have a mathematical assertion which is in fact true, there should be an argument, a proof, a finite sequence…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 1: Is There Anything Computers Can't Do?▶︎ watch 7:22 · read ↗︎
completeness
“Reason has the demand for completeness. When reason looks at knowledge produced by intuition in math, by understanding in science, it says, "That's not good enough.” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 6: How Your Mind Builds Reality▶︎ watch 27:12 · read ↗︎
complexity theorists
“or negative results, and those researchers might self-identify as complexity theorists or as lower bounds researchers, because they're focused on sort of you know, difficulty, okay, proving levels of…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 4: Two Worlds We Might Live In▶︎ watch 7:44 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 5: AI, Quantum Computing, and Beyond▶︎ watch 13:28 · read ↗︎
computable real numbers
“those sets are all countable. And on the other hand, we also have many instances of sets of reals of size continuum, sort of the intervals, the non-trivial intervals, the open sets, the uncountable…” (Joel David Hamkins)
Lectures on Infinity · Lecture 10: Set Theory's Deepest Mystery▶︎ watch 30:10 · read ↗︎
computably undecidable
“and we know now that the halting problem, the question of whether a given computer program ever halts and gives output is computably undecidable. It's similar to the Kolmogorov complexity problem. So…” (Joel David Hamkins)
Lectures on Infinity · Lecture 4: The Largest Tweetable Number▶︎ watch 43:33 · read ↗︎
computation
“So today, I wanna talk about computation. And I say computation, probably that sounds like it has something to do with computers. And you know, in a way it does, but really, computation is a…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 1: Is There Anything Computers Can't Do?▶︎ watch 0:02 · read ↗︎
computation and its limits
“Hi, everyone. My name is Tim Roughgarden, and I'm gonna be your guide for this series on Computation and its Limits. So, those may sound like topics that are fundamentally about computers and…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Intro: Computation and Its Limits▶︎ watch 0:01 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 5: AI, Quantum Computing, and Beyond▶︎ watch 49:43 · read ↗︎
Computation transcends technology
“cutting edge technology of 2026 to where we began. Computation transcends technology. Doesn't matter, at some point in the future there's data centers orbiting the earth, robot colonies on Mars.” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 5: AI, Quantum Computing, and Beyond▶︎ watch 1:03:55 · read ↗︎
computational complexity
“scheduling tasks, solving puzzles, tons of these problems have exactly the same computational complexity, which means the difficulty of carrying out those computational tasks is the same. In fact,…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Intro: Computation and Its Limits▶︎ watch 3:52 · read ↗︎
computer science's fight for recognition
“Another thing we'll learn to talk about, as a byproduct of some of the other historical development, is computer science's fight for recognition, for respect. So, once upon a time, computer science…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Intro: Computation and Its Limits▶︎ watch 10:49 · read ↗︎
concepts
“And instead of forms, the intuition has forms, the understanding has concepts. And instead of two, it's got 12 of them, and we're not gonna get into them. We're only gonna talk about one of” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 6: How Your Mind Builds Reality▶︎ watch 22:06 · read ↗︎
concepts of the understanding
“exactly what Kant says, that we have created the world for us, that our minds have imposed the forms of intuition and the concepts of understanding to create the world for us. This is a world for…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 7: Nietzsche's Warning to the Future▶︎ watch 24:49 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 6: How Your Mind Builds Reality▶︎ watch 45:09 · read ↗︎
conceptual framework
“that the framework that he has, the conceptual framework, the overall view of the universe that he has, is right. Because if it's wrong, then everything that gets filtered through that is going to be…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 1: Descartes Reboots Everything▶︎ watch 9:27 · read ↗︎
conceptual lens
“What you are seeing is the light through a conceptual lens. The conceptual lens being a heliocentric model of the solar system. Meaning, you think the sun is” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 1: Descartes Reboots Everything▶︎ watch 6:50 · read ↗︎
conditionally convergent
“So now I wanna tell you about something amazing about this kind of series. This is called a conditionally convergent. It's a series that converges to a finite answer,” (Joel David Hamkins)
Lectures on Infinity · Lecture 1: Zeno's Paradox and Infinite Sums▶︎ watch 35:35 · read ↗︎
conditionals
“or if-then-else, right? Like, if the hamburger patties are frozen, you follow one set of instructions. If they're not, you follow some other set of instructions. And if you've ever done any kind of…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 2: How Algorithms Outsmart Complexity▶︎ watch 1:25 · read ↗︎
configuration space
“wave function goop is floating around in is no longer three-dimensional space, but a so-called configuration space whose dimensionality in the case of, say, an n-particle system, is 3 times n, okay?…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 5: Three Ways to Save Reality▶︎ watch 1:10:55 · read ↗︎
consciousness
“a principled place to draw the line might be at the level of consciousness, okay? That consciousness might have something important to do with this.” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 3: Two Laws That Can't Both Be True▶︎ watch 29:06 · read ↗︎
consequent conjunctions
“precisely the consequent conjunctions, but that's all that we can do. All that science is, is finding the consequent conjunctions, first this and then this. All that science is, is finding,” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 4: Why You Can't Prove Tomorrow▶︎ watch 32:16 · read ↗︎
Conservation of Energy
“won't be conserved, okay? There will be situations where you have charged particles coming near one another and then moving away from one another, and you add up the total energy of the particles…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 4: Bell's Impossible Proof▶︎ watch 34:43 · read ↗︎
Conservation of Momentum
“won't be conserved, okay? There will be situations where you have charged particles coming near one another and then moving away from one another, and you add up the total energy of the particles…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 4: Bell's Impossible Proof▶︎ watch 34:43 · read ↗︎
constant conjunction
“constant conjunction, meaning two things, when one happens, the other one does, they, they're conjoined consistently and in the same order, after a” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 4: Why You Can't Prove Tomorrow▶︎ watch 29:59 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 5: Kant Wakes from His Dogmatic Sleep▶︎ watch 8:03 · read ↗︎
constitutive
“The transcendental illusion uses, and he has to come up with technical difficult words, he's Kant, uses the ideas in what he calls a constitutive way. That means it treats these as if they're out” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 6: How Your Mind Builds Reality▶︎ watch 40:31 · read ↗︎
constructible universe
“of submodel of that model, and then he proved that, in that submodel, it's known now as the constructible universe, or L, Godel's L, the constructible universe has the property that the continuum…” (Joel David Hamkins)
Lectures on Infinity · Lecture 10: Set Theory's Deepest Mystery▶︎ watch 31:32 · read ↗︎
contingent
“Matters of fact are empirical because there's something else, and it's a very important term. They are contingent. To be contingent means could have been a different way.” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 3: Hume's Map of the Mind▶︎ watch 32:24 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 4: Why You Can't Prove Tomorrow▶︎ watch 3:01 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 5: Kant Wakes from His Dogmatic Sleep▶︎ watch 26:12 · read ↗︎
continuous functions
“And that is, say, how many continuous functions are there on the real numbers. I mean, we know how many functions there are on the real numbers. There's a lot, because there's at least this many, and…” (Joel David Hamkins)
Lectures on Infinity · Lecture 10: Set Theory's Deepest Mystery▶︎ watch 15:47 · read ↗︎
continuum hypothesis
“I'd like to tell you about a certain confounding mystery at the center of set theory, and that is concerned with Cantor's continuum hypothesis. We saw how Cantor proved that the set of real numbers…” (Joel David Hamkins)
Lectures on Infinity · Lecture 10: Set Theory's Deepest Mystery▶︎ watch 0:01 · read ↗︎
contradiction
“This is, uh, necessary because any other possible answer would be a contradiction. If you were to say...” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 3: Hume's Map of the Mind▶︎ watch 26:04 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 5: Kant Wakes from His Dogmatic Sleep▶︎ watch 20:22 · read ↗︎
contrapositive
“be the contrapositive, but it's somehow a much, most people find this much less intuitive, a little bit mind-bending even. Which is that suppose you actually cannot solve problem A. And again, we're…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 1: Is There Anything Computers Can't Do?▶︎ watch 45:05 · read ↗︎
converge
“just by taking N large enough. By taking enough terms, we're gonna make it as close to 1 over 1 minus R as we like. And therefore, what that means, is that the total value of the geometric sum is 1…” (Joel David Hamkins)
Lectures on Infinity · Lecture 1: Zeno's Paradox and Infinite Sums▶︎ watch 22:08 · read ↗︎
convergent form of potentialism
“and maybe still more growing one way or the other, but still we can encompass both. So this would be a convergent form of potentialism in the sense that given any world in the potentialist system,…” (Joel David Hamkins)
Lectures on Infinity · Lecture 5: Potential vs Actual Infinity▶︎ watch 49:20 · read ↗︎
Cook
“Cook at, you know, at Berkeley but then moving to Toronto a very much a lower bounds person, okay? Really kind of, really rooted in the traditions of logic and of touring.” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 4: Two Worlds We Might Live In▶︎ watch 18:18 · read ↗︎
Cook-Levin theorem
“parallel on both sides of what was then the Iron Curtain, so happening kind of in parallel in North America and in the Soviet Union, and something known as the Cook-Levin theorem.” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 3: Easy Problems, Hard Problems▶︎ watch 54:12 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 5: AI, Quantum Computing, and Beyond▶︎ watch 11:32 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 4: Two Worlds We Might Live In▶︎ watch 18:09 · read ↗︎
Copenhagen
“and his circle in Copenhagen, was, it was argued, inevitably gonna collapse into paradox or self-contradiction or something like that. And it's quite astounding to think that anybody could even have…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Intro: The Crisis In Physics▶︎ watch 6:36 · read ↗︎
Copernicus
“And then Copernicus came along and said, "No, no, no, no. The sun's at the center and we're just a rock that's going around the sun among a whole bunch of other rocks, and the sun is just one star…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 7: Nietzsche's Warning to the Future▶︎ watch 9:37 · read ↗︎
correspondence
“Right. One traditional understanding of truth is that it's a sort of correspondence, right? That it's a correspondence between your judgment and the way things are, the being of things. And what does…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 4: The Soul Behind the Senses▶︎ watch 43:23 · read ↗︎
corrupting the youth
“put on trial, charged with impiety and corrupting the youth, which are always good charges against philosophers. In fact, recently in Texas, a professor was banned from teaching Plato's Symposium…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 1: Is Knowledge Just Perception?▶︎ watch 3:04 · read ↗︎
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 5: Defeat as Philosophical Victory▶︎ watch 37:10 · read ↗︎
Coulomb Force
“the Coulomb force. This force is repulsive, this is a force that operates between charged particles, okay? Unlike gravitation, this force can be either attractive or repulsive. It's repulsive if you…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 4: Bell's Impossible Proof▶︎ watch 26:11 · read ↗︎
countable
“So really, what Hilbert's Hotel is about is the concept of countability. So a set is said to be countable basically if it fits in Hilbert's Hotel. A set is countable when it can be placed into…” (Joel David Hamkins)
Lectures on Infinity · Lecture 8: Hilbert's Hotel Is Always Open▶︎ watch 15:22 · read ↗︎
countable choice
Lectures on Infinity · Lecture 7: What Does Finite Really Mean?▶︎ watch 50:09
Lectures on Infinity · Lecture 8: Hilbert's Hotel Is Always Open▶︎ watch 36:42 · read ↗︎
countable infinity
“And the answer has to do with the philosophy of probability and the fact that the number of balls is only a countable infinity, whereas the number of points in the dart board is an uncountable…” (Joel David Hamkins)
Lectures on Infinity · Lecture 2: Supertasks: Doing Infinitely Many Things▶︎ watch 29:08 · read ↗︎
Lectures on Infinity · Lecture 9: Beyond Countable Infinity▶︎ watch 0:58 · read ↗︎
Lectures on Infinity · Lecture 10: Set Theory's Deepest Mystery▶︎ watch 0:00 · read ↗︎
countable union of countable sets
“countable sets and you take their union, you put all those individuals together, then that makes a countable set. But what I claim now is that if you have countably many, countably infinitely many…” (Joel David Hamkins)
Lectures on Infinity · Lecture 8: Hilbert's Hotel Is Always Open▶︎ watch 32:35 · read ↗︎
countably additive
“of measure zero events, they are still measure zero The probability theory is countably additive, but it's not uncountably additive. So when we have countably many, when we have a list of countably…” (Joel David Hamkins)
Lectures on Infinity · Lecture 2: Supertasks: Doing Infinitely Many Things▶︎ watch 29:29 · read ↗︎
countably creative
“Okay. So, if the chocolatier... In other words, if the chocolatier is merely countably creative in the sense that the space of possible chocolates that they could serve, that the chocolatier could…” (Joel David Hamkins)
Lectures on Infinity · Lecture 2: Supertasks: Doing Infinitely Many Things▶︎ watch 43:29 · read ↗︎
countably infinite
“between the countably infinite and the uncountably infinite, a profound idea due to Cantor. We'll start with Zeno and the classical ideas of Aristotle and Archimedes, but eventually, we'll move…” (Joel David Hamkins)
Lectures on Infinity · Intro: Infinity Has a Story to Tell▶︎ watch 0:21 · read ↗︎
Lectures on Infinity · Lecture 8: Hilbert's Hotel Is Always Open▶︎ watch 16:14 · read ↗︎
Lectures on Infinity · Lecture 9: Beyond Countable Infinity▶︎ watch 0:01 · read ↗︎
countably infinite subset
Lectures on Infinity · Lecture 7: What Does Finite Really Mean?▶︎ watch 47:56
Cratylus
“but interestingly, the Greek philosophers never, never point out that it means non-lethe, non-concealment. There's one passage in Plato in the Cratylus which is all about language and etymology where…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 4: The Soul Behind the Senses▶︎ watch 44:30 · read ↗︎
creativity
“he thought that our greatest strength is our creativity. Our greatest strength is our ability to always come up with new ideas, new values, new avenues to explore” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Recap: Making Your Beliefs Your Own▶︎ watch 7:27 · read ↗︎
crisis of representation
“like painting, so on and so forth. And it seems to me that at least part of what must have been going on with Bohr was some kind of idea like, you think you have a crisis of representation, you know?” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 2: When Physics Stops Making Sense▶︎ watch 4:03 · read ↗︎
critical philosophy
“This is what Kant will call critical philosophy. Kant wrote three books, each one he called a critique. Uh, and Kant, as we'll see in the next lecture, was profoundly influenced by Hume, had enormous…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 3: Hume's Map of the Mind▶︎ watch 10:58 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 5: Kant Wakes from His Dogmatic Sleep▶︎ watch 39:25 · read ↗︎
critique
“Kant wrote three books, each one he called a critique. Uh, and Kant, as we'll see in the next lecture, was profoundly influenced by Hume, had enormous respect for Hume because he thought Hume didn't…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 3: Hume's Map of the Mind▶︎ watch 11:04 · read ↗︎
Critique of Pure Reason
“His, he's most famous for his first big book, and I do mean big, 800-page tome, of a book, the Critique of Pure Reason, which he published in 1781. But it wasn't read a great deal.” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 5: Kant Wakes from His Dogmatic Sleep▶︎ watch 1:26 · read ↗︎
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 4: The Soul Behind the Senses▶︎ watch 18:09 · read ↗︎
cross-sectional area
“area because the fibers of the wood are going lengthwise in the beam, and when the beam breaks, it breaks along the cross-section. And so it's the strength of the fibers going through those…” (Joel David Hamkins)
Lectures on Infinity · Lecture 3: The Paradox of Giants: Strange Consequences in High Dimension▶︎ watch 3:28 · read ↗︎
cubists
“inheritors of Bohr, they're called, they're called cubists in the lingo, say, "Fine. Maybe the stories are intelligible. They're not believable," okay? "They're too weird.” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 5: Three Ways to Save Reality▶︎ watch 1:22:50 · read ↗︎
cumulative hierarchy
“There is a unique cumulative hierarchy of sets that one achieves by starting with nothing and then constructing in a sequence of levels by adding all possible subsets of earlier elements. So, we…” (Joel David Hamkins)
Lectures on Infinity · Lecture 10: Set Theory's Deepest Mystery▶︎ watch 39:40 · read ↗︎
custom or habit
“psychological feature of human nature. He calls this custom or habit. This is a fact about the way” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 4: Why You Can't Prove Tomorrow▶︎ watch 27:38 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 5: Kant Wakes from His Dogmatic Sleep▶︎ watch 8:45 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Recap: Making Your Beliefs Your Own▶︎ watch 3:19 · read ↗︎