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S
S4.2
“potentialist conceptions that I had described. This is the central axiom of what's known as S4.2. So, let's talk about one more principle that will distinguish these two cases.” (Joel David Hamkins)
Lectures on Infinity · Lecture 5: Potential vs Actual Infinity▶︎ watch 44:37 · read ↗︎
Lectures on Infinity · Lecture 9: Beyond Countable Infinity▶︎ watch 34:06 · read ↗︎
S4.3
“If phi is possible and psi is possible, so I have these two possible statements, then it's possible that the first is true and the second is” (Joel David Hamkins)
Lectures on Infinity · Lecture 5: Potential vs Actual Infinity▶︎ watch 45:20 · read ↗︎
salvation
“through it to the other side, we can realize that this is the salvation. We can realize that our ability to create these values, which is what we've had all along, is what also enables us to create…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Recap: Making Your Beliefs Your Own▶︎ watch 6:57 · read ↗︎
Salviati
“figures in Galileo's work, particularly in his dialogues between Salviati and Simplicio in the, Dialogue Concerning Two New Sciences in 1638. But, actually, I wanna go much further back and talk…” (Joel David Hamkins)
Lectures on Infinity · Lecture 6: Galileo's Paradox of Infinity▶︎ watch 4:08 · read ↗︎
satisfiability
“which is a problem in logic, and another problem called subgraph isomorphism, which is a problem in networksAnd you know, I I don't know this for sure, but I could imagine that to a complexity…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 4: Two Worlds We Might Live In▶︎ watch 24:20 · read ↗︎
scholē
“haven't we, Socrates?" This is a great word that he uses, by the way. "Scholei," which looks like school, and in fact, it is the root of our word "school." It means leisure, it means free time.” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 3: Does Relativism Refute Itself?▶︎ watch 16:13 · read ↗︎
Schrodinger
“to very early attempts on the parts of people like von Neumann and Schrodinger and Wigner and so on and so forth to push back against this a little bit, to try to see” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Intro: The Crisis In Physics▶︎ watch 9:43 · read ↗︎
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 2: When Physics Stops Making Sense▶︎ watch 6:27 · read ↗︎
Schrodinger equation
“is give you equations of motion like the Schrodinger equation, which determine how these wave functions evolve in time, okay? Just as Newton's equations of motion told us how the positions of…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 2: When Physics Stops Making Sense▶︎ watch 27:28 · read ↗︎
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 3: Two Laws That Can't Both Be True▶︎ watch 11:40 · read ↗︎
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 5: Three Ways to Save Reality▶︎ watch 1:45 · read ↗︎
Schroeder
“But then finally, it was proved by Schroeder, in 1896 as a corollary to a certain theorem of Jevons, and then in 1897 independently, and then finally by Bernstein in 1897. And so the earlier proofs,…” (Joel David Hamkins)
Lectures on Infinity · Lecture 6: Galileo's Paradox of Infinity▶︎ watch 32:58 · read ↗︎
scientific notation
“That's what the notation means. So we can write this out in scientific notation. 8 times 10 to the 3, plus 5 times 10 squared, plus 4 times 10 to the 1, plus 7 times 10 to the 0, which is really just…” (Joel David Hamkins)
Lectures on Infinity · Lecture 1: Zeno's Paradox and Infinite Sums▶︎ watch 12:09 · read ↗︎
scientific project
“So, over and above being a set of discoveries, like I say, about the behaviors of subatomic particles, about the kinds of mathematical apparatus that are required in order to describe those…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Intro: The Crisis In Physics▶︎ watch 1:39 · read ↗︎
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 3: Two Laws That Can't Both Be True▶︎ watch 42:32 · read ↗︎
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 4: Bell's Impossible Proof▶︎ watch 13:08 · read ↗︎
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 5: Three Ways to Save Reality▶︎ watch 1:20:24 · read ↗︎
scientific realism
“A certain, a certain idea of what was called scientific realism, okay, as an attitude toward the scientific activity and toward the aspirations of the scientific activity was collapsing” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 1: The Experiment That Broke Reality▶︎ watch 56:12 · read ↗︎
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 2: When Physics Stops Making Sense▶︎ watch 21:37 · read ↗︎
scientific revolution
“The reason why it became so crucial at that point was because this was the beginning of the scientific revolution. For a long time, there was one picture of the universe, one sense of how things…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Intro: When the Old Map Stopped Working▶︎ watch 0:33 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 7: Nietzsche's Warning to the Future▶︎ watch 5:03 · read ↗︎
Quantum Mechanics and the Crisis of Scientific Realism · Intro: The Crisis In Physics▶︎ watch 0:55 · read ↗︎
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 1: The Experiment That Broke Reality▶︎ watch 0:41 · read ↗︎
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 4: Bell's Impossible Proof▶︎ watch 10:55 · read ↗︎
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 5: Three Ways to Save Reality▶︎ watch 43:44 · read ↗︎
sealing wax
“Yeah. Easier to use though. Yeah. And another common thing would be sealing wax for a letter, right? And then you have a signet ring with your unique pattern that you can stamp into the wax to show…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 4: The Soul Behind the Senses▶︎ watch 33:49 · read ↗︎
second meditation
“for sure." And this is where he begins the second meditation, where he's gonna try to start building, building things back up. And he's gonna get there with what is almost certainly the most famous…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 1: Descartes Reboots Everything▶︎ watch 31:40 · read ↗︎
second order assertion
Lectures on Infinity · Lecture 7: What Does Finite Really Mean?▶︎ watch 52:25
second order logic
Lectures on Infinity · Lecture 7: What Does Finite Really Mean?▶︎ watch 52:25
secondary qualities
“hitting the retina or something like that. And so this is very plausible with, when it comes to colors or other so-called secondary qualities. Things that we assume are subjective. But what's radical…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 2: When Every Perception is True▶︎ watch 18:11 · read ↗︎
secret doctrine
“He says he's initiating us into a secret doctrine. Here's the secret truth. For instance, at 155E, "Have a look around. See that none of the uninitiated are listening to us. I mean, the people who…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 2: When Every Perception is True▶︎ watch 19:22 · read ↗︎
Secrets of LLM Performance
“I'm just teasing out three particular phenomena that I find interesting. So Secrets of LLM Performance. And what” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 5: AI, Quantum Computing, and Beyond▶︎ watch 54:30 · read ↗︎
self-evident
“That's my method. I would say that, that Descartes avoids this trap though, because he doesn't say you have to understand everything by analyzing it. He says some things are simply self-evident. You…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 5: Defeat as Philosophical Victory▶︎ watch 30:18 · read ↗︎
self-referentiality
“So the key thing that Godel showed, Godel showed that you could take statements about the integers, statements in arithmetic, and encode them themselves as integers, give them numbers in a sense. So…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 1: Is There Anything Computers Can't Do?▶︎ watch 39:27 · read ↗︎
self-refutation argument
“One was the self-refutation argument. You know, if everybody's right, then people who disagree with you are right, so you're wrong. Maybe a little bit cheap, but interesting. There was, you know,…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 4: The Soul Behind the Senses▶︎ watch 0:19 · read ↗︎
self-similar fractal
“This is an instance of a kind of fractal with self-similar, it's a self-similar fractal, because the whole thing is just a scaled-up version of each leg of it. So, it's done similar to itself at a…” (Joel David Hamkins)
Lectures on Infinity · Lecture 3: The Paradox of Giants: Strange Consequences in High Dimension▶︎ watch 33:59 · read ↗︎
sensory deception
“classical skeptical argument, which is called sensory deception. The senses lie to you.” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 1: Descartes Reboots Everything▶︎ watch 20:52 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 2: The Birth of Modern Science▶︎ watch 31:58 · read ↗︎
set theoretic pluralism
“that there are multiple distinct concepts of set. There isn't just one set theoretic reality, but rather multiple independent set theoretic worlds, and some of them have the continuum hypothesis…” (Joel David Hamkins)
Lectures on Infinity · Lecture 10: Set Theory's Deepest Mystery▶︎ watch 41:12 · read ↗︎
Seth Benedetti
“Well, so using this sort of diagram, which by the way, I'm borrowing from Seth Benedetti who has a very interesting translation and commentary on the Theaetetus which is often quite intricate, but…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 4: The Soul Behind the Senses▶︎ watch 35:21 · read ↗︎
seventh letter
“So I wanted to run a few things by you, that Plato says about writing. In the seventh letter, which is the most interesting and important and longest letter that we have by Plato, he says, "I've…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 1: Is Knowledge Just Perception?▶︎ watch 3:56 · read ↗︎
shocking claim
“What is this arrow? How does experience underwrite it? And his answer, his shocking answer is, it's not a reasoning inference.” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 4: Why You Can't Prove Tomorrow▶︎ watch 12:17 · read ↗︎
shortest path
“So what we just did, the way we determined the quickest or shortest path from A to B in this example is something known as exhaustive search, which is if you have a whole bunch of options like” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 2: How Algorithms Outsmart Complexity▶︎ watch 33:43 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 3: Easy Problems, Hard Problems▶︎ watch 0:11 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 5: AI, Quantum Computing, and Beyond▶︎ watch 0:01 · read ↗︎
shortest path problem
“by fast algorithms as we have, for example, specifically in the shortest path problem? So, is every NP problem problems with you-know-it-when-you-see-it solutions also solvable by a fast algorithm?…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 5: AI, Quantum Computing, and Beyond▶︎ watch 0:33 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 2: How Algorithms Outsmart Complexity▶︎ watch 42:59 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 3: Easy Problems, Hard Problems▶︎ watch 2:13 · read ↗︎
Sidney Coleman
“You take Sidney Coleman, who was a very famous physicist at Harvard up until 10 or so years ago, used to call this way of talking "quantum mechanics in your face." Okay?” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 5: Three Ways to Save Reality▶︎ watch 47:01 · read ↗︎
SIGACT News
“computer scientists read called SIGACT News. And so Don Knuth, you know, put out a call for suggestions for what should we call, you know, the, what we now call NP-complete. So at that time it was,…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 4: Two Worlds We Might Live In▶︎ watch 41:41 · read ↗︎
simplex method
“would be the simplex method. Invented, I don't know if you say invented, I don't know if you wanna say discovered, up to you. So the simplex method for linear programming. So that was discovered by…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 2: How Algorithms Outsmart Complexity▶︎ watch 50:09 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 4: Two Worlds We Might Live In▶︎ watch 13:59 · read ↗︎
Simplicio
“figures in Galileo's work, particularly in his dialogues between Salviati and Simplicio in the, Dialogue Concerning Two New Sciences in 1638. But, actually, I wanna go much further back and talk…” (Joel David Hamkins)
Lectures on Infinity · Lecture 6: Galileo's Paradox of Infinity▶︎ watch 4:08 · read ↗︎
simulation
“to diagonalization, to reductions, to show you Turing's original argument that indeed, there are problems, even natural problems you'd really like to solve, like the famous one being the halting…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Intro: Computation and Its Limits▶︎ watch 1:13 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 2: The Birth of Modern Science▶︎ watch 10:10 · read ↗︎
single-cell amoeba
“Evolution is our true creator for Nietzsche, rather than God. And the single-cell amoeba that begins life could not conceive of” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Recap: Making Your Beliefs Your Own▶︎ watch 8:09 · read ↗︎
single-celled being
“you have done in your life. You started out as a single-celled being, and then you breathed liquid in the womb, and then you crawled on land, and then you thought, became a thinking being.” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Recap: Making Your Beliefs Your Own▶︎ watch 9:33 · read ↗︎
six dice
“Let me cut to an example he gives which is a kind of a neat parlor trick. So he says, "We have six dice." And you put four next to them. Greater than four. Now, let's increase” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 2: When Every Perception is True▶︎ watch 13:43 · read ↗︎
skeptical arguments
“he'll come up with a reason to doubt. And the reason to doubt, these are called skeptical arguments, because there was an ancient Greek philosophical school, the Skeptical School, which was a group…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 1: Descartes Reboots Everything▶︎ watch 18:50 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 2: The Birth of Modern Science▶︎ watch 9:27 · read ↗︎
Skeptical School
“And the reason to doubt, these are called skeptical arguments, because there was an ancient Greek philosophical school, the Skeptical School, which was a group of philosophers who thought that we…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 1: Descartes Reboots Everything▶︎ watch 18:52 · read ↗︎
skepticism
“There are worries about... there are worries to the effect that it can't refute skepticism. There are worries about the kind of image of ourselves that something like” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Intro: The Crisis In Physics▶︎ watch 4:02 · read ↗︎
Skolem paradox
Lectures on Infinity · Lecture 7: What Does Finite Really Mean?▶︎ watch 53:16
small forcing extensions
“that all of the large cardinal axioms are preserved by what's called small forcing extensions, forcing using a partial order that is of size less than the large cardinal in question. And now, the…” (Joel David Hamkins)
Lectures on Infinity · Lecture 10: Set Theory's Deepest Mystery▶︎ watch 37:53 · read ↗︎
snub-nosed
“Mm-hmm. Because I don't think there are many descriptions of Socrates in Plato or elsewhere, so this is one talking about him being snub-nosed. Yeah, there are a few in Plato, and he's usually…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 1: Is Knowledge Just Perception?▶︎ watch 15:36 · read ↗︎
Socrates
“Socrates was Plato's mentor and teacher and hero, and he died when Plato was in his 20s. He did not die a natural death. In case you don't know, he was put on trial, charged with impiety” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 1: Is Knowledge Just Perception?▶︎ watch 2:51 · read ↗︎
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 2: When Every Perception is True▶︎ watch 0:32 · read ↗︎
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 4: The Soul Behind the Senses▶︎ watch 0:32 · read ↗︎
Socratic fallacy
“This is another move that could be questioned. Some people call it the Socratic fallacy. Why can't these things belong together in a sort of rough, family-resemblant sort of way without all having…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 1: Is Knowledge Just Perception?▶︎ watch 20:10 · read ↗︎
Socratic wisdom
“That's huge, right? Because now he's like Socrates, not just in face, but in mind. So Socrates knows his own ignorance. Now Theaetetus too is at least not going to assume he knows something he…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 5: Defeat as Philosophical Victory▶︎ watch 38:05 · read ↗︎
source of knowledge
“If you have a book written by an omniscient being, all-knowing, who is the creator of the universe, the creator of you, the creator of humanity, and who wants what's best for you, then there is no…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Intro: When the Old Map Stopped Working▶︎ watch 1:47 · read ↗︎
space
“Intuition has forms, two forms, space and time. What that means is we get all this sensory data coming at us, and it's chaotic and it's overwhelming. And our minds put all” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 6: How Your Mind Builds Reality▶︎ watch 17:27 · read ↗︎
Spacetime Curvature
“around in the way they do. This is the really profound revolution of general relativity. That's not the aspect of it I want to focus on here. Another thing that general relativity does, it turns out,” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 4: Bell's Impossible Proof▶︎ watch 55:49 · read ↗︎
special theory of relativity
“about what to do with the special theory of relativity and so on and so forth. A version of this algorithm is developed over the course of the 1920s and is more or less in place by the end of the…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 2: When Physics Stops Making Sense▶︎ watch 20:15 · read ↗︎
St. Anselm
“It's known as the ontological proof. It was created by a 12th century, I believe, monk named St. Anselm. I used to drive by a church of St. Anselm Church. I always wondered if they chanted this…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 2: The Birth of Modern Science▶︎ watch 12:09 · read ↗︎
start from scratch
“And when I say everything, I mean everything. He wanted to go back to the very beginning, to scr- thr- he wanted to start from scratch, and he wanted to bring all of Western civilization with him, to…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Intro: When the Old Map Stopped Working▶︎ watch 5:25 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 1: Descartes Reboots Everything▶︎ watch 1:52 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 6: How Your Mind Builds Reality▶︎ watch 48:39 · read ↗︎
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 1: Is Knowledge Just Perception?▶︎ watch 22:30 · read ↗︎
statistical correlations
“connected with one another in some way? An easy way to find out if that's true, or at least to begin to get a handle on whether or not that's true, is to look for statistical correlations between the…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 1: The Experiment That Broke Reality▶︎ watch 7:55 · read ↗︎
step function
“of, a task involving infinitely many steps? I mean, mathematically, for example, we can easily make a kind of step function. If I draw the light, okay, it's on between zero and a half, and then it's…” (Joel David Hamkins)
Lectures on Infinity · Lecture 2: Supertasks: Doing Infinitely Many Things▶︎ watch 3:16 · read ↗︎
Stephanus numbers
“And we'll refer to the text by the marginal numbers and letters, which are called Stephanus numbers after an early printed edition of Plato. So it begins with a couple of pages of prologue where you…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 1: Is Knowledge Just Perception?▶︎ watch 10:47 · read ↗︎
Stephen Cook
“from the 20th century. So, names like David Hilbert, Kurt Godel, John von Neumann, George Dantzig, Andrei Kolmogorov, Jack Emmons, Stephen Cook, Leonid Levin, Richard Karp, Don Knuth, all of those…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Intro: Computation and Its Limits▶︎ watch 8:04 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 3: Easy Problems, Hard Problems▶︎ watch 55:31 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 4: Two Worlds We Might Live In▶︎ watch 18:09 · read ↗︎
STOC
“And in the 2021 version of STOC, that was the 50th anniversary of the Cook-Levin theorem, so it was an idea of Stefano Leondardo's that we assembled an anniversary session of the Cook-Levin theorem.…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 4: Two Worlds We Might Live In▶︎ watch 28:37 · read ↗︎
stochastic
“about this balls in a sack puzzle, a stochastic way, which means thinking of it as a random process. So let's think, well, what would happen if you put two balls in the sack and then the ball that…” (Joel David Hamkins)
Lectures on Infinity · Lecture 2: Supertasks: Doing Infinitely Many Things▶︎ watch 17:05 · read ↗︎
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 5: Three Ways to Save Reality▶︎ watch 6:59 · read ↗︎
stock rotation
“will just go at the back. This is the same process that the your local restaurant uses when they're doing stock rotation. You know, they get new items coming in, you know, that they're gonna be…” (Joel David Hamkins)
Lectures on Infinity · Lecture 2: Supertasks: Doing Infinitely Many Things▶︎ watch 34:02 · read ↗︎
Stoeckl finite
Lectures on Infinity · Lecture 7: What Does Finite Really Mean?▶︎ watch 13:23
straightedge and compass
“But you will never have the whole thing. And if you think, of course, about the geometric tools of straightedge and compass, then, you know, the straight edge typically has a finite length, so you…” (Joel David Hamkins)
Lectures on Infinity · Lecture 5: Potential vs Actual Infinity▶︎ watch 4:18 · read ↗︎
Strassen's algorithm
“should really look into Strassen's algorithm for matrix multiplication. algorithm for matrix multiplication. Okay, so some of you will remember what matrix multiplication is, some of you won't,…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 2: How Algorithms Outsmart Complexity▶︎ watch 29:34 · read ↗︎
strictly larger
“this notion, then you might wanna say, "Well, when do we wanna say that one set is strictly larger than another?" So we would say X is strictly less than Y or Y is strictly larger than X if and only…” (Joel David Hamkins)
Lectures on Infinity · Lecture 6: Galileo's Paradox of Infinity▶︎ watch 27:47 · read ↗︎
Lectures on Infinity · Lecture 9: Beyond Countable Infinity▶︎ watch 27:44 · read ↗︎
Lectures on Infinity · Lecture 10: Set Theory's Deepest Mystery▶︎ watch 0:00 · read ↗︎
strong double arrow
“the strong double arrow, which is different from an ordinary Knuth double arrow. So, I wanna define the strong double arrow. So, A strong double arrow B means that I do the B fold up” (Joel David Hamkins)
Lectures on Infinity · Lecture 4: The Largest Tweetable Number▶︎ watch 28:13 · read ↗︎
strong induction
Lectures on Infinity · Lecture 7: What Does Finite Really Mean?▶︎ watch 33:04
subatomic particles
“discoveries about the bizarre behaviors of subatomic particles that led to the development of quantum theory represented a sort of really decisive collapse of the traditional” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Intro: The Crisis In Physics▶︎ watch 1:17 · read ↗︎
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 3: Two Laws That Can't Both Be True▶︎ watch 0:00 · read ↗︎
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 5: Three Ways to Save Reality▶︎ watch 10:17 · read ↗︎
subgraph isomorphism
“which is a problem in logic, and another problem called subgraph isomorphism, which is a problem in networksAnd you know, I I don't know this for sure, but I could imagine that to a complexity…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 4: Two Worlds We Might Live In▶︎ watch 24:20 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 5: AI, Quantum Computing, and Beyond▶︎ watch 13:28 · read ↗︎
subject and a predicate
“doing is you're making a judgment, and a judgment is the connection basically of a subject and a predicate. So for Hume's issue, causality, what you're doing is you're connecting a cause and effect.…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 5: Kant Wakes from His Dogmatic Sleep▶︎ watch 9:35 · read ↗︎
subjective
“It's too subjective. It's too variable. People will find different answers. We don't get the same answers from it. And it's too vague. What would I say the room is like? It's kinda warm. That's not a…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 2: The Birth of Modern Science▶︎ watch 33:57 · read ↗︎
successor relation
Lectures on Infinity · Lecture 7: What Does Finite Really Mean?▶︎ watch 18:43
Sudoku
“So informally, the P versus NP question asks whether every single problem for which you can easily recognize solutions, right? Think about Sudoku. Someone shows you their alleged solution to a Sudoku…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Intro: Computation and Its Limits▶︎ watch 13:16 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 3: Easy Problems, Hard Problems▶︎ watch 35:28 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 4: Two Worlds We Might Live In▶︎ watch 1:54 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 5: AI, Quantum Computing, and Beyond▶︎ watch 0:22 · read ↗︎
super box
“Suppose that we wanted to somehow put ourselves in a position, that is suppose we wanted to build what you might call a super box. This will be a box with not three apertures, but I guess five…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 1: The Experiment That Broke Reality▶︎ watch 28:48 · read ↗︎
Superposition
“and so on and so forth. The amazing thing is that it emerges 30 years later in the work of John Bell, okay, that this time the story doesn't come out that way.” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 4: Bell's Impossible Proof▶︎ watch 1:05:23 · read ↗︎
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 5: Three Ways to Save Reality▶︎ watch 29:13 · read ↗︎
Computation as a Universal and Fundamental Concept · Lecture 5: AI, Quantum Computing, and Beyond▶︎ watch 41:05 · read ↗︎
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 2: When Physics Stops Making Sense▶︎ watch 13:23 · read ↗︎
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 3: Two Laws That Can't Both Be True▶︎ watch 4:54 · read ↗︎
supertasks
“We're gonna see Zeno's paradox, and the paradox of supertasks, Galileo's paradox, the distinction between the potentially infinite and the actually infinite. Eventually, we'll find the distinction…” (Joel David Hamkins)
Lectures on Infinity · Intro: Infinity Has a Story to Tell▶︎ watch 0:11 · read ↗︎
Lectures on Infinity · Lecture 1: Zeno's Paradox and Infinite Sums▶︎ watch 3:58 · read ↗︎
Lectures on Infinity · Lecture 2: Supertasks: Doing Infinitely Many Things▶︎ watch 0:01 · read ↗︎
supremely perfect being
“Okay, third step. Among my ideas is an idea of God. What is the essence of that idea? The essence of the idea of God, according to this proof, is to be a supremely perfect being. A supremely perfect…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 2: The Birth of Modern Science▶︎ watch 18:18 · read ↗︎
supremum
“In fact, we can specify it exactly in this case, because the supremum of the As, there will be a least number that's larger than all the As. That will have to be inside. The sup on N of A sub-N will” (Joel David Hamkins)
Lectures on Infinity · Lecture 9: Beyond Countable Infinity▶︎ watch 21:19 · read ↗︎
surface of revolution
“manner, you imagine sort of slicing it into cross-sections. So we're gonna slice this horn into these kind of disks. Yeah. I'm thinking of the solid, the volume of the solid, the part inside the horn…” (Joel David Hamkins)
Lectures on Infinity · Lecture 3: The Paradox of Giants: Strange Consequences in High Dimension▶︎ watch 13:59 · read ↗︎
surface tension
“for it to stick to the wall and so on. A bug that crawls on the surface of the water, the surface tension effects simply aren't, don't scale in the right way. And so the paradox of these giants is…” (Joel David Hamkins)
Lectures on Infinity · Lecture 3: The Paradox of Giants: Strange Consequences in High Dimension▶︎ watch 8:29 · read ↗︎
surprising claim
“And here we get to the first surprising claim. So imagine that you're in a pool hall, and you see one” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 4: Why You Can't Prove Tomorrow▶︎ watch 5:27 · read ↗︎
Suslin
“So this was generalized by Suslin to the Borel sets, which is a sort of continuation of Cantor's program of sort of working his way up in complexity, and I think analytic sets also by Suslin. But the…” (Joel David Hamkins)
Lectures on Infinity · Lecture 10: Set Theory's Deepest Mystery▶︎ watch 28:02 · read ↗︎
Symposium
“In fact, recently in Texas, a professor was banned from teaching Plato's Symposium because it espoused "Radical gender ideology." So Plato is still corrupting the youth, I'm happy to say. So Socrates…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 1: Is Knowledge Just Perception?▶︎ watch 3:14 · read ↗︎
synesthesia
“should talk about this a little bit. I was thinking of synesthesia originally. But as far as I understand, that's more of, like, a psychological confusion of different sensory inputs, and it happens…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 4: The Soul Behind the Senses▶︎ watch 7:44 · read ↗︎
syntax-semantics dichotomy
“So this is, this distinction between number and numeral is sometimes called the semantics, the syntax-semantics dichotomy, and there's another way to talk about this. Once I was at high table at…” (Joel David Hamkins)
Lectures on Infinity · Lecture 4: The Largest Tweetable Number▶︎ watch 8:14 · read ↗︎
synthetic
“Kant adds synthetic and analytic. And this one we haven't seen before. We've seen something pretty similar to” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 5: Kant Wakes from His Dogmatic Sleep▶︎ watch 18:45 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 6: How Your Mind Builds Reality▶︎ watch 1:46 · read ↗︎
synthetic a priori
“there's a priori analytic, there's this type, synthetic empirical, and there are a priori synthetic judgments. That should be surprising.” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 5: Kant Wakes from His Dogmatic Sleep▶︎ watch 29:10 · read ↗︎
synthetic empirical
“Synthetic empirical. Yeah. My dog is brown. This chalk is red. I am standing here. The vast majority of beliefs are synthetic empirical, and these are basically what” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 5: Kant Wakes from His Dogmatic Sleep▶︎ watch 28:16 · read ↗︎