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I delta zero
“So one forms the theory that's known as I delta zero, which asserts the induction axiom, that's the I part, for delta zero assertions, which are assertions that involve only bounded quantifiers. So…” (Joel David Hamkins)
Lectures on Infinity · Lecture 5: Potential vs Actual Infinity▶︎ watch 23:40 · read ↗︎
I think, therefore I am
“And he talks about his famous line, of course, is, "I think, therefore I am." But you could kind of think of that as, "I think for myself for the first time,” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Recap: Making Your Beliefs Your Own▶︎ watch 1:40 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 1: Descartes Reboots Everything▶︎ watch 34:52 · read ↗︎
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 5: Defeat as Philosophical Victory▶︎ watch 30:17 · read ↗︎
idea
“What's rattling around in there?And like, uh, Descartes, like many early modern philosophers, the period from 1600 to 1800, he used the word idea. We have all these ideas in our head. Uh, but he says…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 3: Hume's Map of the Mind▶︎ watch 12:10 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 1: Descartes Reboots Everything▶︎ watch 41:51 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 6: How Your Mind Builds Reality▶︎ watch 26:39 · read ↗︎
immediate impression
“Well, there are some matters of fact we have an immediate impression of, right? We can directly see. How do I know that my shirt is blue? Just because I see it. Again, uninteresting, obvious, no big…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 4: Why You Can't Prove Tomorrow▶︎ watch 0:48 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 3: Hume's Map of the Mind▶︎ watch 12:32 · read ↗︎
immortality of the soul
“immortality of the soul, but that's different. So metaphysics is an organic, natural growth, culmination, conclusion of physics itself. Our minds are such that we” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 6: How Your Mind Builds Reality▶︎ watch 35:23 · read ↗︎
impossible event
“probability zero event and an impossible event, those are not the same thing. Just because something is probability zero doesn't mean that it is logically impossible for it to happen. It could be,…” (Joel David Hamkins)
Lectures on Infinity · Lecture 2: Supertasks: Doing Infinitely Many Things▶︎ watch 22:54 · read ↗︎
impression
“Okay, of course he doesn't mean this literally, you know, the only wax in your head is in your ear canal. But don't we still talk this way, right? We talk about, "It made a big impression on me," or…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 4: The Soul Behind the Senses▶︎ watch 32:16 · read ↗︎
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 3: Hume's Map of the Mind▶︎ watch 12:41 · read ↗︎
incompatible
“We call observable properties like color and hardness incompatible with one another because our experience is that there is no procedure by means of which we can put ourselves in a position to…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 1: The Experiment That Broke Reality▶︎ watch 33:42 · read ↗︎
indelible
“Or once recordings of the outcome of the experiment have become indelible, okay, then law number two kicks in. You mean it matters what kinda ink you use? I mean, I don't... You know, it's really” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 3: Two Laws That Can't Both Be True▶︎ watch 27:52 · read ↗︎
independent
“and so the situation is that not only is the continuum hypothesis independent — to be independent means you can neither prove it nor refute it from the other axioms if those axioms are consistent.…” (Joel David Hamkins)
Lectures on Infinity · Lecture 10: Set Theory's Deepest Mystery▶︎ watch 36:10 · read ↗︎
indubitable
“be false, that is indubitable. That means it cannot be doubted. There are no grounds for doubt at all. There's no way you can doubt it. That's how true it is. And so, like the bulletproof material,” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 1: Descartes Reboots Everything▶︎ watch 15:33 · read ↗︎
induction
Lectures on Infinity · Lecture 7: What Does Finite Really Mean?▶︎ watch 20:16
induction scheme
“basic axioms about addition and multiplication and the recursive formulas that define multiplication over addition and so on. And then piano arithmetic has what's called the induction scheme, which…” (Joel David Hamkins)
Lectures on Infinity · Lecture 5: Potential vs Actual Infinity▶︎ watch 21:28 · read ↗︎
inference
“sort of preprocessing step, then you do inference, and this is the part you and I experience every day when we issue a query to, for example, a large language model and it gives us a response, that's…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 5: AI, Quantum Computing, and Beyond▶︎ watch 37:30 · read ↗︎
infinite
Lectures on Infinity · Lecture 7: What Does Finite Really Mean?▶︎ watch 0:01
infinite matrix
“do is imagine the chocolates on the serving platter filling up an infinite matrix, okay? So the first-round chocolates are placed on the first row, okay? Each one of these is a little chocolate.…” (Joel David Hamkins)
Lectures on Infinity · Lecture 2: Supertasks: Doing Infinitely Many Things▶︎ watch 37:11 · read ↗︎
infinite regress
“time itself seems to drive us towards, 'cause it's before and before and before and before. It's what philosophers call an infinite regress. 'Cause it just keeps going back and back and back forever,…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 6: How Your Mind Builds Reality▶︎ watch 31:53 · read ↗︎
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 5: Defeat as Philosophical Victory▶︎ watch 8:12 · read ↗︎
infinite series
“total length of all of these segments will exhaust the original interval, and so this infinite series is adding up to one, the total original length. This is a kind of contemporary way of…” (Joel David Hamkins)
Lectures on Infinity · Lecture 1: Zeno's Paradox and Infinite Sums▶︎ watch 6:18 · read ↗︎
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 3: Does Relativism Refute Itself?▶︎ watch 48:32 · read ↗︎
infinite sum
“one-quarter plus one-eighth plus one-sixteenth and so on. And so we're adding up infinitely many numbers, and what does that really mean to add up infinitely many numbers? Well, it's quite clear,…” (Joel David Hamkins)
Lectures on Infinity · Lecture 1: Zeno's Paradox and Infinite Sums▶︎ watch 5:58 · read ↗︎
Lectures on Infinity · Lecture 5: Potential vs Actual Infinity▶︎ watch 7:06 · read ↗︎
infinitude of primes
“So, let's talk about another classical mathematical result that exhibits this distinction between potential and actual infinity, and that has to do with the infinitude of primes. So, there are…” (Joel David Hamkins)
Lectures on Infinity · Lecture 5: Potential vs Actual Infinity▶︎ watch 7:59 · read ↗︎
infinity
“to this series of lectures on infinity. I wanna show you all my favorite conundrums and paradoxes of infinity. We're gonna see Zeno's paradox, and the paradox of supertasks, Galileo's paradox, the…” (Joel David Hamkins)
Lectures on Infinity · Intro: Infinity Has a Story to Tell▶︎ watch 0:04 · read ↗︎
Lectures on Infinity · Lecture 1: Zeno's Paradox and Infinite Sums▶︎ watch 0:01 · read ↗︎
information
“got into your head, but the form of it. And this is why we talk about information. We're getting information from things which forms something in our neurons, our wax, whatever you want to talk…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 4: The Soul Behind the Senses▶︎ watch 32:47 · read ↗︎
injective maps
“It's not so difficult. It's challenging, but not so difficult. The situation is you have these two injective maps, these two one-to-one correspondences, and you need to assemble them together to make…” (Joel David Hamkins)
Lectures on Infinity · Lecture 6: Galileo's Paradox of Infinity▶︎ watch 33:19 · read ↗︎
injustice as its own punishment
“be not a superficial thing like, "Oh, you're gonna get caught and you're gonna be thrown in jail, or you're gonna go to hell." But the punishment is, living an unjust life. In itself, it's an unhappy…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 3: Does Relativism Refute Itself?▶︎ watch 39:50 · read ↗︎
Inquiry Concerning Human Understanding
“We're going to be talking primarily about, uh, this book, the Inquiry Concerning Human Understanding, uh, published in 1748, and there's, uh, good news and bad news about, about the book. Uh, the…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 3: Hume's Map of the Mind▶︎ watch 0:41 · read ↗︎
instrumentalism
“to the final effectSomething we do know about quantum mechanics now is that any attempt to push back against the sort of radical instrumentalism that I was talking about before, any attempt to push…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Intro: The Crisis In Physics▶︎ watch 12:17 · read ↗︎
instrumentalist
“try to tell a story. You just forget about it. You adopt a sort of instrumentalist picture of science. What science is for is to predict the outcomes of later measurements from the outcomes of…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 2: When Physics Stops Making Sense▶︎ watch 18:18 · read ↗︎
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 3: Two Laws That Can't Both Be True▶︎ watch 2:52 · read ↗︎
integer programming
“Because, for example, current technology trends you've probably heard about, right? There's quantum computing, there's sort of powerful optimization solvers, like if you've ever heard of integer…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Intro: Computation and Its Limits▶︎ watch 5:56 · read ↗︎
integers
“Okay, so the union of two countable sets is countable. Well, it follows from that, for example, that the integers, meaning the natural numbers together with the negatives, is a countably infinite…” (Joel David Hamkins)
Lectures on Infinity · Lecture 8: Hilbert's Hotel Is Always Open▶︎ watch 20:56 · read ↗︎
intelligibility
“really about the intelligibility of the supertask. What is the state of the lamp after one minute? Is it on or off? Okay. And okay, there's all kinds of physics-based objections that one can make to…” (Joel David Hamkins)
Lectures on Infinity · Lecture 2: Supertasks: Doing Infinitely Many Things▶︎ watch 1:23 · read ↗︎
interactive dualist
“It's not an epiphenomenalist position, it's not a parallelist position. It's what's called an interactive dualist position. It's the kind of dualist position that Descartes had, okay? And that not…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 3: Two Laws That Can't Both Be True▶︎ watch 38:14 · read ↗︎
interference effects
“okay, the fact that you have at the end these interference phenomena, okay, which both the state corresponding to the electron taking the hard path and the state corresponding to the electron taking…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 5: Three Ways to Save Reality▶︎ watch 37:27 · read ↗︎
interference pattern
“Good. So the thought was, when both slits are open, okay? And there's no detector to tell you which slit the thing is going through, that's when you're gonna get this interference pattern, okay?” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 3: Two Laws That Can't Both Be True▶︎ watch 23:53 · read ↗︎
interleaving
“union set is countable, but I can do that simply by interleaving, yeah. So I can take the first element from the first one and then the first one of the second one, so A0, B0, A1, B1, A2, B2, and so…” (Joel David Hamkins)
Lectures on Infinity · Lecture 8: Hilbert's Hotel Is Always Open▶︎ watch 19:53 · read ↗︎
interleaving the digits
“So pi and e, for example, or given any two reals, I'm going to associate this pair of real numbers with a single real number, and the way I'm gonna get that real number is simply by interleaving the…” (Joel David Hamkins)
Lectures on Infinity · Lecture 10: Set Theory's Deepest Mystery▶︎ watch 7:16 · read ↗︎
International Congress of Mathematicians
“back in 1900, so he gave a sort of keynote address at the International Congress of Mathematicians, 1900. This was one of the first ICMs. It was in Paris. And in his talk, he presented a list......…” (Tim Roughgarden)
Computation as a Universal and Fundamental Concept · Lecture 1: Is There Anything Computers Can't Do?▶︎ watch 5:50 · read ↗︎
intrinsic spin
“For people who wanna look into it more deeply, the properties I'm gonna be talking about measuring are different components of the intrinsic spin of electrons. But here, we'll refer to them by…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 1: The Experiment That Broke Reality▶︎ watch 1:43 · read ↗︎
intrinsic value
“Why not take classes that you want to take because of the class, that have intrinsic value, instead of merely for something else? Working jobs that have quality, that are something you desire.” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 7: Nietzsche's Warning to the Future▶︎ watch 49:14 · read ↗︎
intuition
“The first faculty of the mind is what's called intuition, and this is a very unfortunate translation. Someone translated it that way early on, and it's just stuck, but it has nothing to do with the…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 6: How Your Mind Builds Reality▶︎ watch 15:59 · read ↗︎
Inverse Square Law
“between these two material bodies. If you do a quick calculation of how you would expect this apparent force to fall off in, if a theory like this were true, it wouldn't fall off as one over R…” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 4: Bell's Impossible Proof▶︎ watch 22:58 · read ↗︎
irony
“Is it... Well, the word usually used is irony. Ah. And there are different interpretations of what irony means exactly. Is it a sort of deception or is it a kind of polite, self-deprecating attitude…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 2: When Every Perception is True▶︎ watch 26:49 · read ↗︎
irrational
“That's not irrational. Irrational means it's bad reasoning, you should not think it that way. Arational means it has nothing to do with reason. Your digestion is arational.” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 4: Why You Can't Prove Tomorrow▶︎ watch 33:42 · read ↗︎
irrational numbers
“and the Greek mathematicians, a great achievement was to show that there are irrational numbers. You cannot express them in a logos. This will be an important word later on. Very fundamental Greek…” (Richard Polt)
Plato’s Theaetetus: An Inquiry into Knowledge · Lecture 1: Is Knowledge Just Perception?▶︎ watch 25:10 · read ↗︎
Lectures on Infinity · Lecture 9: Beyond Countable Infinity▶︎ watch 41:12 · read ↗︎
irreducibly chances
“which are genuinely irreducibly chances, okay? Another side remark. Suppose that we wanted to somehow put ourselves in a position, that is suppose we wanted to build” (David Albert)
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 1: The Experiment That Broke Reality▶︎ watch 28:38 · read ↗︎
Isaac Newton
“Even afterwards, Isaac Newton, arguably the greatest scientist who ever lived, when we went through his papers afterwards, what we found was that the amount he wrote on science... This is the man who…” (Lee Braver)
From Descartes to Nietzsche: The Birth of Science and the Death of God · Lecture 1: Descartes Reboots Everything▶︎ watch 3:52 · read ↗︎
Quantum Mechanics and the Crisis of Scientific Realism · Lecture 4: Bell's Impossible Proof▶︎ watch 13:18 · read ↗︎
isolated points
“might have some isolated points in it though. So in the general case, maybe we have some isolated points, but if I have a lot of isolated points, say, in a bounded region, then they would have to…” (Joel David Hamkins)
Lectures on Infinity · Lecture 10: Set Theory's Deepest Mystery▶︎ watch 21:09 · read ↗︎
isomorphic
Lectures on Infinity · Lecture 7: What Does Finite Really Mean?▶︎ watch 24:07
iterated exponentials
“100 is a pretty big number, or 2 to the 1,000, that's a big number, but we could also do what's called iterated exponentials. For example, I could do 2 to the 3 to the, to the 100, and so on, or in…” (Joel David Hamkins)
Lectures on Infinity · Lecture 4: The Largest Tweetable Number▶︎ watch 13:48 · read ↗︎