Mind Matters Natural and Artificial Intelligence News and Analysis

TagKurt Gödel

solving algebra equation on whiteboard in classroom

How Eccentric Mathematician Kurt Gödel Opened the World

Science writer: As often happens, few people understood the significance of what had just happened. The one exception was John von Neumann.

Albert Einstein, Jogalekar tells us, considered it a privilege to walk home with Gödel every day. Why?: In an exceptionally elegant essay, science writer Ashutosh Jogalekar (no stranger to controversy) talks about the huge difference Kurt Gödel (1906–1978) made by eliminating the idea that some single, simple explanation would put an end to all questioning about the nature of the universe in favor of some simple materialism. In a review of Stephen Budiansky’s biography of Gödel, Journey to the Edge of Reason (Harvard 2021), Jogalekar explains how Gödel dashed such hopes: In September 1930, a big conference was going to be organized in Königsberg. German mathematics had been harmed because of Germany’s instigation of the Great War, and Hilbert’s decency…

Statue of Saint Anselm and the towers of the Cathedral of Aosta, the Cattedrale di Aosta de Corso Pere-Laurent in Aosta. Aosta Valley. Italy. Europe

Gödel Says God Exists and Proves It

Here is a line-by-line explanation of his proof

Kurt Gödel, an intellectual giant of the 20th century, offered a mathematical proof that God exists. Those who suffer from math anxiety admire what the theorem (shown below) claims to do, but have absolutely no idea what it means. Our goal is to explain, in English, what Gödel’s existence of God proof says. Gödel’s proof shows the existence of God is a necessary truth. The idea behind the truth is not new and dates back to Saint Anselm of Canterbury (1033-1109). Great scientists and philosophers, including Descartes and Leibniz, have reconsidered and refined Anselm’s argument. Gödel appears to be the first, however, to present the argument using mathematical logic. Lexicography In any development of a mathematical theory, there are foundational axioms…


How Materialism Proves Unbounded Scientific Ignorance

There is an infinite number of things that are true that we cannot prove scientifically and never will

Science is based on a glut of laws from physics, chemistry, mathematics, and other areas. The assumption of scientific materialism, as I understand it, is that science has explained or will explain everything. The final conclusion of scientific materialism, also known as scientism, is nicely captured in a question chemist Peter Atkins asked philosopher William Lane Craig in a debate: “Do you deny that science can account for everything?” Scientism’s assumption that science can establish everything is self-refuting. Careful analysis shows that there is an infinite number of things that are true that we cannot prove scientifically and never will. Stephen Hawking saw the tip of the iceberg of this truth when he said, “Up to now, most people have…

connect the dots.jpg
Anti social man, business connection or social network concept, miniature people businessman standing on colorful pastel chalk line link and connect between multiple dot or tiers on blackboard

What Is the Essential Feature of Creative Intelligence?

Creative intelligence is easier to describe by what it is not than by what it is. But there is a clue in that very fact…

I’ve spent the past couple articles debunking artificial intelligence. It is just as artificial as its name suggests. It takes on the appearance of intelligence through speed but it lacks the fundamental ability to create a well-matched start and end. So a perceptive reader has returned with another good question: “What is creative intelligence?” The reader is right to ask. Yes, telling someone that the exquisite dessert is not celery and not cod liver oil does not help us understand what the dessert itself is. There is a mystery regarding the very nature of human intelligence. Like its antithesis, randomness, creative intelligence is easier to describe by what it is not than by what it is. But, we can try!…

SpaceX Concept Spacecraft in orbit of the Earth. SpaceX Elon Musk Mars programm 3d render

Why Elon Musk and Other Geniuses Can’t Afford To Follow Rules

Mathematician Gregory Chaitin explains why Elon Musk is, perhaps unexpectedly, his hero

In last week’s podcast, “The Chaitin Interview III: The Changing Landscape for Mathematics,” Walter Bradley Center director Robert J. Marks interviewed mathematician and computer scientist Gregory Chaitin on many things mathematical, including why great books on math, advancing new theorems, aren’t written much any more. This week, we look at why geniuses like Musk (whose proposed Mars Orbiter is our featured image above) simply can’t just follow the rules, for better or worse: https://episodes.castos.com/mindmatters/Mind-Matters-126-Gregory-Chaitin.mp3 This portion begins at 7:57 min. A partial transcript, Show Notes, and Additional Resources follow. Gregory Chaitin: Look at Elon Musk (pictured). He’s my great hero. He’s a wonderful engineer and he’s a wonderful entrepreneur and he doesn’t follow the rules. Robert J. Marks: He doesn’t,…

Close up cute little child girl spinning a coin to make decision. Heads or tails game.

The Chaitin Interview II: Defining Randomness

In the 1960s, mathematician and computer scientist Gregory Chaitin published a landmark paper in the field of algorithmic information theory in the Journal of the ACM – and he was only a teenager. Listen in as Robert J. Marks explores that paper with Chaitin, covering Chaitin’s definition of randomness and his philosophical interest in algorithmic information theory. Show Notes 00:27…

mandelbrot set abstract mathematics computer generated

Gregory Chaitin’s “Almost” Meeting With Kurt Gödel

This hard-to-find anecdote gives some sense of the encouraging but eccentric math genius

In this week’s podcast, “The Chaitin interview I: Chaitin chats with Kurt Gödel,” Walter Bradley Center director Robert J. Marks interviewed mathematician and computer scientist Gregory Chaitin. Yesterday, we noted his comments on the almost supernatural awareness that the great mathematicians had of the foundations of reality in the mathematics of our universe. This time out, Chaitin recounts how he (almost) met the eccentric genius Kurt Gödel (1906–1978): https://episodes.castos.com/mindmatters/Mind-Matters-124-Gregory-Chaitin.mp3 This portion begins at 12:42 min. A partial transcript, Show Notes and Additional Resources follow. Robert J. Marks: You mentioned that you read the article about Gödel’s Incompleteness Theorem in Scientific American I also know that you had a near brush with Gödel and I’ve heard the story from you. But…

Silhouette of human with universe and physical, mathematical formulas

Gregory Chaitin on the Great Mathematicians, East and West

Himself a “game-changer” in mathematics, Chaitin muses on what made the great thinkers stand out

In this week’s podcast, “The Chaitin interview I: Chaitin chats with Kurt Gödel,” Walter Bradley Center director Robert J. Marks interviewed mathematician and computer scientist Gregory Chaitin on the almost supernatural awareness that the great mathematicians had of the foundations of reality in the mathematics of our universe: https://episodes.castos.com/mindmatters/Mind-Matters-124-Gregory-Chaitin.mp3 This discussion begins at 8:26 min. A partial transcript, Show Notes and Additional Resources follow. Robert J. Marks: There are few people who can be credited without any controversy with the founding of a game changing field of mathematics. We are really fortunate today to talk to Gregory Chaitin (pictured) who has that distinction. Professor Chaitin is a co-founder of the Field of Algorithmic Information Theory that explores the properties of…

Close-up Shot of a Hand Holding Chalk and Writing Complex and Sophisticated Mathematical Formula/ Equation on the Blackboard.

The Chaitin Interview I: Chaitin Chats with Kurt Gödel

In this week’s Mind Matters episode, Robert J. Marks begins a conversation with mathematician and computer scientist Gregory Chaitin. The two discuss Chaitin’s beginnings in computer science, his thoughts on historic scientists in his field such as Leonard Euler and Kurt Gödel, and even the story of how a cold call to Gödel almost led to Chaitin meeting the famed…

Guérilla urbaine

Gödel’s Incompleteness Theorems: The Cause—and Cure—of Wokeness?

Why do so many people today think there are only arguments, not facts?

In modern “woke” ideology, there are no facts, only arguments which express cultural power— based on the acceptance of those arguments by current society. In such ideologies, it is not important whether or not the arguments are logically consistent or if they are true in any real sense. What is important is whether or not they achieve the desired results in politics and society. This is not a criticism. It is a description of their methodology (for a review of the academic literature on the subject, see the book Cynical Theories by Helen Pluckrose and James Lindsay. Many people wonder how we got here. Why do so many scholars actively reject logic as a method of finding the truth, and…

schematic of human brain and communication via circuit-board, artificial intelligence

George Gilder on Superintelligent AI

George Gilder and Robert J. Marks discuss the human brain, superintelligent machines, artificial intelligence, and George Gilder’s new book Gaming AI: Why AI Can’t Think but Can Transform Jobs (which you can get for free here). Show Notes 00:29 | Introducing George Gilder 01:00 | An “Indian summer” in AI? 03:45 | Superintelligence 06:04 | The future of computing technology…

Bitcoin statistics

Artificial Intelligence Gaming the Stock Market

What are some assumptions about artificial intelligence? How does artificial intelligence affect the stock market? George Gilder and Robert J. Marks discuss assumptions about artificial intelligence, the stock market, and George Gilder’s new book Gaming AI: Why AI Can’t Think but Can Transform Jobs (which you can get for free here). Show Notes 00:30 | Introducing George Gilder 01:02 |…

The robot writes with a pen and looks at the computer monitor. Artificial Intelligence

Bingecast: Selmer Bringsjord on the Lovelace Test

The Turing test, developed by Alan Turing in 1950, is a test of a machine’s ability to exhibit intelligent behaviour indistinguishable from a human. Many think that Turing’s proposal for intelligence, especially creativity, has been proven inadequate. Is the Lovelace test a better alternative? What are the capabilities and limitations of AI? Robert J. Marks and Dr. Selmer Bringsjord discuss…

man jumping on rock formation

Is Materialism Falsifiable? Yes, Easily.

Neurologist Steven Novella is sure that materialism is not falsifiable by science

Contrary to Steven Novella's claims, cosmological singularities refute materialism. Kurt Gödel can explain

Read More ›
If Then logic statement written in white chalk on a black chalkboard isolated on white

Gödel and God: A Surprising History

A thought-provoking account of master logician Gödel’s largely unknown proof of the existence of God

In an unsanitized, politically incorrect (but factual) history, Selmer Bringsjord talks about how the tormented genius Kurt Gödel took up a quest that dated back a thousand years to prove the existence of God by formal logic. His original version didn’t quite work but his editor’s version passed an important logic test.

Read More ›
E-mc2 written on chalkboard

Kurt Gödel’s Proof of the Existence of God

Kurt Gödel toppled a tall tower of mathematical reasoning with publication of his work showing no formal system of math could be both complete and consistent. He also gave a mathematical proof of the existence of God. Is Gödel’s proof valid? Robert J. Marks and Dr. Selmer Bringsjord discuss mathematics, Kurt Gödel, and the ontological argument. Show Notes 01:05 |…

Digital mind

Why Our Minds Can’t Really Be Uploaded to Computers

The basic problem is that human minds aren’t “computable.” Peter and Jane are not bits and bytes

The underlying problem with creating immortality by uploading our minds to computers is that people are conscious and even the most sophisticated foreseeable computers are not. And we are not at all sure what consciousness even IS.

Read More ›

Math Shows Why the Mind Is Not Just a Formula

The Liar’s Paradox shows that even mathematics cannot be reduced to a fixed set of axioms

Gödel’s discovery brought back a sense of wonder to mathematics and to the rest of human knowledge. His incompleteness theorem underlies the fact that human investigation can never exhaust all that can be known. Every discovery builds a path to a new discovery.

Read More ›
black mathematics board with formulas

Faith Is the Most Fundamental of the Mathematical Tools

An early twentieth century clash of giants showed that even mathematics depends on some unprovable assumptions

David Hilbert wanted all mathematics to be proved by logical steps. Kurt Gödel showed that no axiomatic system could be complete and consistent at the same time.

Read More ›
Crystal ball with building from antiquity

Futurism Doesn’t Learn from Past Experience

Technological success stories cannot be extrapolated into an indefinite future

The limits of science can be as instructive as the discoveries. If science someday proved that computer systems could never reproduce some aspect of mind, we'd have learned something important about the nature of mind.

Read More ›