_{Science writer: As often happens, few people understood the significance of what had just happened. The one exception was John von Neumann.}_{
News
July 19, 2021
Mathematics
}

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…

^{
Type
post
Author
Robert J. Marks
Date
June 7, 2021
Categorized
Mathematics, Religion
Tagged
Anselm of Canterbury, Axioms, Definitions, Descartees, God's existence, Gottfried Wilhelm Leibniz, Kurt Gödel, Kurt Gödel (belief in God), ontological proof, Theorems
}

_{Here is a line-by-line explanation of his proof}_{
Robert J. Marks and Samuel Haug
June 7, 2021
Mathematics, Religion
}

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…

^{
Type
post
Author
Robert J. Marks
Date
April 18, 2021
Categorized
Philosophy, Science
Tagged
Creator, Daniel Andrés Díaz Pachón, god, Goldbach's Conjecture, Incompleteness theorems (Gödel), Kurt Gödel, Peter Atkins, Proof (in mathematics), Scientific materialism, Scientism, Stephen Hawking, String theory, Theism, Theory of Everything, William Lane Craig
}

_{There is an infinite number of things that are true that we cannot prove scientifically and never will}_{
Robert J. Marks
April 18, 2021
Philosophy, Science
}

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…

^{
Type
post
Author
Eric Holloway
Date
April 9, 2021
Categorized
Artificial Intelligence, Creativity, Philosophy of Mind
Tagged
__featured, Creative intelligence, Creative intelligence (cluttered attic analogy), Creative intelligence (connect the dots analogy), Creative intelligence (puzzle analogy), Creativity, Incompleteness theorems (Gödel), Kurt Gödel
}

_{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… }_{
Eric Holloway
April 9, 2021
Artificial Intelligence, Creativity, Philosophy of Mind
}

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!…

^{
Type
post
Author
News
Date
March 21, 2021
Categorized
Artificial Intelligence, Mathematics, Neuroscience, Programming
Tagged
__featured, Brain-Computer Interface (BCI), Computer sim universe, Computers (creativity limits), Creativity, Elon Musk, Georg Cantor (illness), Gregory Chaitin, Kurt Gödel, Kurt Gödel (illness), Neuralink, Proof checkers (software), Robert J. Marks
}

_{Mathematician Gregory Chaitin explains why Elon Musk is, perhaps unexpectedly, his hero}_{
News
March 21, 2021
Artificial Intelligence, Mathematics, Neuroscience, Programming
}

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,…

^{
Type
podcast
Author
Robert J. Marks
Date
March 11, 2021
Tagged
Algorithmic Information Theory, Computer science, Fermat's Last Theorem, Gregory Chaitin, Kurt Gödel, Mathematics, 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…

^{
Type
post
Author
News
Date
March 6, 2021
Categorized
Mathematics
Tagged
__featured, Berry Paradox, Emil Post, Epimenides' Paradox, Gregory Chaitin, Kurt Gödel, Liar's Paradox, Robert J. Marks
}

_{This hard-to-find anecdote gives some sense of the encouraging but eccentric math genius}_{
News
March 6, 2021
Mathematics
}

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…

^{
Type
post
Author
News
Date
March 5, 2021
Categorized
Artificial Intelligence, Mathematics, Religion
Tagged
__featured, Carl Friedrich Gauss, Georg Cantor, God's existence, Gödel ’s Proof, Gregory Chaitin, infinity, Kurt Gödel, Leonhard Euler, Niels Henrik Abel, Robert J. Marks, Srinivasa Ramanujan
}

_{Himself a “game-changer” in mathematics, Chaitin muses on what made the great thinkers stand out}_{
News
March 5, 2021
Artificial Intelligence, Mathematics, Religion
}

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…

^{
Type
podcast
Author
Robert J. Marks
Date
March 4, 2021
Tagged
Algorithmic Information Theory, Computer science, Gregory Chaitin, Kurt Gödel, Leonard Euler, Mathematics
}

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…

^{
Type
post
Author
Jonathan Bartlett
Date
December 31, 2020
Categorized
Education
Tagged
Alfred North Whitehead, Bertrand Russell, Kurt Gödel, Rene Descartes
}

_{Why do so many people today think there are only arguments, not facts?}_{
Jonathan Bartlett
December 31, 2020
Education
}

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…

^{
Type
podcast
Author
Robert J. Marks
Date
November 5, 2020
Tagged
Alan Turing, Artificial General Intelligence (AGI), Artificial Intelligence, Connectome, DeepMind, Ergodicity, George Gilder, Kurt Gödel, Life after Google (book), Nematode worm, Neural networks, Ray Kurzweil, Singularity, Superintelligence, Tony Stretton, Turing Machine, zettabyte
}

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…

^{
Type
podcast
Author
Robert J. Marks
Date
October 29, 2020
Tagged
Alan Turing, Artificial Intelligence, Big Data, Data Mining, Ergodicity, front running, Gaming AI (book), George Gilder, Gregory Chaitin, John von Neumann, Kurt Gödel, Life after Google (book), Mind Brain, stock market, Turing Machine
}

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 |…

^{
Type
podcast
Author
Robert J. Marks
Date
September 24, 2020
Tagged
Abstract thought, Ada Lovelace, Alan Turing, Algorithm-of-the-Gaps, AlphaGo, Charles Babbage, Claude Shannon, Cognition, computer, Computers, Consciousness, Creativity, David Gelernter, disjunctive syllogism, Eugene Goostman, Gottfried Wilhelm Leibniz, Kurt Gödel, Language, Lovelace test, Marcel Proust, Mathematics, Natural Language Generation, Natural Language Processing, non-algorithmic, novels, ontological argument, ontological proof, Ray Kurzweil, Saint Anselm, Selmer Bringsjord, Singularity, Sports, Theorems, Turing 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…

^{
Type
post
Author
Michael Egnor
Date
May 24, 2020
Categorized
Philosophy of Mind
Tagged
__featured, __focus-north, Cosmological singularities, Kurt Gödel, Materialism, Naturalism, Res extensa, Steven Novella, Supernaturalism
}

^{
Type
post
Author
News
Date
May 10, 2020
Categorized
Artificial Intelligence, Mathematics, Religion
Tagged
___longform, __featured, Formal logic, Gottfried Wilhelm Leibniz, Kurt Gödel, Mathematics, Rene Descartes, Robert J. Marks, Saint Anselm, Selmer Bringsjord
}

_{A thought-provoking account of master logician Gödel’s largely unknown proof of the existence of God }_{
News
May 10, 2020
Artificial Intelligence, Mathematics, Religion
}

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.

^{
Type
podcast
Author
Robert J. Marks
Date
May 7, 2020
Tagged
disjunctive syllogism, Gottfried Wilhelm Leibniz, Kurt Gödel, Mathematics, ontological argument, ontological proof, Saint Anselm, Selmer Bringsjord, Theorems
}

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 |…

^{
Type
post
Author
News
Date
April 22, 2020
Categorized
Artificial Intelligence, Arts & Culture, Philosophy of Mind
Tagged
___longform, __featured, Computers, Consciousness, Kurt Gödel, Mind Uploading, Robert J. Marks, Selmer Bringsjord, uploading consciousness
}

_{The basic problem is that human minds aren’t “computable.” Peter and Jane are not bits and bytes}_{
News
April 22, 2020
Artificial Intelligence, Arts & Culture, Philosophy of Mind
}

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.

^{
Type
post
Author
Eric Holloway
Date
March 29, 2020
Categorized
Mathematics, Philosophy of Mind
Tagged
J. R. Lucas, Kurt Gödel, Leonid Levin, Logicomix (comic book), Vienna Circle
}

_{The Liar’s Paradox shows that even mathematics cannot be reduced to a fixed set of axioms}_{
Eric Holloway
March 29, 2020
Mathematics, Philosophy of Mind
}

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.

^{
Type
post
Author
Daniel Andrés Díaz-Pachón
Date
January 5, 2020
Categorized
Mathematics
Tagged
___longform, Apologetics, David Hilbert, Faith, Featured, Kurt Gödel, Modernity, Philosophy
}

_{An early twentieth century clash of giants showed that even mathematics depends on some unprovable assumptions }_{
Daniel Andrés Díaz-Pachón
January 5, 2020
Mathematics
}

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.

^{
Type
post
Author
Mind Matters Analysis
Date
June 26, 2019
Categorized
Artificial Intelligence
Tagged
Featured, Futurism, Kurt Gödel, Longform, Philosophy, science
}

_{Technological success stories cannot be extrapolated into an indefinite future}_{
Analysis
June 26, 2019
Artificial Intelligence
}

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.