Kurt Gödel’s “Incompleteness Theorem”
For Kurt Gödel, mathematics pointed to a remarkable world of transcendent order and meaningGödel saw the beauty of numbers and associated them with a transcendent order.
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Why Is Theology the Most Important Empirical Science?
Arguing pro or con about the existence of God has resulted in many successful and/or widely accepted theories in scienceIf generating testable theories in empirical science is the standard of success, theology has certainly succeeded, as the record will show.
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Why Logician Kurt Gödel Believed in Life After Death
He saw human folly as an opportunity to reform and learn, because our souls are immortal whether we like it or notIn a deeply rational, ordered universe, Gödel argues, human potential — frustrated in so many ways here — must flower afterward elsewhere.
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The Search for Extraterrestrial Life 18
We are starting to find more different kinds of exoplanets and an unexpected source of water on MarsIn our universe: Time travel? “How a Rotating Universe Makes Time Travel Possible” At Universe Today, Stony Brook astrophysicist Paul Sutter notes that mathematical philosopher Kurt Gödel (1906–1978) wrote a model for Albert Einstein (1879–1955) of a universe that allows time travel into the past: “Gödel constructed a relatively simple and artificial model universe to prove his point. This universe is rotating and contains only one ingredient. That ingredient is a negative cosmological constant that resists the centrifugal force of the rotation to keep the universe static. / Gödel found that if you follow a particular path in this rotating universe you can end up in your own past. ” (January 11, 2023) Our universe, as it happens, is not Read More ›
Why Did Stephen Hawking Give Up on a Theory of Everything?
Daniel Díaz and Ola Hössjer continue their discussion of the fine tuning of the universal constants of nature with Robert J. MarksIn a continuing conversation with Swedish mathematician Ola Hössjer and Colombian biostatistician Daniel Díaz on the fine-tuning of the universe — and Earth — for life, Walter Bradley Center director Robert J. Marks asks them about why a Theory of Everything eludes us and about the life-permitting interval — the narrow window for life that the constants of the universe permit. This is the second part of Episode 3, “The universe is so fine-tuned!” (September 16, 2021). Earlier portions, with transcripts and notes, are listed below. https://episodes.castos.com/mindmatters/Mind-Matters-Episode-152-Hossjer-Diaz.mp3 This portion begins at 12:36 min. A partial transcript, Show Notes, and Additional Resources follow. Robert J. Marks: In truth, there’s a lot of fundamental constants — the electric charge of an electron, Read More ›
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 Read More ›
Gödel Says God Exists and Proves It
Here is a line-by-line explanation of his proofKurt 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 Read More ›
How Materialism Proves Unbounded Scientific Ignorance
There is an infinite number of things that are true that we cannot prove scientifically and never willScience 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 Read More ›
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! Read More ›
Why Elon Musk and Other Geniuses Can’t Afford To Follow Rules
Mathematician Gregory Chaitin explains why Elon Musk is, perhaps unexpectedly, his heroIn 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, Read More ›
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 Additional Read More ›
Gregory Chaitin’s “Almost” Meeting With Kurt Gödel
This hard-to-find anecdote gives some sense of the encouraging but eccentric math geniusIn 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 Read More ›
Gregory Chaitin on the Great Mathematicians, East and West
Himself a “game-changer” in mathematics, Chaitin muses on what made the great thinkers stand outIn 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 Read More ›
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 Read More ›
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 Read More ›
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 Additional Resources
Is Materialism Falsifiable? Yes, Easily.
Neurologist Steven Novella is sure that materialism is not falsifiable by scienceContrary to Steven Novella’s claims, cosmological singularities refute materialism. Kurt Gödel can explain
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Gödel and God: A Surprising History
A thought-provoking account of master logician Gödel’s largely unknown proof of the existence of GodIn 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.
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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 | Read More ›
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 bytesThe 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.
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