Mind Matters Natural and Artificial Intelligence News and Analysis

TagGottfried Wilhelm Leibniz

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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…

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Evolving Abstract Visualization

Can Mathematics Help Us Understand Consciousness?

Gregory Chaitin asks, what if the universe is information, not matter?

In last week’s podcast, “The Chaitin Interview IV: Knowability and Unknowability,” Walter Bradley Center director Robert J. Marks interviewed mathematician Gregory Chaitin, best known for Chaitin’s Unknowable Number, on, among other things, consciousness. What can mathematics contribute to the discussion. Also, what does Chaitin think about panpsychism (everything is conscious”)? The discussion began with reference to David Chalmers’s 1996 book, The Conscious Mind: In Search of a Fundamental Theory, in which Chalmers coined the term “Hard Problem of Consciousness.” The term acknowledged what everyone knew, that human consciousness is a very difficult problem to understand, especially from a materialist perspective.Are there other approaches? Chaitin offers a look at the challenge panpsychism presents to materialism: https://episodes.castos.com/mindmatters/Mind-Matters-127-Gregory-Chaitin.mp3 This portion begins at 28:25…

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Abstract virtual binary code illustration on blurry modern office building background. Big data and coding concept. Multiexposure

The Chaitin Interview V: Chaitin’s Number

Listen in as Robert J. Marks picks the mind of Professor Gregory Chaitin about Chaitin’s number – a number that has been called “mystical and magical”. How does this number work? Why do some people call it “Chaitin’s constant”? What is the usefulness of philosophizing in mathematics? Show Notes 00:27 | Introducing Gregory Chaitin and Chaitin’s number 01:32 | Chaitin’s…

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Omega, the letter of a Greek alphabet. Greek numerals, mathematical eight hundred number concept. Abstract, digital, wireframe, low poly mesh, Raster blue neon 3d illustration. Triangle, line dot

The Chaitin Interview IV: Knowability and Unknowability

What does it mean for something to be unknowable? Is creativity non-computable? Do all things have a level of consciousness? Jump into today’s podcast, where Robert J. Marks continues his discussion with Gregory Chaitin about mathematical theory and philosophy. Show Notes 00:23 | Introducing Gregory Chaitin 00:40 | What is unknowability? 06:07 | Does non-computable mean unknowable? 09:43 | A…

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Online education concept

How Stephen Wolfram Revolutionized Math Computing

Wolfram has not made computers creative but he certainly took a lot of the drudgery out of the profession

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 math or engineering geniuses (Elon Musk came to mind, of course) can’t just follow the rules. This week, we look at Stephen Wolfram’s new program that checks your hard math. What can — and can’t — it do for mathematicians? https://episodes.castos.com/mindmatters/Mind-Matters-126-Gregory-Chaitin.mp3 This portion begins at 13:22 min. A partial transcript, Show Notes, and Additional Resources follow. Gregory Chaitin: Now, there is what I regard as a piece of AI, so it might be interesting to talk about it. My friend Stephen Wolfram (pictured), the system he’s created,…

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Infinite random numbers, original 3d rendering background, technology and science concepts

Chaitin’s Discovery of a Way of Describing True Randomness

He found that concepts from computer programming worked well because, if the data is not random, the program should be smaller than the data

In this week’s podcast, “The Chaitin Interview II: Defining Randomness,” Walter Bradley Center director Robert J. Marks interviewed mathematician and computer scientist Gregory Chaitin on randomness. It’s a subject on which Chaitin has thought deeply since his teenage years (!), when he published a journal paper on the subject. How do we measure randomness? Chaitin begins by reflecting on his 1969 paper: https://episodes.castos.com/mindmatters/Mind-Matters-125-Gregory-Chaitin.mp3 This portion begins at 1:12 min. A partial transcript, Show Notes, and Additional Resources follow. Gregory Chaitin: In particular, my paper looks at the size of computer programs in bits. More technically you ask, what is the size in bits of the smallest computer program you need to calculate a given digital object? That’s called the program…

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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…

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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.

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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 |…