Could an android at a child’s funeral read the mourners’ thoughts and emotions? Or would it view the death as a mere rearrangement of atoms in a wooden box?
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Some think math is invented. (See the article by Peter Biles.) Evidence, though, points towards discovery. Simultaneous mathematical discovery supports this viewpoint. Many mathematical breakthroughs are sometimes independently reported by two or more mathematicians at roughly the same time. The most famous is the simultaneous discovery of calculus by Isaac Newton and Gottfried Wilhelm Leibniz. Newton was secretive about his discovery and shared his results with only a few members of the Royal Society. When Leibnitz published his discovery of the calculus, Newton charged him with plagiarism. Today, historians agree that the discoveries were independent of each other. Here are some other lesser-known examples of simultaneous discovery. The Papoulis-Gerchberg Algorithm (PGA). The PGA is an ingenious method for recovering lost Read More ›
This story was #3 in 2022 at Mind Matters News in terms of reader numbers. As we approach the New Year, we are rerunning the top ten stories of 2022, based on reader interest. In “Mathematics can prove the existence of God” (July 31, 2022), neurosurgeon Michael Egnor offers this thought: Because mathematics can show infinity, eternity, and omnipotence, it can only have proceeded from a mind with those characteristics. That’s God. In a recent post, atheist biologist Jerry Coyne takes issue with a commenter who asserts that God exists in the same sort of way mathematics exists. Here’s the analogy the commenter offered, as quoted by Coyne: Think of numbers for example, or mathematical equations, these are metaphysical things, Read More ›
In a recent post, atheist biologist Jerry Coyne takes issue with a commenter who asserts that God exists in the same sort of way mathematics exists. Here’s the analogy the commenter offered, as quoted by Coyne: Think of numbers for example, or mathematical equations, these are metaphysical things, that have not been created, however were discovered. The number 7 was the number 7 before anything at all came into existence. This is also true concerning the nature of God. He is not some material being that has come into existence, he is like a number that has always existed, (and by the way nobody will deny this logic with the number, however when someone mentions God a problem occurs). Jerry Read More ›
“Does God exist?” On September 17, in a dramatic debate, Christian neurosurgeon Michael Egnor and atheist broadcaster Matt Dillahunty squared off on the question at Theology Unleashed. The debate hosts are Arjuna Das for Theology Unleashed and Nathan from Digital Gnosis as the moderator. A partial transcript and notes follow. Egnor has been a guest at Theology Unleashed, before, debating materialist philosopher David Papineau. The ten proofs of God that he presents as his opening argument below are not drawn from sacred texts but from philosophical reasoning: Michael Egnor: There are, broadly speaking, two different kinds of theology. There’s natural theology and there’s revealed theology. Revealed theology is the use of scripture, personal experiences, or relationships to God. And that’s Read More ›
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 Read More ›
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 Read More ›
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, Read More ›
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 Read More ›
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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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 ›