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TagLaw of non-contradiction

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Why the Unknowable Number Exists But Is Uncomputable

Sensing that a computer program is “elegant” requires discernment. Proving mathematically that it is elegant is, Chaitin shows, impossible

In this week’s podcast, “The Chaitin Interview IV: Knowability and Unknowability,” Walter Bradley Center director Robert J. Marks interviewed mathematician Gregory Chaitin on his “unknowable number.” That’s the topic of this series, based on the fourth podcast. Last week, we tried getting to know the unknowable number. Today, let’s look at the question of how we know that the number is unknowable — instead of merely non-computable. Lots of things are non-computable but we do not expect that to be true of numbers. Let’s see what’s happening here, as Chaitin offers a walk through his proof that it really is unknowable: https://episodes.castos.com/mindmatters/Mind-Matters-127-Gregory-Chaitin.mp3 This portion begins at 09:43 min. A partial transcript, Show Notes, and Additional Resources follow. Robert J. Marks:…

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How Do You Know You Are Not the Only Human Who Ever Existed?

Can evidence or logic help you decide? You might be surprised…

Solipsism is the belief that you are the only human being who has ever existed; all others are the inventions of your imagination. G.K. Chesterton famously received a letter from a reader who commented (I paraphrase), ‘Solipsism is a compelling metaphysical position. I’m surprised more people don’t believe it.” At Scientific American, columnist John Horgan describes solipsism as a central dilemma of human life. In a recent essay, “How do I know I’m not the only conscious being in the universe?”, he writes, It is a central dilemma of human life—more urgent, arguably, than the inevitability of suffering and death. I have been brooding and ranting to my students about it for years. It surely troubles us more than ever…