Top News, Articles, and Interviews in Philosophy

I was intending to post Chapter 17 today — the final chapter, dealing with Löb’s Theorem and related results. But looking again at my draft version yesterday, I thought it was/is rather a [More]
Today’s chapter is optimistically entitled ‘Proving the Second Incompleteness Theorem’. Of course we don’t actually do that! But we do say something more about what it takes to prove it (stating the s [More]
Today’s short episode is a second ‘Interlude’, separating the chapters on the first incompleteness theorem from the final three chapters on the second theorem. But it mentions (or at least, gestures at) enough interesting points for it to be worth … Continue reading → The post Gödel Without Tears, slowly, Interlude appeared first on Logic [More]
Today’s short episode is a second ‘Interlude’, separating the chapters on the first incompleteness theorem from the final three chapters on the second theorem. But it mentions (or at least, gestures at) enough interesting points for it to be worth … Continue reading → The post Gödel Without Tears, slowly, 15 appeared first on Logic [More]
In this last (and short!) chapter related to the first incompleteness theorem, we meet ‘Tarski’s Theorem’. And so we arrive at what might be thought of as the Master Argument for incompleteness — for appropriate theories, provability-in-T  is expressible in … Continue reading → The post Gödel Without Tears, slowly, 14 appeared first on Logic [More]
We get today to Chapter 13, called ‘The Diagonalization Lemma, and Rosser’s Theorem’. Not that we actually prove Rosser’s theorem in detail, as this is fiddly. But I do establish the Lemma, show how it can be used to derive … Continue reading → The post Gödel Without Tears, slowly, 13 appeared first on Logic [More]
And, at last …. Cue drumroll … ‘The First Incompleteness Theorem, syntactic version’ This is the version of the theorem that Gödel highlights in his epochal 1931 paper, and which people usually have in mind when they talk of ‘the’ … Continue reading → The post Gödel Without Tears, slowly, 12 appeared first on Logic [More]
And at last, we get to a proof of ‘The First Incompleteness Theorem, semantic version’, uisng pretty much Gödel’s materials. And given our background work over previous chapters, it is very easy. Grasp the trick in constructing the described Gödel … Continue reading → The post Gödel Without Tears, slowly, 11 appeared first on Logic [More]
A good time to join the party, if you haven’t yet been following along with this chapter-by-chapter posting of a new version of Gödel Without (Too Many) Tears. Along with revised versions of early chapters (thanks to all those who … Continue reading → The post Gödel Without Tears, slowly, 10 appeared first on Logic [More]
Today’s chapter is about ‘Expressing and capturing the primitive recursive functions’. We prove (in reasonable detail) that although the language of basic arithmetic only has the successor, addition and multiplication functions built in, we can in fact form a wff … Continue reading → The post Gödel Without Tears, slowly, 9 appeared first on Logic [More]

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## Interview with

Dr. Robert McKim
• on Religious Diversity
• Professor of Religion and Professor of Philosophy
• Focuses on Philosophy of Religion
• Ph.D. Yale

## Interview with

Dr. Alvin Plantinga
• on Where the Conflict Really Lies
• Emeritus Professor of Philosophy (UND)
• Focuses on Epistemology, Metaphysics, Philosophy of Religion
• Ph.D. Yale

## Interview with

Dr. Peter Boghossian
• on faith as a cognitive sickness
• Teaches Philosophy at Portland State University (Oregon)
• Focuses on atheism and critical thinking
• Has a passion for teaching in prisons
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