Top News, Articles, and Interviews in Philosophy

Kripke on diagonalization

Having thought a bit more about Kripke’s short note on diagonalization, linked in the last post, it seems to me that the situation is this, in rough headline terms. How do we get from a Diagonalization Lemma to the incompleteness … Continue reading → The post Kripke on diagonalization appeared first on Logic [More]

Gödel Without Tears, slowly, 16

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 so-called derivability conditions, and saying what it takes … Continue reading → The post Gödel Without Tears, slowly, 16 appeared first on Logic [More]

Gödel Without Tears, slowly, Interlude

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]

Gödel Without Tears, slowly, 15

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]

Gödel Without Tears, slowly, 14

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]

Gödel Without Tears, slowly, 13

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]

Gödel Without Tears, slowly, 12

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]

Gödel Without Tears, slowly, 11

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]

Gödel Without Tears, slowly, 10

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]

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

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

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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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