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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]

Gödel Without Tears, slowly, 9

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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