Tag: Logic and Foundations

Wikistyle maths
Wikistyle cooperative mathematics can work for even the highest levels of maths research, reports (subscribers only) the New Scientist (subscription offer) – challenging the idea that maths advances can only come from tortured geniuses working alone. The system, called Polymath (there is a blog about it here) was tested out on the “density HalesJewett theorem” […]

Gödel, Turing and decidability
I am still wandering around in the world opened to me by The Annotated Turing – perhaps a little lost, but I have been reading some guide books. The most recent of these has been Gödel’s Proof which gives a gentle(ish) introduction to Gödel’s incompleteness theorem. This is a short, but fascinating book that I repeatedly […]

Even more confused
Still on The Annotated Turing: and now (I am up to page 260) I have to admit I am finding the maths part quite hard going, though I guess there is no particular shame in that – after all this was the very bleeding edge of the discipline 70 years ago. Well, yesterday I pointed […]

For all you first order/predicate logic fans out there
From The Annotated Turing: now reached page 226 and it is still good. I think Charles Petzold has made a mistake – has he? Please read on and let me know. Petzold says these three axioms come from Hilbert and Bernays and they mean: Every member has a successor There exists a number that does […]

Bought on a whim but seems like a good one
I bought this book this evening on the way home from work – The Annotated Turing – and have already got through fifty pages. (Actually I wish I had bought it from Amazon because the price there is less than half I paid for it). Those pages covered much of the same ground as the […]