Sleeping beauty problem III

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I am writing a third post about the sleeping beauty problem partly because I have seen Sean Carmody's post  (26th August) in which he describes the problem and expresses his uncertainty about it, and promises an opinion in a future post. We are waiting, Sean, for your ideas on the matter!


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Opera d'abbaco del reverendo padre don Smiraldo Borghetti

Here are some pages from a book I bought some years ago on arithmetic, published in 1594.

It is interesting to read that without numbers the world would be without order,  and a horrible chaos.

Strangely the current popular view (which I do not share) is that the world is chaos, even to the extent that the laws of physics are the casual effect of which universe of the multiverse we happen to inhabit.

Giuseppe Peano

On Saturday I  bought for 2 euros  at the mercatino of Lavello a little book by Giuseppe Peano of numerical tables. It has an interesting preface by Peano.

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Ricordo di Aurelio Carboni, Matematico e Filosofo

I have just received a volume of "Il Protagora" in which there is a section devoted to Aurelio's memory.

There are four articles all in
Il Protagora, Volume XL, July-December 2013, sesta serie, n. 20

The articles are

Fabio Minazzi, Un ricordo di Aurelio Carboni, pp. 489-494

F. William Lawvere, Farewell to Aurelio, pp. 495-498

R.F.C. Walters, Working with Aurelio - Tangled Lives, pp. 499-504

George Janelidze, An open letter to Aurelio Carboni and all Mathematicians who remember him, pp. 505-513

Prepublication versions of three of the papers are at the Como Category Archive.

Lex total categories and Grothendieck toposes IV

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The aim of this post is to complete the proof that well-powered lex total categories are elementary toposes, by proving that they have subobject classifiers.

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Span(Graph) III: Circuits with feedback

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The two main operations in $\bf Circ$ are composition and parallel as for straight-line circuits, and there are a variety of constants.

Today we describe the operation of composition of circuits with feedback in $\bf Circ$.

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Lex total categories and Grothendieck toposes III

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Today I want to give an application of the adjoint functor theorem for totally complete categories, namely to show that lex total categories are cartesian closed. The proof should be a generalization of the proof that locales are cartesian closed so we should look at that before attempting the case of lex total categories. We will be repeating some of the discussion of the first post in this series.

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