# Covered in blue …

So here’s the cover for IFL2 (click for a larger version).  The painting, my choice, is Kandinsky’s Blue Painting (Blaues Bild) from January 1924. It has been slightly cropped by CUP’s designers but I do think it still makes for a good-looking cover. I’m really very pleased with the result.

I’m working away putting answers to end-of-chapter exercises online (currently I’m having fun with quantifier natural deduction).  This is actually rather a good task to have on the go right now. It is distracting enough to keep my mind off other things during a long afternoon stuck at home; but it hardly demands prolonged concentration trying to get my head round Difficult Stuff.  I’m making some very slight improvements to the exercises as I go along which can be incorporated into the final final book version when CUP call for it in a week or two. And so  on we go.

I’d like, though, to get back to thinking about category theory. Here’s one question: category theorists, or some influential ones among them at any rate, seemingly work with a non-standard conception of sets: but what is it, exactly (when you try to cash out the ‘bag of dots’ metaphor that gets trotted out)? As a warm up exercise (although I don’t think he tackles this question) I’m going to be sitting down to read carefully Luca Incurvati’s recent Conceptions of Set and the Foundations of Mathematics. If your library subscribes to the Cambridge Core system, you should be able to get it online. I’ll start posting about this book, chapter by chapter, in the next few days.

### 3 thoughts on “Covered in blue …”

1. Jan von Plato

Dear Peter, belated congratulations for the choice of cover picture! It is not nice, that’s a stupid word, it’s, perhaps, sublime?

2. I like the blue cover (and prefer that picture to the ones you were considering a while back).

The Incurvati book looks very interesting — in part (from my pov) because says very little about category theory.

Explaining category theory’s approach to sets may be more a job for sociologists, psychologists, and perhaps political scientists than for mathematicians or philosophers. Lawvere is explicitly ideological:

When the main contradictions of a thing have been found, the scientific procedure is to summarize them in slogans which one then constantly uses as an ideological weapon for the further development and transformation of the thing. Doing this for “set theory” requires taking account of the experience that the main pairs of opposing tendencies in mathematics take the form of adjoint functors, and frees us of the mathematically irrelevant traces (∈) left behind by the process of accumulating (∪) the power set (P) at each stage of a metaphysical “construction”.

According to Lawvere, the scientific procedure — the scientific procedure! — is to summarise contradictions in slogans to use as an ideological weapon.

(This is from “Quanifiers and Sheaves”, which has Mao’s On Contradiction. Where do correct ideas come from? as the first of only four references.) (They’re not in alphabetical order.)

1. I do agree that lots of what I’ve seen by way of passing remarks on sets by category theorists does seem to recycle some confused ideas. And it seems that Lawvere (whom I certainly wouldn’t trust on conceptual/philosophical matters — witness your quote!!!) is the source of those. But I’d still like to be in a better position to sort the wheat (if any) from the chaff here.

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