3rd Tape of discussions, incl. FW Lawvere, A Peruzzi & M Wright (contd.)

0:00 If they just reject, I must have got the address wrong somehow. Let me get it off. Yeah, well, that's what I've been sending to you. Yeah. Well, he keeps saying that, you know, it's hard to establish a connection. That must be something. I'll talk to you about it another time. R. Roseborough. I haven't actually written it. O-S-E-B-R-U-G-H, right. Look, I'll get the address off you. That's R. Roseborough. That's B-R-U-G-H. Or is it Berg? Because I sent an email in July and got absolutely nothing back. The archive, the old archive, that I'm maintaining it. And now you have to get it through the main categories list. So I haven't been able to look at anything that's been posted. Take you off the beam. There's a remark you made about Stalin's art. The other one, which is... When you say that, you understand that concerns those few topos in which all magnetic objects are two objects, in which all magnetic objects are two objects.

2:30 When you say that, you understand that you apply only this to such topics. If I can just say quickly that there's a quite good explanation of that point in Colin's article in the JSL, He published a paper published about four, five, six years ago. He has a discussion of the, in the context of the weekly Decidable Sub-Object Conditioning that all governments, localities, and governments, very short papers, only about three pages. And he has this, yeah, yeah, sure, I'm surprised they haven't got it. It's the paper that comes with the value. I couldn't judge it on a symbolic logic. Colin published a paper in there which is, A full of mathematical amplification of his sets of points of years back now this much, and goes back. Which you certainly did. Well, he wrote a mathematical version of that for the journal Symbolic Logic, which appeared about a year later. I think it was in 1991, I think it's 1991. Yeah, I'll send it to you. But he has a discussion of this. You mentioned a paper by E.K. Maurelio and Martha Womberg. I didn't invest. What then would the term that I suggested? Maybe it's not a good one. It doesn't suggest the right thing at all because the symmetric elements are a part of the vector space rather than the basis for it. If you had a basis for the vector space, well, symmetric is a non-communicative version. In other words, I think Chevalier's extensive quantity, one interpretation of extensive quantity on the spectrum of A, where A is...

5:00 Let's say a commutative algebra over k is just a k-linear map. These could be a linear combination of points or more generally linear. In fact, it could have values that represents on spec a are the same as points of spec of s of a. On the measures on the give and take, that's exactly what would be a point.

7:30 So I shouldn't have never have done this. It's such a bad word. ...the geometric roots.

57:30 Oh he must have thought this. He could imagine that. There seems to be, the chief points out, I would not, was setting, he established some very nice results there, basic, you know, geometry, geometric ideas, or, oh, you mean the, what, the conceptual, yeah, that's a lovely book, conceptual, Lorver and Schaniel, is that the book you're talking about, Lorver and Schaniel, conceptual mathematics?

1:17:30 Yeah, exactly. Yes, yes, yes, that's a lovely book. It's, although it is presented as an introductory, very introductory, it's a wonderful book, although it's, you know, the actual. It is actually deep suggestive ideas at the end. I haven't read that yet. It's a primer infinitesimal analysis it's called, isn't it?

1:20:00 I haven't read it yet. It's bound to be good. I mean, John Bell usually gives a lot of historical and philosophical motivation with the Goldblatt book. Read it by all means, and nothing could be less true. Historically, it's a complete distortion. It came out of in a form which was so hairy. I took it and simplified it. The main model theory is Tarski, where mathematics is a set of theory from you and models on the spaces that you're in, in which the models naturally live. For instance, the axiom of choice just turns out to have a very big, it's just got a kind of notion of one. You can think of the domain as consisting of, which are just there to be the same or different, absolutely, to be the variables. The whole way that you, you have to start from that, you have to start from a set of theoretical ontology and the standard approach.

1:22:30 Where else would the domains of your models come from? I would say, you know, deeper. The quantifiers themselves turn out to have a very, and the really important structures in logic turn out to be the one that's by this gym, which is just a restricted, an unrestricted quantification factor. It's easy to treat that entirely in terms of this kind of underlying, that's increasingly used now by people in logic, which suggests, which is the really big, you know, philosophical part, that there isn't, that there's something wrong about what shows up as the various pathologies, including, of course, the completeness. So, seeing if reconstructing topology on a basis does in fact have deep philosophical... It is hairy stuff, and it's taken me about 20 years to... All of that was just to say, yeah, the Bible I'm sure is excellent. One about my Goldblum... It's not a bad book. I'm not saying there's anything specific. No, it's not. You see all of the structure. There wasn't anything in between, but about five years ago, no, four or five years ago, Colin McLarty, he wrote a mathematical introduction to the subject, but it's written at a sort of much more accessible level than Johnston, but it's historically, and I would say also philosophically, much better.

1:25:00 Bring at it from the category theoretic end rather than from the... I recommend that as well. But no, a good general presentation of the significance of... The problem is that the subject is so huge in mathematics and with the way that you see things fitting together in the big pictures themselves, I wouldn't presume.