p. 5: “Freedman Dyson” should be “Freeman Dyson”

p.6: Feynman admitted that Feynman diagrams were somewhat ad hoc, but he had no great interest in the attempts of orthodox mathemasticians to “clean up” the mathematics, which attempts have proceeded in several different directions. Similarly, once could say that Newton’s fluxions were somewhat ad hoc, but that Calculus has been cleaned up since then.

Feynman did not necessarily believe or disbelieve in von Neumann’s quantum logic, but had his own “internal” reasons for suggesting that quantum computers might be the proper substrate in which to ds quantum calculations.

Worth mentioning the von Neumann universe? “…In set theory and related branches of mathematics, the von Neumann universe, or von Neumann hierarchy of sets is the class of all sets, divided into a transfinite hierarchy of individual sets. It is also sometimes called the cumulative hierarchy….”

As wikipedia comments on this:

“There are two distinct approaches to understanding the relationship of the von Neumann universe V to ZFC (and many variations of each approach, and shadings between them). Roughly, formalists will tend to view V as something that flows from the ZFC axioms (for example, ZFC proves that every set is in V). On the other hand, realists are more likely to see the von Neumann hierarchy as something directly accessible to the intuition, and the axioms of ZFC as propositions for whose truth in V we can give direct intuitive arguments in natural language. A possible middle position is that the mental picture of the von Neumann hierarchy provides the ZFC axioms with a motivation (so that they are not arbitrary), but does not necessarily describe objects with real existence.”

On Grothedeick, is it worth mentioning his “inner life” moved from Math to leftist French politics?

Lakatos on polyhedra might need comment on star polyhedra, infinite polyhedra, sections of polytopes, and other things that Plato or Pythagoras might not have taken as Math.

Today (3 March) is the birthday of Georg Cantor, by the way.

Worth going from Ising models to Lattice models in general, and of higher dimensionality?

p.15: I’d be interested to see more on Habermas, not just as filtered through Friedman. Habermas appeals to people I know who are trying to develop meta-theories of communicative networks in online collaboration, random graphs in the in social network theory, and phase changes in random networks somewhat different from the Renormalization Group.

## Re: Dynamics of Mathematical Reason

Take these comments with a large bucket of salt, because I know from embarrassing experience that I am sometimes a very peculiar reader, but:

What is the central line of argument of this paper? It seems very digressive and discursive, and I’m having trouble keeping track of what you’re arguing for at various points.

Given that your review is kind of a negative reaction to the book, I’d feel more comfortable if I felt you engaging more directly with Friedman’s arguments. I realise you don’t want to be incorporating a review of his book inside your paper, but at the moment it gives me the feeling of “Friedman didn’t write about all these cool things that I’m interested in!” This is a legitimate reaction, but it doesn’t necessarily give a paper a strong narrative drive, so it’s possibly not the main thing that you want to come across to the reader.

There’s a lot of interesting material in there, but at the moment I’m finding it difficult to see what the strategy is behind the way you’re deploying it.

But this may just be me being dense. Keep the buckets of salt on hand.