This is a detailed book, and I felt it wasn't really aimed at a non-specialist like me, but I did feel that I got something out of the book. My understanding of what the book is saying is as follows. In his 1976 Nobel lecture, Milton Friedman claimed that economists had promoted inflationist policies on the basis that the Phillips curve meant that this would lower unemployment, and he explained that in reality inflation would produce expectations of further inflation which would cancel out any benefit. Forder argues that Friedman's claim is a myth. In the 1960s and 1970s hardly anyone was promoting inlationist policies, and the Phillips curve wasn't seen as something that was set in stone. Some people put forward the 'lubrication' argument for a moderate level of inflation. This argued that since workers are understandably very resistant to a cut in (money) wages, a reasonable level of inflation would allow real wages to drop slightly in weak sectors of the economy, rather than having large scale business closures. Also when the Phillip's curve was mentioned people asked what policies would shift it to allow lower unemployment whilst still maintaining low inflation. Indeed lowering inflation was always seen as a policy goal.
I did feel that there were a few things Forder could have done to make it more readable by the non-specialist.
A central theme in the book is that economists weren't promoting inflationist policies. But inflation grew anyway, so a discussion of why this happened would be useful. (To be fair he does mention the cost of the Vietnam War). Also this is a book about a graph, and arguments such as whether the curve is really vertical. I felt a few graphics illustrating the curves being talked about wouldn't have gone amiss. A bit biographical information about Phillips would also have been interesting, for example his job as a crocodile hunter, but more importantly, the economic models he constructed. Nowadays you might use a spreadsheet, but this was long before spreadsheets were invented, and most of the computers around were being used for designing bombs. So Phillips designed a
hydraulic computer
https://en.wikipedia.org/wiki/MONIAC. Forder does mention Phillips 1954 paper, which looks like it has a lot of Moniac-style flowcharts, and I think that it would have been useful to see how much Phillips was into computer modelling. Forder tells us that one of the reasons the Phillips curve became well known was because it was thought to offer a falsifiable prediction, so fitting in to Popperian philosophy of science. But computer modelling provides a different philosophy, models can always be tuned to fit new data, so there's the question of what tuning is acceptible. I thought some discussion of this in the book would have been interesting.
I can't help seeing parallels between the story of the Phillips curve and that of the Higgs Boson (Phillips' paper was published in 1958, Higgs' in 1964) Phillips had done mathematical work on the inflation-unemployment relationship, but became known for a curve which people could put his name to. Higgs had done mathematical work on how particles get their mass, but it was when he mentioned a boson - something that people could attach his name to - that his work got published. In an explanation of the Higgs mechanism we're asked to imagine Mrs Thatcher walking across a room of party workers, and being impeded as they clustered around her. However, this would seem to imply that she would be slowed down. Friedman claimed that you couldn't trade off unemployment with the first derivative of prices (inflation), but rather the second derivative. You could imagine a Nobel laureate in physics explaing how he had put people right because, given the explanation of the Higgs boson, they believed that moving objects would slow down (first defivative of position) rather than exhibit resistance to acceleration (second derivative). But of course all of that was sorted out by Galileo (unless anyone has evidence that that's a myth too)
So although I didn't follow all of Forder's arguments in detail, I felt that I got a lot out of the book. Most of all I see this book as an example of how digging into the literature can help to show inaccuracies in our current beliefs about an earlier period of time.