Lakoff has spent decades promoting his generative semantics over Chomsky's generative grammar.
You've made a category error here. "Generative semantics" does not contrast with "generative grammar"; it contrasts with "interpretive semantics". See the Wikipedia article, which says:
The controversy surrounding generative semantics stemmed in part from the competition between two fundamentally different approaches to semantics within transformational generative syntax.
Note that "grammar" in linguistics is not a synonym for "syntax"; it is the comprehensive term for the rules of a language, including syntax, semantics, morphology, phonology, etc.
Summary: generative semantics is a school of thought within "generative grammar".
Thanks for the correction. Lakoff and Johnson don't oppose the two terms in their book, and my brief glance at Wikipedia misled my impression of how linguists are drawing up the boundaries around their categories.
The chapter on Chomsky is contrasting the generative grammar approach, which Lakoff used to work within, to the cognitive science inspired cognitive linguistics approach, which Lakoff has been working in for the last few decades. Cognitive linguistics includes cognitive semantics which is rather different to generative semantics.
I largely agree with your critique, but more as a description of a different book that could have been written in this book's place. For example, a book on philosophy applying the results of this book's methodology, of which chapter 25 is a poor substitute. Or books drilling into one particular area in more detail with careful connections to the literature. This book serves better as an inspiring manifesto.
While these chapters are enlightening, they depend too heavily on the earlier account of metaphor, rarely draw upon other findings in cognitive science that are likely relevant, are sparse in scientific citations, and (as I've said) rarely cite actual philosophers claiming the things they say that philosophers claim.
Why is the dependence on the earlier theory of metaphor a problem?
Do you think the authors misrepresent what philosophers claim, in those chapters addressing philosophy (15-24) rather than (informal) philosophical ideas (9-14)?
Lakoff & Johnson's Philosophy in the Flesh (1999) is an ambitious 550-page attempt to rewrite philosophy from scratch given what we now know from the cognitive sciences about how human reasoning works. After reading the first page, I had some hope it would be the book I could hand to somebody who wanted to study philosophy without being corrupted by studying 2500 years worth of bad methods and wrong answers.
Yet, while I agree with the book in broad strokes and in many particular details, it has several weaknesses that make it difficult to engage at a technical level. These problems may be part of why the book has 1400+ citations on Google Scholar even though there are almost no books or articles that engage its contents in detail.
The biggest problem is that Lakoff and Johnson cover too much ground, and therefore don't have the space to defend or even explain the precise nature of the thousands of claims they make in the book. E.g.: Several times per chapter, they claim that philosophers assume X without citing a single philosopher in the business of claiming X, or even someone else claiming that philosophers often assume X.
The majority of the book (chapters 9-24) engages directly in what Eliezer calls "dissolving the question" — at least, the part where one explains the cognitive science of how particular philosophical confusions and debates arise. While these chapters are enlightening, they depend too heavily on the earlier account of metaphor, rarely draw upon other findings in cognitive science that are likely relevant, are sparse in scientific citations, and (as I've said) rarely cite actual philosophers claiming the things they say that philosophers claim.
The authors are also too unclear about their positive project: "embodied philosophy." Nowhere do they state the propositions that make up what they call "embodied philosophy," nowhere do they explicate those propositions in precise detail, and nowhere do they defend those propositions in detail from misinterpretation and objection. The reader is left with only a vague sense of what they mean by embodied philosophy, or why it should be favored over other forms of naturalistic philosophy that have been defined and defended more precisely by their proponents. (Compare, for example, Bishop & Trout's clear explication and defense of "strategic reliabilism" in Epistemology and the Psychology of Human Judgment.)
There are only two subjects the authors treat in sufficient detail. The first is the section on how thoroughly human thought is metaphorical, which builds on their earlier Metaphors We Live By (1980). This section (chapters 4 & 5) is excellent, and worth reading if you read nothing else of the book.
The other subject treated in sufficient detail is Noam Chomsky (chapter 22). This is not surprising because it is the other major subject of Lakoff's career. Lakoff has spent decades promoting his generative semantics over Chomsky's generative grammar.
The book's deficiencies are frustrating to someone of a "scholarly technical cogsci/philosophy" bent like myself, but they may actually make the book more readable to those whose primary interest isn't technical philosophy. Philosophy in the Flesh is full of ideas, many of them correct or half-correct, and may be worth reading just to get a broad picture of what philosophy might look like when you start from scratch with the latest cognitive science.