From Molecule to Metaphor (2006), chapters 15-17

These three chapters in Feldman's book are based on the classes he and George Lakoff give together at Berkeley. They describe Lakoff's theory of metaphor as we know it from countless other sources.

Primary Metaphor and the Basis of Meaning
Feldman begins by repeating the well-known theory that meaning grows out of first-hand experience:

For perception, action, emotions, and so on, human experience and the social relations shared by all people provide the basis for learning words. (p. 185)

[...] abstract, cultural, and technical words and concepts arise from the opulent substrate of direct experience. [...] people, as neural systems, understand abstract ideas because these concepts are mapped to and actiavte brain curcuits involved in embodied experience. (p. 185)

There is now very strong evidence that essentially all of our cultural, abstract, and theoretical concepts derive their meanings by mapping, through metaphor, to the embodied experiential concepts we explored in earlier chapters. (p. 199)

Bi-directional Metaphor and Scaffolding
Lakoff (through Feldman) makes a curious remark in the middle of chapter 16:

Once a domain of knowledge becomes well known, it can itself serve as a source domain (basis) for understanding more novel concepts. We sometimes get metaphors mapping both ways, for example, between war and sports. These create no difficulty---the appropriate concepts in each domain are activated and inferences are drawn from the combined activation. (p. 209)

And nothing more is said of that matter. This seem to be essentially Lakoff falsifying Lakoff: Saying at once that metaphors need not go "all the way down" and still claiming that they do.

More concretely, the first sentence seems to oscillate between to claims depending on which way the evidence goes: Either it means that we learn new things by comparing them to old (which everyone agrees on); or else it means that the connection between the new subject matter and the old are permanently established and remain in use (which is false).

I don't know exactly what it means that "the appropriate concepts in each domain are activated and inferences are drawn from the combined activation," and Feldman/Lakoff doesn't explain. Is the target domain known or not known? Is any information actually transferred, and if so, what?

The Invariance Principle Returns
They also repeat what Lakoff said twenty years ago:

Metaphorical mappings preserve the cognitive topology (that is, the frame and schema structure) of the source domain, in a way consistent with the inherent structure of the target domain. This is called the invariance principle. (p. 209-10)

Or, equivalently: metaphors preserve structure except when they don't. They continue:

As a consequence, the image-schematic structure of the target domain cannot be violated: one cannot find cases in which a source domain interior is mapped onto a target domain exterior, or a source domain exterior is mapped onto a target domain path. This simply does not happen. (p. 210)

But since the target domains don't have literal paths, this could hardly be more than a tautology. There would be no way to identify whether the thing we map the interior onto actually is an "interior," since no such thing is there.

The only way we could in principle falsify this claim would be if we could find some case where the metaphorical outside of the target domain could also be the metaphorical inside. Such cases do indeed exist and thus falsify Lakoff's claim. Examples are HOT/COOL IS FASHIONABLE, UPHILL/DOWNHILL IS DIFFICULT, and THICK/THIN IS IMPLAUSIBLE.