I've taught the Lakoff and Johnson in IB Theory of Knowledge classes.
Their assertion is so simple it's revolutionary: metaphors aren't embellishment. They are the engine that drives the train. From Aristotle through the 20th century metaphors were given short shrift. L and J bring them to the epistimological forefront. Even the most abstract expressions are fodder for L and J. For example:
Who put that idea into your head?
Here "your head" is a container. "Idea" in an object that goes into the container.
This type of statement falls into their "conduit category" which applies to but doesn't exhaust abstract thought.
In general the mind is filled (metaphor) with metaphorical domains
The domains may or may not inter-relate. Take "fishing."
He took the bait.
He's a sucker; just reel him in.
He's a shrink. He fishes in deep water.
and so on.
THinkl of the language we use to deal with an argument:
I blew him out of the water.
I destroyed him.
To argue we use the language of war. L and J put the question: what if we used the language of dance? Instead of destruction we might talk about in synch, harmony, moving together, in rhythm.
I don't think L and J are engaging the "what is a metaphor" discussion per se. As the name "cognitive" suggests, they're claiming that we think by metaphor.
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