What are the key differences between Conceptual Metaphor and Propositional Metaphor?
Both, I think, can be justly pictured thusly:
Mapping between source and target domains
The difference is in (1) what sentences are *for* and (2) what reasoning happens where.
**What sentences are for**
In Propositional Metaphor, sentences/statements/utterances are *truth-valued* statements.
In Conceptual Metaphor, sentences don't have to be truth-valued. Their purpose is to support decision-making, ultimately causing action in the world.
**What reasoning happens where**
In Propositional Metaphor, a statement in the Source Domain is *false*. When a speaker says, "What you just said flew right over my head," nothing of the sort happened.
The brain has the responsibility of solving the puzzle "What true statement might the speaker have meant?"
In the context of a conversation, and assuming an interlocutor who's playing by the rules, the brain can deduce that what was meant was the *true* statement "I didn't understand."
If the listener wants to reason about what to do with that new information, the reasoning is done in the Target Domain of the translated sentence, using the true version. Nothing further happens in the Source Domain.
In Conceptual Metaphor, reasoning – problem-solving – happens primarily in the Source Domain. The brain reasons from its prior understanding of things going over other things. Things that fly over other things are not accessible once they're past. If the brain is viewed as a container, they did not become contained by it.
*After* that reasoning, the conclusions are mapped into the Target Domain, and the brain "asks" "What might they mean here?... Ah, the content of the message was not retained by my interlocutor's brain."
Thereafter, the answer to the question "What to do about it?" is at least informed by the Target Domain." For example, one thing you could do with a thing that goes too far is to throw it more slowly." That's not very helpful. Perhaps – I admit this is a stretch – the answer could be "throw it more directly at what you want to hit," which could arguably be interpreted in the Target Domain as "Tailor the message better to the listener."