Invariance Again
The metaphors I have discussed primarily map three kinds of image-schemas:
Because of the complexity of the sub-cases and interactions, the details are intricate, to say the least. However, the Invariance Principle does make claims in each case as to what image-schemas get mapped onto target domains. I will not go through most of the details here, but so far as I can see, the claims made about inferential structure are reasonable ones. For example, the logic of force dynamics does seem to map, via the submapping CAUSES ARE FORCES, onto the logic of causation. The following are inferences from the logic of forces inherent in force dynamics:
These are among the classic inferential conditions on causation: spatial contiguity, temporal precedence, and that A caused B only if B wouldn't have happened without A. At this point, I would like to take up the question of what else the Invariance Principle would buy us. I will consider two cases that arose while Mark Turner and I were writing More Than Cool Reason (Lakoff & Turner, 1989). The first concerns image-metaphors and the second, generic-level metaphors. But before I move on to those topics, I should point an important consequence of invariance. Johnson and I argued in Metaphors We Live By (Lakoff & Johnson, 1980) that a complex propositional structure could be mapped by metaphor onto another domain. The main example we gave was ARGUMENT AS WAR. Kovecses and I, in our analysis of anger metaphors (Lakoff, 1987, case study 1, Kovecses, 1990), also argued that metaphors could map complex propositional structures. The Invariance Principle does not deny this, but it puts those claims in a very different light. Complex propositional structures involve concepts like time, states, changes, causes, purposes, quantity scales, and categories. If all of these abstract concepts are characterized metaphorically, then the Invariance Principle claims that what we had called propositional structure is really image-schematic structure. In other words: So-called propositional inferences arise from the inherent topological structure of the image-schemas mapped by metaphor onto concepts like time, states, changes, actions, causes, purposes, means, quantity, and categories. The reason that I have taken the trouble to discuss all those abstract concepts is to demonstrate this consequence of the Invariance Principle; namely, that what have been seen in the past as propositional inferences are really image-based inferences. If the Invariance Principle is correct, it has a remarkable consequence, namely that: Abstract reasoning is a special case of imaged-based reasoning. Image-based reasoning is fundamental and abstract reasoning is image-based reasoning under metaphorical projections to abstract domains. To look for independent confirmation of the Invariance Principle, let us turn to image-metaphors.
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