Abstract
We’re now ready to use the analogies we’ve generated. Analogies are used to generate and interpret metaphors. For those uses, it’s necessary to move knowledge from the source description to the target (it’s especially important to move source rules). This movement is analogical transference. Analogical transference is ampliative: it creates new propositions in the target description. These may be literal or metaphorical, true or false.
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Notes
Kittay’s metaphorical function as fm should not be confused with my analogical mapping function fM. Kittay defines her fM like this: “When we interpret a metaphor whose topic domain is already structured, we make that function homomorphic, that is, we make the function a relation-preserving mapping from some subset of the semantic field of the vehicle to a subset of the content domain of the topic. If the metaphor’s target (or the relevant portion thereof) is unstructured, the function induces the structure of the relations from the relevant portion of the field of the vehicle” (pp. 168–9; emphasis original). But this is exactly the description of my analogical transference operator a.
Contradiction is relative to the map fM- In the SOCRATES IS A MIDWIFE analogy, inversion on the gender axis [male / female] and inversion on the ontological axis [intellectual / material] are significant (the analogy asserts that males are to intellectual things as females are to material things). The map fM captures these inversions by mapping [female] onto [male] and [material] onto [intellectual] so that [female] is to [male] as [material] is to [intellectual] — an aspect of Greek misogyny. The more logical result is that source and target are symmetric under inversion of gender and ontology, so that [woman] and [material] belong to the positive analogy.
Abstract concepts transferred from the source are often literal in the target.
According to Kittay (1987), subsymbolic analogical transference induces a metaphorical lexical articulation over the target content domain. According to Fillmore (1977), “metaphor consists in using, in connection with one scene, a word — or perhaps a whole frame — that is known by both speaker and hearer to be more fundamentally associated with a different scene” (p. 70). Fillmore’s scene (the source scene) is a source content domain; Fillmore’s frame (the topic frame) is part of the target conceptual field. Metaphor based on subsymbolic analogical transference involves transference of some part of the source frame to the target based on an analogy between source and target scenes.
The metaphorical application of terms from non-auditory modalities to the auditory modality has been extensively studied (cf. Brown, Leiter & Hildum, 1957). Transferring a contrast from the gustatory modality, one speaks of “sour notes” and “sweet refrains”. Transferring a contrast from the tactile modality, one speaks of “flat” and “sharp” notes. But the most pervasive and extensive transference comes from vision. The cross-modality mapping from the visual modality to the auditory modality supports a projective analogy that produces a visual language for sound and music. Sound is spoken of as if it were seen. We speak of “high” and “low” notes. Musical tunes seem to occupy an auditory space with a Euclidean geometry, to rise and fall, to weave in and out of each other. Two classical studies by Odbert and Karwoski on synesthetic thinking reveal the use of metaphorical observational language. In their first study, Odbert, Karwoski & Eckerson (1942) reveal how a cross-modal analogy between vision and audition supports the metaphorical application of color terms to music. In their second study, Karwoski, Odbert & Osgood (1942) discuss how the cross-modal analogy between vision and audition supports metaphorical language for music such as “angular” or “rounded”.
Because it is possible to understand a given target first in terms of one source, and second in terms of another, the concepts and connections added by analogical transference cannot initially be permanent. If they were, the changes introduced by the first analogy would interfere with comprehension of the second. For example, when reading Plato’s Theaetetus we are first offered the analogy MEMORY IS A WAX TABLET and then the analogy MEMORY IS AN AVIARY. It is clear that we are able to first comprehend the MEMORY IS A WAX TABLET analogy and then to comprehend the MEMORY IS AN AVIARY analogy based on essentially the same understanding of the target field [memory]. In order to be able to do this, the concepts and connections first added by analogical transference for the MEMORY IS A WAX TABLET analogy must be deleted from long-term memory prior to processing the MEMORY IS AN AVIARY analogy. To be able to delete the connections added by analogical transference when required, it is necessary to distinguish them from other connections in long-term memory. So I label those connections TEMPORARY; such connections are deletable. Deletion of all the connections in which a concept participates causes deletion of the concept. If all the TEMPORARY connections introduced by analogical transference are removed, the transferred concepts are removed (from the target).
It is expected that rules encode either formal or well-justified relations among source propositions, such as lexical entailments or (idealized) causal relations. The rules transferred are just those native to the source.
In Figure 10, double-arrowed lines indicate analogical correspondence, and [menstrual-cycle] has been abbreviated to [cycle].
One reason to think that inductive arguments justify their conclusions is that they are deductively valid in their limiting cases. The limiting case of an argument by similarity occurs if either its two objects x and y are numerically identical or if the features in premises of the argument necessarily determine the features in the conclusion. Necessary determination occurs in mathematics: X has 3 sides & is a plane figure & has angles that sum to 180; Y has 3 sides & is a plane figure; therefore, Y has angles that sum to 180 degrees. The limiting case of an argument by analogy occurs if the source and target are isomorphic (perfect analogy) and if the corresponding objects are exactly of the same type (e.g. there are isomorphic games, and in abstract algebra, isomorphic groups). Since the limiting cases of arguments by similarity and analogy are deductively valid, it seems reasonable to infer that there are cases that converge to these limits.
The probability of the transferred source proposition is not necessarily the same as that of the source proposition itself. The probability of the transferred proposition depends on a complete statistical analysis of the two domains and their determination relations.
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Steinhart, E.C. (2001). Analogical Transference. In: The Logic of Metaphor. Synthese Library, vol 299. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9654-1_5
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