01 April 2005

Questions for the Audience, and For Readers

In a somewhat novel twist, at one point O'Rourke interrupted the question-and-answer session in order to pose questions to the audience. I'll pose them to you.

1. It's easy to think of examples of metaphors where a word for something perceptible is used to talk about something ostensibly imperceptible. But are there any metaphors where a word for some imperceptible thing is used to talk about some other imperceptible thing? (Construe 'perceptible' broadly, so that, for instance, the sequence of time in a day, already mentioned, counts as perceptible.)

2. There seems to be an aspect of 'impropriety' (as it is called) in a metaphor, because a metaphor implies the transfer of a term from its proper domain to some domain in which it does not belong. (The proper domain is that in which the term is used 'strictly' or 'literally', kuriws.) What licenses the transfer, despite the impropriety, is some action or function of what we wish to talk about (or so O'Rourke wished to claim). Or is this not true--Can one think of some metaphorical use of term, where the metaphor is not underwritten by the action or function of what one wants to talk about?

3. A similarity of relations is an analogy, e.g. cup:Dionysus::shield:Ares. But should an identity of relations also be counted as an analogy, e.g. 2:4::3:6 ? And, if so, would it license a metaphor? What would be an example of this?


Wes DeMarco said...

I want to post the case of Gell-Mann’s use of symmetry groups as example of a metaphor not grounded in sensation. The original proposal of the existence of an omega minus particle was based on a pure structural analogy that ought to be called metaphorical in the way Fran used the term. For one thing, the theory itself was based on a purely abstract structural similarity between symmetry groups (SU(2)) and (SU(3)). Moreover, this is usefully styled a metaphor in his sense (though not, I argue elsewhere, in Lakoff’s sense!) because what suggested the analogy was certain formal features of the notation. That is, at issue here are purely incidental features of the source structure. This is a fairly well known case in phil of science circles. Mark Steiner provides the best discussion, and it is one that emphasizes the role of notation and the sheerly incidental character of the features that suggested the analogy. See The Applicability of Mathematics as a Philosophical Problem, especially pp. 70-2, 116-35, 136-76. Other examples discussed in his book may be worth considering in connection with the question, since Steiner defines a formal analogy as “one based on the syntax or even orthography of the language or notation of physical theories, rather than what (if anything) it expresses” (54, emph. added).
In sum, I maintain that the Gell-Mann symmetry group example is better than Michael Pakaluk’s example of the use of denumeration in the context of rational numbers, since most mathematicians who use it at all believe that it is a proper use and not at all based on incidentals.
There are other examples of structural transfer. An ecological biologist whose name escapes me at the moment (I could look it up) has been inspired by the periodic table of elements to generate a systematic table of types ecological niche. That is not the only grid inspired by the periodic table. Though the table can be arranged a number of different ways, any useful ordering will still reflect some intrinsic feature of the elements—atomic number, for instance. This transfer is metaphorical if the corresponding features of the new table are not similarly intrinsic; if not, then not.
Lakoff and Nunez’s Where Mathematics Comes From is chock full of cases that they claim are metaphorical and which, if metaphorical would provide you with examples. They speak of Boole’s metaphor, Weiserstrass’ metaphorical masterpiece, etc., etc. The issue is whether these are really metaphors in the sense that interests you or not. I have an unsolicited critical essay on this work (“Math in the Flesh”), conference-size, if anyone’s interested.
Some of the most interesting cases are philosophical. Leibniz takes an operation of mind (perception) as an operation of being. Whitehead does something similar with prehension. These authors would not agree that the mental aspect is already a metaphor grounded in sensation, but would insist it is instead immediately intuited in its character. For an example even more clearly removed from sensation, we could consider Whiteheadian creativity, which is arguably based on a generalized notion of function. Pepper, notoriously, claimed that a ‘root metaphor’ underlies every grand philosophical scheme. The trouble with Pepper’s claim, as with all these others, is that what the outsider or critic claims is metaphorical, the insider or advocate claims is analogous or literal. Aristotle claimed ‘participation’ is metaphorical and ‘teleology’ is not; most today would claim that teleology too is metaphorical because purposiveness is not proper to nonhuman nature. Is metaphysical organicism a metaphor writ large, or is it a proper analogy? The philosophical cases all raise this issue.
At long last, I want to remark on the second of Fran’s questions, reiterated by Michael, concerning the role of metaphor in the description of mental functions. I argue that there are certain operations that function on the side of ‘mental’ being and also on the side of ‘physical’ being. Examples include inclusion and exclusion, segmenting and sequencing, inversion and reversal, expansion and contraction, gathering and scattering. On this view, talk of gathering thoughts or reversing sense, or expanding meaning is not metaphorical even though we may learn first about such operations by means of sensible examples in physical domains. That is just to say such examples are ‘first for us,’ though I argue that we may also experience them directly as mental operations. Plainly segmenting and sequencing, inclusion and exclusion and so on play different roles in the several domains. But I believe it prejudices the issue to suppose that because we can point to physical examples and because these are often (if not always) ‘first for us,’ that the use of them in reference to mental operations must be metaphorical. I mentioned some of these examples at the talk, and Fran retorted that they seemed metaphorical to him, presumably because they do have obvious physical application. As I noted at that time, anyone who claims that an operation is equally at home in mental and physical domains leaves himself open to the charge that it is metaphorical on the mental side, precisely because we can refer to physical examples. However, the inference from the existence of a literal physical application to the metaphorical nature of the mental application is a bogus inference. I offer a more elaborate case in “The Generation and Destruction of Categories,” in Gorman and Sanford (eds.) Categories: Historical and Systematic Essays (CUA Press, 2004), an essay that is, in a way, an effort to make metaphysical hay of the strongest elements of the best empiricist approaches to language and mind.

--Wes DeMarco