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Analog Representation and the Parts Principle

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Analog representation is often cast in terms of an engineering distinction between smooth and discrete systems. The engineering notion cuts across interesting representational categories, however, so it is poorly suited to thinking about kinds of representation. This paper suggests that analog representations support a pattern of interaction, specifically open-ended searches for content across levels of abstraction. They support the pattern by sharing a structure with what they represent. Continuous systems that satisfy the engineering notion are exemplars of this kind because they are uninterpretable unless they are structure-preserving. Analog representations, so understood, include pictures, images, diagrams, and most graphs. This conception of analogicity also fits well with a line of thought about what makes perceptual states distinctive: they satisfy a “parts principle”.

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  1. Haugeland’s paper “Analog and analog” appeared in 1981. Page references are to the anthologized version (Haugeland 1998).

  2. Perhaps some inscriptions are such that we cannot tell whether they are ‘C’s, ‘G’s, or neither. In that case, the Roman alphabet would fail the test of syntactic finite differentiation. See Goodman (1968, 137–139) for discussion. This is not directly relevant to syntactic density, however, so we can leave the point here.

  3. Matthew Katz (2008, 405) also stresses the fact, following Goodman, that in analog representation we cannot know the syntactic identity of any given representation, but he, like Goodman, didn’t notice any semantic consequences of this fact. As we will see in the next section, this is precisely where we find the action in understanding analog representation.

  4. Haugeland conflated the second and third points just made. Analog systems are sensitive, in Haugeland’s sense, when “not only are all variations allowed, but they all matter.” (1998, 83). In line with the second point above, they all matter syntactically, and they also, in line with the third point, matter semantically. At the end of this section it will be clear that this conflation is reasonable, but to see why it’s reasonable these two conditions need to be kept apart.

  5. This suggestion comports poorly with the mechanism behind a mercury thermometer, but we can leave that point to one side for present purposes.

  6. Bach offers this specifically as an amendment to Goodman’s account of pictorial representation. Goodman thought that pictorial representation was simply a species of syntactically and semantically dense representation, in which relatively many qualities—color, shape, shading—matter to a representation’s identity. Pictures are relatively replete (Goodman 1968, 230).

  7. Haugeland avoids semantics talk in his article, because “in my view digital [and analog] devices are not necessarily representational or symbolic” (1998, 88n2). The position of a potentiometer does not represent the brightness of the lights, but dimmers are analog devices. Notice that even if some analog devices are not representational, analogicity is essentially relational. Changes in the states of one thing relate to changes in the states of another in a systematic, structure-preserving fashion. This paper focuses on analog representation, but the phenomenon is not limited to representation.

  8. As one might expect, these two are related, which we will see. Coming at things from a different angle, Philip Kitcher and Achille Varzi say pictures and many maps are worth “a vast infinity of sentences.” (2000, 377)

  9. Notice that there are not indefinitely many abstractions available with the thermometer that has one-degree resolution. This is because there are not indefinitely many ways of abstracting over the finitely many readings the thermometer can muster. There are more than we could ever care about, but there are not indefinitely many. This is how resolution—the maximum information delivered by any given reading—interacts with the number of available abstractions.

  10. I am not claiming that a representation is digital if it fails to be analog. No account of digital representation is on offer here. Analog and digital make a nice contrast, but no account of the distinction suggests that they jointly cover the range of representation. So, one needn’t offer an account of both at once.

  11. These claims are all formulated in terms of “pictures”, but they can actually be understood a lot more broadly, as we will see. Casati and Varzi (1999) appeal to a related claim in working out a semantics of maps and Kulvicki (2006, 59n2) discusses it in relation to pictorial transparency. See Balog (2009) for a critical discussion of Fodor’s proposal and Kulvicki (2014, Ch 8) where I discuss the following way to think of the parts principle, though I did not notice the connection there to analog representation.

  12. Fred Dretske (1981, 135–141) appropriates the analog-digital distinction in the service of understanding the distinction between sensation, on the one hand, and thought-like states, on the other. He uses the terms ‘analog’ and ‘digital’ in a distinctive manner that does not fit with the present proposal. Elsewhere, however, I suggest a way of emending his view that makes it easy to show how the present conception of analog representation fits well with his account of sensory states (Kulvicki 2004, 383–389; 2007, 361–364).

  13. I thank two anonymous referees, the editors of this special issue, and Eliot Michaelson for their very useful comments. Audiences at Dartmouth College, Rice University, the University of Auckland, and the Kunstakademie Düsseldorf also provided helpful feedback. This research was supported by a Dartmouth College Scholarly Research and Advancement Award.


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Kulvicki, J. Analog Representation and the Parts Principle. Rev.Phil.Psych. 6, 165–180 (2015).

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