Abstract
The thesis of the paper is that semiotic processes are intrinsic to computation and computational systems. An explanation of computation that does not take this semiotic dimension into account is incomplete. Semiosis is essential to computation and therefore requires a rigorous definition. To prove this thesis, the author analyzes two concepts of computation: the Turing machine and the mechanistic conception of physical computation. The paper is organized in two parts. The first part (Sects. 2 and 3) develops a re-interpretation of the Turing machine starting from Peirce’s semiotics. The author shows how this reinterpretation allows overcoming the dualism between a purist and a realist version of the Turing machine. The second part of the paper (Sect. 4) shows how a mechanistic explanation of physical computation such as the one developed by Piccinini is incomplete without considering semiotic relations. The paper intends to be a contribution to the philosophical debate on computation.
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15 November 2022
A Correction to this paper has been published: https://doi.org/10.1007/s10699-022-09884-8
Notes
This paper is a re-formulation and development of Possati (2022, Chap. 5).
Peirce played a small role in the history of the computer along with his disciple Alan Marquand. Peirce was the first to propose a computer built from electric circuits, and thus saw his own theory as amenable to computation. I thank the anonymous reviewer for this note.
Here a purist description of TM: “A Turing machine is a specific kind of idealized machine for carrying out computations, especially computations on positive integers represented in monadic notation. We suppose that the computation takes place on a tape, marked into squares, which is unending in both directions—either because it is actually infinite or because there is someone stationed at each end to add extra blank squares as needed. Each square either is blank, or has a stroke printed on it. (We represent the blank by S0 or 0 or most often B, and the stroke by S1 or | or most often 1, depending on the context.) And with at most a finite number of exceptions, all squares are blank, both initially and at each subsequent stage of the computation. At each stage of the computation, the computer (that is, the human or mechanical agent doing the computation) is scanning some one square of the tape.” (Boolos et al., 2007, 25).
For a comment on the passage, see Spinks (1991, 52–53).
I do not want to analyze the oscillation, very present in Peirce’s texts, between a psychological reading and a communicative and non-psychological reading of the concept of semiosis. See Fadda (2013, 173–175).
I cannot analyze here, for reasons of space, on the debate on iconism in 1970–1980 semiotics. I only mention the famous criticisms of Goodman and Eco. I quote, in response to these criticisms, the position of Deacon (a long but important passage): “When we apply these terms to particular things, for instance, calling a particular sculpture an icon, a speedometer an indicator, or a coat of arms a symbol, we are engaging in a sort of tacit shorthand. What we usually mean is that they were designed to be interpreted that way, or are highly likely to be interpreted that way. So, for example, a striking resemblance does not make one thing an icon of another. Only when considering the features of one brings the other to mind because of this resemblance is the relationship iconic. Similarity does not cause iconicity, nor is iconicity the physical relationship of similarity. It is a kind of inferential process that is based on recognizing a similarity. As critics of the concept of iconicity have often pointed out, almost anything could be considered an icon of anything else, depending on the vagueness of the similarity considered. The same point can be made for each of the other two modes of referential relationship: neither physical connection nor involvement in some conventional activity dictates that something is indexical or symbolic, respectively. Only when these are the basis by which one thing invokes another are we justified in calling their relationship indexical or symbolic” (Deacon, 1997, 71).
I refer here to the manuscripts cited by Bellucci (2017). By the abbreviation R I refer to A Harvard manuscript (Charles S. Peirce Papers, 1787–1951, MS Am 1632, Houghton Library, Harvard University) as listed in Richard Robin, Annotated Catalog of the Papers of Charles S. Peirce (Amherst: University of Massachusetts Press, 1967); the abbreviation CSP refers to the Peirce pagination.
Piccinini does not deny that computational systems can be semantic. He only states that these systems do not presuppose semantics. “Of course, many (though not all) computational vehicles do have semantic properties, and such semantic properties can be used to individuate computing systems and the functions they compute. The functions computed by physical systems that operate over representations can be individuated either semantically or non-semantically; the mechanistic account provides non-semantic individuation conditions” (Piccinini, 2015, 118).
The vehicles are not exactly identical to the components; vehicles are not objects with a fixed state, but concrete or abstract variables; see Piccinini (2015, 119).
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Possati, L.M. From Turing to Peirce. A semiotic interpretation of computation. Found Sci 28, 1085–1110 (2023). https://doi.org/10.1007/s10699-022-09878-6
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DOI: https://doi.org/10.1007/s10699-022-09878-6