Abstract
Kripke’s argument against functionalism extended to physical computers poses a deep philosophical problem (not previously addressed in the literature) for understanding the standard view of what computers are. The problem puts into jeopardy the definition in the standard view that computers are physical machines for performing physical computations. Indeed, it is entirely possible that, unless this philosophical problem is resolved, we will never have a good understanding of computers and may never know just what they are.
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Three well-known computer science texts which express the standard view of what computers are: Hennessy and Patterson (1994), Aho et al. (1982) and Sedgewick and Wayne (2017). Hennessy and Patterson define the classical components of a computer as: memory, processor (control and the datapath), input and output.
Since there are different philosophical views concerning the nature of (abstract) computation and physical computation, there are correspondingly different philosophical views as to what is a physical computer (compatible with the standard view’s definition of a physical computer). Although my target is the view of computers held by most computer scientists (the standard view), I will examine some of the philosophical views on the nature of physical computation. The problem which I pose for the standard view arises on these different philosophical views about the nature of physical computation. For a first-rate exposition of different philosophical views on the nature of physical computation, see Piccinini (2015).
Turing (1936–1937).
See, for example, an important work on explicating the concept of an algorithm, Dean (2007).
Scott and Strachey (1971).
vanBenthem (1995). It would be a mistake to claim that a logic viewed in this way is a computer. The rules of inference in, say, sentential calculus (embodying various truth-functions) direct the flow of information through the proofs in which they are employed. However, we can program a physical computer to make those inferences by performing various physical computations.
McCune (1997).
Haken and Appel (1977).
One might object that computers are more than just physical devices for performing physical computations—that they are used to, for example, communicate (the Internet), display images and sounds, store and record information (including images and sounds). This objection can be easily defused. For instance, images and sounds are data structures which can be manipulated by a physical computation.
Teller (1980).
John H. Conway is quoted in an article in the New York Times on the use of computers in mathematical proofs, by Kenneth Chang, April 6, 2004, In math, computers don’t lie. Or do they?
Davis and Cerutti (1969).
Wittgenstein (2009).
For a full exposition of Kripke’s argument against functionalism as it applies to both human minds and to physical computers (that are not human beings), see Buechner (2011). Kripke’s argument against functionalism has never been published—the exposition of it in Buechner (2011) uses, among other things, a transcript of a talk Kripke gave in 1984 and tape recordings of different versions of the talk he gave in the early 1980s. Buechner (2011) does not (except when directly quoting) separate what Kripke says from what Buechner says about what Kripke says about how to refute functionalism. Additionally, Kripke in his talks applies his argument to the use of functionalism to describe human mental states (including mental states in which computations are performed). In this paper I show how his argument can be applied to physical computers (that are not human beings).
Which user of a given physical computer gets to make such stipulations? What competence(s) must such a user possess? These are difficult questions which will not be addressed here. For analogous questions concerning who gets to make the conventions as to what words mean in a community of language users, see Kripke (1982, especially Chapter Three).
I thank an anonymous referee for comments which helped me formulate this weak version of skepticism and for asking for an argument which shows that it is false that Kripke’s argument against functionalism extended to physical computers is nothing more than a form of weak skepticism. My definition of weak skepticism is that it is a skeptical claim against some knowledge claim which leaves open evidence sources which can be used to justify that knowledge claim. Strong skepticism is a skeptical claim against some knowledge claim which leaves open no sources of evidence which could be used to justify that knowledge claim. The material in this section is not in Buechner (2011).
I have considerably simplified this discussion in two ways. First, at each node there will be four pathways exiting it: normal in computation of F, breakdown in computation of G, breakdown in computation of F, normal in computation of G. Second, the introduction of new functions growth will be, for instance, 3N where there are two different kinds of physical breakdown, in each one of which a different function is physically computed. I assume in the discussion only one kind of breakdown and two pathways exiting each node.
Putnam (1981).
See Piccinini (2015), op. cit. I thank an anonymous referee of this paper for motivating the inclusion of this section.
Piccinini (2015), op. cit., p. 10.
See Piccinini (2015), op. cit., pp. 44–45.
Kripke (1982), op. cit.
Stabler (1987).
Monty Python Flying Circus Episode 35 Chapter 5: Mystico and Janet—Flats Built By Hypnosis https://www.youtube.com/watch?v=1ujRE2IkEIo.
Many thanks to the two anonymous referees whose comments were a great help in improving this paper.
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Buechner, J. Does Kripke’s Argument Against Functionalism Undermine the Standard View of What Computers Are?. Minds & Machines 28, 491–513 (2018). https://doi.org/10.1007/s11023-018-9466-5
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DOI: https://doi.org/10.1007/s11023-018-9466-5