Abstract
This paper argues that the idea of a computer is unique. Calculators and analog computers are not different ideas about computers, and nature does not compute by itself. Computers, once clearly defined in all their terms and mechanisms, rather than enumerated by behavioral examples, can be more than instrumental tools in science, and more than source of analogies and taxonomies in philosophy. They can help us understand semantic content and its relation to form. This can be achieved because they have the potential to do more than calculators, which are computers that are designed not to learn. Today’s computers are not designed to learn; rather, they are designed to support learning; therefore, any theory of content tested by computers that currently exist must be of an empirical, rather than a formal nature. If they are designed someday to learn, we will see a change in roles, requiring an empirical theory about the Turing architecture’s content, using the primitives of learning machines. This way of thinking, which I call the intensional view of computers, avoids the problems of analogies between minds and computers. It focuses on the constitutive properties of computers, such as showing clearly how they can help us avoid the infinite regress in interpretation, and how we can clarify the terms of the suggested mechanisms to facilitate a useful debate. Within the intensional view, syntax and content in the context of computers become two ends of physically realizing correspondence problems in various domains.
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Notes
The test compares two physical medium-independent verbal exchanges with a machine and a human, and which is which is decided by a human questioner.
The combinators S and K are respectively the lambda terms \(\lambda x\lambda y\lambda z.xz(yz)\) and \(\lambda x\lambda y.x\).
A compiler is a program which translates from one programming language to another. Typically, the target language is a lower-level language than the source language. The final process in compiling is called code generation, by which all intermediate representations of levels of translations are dispensed with, and the code is solely in the form of the primitive instruction set of the intended architecture. There is no syntactic translation at run-time of compiled programs; it is just execution.
Take f to be the representation relation. It can be for example \(f(\text{ low } \text{ voltage })=0\), meaning we map the physical property of low voltage to bit 0. Decoding and encoding are different uses of a representation. Decoding is essentially using f. Encoding is using \(f^{-1}\). For example, when we type ’a’ in our word processor, we encode whatever physical property—some voltage levels—is assigned to it down below. Therefore good representations are needed technologically, both in digital and analog computers, to be sure about the physical component.
The authors note that the compute cycle is the reverse of the experiment cycle in for example physics. In physics we let the abstract level do its work, then encode its result in some physical object to see if the theory predicted its presence, location etc. correctly, as in Fig. 2a. The physical level does not do the work; its work is predicted. In the case of computers, the physical layer does the work—therefore it is not a simulation, and the result is tried to be predicted by an algorithm or an analogy (implicitly computes relation) of Fig. 1, as in Fig. 2b. Notice that what allows the physical layer to carry out its work is a series of translations of say the averaging algorithm or equations to the terms of the computer. We compare its physical work with the prediction at the abstract level, i.e. by an algorithm or equation.
Notice also that a computer scientist seeking an explanation has to reverse the modeling relation too, after it is established. Because it only serves to establish the correctness of the algorithm, assuming the underlying physical machinery was confirmed. What we do with the corrected algorithm afterwards is much like the diagram in Fig. 2a. Therefore physics and computer science may differ on how they use the model-theory-technology cycles, but it is clear that what amounts to theory in physics and computer science is based on the same process of thinking.
One implication of this result is that nothing computes in nature unless we map it to a computational problem in our thinking. Pancomputationalism and born-again computationalism seem to be some form of analogical (if not romantic) reasoning. ACM’s (2012) centenary celebration of Turing by all the living Turing-award winners makes the point quite clear: “This development [algorithmic thinking outside computer science] is an exquisite unintended consequence of the fact that there is latent computation underlying each of these phenomena [cells, brains, market, universe, etc.], or the ways in which science studies them.” [emphasis added]
Nature-inspired computing is not to be confused with ‘nature computes’ movement. Personally, I would not lose too much sleep if some problems are not amenable to computationalist understanding. Discovery by method has its limits.
Algorithmic complexity theory is based on Turing’s notion of ‘next’, such as the next step, next state, and next input. Problem size in the theory is measured with this concept. It is not a physical concept, but obviously physically realizable; see Bozşahin (2016) for more philosophical implications.
Problems in P have polynomial solutions, where polynomial is on the problem size in the sense of footnote 7. NP problems can check a given solution with polynomial effort. Whether P and NP are the same is an open problem in computer science, with serious implications in economics, social sciences and natural sciences; see Fortnow (2013) for an entertaining coverage of these aspects.
To avoid a cryptic mathematical exposition of the problem, I follow the authors’ informal description: The Steiner Tree Problem is equivalent in real life to building a road system of minimum length for n towns, possibly making intersections outside of towns. If the number of vertices that can be formed outside of towns (called Steiner vertices) is not known, the problem is NP-hard. If the question is whether we have a solution with length m then it is NP-complete. We are discussing the latter problem.
For example, winning at chess every time in maximum of n moves from any starting move would be as easy as testing a checkmate on the board. If the opponent also knows the algorithm, then winning the game reduces to who starts the game. Even a non-player can undertake the test (checkmate condition) without understanding the game, if the rules are given on a piece of paper.
For semantic content, we can take the perspective of the Language of Thought (LOT) hypothesis of Fodor (1975), which requires primitives (or core concepts), to support LOT as its primitives, or its rival, map theory, which states that we have a system of belief maps by which we steer our cognitive functions, rather than individuated sentential statements of LOT. Something has to support the system of belief and the maps. “The brain can do this” is no more an empirical theory than Turing’s “being suitably programmed” was for intelligence and understanding. A good place to start for both is by giving them a process ontology. Although map-theorists shun the computer analogy, the intensional view is not an analogy but a constitutive principle, so it might also help those theorists.
Rogers (1959):115 provided the first Chinese Room-like argument where the input-output materials are not Chinese symbols but numbers. He was interested in computing number-theoretic functions by a human. He placed a man in the room equipped with a finite set of instructions to compute numbers, who outputted them for checking. He did not suggest a test to decide between man and machine. His test was to be able to compute any number-theoretic function in a finite amount of time. He assumed that the person inside the room is inexhaustible.
The Robot Reply suggested that a computer with a body would be like a child learning language.
I first saw the use of this mythological ‘word turtle’ idea in the sense closest to the current discussion in Ross (1967), who attributes it to William James. Its significance for the intensional view is that Ross recalls it with a “bull’s eye relevance to the study of syntax.”
Without this assumption, we would not be too far from linguistic relativism of the Sapir variety, in which we would think in a language. Although there are many cases in which linguistic terminology is deeply cultural; for example, basicness of color terms, this is not a causal link from language to thought, because we have seen tragic cases of having thought but not language, at least quite unexpected cases of inferential ability (if language caused thought), in the light of little (almost no) linguistic exposure up to puberty. One such case is Genie (Fromkin et al. 1974; Curtiss et al. 1974). Assuming that language is an expression of thought seems to avoid these problems. In the current argument, it is not only empirically on better grounds, but also a necessary consequence of thinking that language is a computational mechanism. On the other hand, syntactic semantics require it as an extra assumption; but, let me stress that nobody is denying the role of compositional semantics in syntax. The question is whether syntax alone can cause semantics.
Ford (2011):70, who defended Searle’s views against Rapaport, is less apathetic, but still analogical in thinking about computers: “if we can get a computer to have meaningful conscious experiences—the road to natural language acquisition and understanding would be clear (as far as Searle is concerned).”
Keller’s case is different from that of a child who is deaf or blind in the critical period of acquisition. The child in these circumstances can have some access to meanings out there by his own initiative, to relate them to forms. In fact blind children create form differences for the semantic distinction of look and see, although they cannot experience visual looking or visual seeing. Deaf or hearing children who are born to deaf parents acquire their sign language in the normal time course of language acquisition. Blind children follow a normal course too as long as they are exposed to language; see Gleitman and Elissa (1995) for a summary.
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Acknowledgements
I thank five reviewers of Minds and Machines for their comments, which significantly improved the paper. Thanks also to Halit Oğuztüzün and Umut Özge for feedback on an earlier draft, which led to some new sections, and to Vincent Nunney for last minute help with some pieces of text. All errors and misunderstandings are mine.
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The paper is dedicated to my Arizona State classmate Jonathan Mills, 1952–2016, whose work led me to some rethinking which eventually led to this paper, who had taught me one day in class what it means to be a computer science graduate student.
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Bozşahin, C. Computers Aren’t Syntax All the Way Down or Content All the Way Up. Minds & Machines 28, 543–567 (2018). https://doi.org/10.1007/s11023-018-9469-2
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DOI: https://doi.org/10.1007/s11023-018-9469-2