Little, Brown, 1992 Review by Glenn Branch on Jul 5th 1999 Volume: 3, Number: 27.

A survey of the field of hypercomputation, including discussion of a variety of objections.

Accelerating Turing machines have attracted much attention in the last decade or so. They have been described as “the work-horse of hypercomputation” (Potgieter and Rosinger 2010: 853). But do they really compute beyond the “Turing limit”—e.g., compute the halting function? We argue that the answer depends on what you mean by an accelerating Turing machine, on what you mean by computation, and even on what you mean by a Turing machine. We show first that in the current literature the term (...) “accelerating Turing machine” is used to refer to two very different species of accelerating machine, which we call end-stage-in and end-stage-out machines, respectively. We argue that end-stage-in accelerating machines are not Turing machines at all. We then present two differing conceptions of computation, the internal and the external, and introduce the notion of an epistemic embedding of a computation. We argue that no accelerating Turing machine computes the halting function in the internal sense. Finally, we distinguish between two very different conceptions of the Turing machine, the purist conception and the realist conception; and we argue that Turing himself was no subscriber to the purist conception. We conclude that under the realist conception, but not under the purist conception, an accelerating Turing machine is able to compute the halting function in the external sense. We adopt a relatively informal approach throughout, since we take the key issues to be philosophical rather than mathematical. (shrink)

I articulate a novel modal argument for P=NP.

What psychological and philosophical significance should we attach to recent efforts at computer simulations of human cognitive capacities? In answering this question, I find it useful to distinguish what I will call "strong" AI from "weak" or "cautious" AI. According to weak AI, the principal value of the computer in the study of the mind is that it gives us a very powerful tool. For example, it enables us to formulate and test hypotheses in a more rigorous and precise fashion. (...) But according to strong AI, the computer is not merely a tool in the study of the mind; rather, the appropriately programmed computer really is a mind, in the sense that computers given the right programs can be literally said to. (shrink)

I propose to consider the question, "Can machines think?" This should begin with definitions of the meaning of the terms "machine" and "think." The definitions might be framed so as to reflect so far as possible the normal use of the words, but this attitude is dangerous, If the meaning of the words "machine" and "think" are to be found by examining how they are commonly used it is difficult to escape the conclusion that the meaning and the answer to (...) the question, "Can machines think?" is to be sought in a statistical survey such as a Gallup poll. But this is absurd. Instead of attempting such a definition I shall replace the question by another, which is closely related to it and is expressed in relatively unambiguous words. The new form of the problem can be described in terms of a game which we call the 'imitation game." It is played with three people, a man (A), a woman (B), and an interrogator (C) who may be of either sex. The interrogator stays in a room apart front the other two. The object of the game for the interrogator is to determine which of the other two is the man and which is the woman. He knows them by labels X and Y, and at the end of the game he says either "X is A and Y is B" or "X is B and Y is A." The interrogator is allowed to put questions to A and B. We now ask the question, "What will happen when a machine takes the part of A in this game?" Will the interrogator decide wrongly as often when the game is played like this as he does when the game is played between a man and a woman? These questions replace our original, "Can machines think?". (shrink)

What is computer-science about? CS is obviously the science of computers. But what exactly are computers? We know that there are physical computers, and, perhaps, also abstract computers. Let us limit the discussion here to physical entities and ask: What are physical computers? What does it mean for a physical entity to be a computer? The answer, it seems, is that physical computers are physical dynamical systems that implement formal entities such as Turing-machines. I do not think that this answer (...) is false. But it invites another, and troubling, question: What distinguishes computers from other physical dynamical systems? The difficulty is that, on the one hand, every physical system im-plements abstract formal entities such as sets of differential equations, while on the other hand we certainly do not want to count every dynamical system as a computer. After all, if CS is somehow distinctive, then there must be a difference between computers and other systems such as solar systems, stomachs, and carburetors. But what is the difference? (shrink)

What is computer-science about? CS is obviously the science of computers. But what exactly are computers? We know that there are physical computers, and, perhaps, also abstract computers. Let us limit the discussion here to physical entities and ask: What are physical computers? What does it mean for a physical entity to be a computer? The answer, it seems, is that physical computers are physical dynamical systems that implement formal entities such as Turing-machines. I do not think that this answer (...) is false. But it invites another, and troubling, question: What distinguishes computers from other physical dynamical systems? The difficulty is that, on the one hand, every physical system im-plements abstract formal entities such as sets of differential equations, while on the other hand we certainly do not want to count every dynamical system as a computer. After all, if CS is somehow distinctive, then there must be a difference between computers and other systems such as solar systems, stomachs, and carburetors. But what is the difference? (shrink)

There are different ways to present a Presidential Address to the APA; the one I have chosen is simply to report on work that I am doing right now, on work in progress. I am going to present some of my further explorations into the computational model of the mind.\**.

Ford’s Helen Keller Was Never in a Chinese Room claims that my argument in How Helen Keller Used Syntactic Semantics to Escape from a Chinese Room fails because Searle and I use the terms ‘syntax’ and ‘semantics’ differently, hence are at cross purposes. Ford has misunderstood me; this reply clarifies my theory.

A computer can come to understand natural language the same way Helen Keller did: by using “syntactic semantics”—a theory of how syntax can suffice for semantics, i.e., how semantics for natural language can be provided by means of computational symbol manipulation. This essay considers real-life approximations of Chinese Rooms, focusing on Helen Keller’s experiences growing up deaf and blind, locked in a sort of Chinese Room yet learning how to communicate with the outside world. Using the SNePS computational knowledge-representation system, (...) the essay analyzes Keller’s belief that learning that “everything has a name” was the key to her success, enabling her to “partition” her mental concepts into mental representations of: words, objects, and the naming relations between them. It next looks at Herbert Terrace’s theory of naming, which is akin to Keller’s, and which only humans are supposed to be capable of. The essay suggests that computers at least, and perhaps non-human primates, are also capable of this kind of naming. (shrink)

I offer an explication of the notion of computer, grounded in the practices of computability theorists and computer scientists. I begin by explaining what distinguishes computers from calculators. Then, I offer a systematic taxonomy of kinds of computer, including hard-wired versus programmable, general-purpose versus special-purpose, analog versus digital, and serial versus parallel, giving explicit criteria for each kind. My account is mechanistic: which class a system belongs in, and which functions are computable by which system, depends on the system's mechanistic (...) properties. Finally, I briefly illustrate how my account sheds light on some issues in the history and philosophy of computing as well as the philosophy of mind. (shrink)

Traditional combinatory logic uses combinators S and K to represent all Turing-computable functions on natural numbers, but there are Turing-computable functions on the combinators themselves that cannot be so represented, because they access internal structure in ways that S and K cannot. Much of this expressive power is captured by adding a factorisation combinator F. The resulting SF-calculus is structure complete, in that it supports all pattern-matching functions whose patterns are in normal form, including a function that decides structural equality (...) of arbitrary normal forms. A general characterisation of the structure complete, confluent combinatory calculi is given along with some examples. These are able to represent all their Turing-computable functions whose domain is limited to normal forms. The combinator F can be typed using an existential type to represent internal type information. (shrink)

William Rapaport, in “How Helen Keller used syntactic semantics to escape from a Chinese Room,” (Rapaport 2006), argues that Helen Keller was in a sort of Chinese Room, and that her subsequent development of natural language fluency illustrates the flaws in Searle’s famous Chinese Room Argument and provides a method for developing computers that have genuine semantics (and intentionality). I contend that his argument fails. In setting the problem, Rapaport uses his own preferred definitions of semantics and syntax, but he (...) does not translate Searle’s Chinese Room argument into that idiom before attacking it. Once the Chinese Room is translated into Rapaport’s idiom (in a manner that preserves the distinction between meaningful representations and uninterpreted symbols), I demonstrate how Rapaport’s argument fails to defeat the CRA. This failure brings a crucial element of the Chinese Room Argument to the fore: the person in the Chinese Room is prevented from connecting the Chinese symbols to his/her own meaningful experiences and memories. This issue must be addressed before any victory over the CRA is announced. (shrink)

Continuing his exploration of the organization of complexity and the science of design, this new edition of Herbert Simon's classic work on artificial ...

One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In particular, I argue that computational complexity theory---the field that studies the resources needed to solve computational problems---leads to new perspectives on the nature of mathematical knowledge, the strong AI debate, computationalism, the problem of logical omniscience, Hume's problem of induction and Goodman's (...) grue riddle, the foundations of quantum mechanics, economic rationality, closed timelike curves, and several other topics of philosophical interest. I end by discussing aspects of complexity theory itself that could benefit from philosophical analysis. (shrink)

The functionalist view of the nature of the mind is now widely accepted. Like behaviorism and physicalism, functionalism seeks to answer the question "What are mental states?" I shall be concerned with identity thesis formulations of functionalism. They say, for example, that pain is a functional state, just as identity thesis formulations of physicalism say that pain is a physical state.

Selmer Bringsjord & Joshua Taylor∗ Department of Cognitive Science Department of Computer Science The Rensselaer AI & Reasoning (RAIR) Lab Rensselaer Polytechnic Institute (RPI) Troy NY 12180 USA http://www.rpi.edu/∼brings {selmer,tayloj}@rpi.edu..

This essay considers what it means to understand natural language and whether a computer running an artificial-intelligence program designed to understand natural language does in fact do so. It is argued that a certain kind of semantics is needed to understand natural language, that this kind of semantics is mere symbol manipulation (i.e., syntax), and that, hence, it is available to AI systems. Recent arguments by Searle and Dretske to the effect that computers cannot understand natural language are discussed, and (...) a prototype natural-language-understanding system is presented as an illustration. (shrink)