Online research in philosophy

Accelerated Turing machines are Turing machines that perform tasks commonly regarded as impossible, such as computing the halting function. The existence of these notional machines has obvious implications concerning the theoretical limits of computability.

This paper considers undecidability in the imitation game, the so-called Turing Test. In the Turing Test, a human, a machine, and an interrogator are the players of the game. In our model of the Turing Test, the machine and the interrogator are formalized as Turing machines, allowing us to derive several impossibility results concerning the capabilities of the interrogator. The key issue is that the validity of the Turing test is not attributed to the capability of human or machine, but rather to the capability of the interrogator. In particular, it is shown that no Turing machine can be a perfect interrogator. We also discuss meta-imitation game and imitation game with analog interfaces where both the imitator and the interrogator are mimicked by continuous dynamical systems.

A myth has arisen concerning Turing's paper of 1936, namely that Turing set forth a fundamental principle concerning the limits of what can be computed by machine - a myth that has passed into cognitive science and the philosophy of mind, to wide and pernicious effect. This supposed principle, sometimes incorrectly termed the 'Church-Turing thesis', is the claim that the class of functions that can be computed by machines is identical to the class of functions that can be computed by Turing machines. In point of fact Turing himself nowhere endorses, nor even states, this claim (nor does Church). I describe a number of notional machines, both analogue and digital, that can compute more than a universal Turing machine. These machines are exemplars of the class of _nonclassical_ computing machines. Nothing known at present rules out the possibility that machines in this class will one day be built, nor that the brain itself is such a machine. These theoretical considerations undercut a number of foundational arguments that are commonly rehearsed in cognitive science, and gesture towards a new class of cognitive models.

In his PhD thesis (1938) Turing introduced what he described as 'a new kind of machine'. He called these 'O-machines'. The present paper employs Turing's concept against a number of currently fashionable positions in the philosophy of mind.

Since the introduction of the imitation game by Turing in 1950 there has been much debate as to its validity in ascertaining machine intelligence. We wish herein to consider a different issue altogether: granted that a computing machine passes the Turing Test, thereby earning the label of ``Turing Chatterbox'', would it then be of any use (to us humans)? From the examination of scenarios, we conclude that when machines begin to participate in social transactions, unresolved issues of trust and responsibility may well overshadow any raw reasoning ability they possess.

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.

It is not widely realised that Turing was probably the first person to consider building computing machines out of simple, neuron-like elements connected together into networks in a largely random manner. Turing called his networks unorganised machines. By the application of what he described as appropriate interference, mimicking education an unorganised machine can be trained to perform any task that a Turing machine can carry out, provided the number of neurons is sufficient. Turing proposed simulating both the behaviour of the network and the training process by means of a computer program. We outline Turing's connectionist project of 1948.

Accelerating Turing machines are Turing machines of a sort able to perform tasks that are commonly regarded as impossible for Turing machines. For example, they can determine whether or not the decimal representation of contains n consecutive 7s, for any n; solve the Turing-machine halting problem; and decide the predicate calculus. Are accelerating Turing machines, then, logically impossible devices? I argue that they are not. There are implications concerning the nature of effective procedures and the theoretical limits of computability. Contrary to a recent paper by Bringsjord, Bello and Ferrucci, however, the concept of an accelerating Turing machine cannot be used to shove up Searle's Chinese room argument.

In this paper I discuss the topics of mechanism and algorithmicity. I emphasise that a characterisation of algorithmicity such as the Turing machine is iterative; and I argue that if the human mind can solve problems that no Turing machine can, the mind must depend on some non-iterative principle — in fact, Cantor's second principle of generation, a principle of the actual infinite rather than the potential infinite of Turing machines. But as there has been theorisation that all physical systems can be represented by Turing machines, I investigate claims that seem to contradict this: specifically, claims that there are noncomputable phenomena. One conclusion I reach is that if it is believed that the human mind is more than a Turing machine, a belief in a kind of Cartesian dualist gulf between the mental and the physical is concomitant.