This paper investigates the view that digital hypercomputing is a good reason for rejection or re-interpretation of the Church-Turing thesis. After suggestion that such re-interpretation is historically problematic and often involves attack on a straw man (the ‘maximality thesis’), it discusses proposals for digital hypercomputing with Zeno-machines , i.e. computing machines that compute an infinite number of computing steps in finite time, thus performing supertasks. It argues that effective computing with Zeno-machines falls into a dilemma: either they are specified such (...) that they do not have output states, or they are specified such that they do have output states, but involve contradiction. Repairs though non-effective methods or special rules for semi-decidable problems are sought, but not found. The paper concludes that hypercomputing supertasks are impossible in the actual world and thus no reason for rejection of the Church-Turing thesis in its traditional interpretation. (shrink)

For over a decade, the hypercomputation movement has produced computational models that in theory solve the algorithmically unsolvable, but they are not physically realizable according to currently accepted physical theories. While opponents to the hypercomputation movement provide arguments against the physical realizability of specific models in order to demonstrate this, these arguments lack the generality to be a satisfactory justification against the construction of any information-processing machine that computes beyond the universal Turing machine. To this end, I present a more (...) mathematically concrete challenge to hypercomputability, and will show that one is immediately led into physical impossibilities, thereby demonstrating the infeasibility of hypercomputers more generally. This gives impetus to propose and justify a more plausible starting point for an extension to the classical paradigm that is physically possible, at least in principle. Instead of attempting to rely on infinities such as idealized limits of infinite time or numerical precision, or some other physically unattainable source, one should focus on extending the classical paradigm to better encapsulate modern computational problems that are not well-expressed/modeled by the closed-system paradigm of the Turing machine. I present the first steps toward this goal by considering contemporary computational problems dealing with intractability and issues surrounding cyber-physical systems, and argue that a reasonable extension to the classical paradigm should focus on these issues in order to be practically viable. (shrink)

The Turing Test is claimed by many to be a way to test for the presence, in computers, of such ``deep'' phenomena as thought and consciousness. Unfortunately, attempts to build computational systems able to pass TT have devolved into shallow symbol manipulation designed to, by hook or by crook, trick. The human creators of such systems know all too well that they have merely tried to fool those people who interact with their systems into believing that these systems really have (...) minds. And the problem is fundamental: the structure of the TT is such as to cultivate tricksters. A better test is one that insists on a certain restrictive epistemic relation between an artificial agent A, its output o, and the human architect H of A – a relation which, roughly speaking, obtains when H cannot account for how A produced o. We call this test the ``Lovelace Test'' in honor of Lady Lovelace, who believed that only when computers originate things should they be believed to have minds. (shrink)

An effective method is a computational method that might, in principle, be executed by a human. In this paper, I argue that there are methods for computing that are not effective methods. The examples I consider are taken primarily from quantum computing, but these are only meant to be illustrative of a much wider class. Quantum inference and quantum parallelism involve steps that might be implemented in multiple physical systems, but cannot be implemented, or at least not at will, by (...) an idealised human. Recognising that not all computational methods are effective methods is important for at least two reasons. First, it is needed to correctly state the results of Turing and other founders of computation theory. Turing is sometimes said to have offered a replacement for the informal notion of an effective method with the formal notion of a Turing machine. I argue that such a view only holds under limited circumstances. Second, not distinguishing between computational methods and effective methods can lead to mistakes when quantifying over the class of all possible computational methods. Such quantification is common in philosophy of mind in the context of thought experiments that explore the limits of computational functionalism. I argue that these ‘homuncular’ thought experiments should not be treated as valid. (shrink)

We describe an emerging field, that of nonclassical computability and nonclassical computing machinery. According to the nonclassicist, the set of well-defined computations is not exhausted by the computations that can be carried out by a Turing machine. We provide an overview of the field and a philosophical defence of its foundations.

A version of the Church-Turing Thesis states that every effectively realizable physical system can be simulated by Turing Machines (‘Thesis P’). In this formulation the Thesis appears to be an empirical hypothesis, subject to physical falsification. We review the main approaches to computation beyond Turing definability (‘hypercomputation’): supertask, non-well-founded, analog, quantum, and retrocausal computation. The conclusions are that these models reduce to supertasks, i.e. infinite computation, and that even supertasks are no solution for recursive incomputability. This yields that the realization (...) of hypercomputing devices is implausible, and that Thesis P is not essentially different from the standard Church-Turing Thesis. (shrink)

I argue in this article that there is a mistake in Searle's Chinese room argument that has not received sufficient attention. The mistake stems from Searle's use of the Church-Turing thesis. Searle assumes that the Church-Turing thesis licences the assumption that the Chinese room can run any program. I argue that it does not, and that this assumption is false. A number of possible objections are considered and rejected. My conclusion is that it is consistent with Searle's argument to hold (...) onto the claim that understanding consists in the running of a program. (shrink)

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)

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. (shrink)

The aim of this paper is an attempt to give an answer to the question what does it mean that a computational system is intelligent. We base on some theses that though debatable are commonly accepted. Intelligence is conceived as the ability of tractable solving of some problems that in general are not solvable by deterministic Turing Machine.

Brauchen Roboter moralische Kompetenz? Die Antwort lautet ja. Einerseits benötigen Roboter moralische Kompetenz, um unsere Welt aus Regeln, Vorschriften und Werten zu begreifen, andererseits um von ihrem Umfeld akzeptiert zu werden. Wie aber lässt sich moralische Kompetenz in Roboter implementieren? Welche philosophischen Herausforderungen sind zu erwarten? Und wie können wir uns und unsere Kinder auf Roboter vorbereiten, die irgendwann über moralische Kompetenz verfügen werden? André und Iga Maria Schmiljun skizzieren aus einer humanistisch-philosophischen Perspektive erste Antworten auf diese Fragen und entwickeln (...) einen didaktischen Einstieg in das Thema für die Grundschule. (shrink)