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. (shrink)

Some authors have recently suggested that it is time to consider rights for robots. These suggestions are based on the claim that the question of robot rights should not depend on a standard set of conditions for ‘moral status’; but instead, the question is to be framed in a new way, by rejecting the is/ought distinction, making a relational turn, or assuming a methodological behaviourism. We try to clarify these suggestions and to show their highly problematic consequences. While we find (...) the suggestions ultimately unmotivated, the discussion shows that our epistemic condition with respect to the moral status of others does raise problems, and that the human tendency to empathise with things that do not have moral status should be taken seriously—we suggest that it produces a “derived moral status”. Finally, it turns out that there is typically no individual in real AI that could even be said to be the bearer of moral status. Overall, there is no reason to think that robot rights are an issue now. (shrink)

Scriven’s paradox of predictability arises from the combination of two ideas: first, that everything in a deterministic universe is, in principle, predictable; second, that it is possible to create a system that falsifies any prediction that is made of it. Recently, the paradox has been used by Rummens and Cuypers to argue that there is a fundamental difference between embedded and external predictors; and by Ismael to argue against a governing conception of laws. The present paper defends a new diagnosis (...) of the roots of the paradox. First, it is argued that the unpredictability has to be understood in the light of Turing’s famous results about computability, in particular his proof that there is no solution to the ‘halting problem.’ This allows us to see that previous analyses of the paradox were either mistaken or not fully adequate. Second, the sense of paradox that nevertheless remains is traced to the idea that rational behaviour is not dependent on contingent environmental circumstances: that it is always up to us to engage in activities such as rational prediction or rational belief. The paradox of predictability teaches us that this idea, natural though it may be, is mistaken. (shrink)

I examine the abstraction/representation theory of computation put forward by Horsman et al., connecting it to the broader notion of modeling, and in particular, model-based explanation, as considered by Rosen. I argue that the ‘representational entities’ it depends on cannot themselves be computational, and that, in particular, their representational capacities cannot be realized by computational means, and must remain explanatorily opaque to them. I then propose that representation might be realized by subjective experience (qualia), through being the bearer of the (...) structure of abstract objects that are represented. (shrink)

For an arbitrary finite algebra $\g A = (A, f, 0, 1)$ one defines a double sequence $a(i,j)$ by $a(i,0)\!=\!a(0,j)\! =\! 1$ and $a(i,j) \!= \!f( a(i, j-1) , a(i-1,j) )$.The problem if such recurrent double sequences are ultimately zero is undecidable, even if we restrict it to the class of commutative finite algebras.

Every acceptable numbering of an effective domain is complete. Hence every effective domain admits the 2nd recursion theorem of Eršov[1]. On the other hand for every effective domain, the 1st recursion theorem holds. In this note, we establish that for effective domains, the 2nd recursion theorem is strictly more general than the 1st recursion theorem, a generalization of an important result in recursive function theory.

We review and discuss A. H. Louie’s book “More than Life Itself: A Reflexion on Formal Systems and Biology” from an interdisciplinary viewpoint, involving both biology and mathematics, taking into account new developments and related theories.

Hay and, then, Johnson extended the classic Rice and Rice-Shapiro Theorems for computably enumerable sets, to analogs for all the higher levels in the finite Ershov Hierarchy. The present paper extends their work to analogs in the transfinite Ershov Hierarchy. Some of the transfinite cases are done for all transfinite notations in Kleene's important system of notations, equation image. Other cases are done for all transfinite notations in a very natural, proper subsystem equation image of equation image, where equation image (...) has at least one notation for each constructive ordinal. In these latter cases it is open as to what happens for the entire set of transfinite notations in equation image. (shrink)

This paper contributes to the computer ethics debate on software ownership protection by examining the ontological, methodological, and ethical problems related to property right infringement that should come prior to any legal discussion. The ontological problem consists in determining precisely what it is for a computer program to be a copy of another one, a largely neglected problem in computer ethics. The methodological problem is defined as the difficulty of deciding whether a given software system is a copy of another (...) system. And the ethical problem corresponds to establishing when a copy constitutes, or does not constitute, a property right infringement. The ontological problem is solved on the logical analysis of abstract machines, and the latter are argued to be the appropriate level of abstraction for software at which the methodological and the ethical problems can be successfully addressed. (shrink)

The Turing Machine presents itself as the very landmark and initial design of digital automata present in all modern general-purpose digital computers and whose design on computable numbers implies deeply ontological as well as epistemological foundations for today’s computers. These lines of work attempt to briefly analyze the fundamental epistemological problem that rose in the late 19th and early 20th century whereby “machine cognition” emerges. The epistemological roots addressed in the TM and notably in its “Halting Problem” uncovers the tension (...) between determinism and uncertainty, regarded here as the primal and inherent features of machine cognition. Resumen La Máquina de Turing se presenta como el hito y el diseño inicial de un autómata digital presente en todas las computadoras digitales modernas de propósito general y cuyo diseño en números computables establece bases profundamente ontológicas y epistemológicas para las computadoras de hoy. Estas líneas de trabajo intentan analizar brevemente el problema epistemológico fundamental que surgió a finales del siglo XIX y principios del XX mediante el cual emerge la “cognición de la máquina”. Las raíces epistemológicas que se abordan en la TM y, en particular, en su “Problema de detención” ponen al descubierto la tensión entre el determinismo y la incertidumbre, consideradas aquí, como las características primordiales e inherentes de la cognición de la máquina. (shrink)