La filosofía de la ciencia se desarrolló durante la primera mitad del siglo xx bajo el supuesto de que la ciencia podía caracterizarse por la estructura lógica tanto del conocimiento articulado en las teorías más exitosas como de sus explicaciones. En la segunda mitad del siglo xx se cuestiona fuertemente esa idea, pero se sigue asumiendo que la filosofía de la ciencia debe hacerse siguiendo los cánones de una epistemología fundamentalista que considera que el avance de la ciencia pasa por (...) una ontología cada vez mas austera guiada por la idea de "mientras menos mejor". Desde esta perspectiva fundamentalista, el que las diferentes ciencias hablen de diferentes tipos de cosas es un obstáculo al entendimiento, producto de la imperfección del conocimiento actual. Este ideal nos invita a pensar que la epistemología debe hacerse reflexionando sobre el conocimiento articulado en nuestras teorías más austeras y nos compromete con propuestas reduccionistas problemáticas que no permiten explicar la diversidad de recursos epistémicos que de hecho utilizan los científicos. En este libro promovemos una epistemología que no sigue el lema de "mientras menos mejor", sino el de "organizar nuestros recursos epistémicos de manera que se genere entendimiento". Así, la misma estructura de las explicaciones y las prácticas (que incluye métodos y normas respecto de lo que se considera plausible y valioso) es lo que nos da la pauta para responder a la pregunta de qué es lo que hay. Esta estrategia epistémica nos obliga a hacer una filosofía de la ciencia muy cercana a la ciencia, reconociendo la pluralidad de sus métodos, objetivos y prácticas, sin reducir la filosofía de la ciencia a la sociología o a cualquier otra ciencia en particular. (shrink)

This is a review of Mind and Supermind. By KEITH FRANKISH. (Cambridge: Cambridge University Press, 2004. Pp xiv + 255. Price £45.00 (US $75.00). ISBN 0521 812038 (hardback).

Following Nancy Cartwright and others, I suggest that most (if not all) theories incorporate, or depend on, one or more idealizing assumptions. I then argue that such theories ought to be regimented as counterfactuals, the antecedents of which are simplifying assumptions. If this account of the logic form of theories is granted, then a serious problem arises for Bayesians concerning the prior probabilities of theories that have counterfactual form. If no such probabilities can be assigned, the the posterior probabilities will (...) be undefined, as the latter are defined in terms of the former. I argue here that the most plausible attempts to address the problem of probabilities of conditionals fail to help Bayesians, and, hence, that Bayesians are faced with a new problem. In so far as these proposed solutions fail, I argue that Bayesians must give up Bayesianism or accept the counterintuitive view that no theories that incorporate any idealizations have ever really been confirmed to any extent whatsoever. Moreover, as it appears that the latter horn of this dilemma is highly implausible, we are left with the conclusion that Bayesianism should be rejected, at least as it stands. (shrink)

Between Calculability and Non-Calculability. Issues of Calculability and Predictability in the Physics of Complex Systems. The ability to predict has been a very important qualifier of what constitutes scientific knowledge, ever since the successes of Babylonian and Greek astronomy. More recent is the general appreciation of the fact that in the presence of deterministic chaos, predictability is severely limited (the so-called ‘butterfly effect’): Nearby trajectories diverge during time evolution; small errors typically grow exponentially with time. The system obeys deterministic laws (...) and still is unpredictable, seemingly a paradox for the traditional viewpoint of Laplacian determinisms. With the concept of deterministic chaos the epistemological issue about an adequate understanding of predictability is no longer just a mere philosophical topic. Physicists on the one hand recognize the limits of (long term) predictability, computability and even of scientific knowledge, on the other hand they work on concepts for extending the horizon of predictability. It is shown in this paper that physics of complex systems is useful to clarify the jungle of different meanings of the terms ‘predictability’ and ‘computability’ — also with philosophical implications for understanding science and nature. Today, from the physical point of view, the relevance of the concepts of predictability seems to be underestimated by philosophers as a mere methodological topic. In the paper I analyse the importance of predictability and computability in physics of complex systems. I show a way how to cope with problems of unpredictability and noncomputability. Nine different concepts of predictability and computability (i.e. open solution, sensitivity/chaos, redundancy/chance) are presented, compared and evaluated. (shrink)

It is commonly believed that there is no equivalent of the Church–Turing thesis for computation over the reals. In particular, computational models on this domain do not exhibit the convergence of formalisms that supports this thesis in the case of integer computation. In the light of recent philosophical developments on the different meanings of the Church–Turing thesis, and recent technical results on analog computation, I will show that this current belief confounds two distinct issues, namely the extension of the notion (...) of effective computation to the reals on the one hand, and the simulation of analog computers by Turing machines on the other hand. I will argue that it is possible in both cases to defend an equivalent of the Church–Turing thesis over the reals. Along the way, we will learn some methodological caveats on the comparison of different computational models, and how to make it meaningful. (shrink)

The emperor's new mind (hereafter Emperor) is an attempt to put forward a scientific alternative to the viewpoint of according to which mental activity is merely the acting out of some algorithmic procedure. John Searle and other thinkers have likewise argued that mere calculation does not, of itself, evoke conscious mental attributes, such as understanding or intentionality, but they are still prepared to accept the action the brain, like that of any other physical object, could in principle be simulated by (...) a computer. In Emperor I go further than this and suggest that the outward manifestations ofconscious mental activity cannot even be properly simulated by calculation. To support this view, I use various arguments to show that the results of mathematical insight, in particular, do not seem to be obtained algorithmically. The main thrust ofthis work, however, is to present an overview ofthe present state of physical understanding and to show that an important gap exists at the point where, quantum and classical physics meet, as well as to speculate on how the conscious brain might be taking advantage ofwhatever new physics is needed to fill this gap to achieve its nonalgorithmic effects. (shrink)

The purpose of this paper is to provide an account of the epistemology and metaphysics of universe creation on a computer. The paper begins with F.J.Tipler's argument that our experience is indistinguishable from the experience of someone embedded in a perfect computer simulation of our own universe, hence we cannot know whether or not we are part of such a computer program ourselves. Tipler's argument is treated as a special case of epistemological scepticism, in a similar vein to `brain-in-a-vat' arguments. (...) It is argued that the hypothesis that our universe is a program running on a digital computer in another universe generates empirical predictions, and is therefore a falsifiable hypothesis. The computer program hypothesis is also treated as a hypothesis about what exists beyond the physical world, and is compared with Kant's metaphysics of noumena. It is proposed that a theory about what exists beyond the physical world should be formulated with the precise concepts of mathematics, and should generate physical predictions. It is argued that if our universe is a program running on a digital computer, then our universe must have compact spatial topology, and the possibilities of observationally testing this prediction are considered. The possibility of testing the computer program hypothesis with the value of the density parameter Omega_0 is also analysed. The informational requirements for a computer to represent a universeexactly and completely are considered. Consequent doubt is thrown upon Tipler's claim that if a hierarchy of computer universes exists, we would not be able to know which `level of implementation' our universe exists at. It is then argued that a digital computer simulation of a universe cannot exist as a universe. However, the paper concludes with the acknowledgement that an analog computer simulation can be objectively related to the thing it represents, hence an analog computer simulation of a universe could, in principle, exist as a universe. (shrink)

The purpose of this paper is to provide an account of the epistemology and metaphysics of universe creation on a computer. The paper begins with F.J.Tipler's argument that our experience is indistinguishable from the experience of someone embedded in a perfect computer simulation of our own universe, hence we cannot know whether or not we are part of such a computer program ourselves. Tipler's argument is treated as a special case of epistemological scepticism, in a similar vein to `brain-in-a-vat' arguments. (...) It is argued that the hypothesis that our universe is a program running on a digital computer in another universe generates empirical predictions, and is therefore a falsifiable hypothesis. The computer program hypothesis is also treated as a hypothesis about what exists beyond the physical world, and is compared with Kant's metaphysics of noumena. It is proposed that a theory about what exists beyond the physical world should be formulated with the precise concepts of mathematics, and should generate physical predictions. It is argued that if our universe is a program running on a digital computer, then our universe must have compact spatial topology, and the possibilities of observationally testing this prediction are considered. The possibility of testing the computer program hypothesis with the value of the density parameter Omega_0 is also analysed. The informational requirements for a computer to represent a universeexactly and completely are considered. Consequent doubt is thrown upon Tipler's claim that if a hierarchy of computer universes exists, we would not be able to know which `level of implementation' our universe exists at. It is then argued that a digital computer simulation of a universe cannot exist as a universe. However, the paper concludes with the acknowledgement that an analog computer simulation can be objectively related to the thing it represents, hence an analog computer simulation of a universe could, in principle, exist as a universe. (shrink)

The purpose of this paper is to elucidate, by means of concepts and theorems drawn from mathematical logic, the conditions under which the existence of a multiverse is a logical necessity in mathematical physics, and the implications of Gödel’s incompleteness theorem for theories of everything.Three conclusions are obtained in the final section: (i) the theory of the structure of our universe might be an undecidable theory, and this constitutes a potential epistemological limit for mathematical physics, but because such a theory (...) must be complete, there is no ontological barrier to the existence of a final theory of everything; (ii) in terms of mathematical logic, there are two different types of multiverse: classes of non-isomorphic but elementarily equivalent models, and classes of model which are both non-isomorphic and elementarily inequivalent; (iii) for a hypothetical theory of everything to have only one possible model, and to thereby negate the possible existence of a multiverse, that theory must be such that it admits only a finite model. (shrink)

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. (shrink)

We explore the possibility of using quantum mechanical principles for hypercomputation through the consideration of a quantum algorithm for computing the Turing halting problem. The mathematical noncomputability is compensated by the measurability of the values of quantum observables and of the probability distributions for these values. Some previous no-go claims against quantum hypercomputation are then reviewed in the light of this new positive proposal.

Continuity as appears to us immediately by intuition differs from its current formalization, the arithmetical continuum or equivalently the set of real numbers used in modern mathematical analysis. Motivated by the known mathematical and physical problems arising from this formalization of the continuum, our aim in this paper is twofold. Firstly, by interpreting Chaitin’s variant of Gödel’s first incompleteness theorem as an inherent uncertainty or fuzziness of the arithmetical continuum, a formal set-theoretic entropy is assigned to the arithmetical continuum. Secondly, (...) by analyzing Noether’s theorem on symmetries and conserved quantities, we argue that whenever the four dimensional space-time continuum containing a single, stationary, asymptotically flat black hole is modeled by the arithmetical continuum in the mathematical formulation of general relativity, the hidden set-theoretic entropy of this latter structure reveals itself as the entropy of the black hole, indicating that this apparently physical quantity might have a pure set-theoretic origin, too. (shrink)

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)

Sumário Mostramos que, em virtude dos limites teóricos da computação, nem toda a ciência formulada com carácter preditivo pode ser simulada. Em particular, evidencia- se que a Fisica Clássica, nomeadamente a Físíca Newtoniana, padece deste mal, encerrando processos de Zenão.

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.