Church's Thesis asserts that the only numeric functions that can be calculated by effective means are the recursive ones, which are the same, extensionally, as the Turing-computable numeric functions. The Abstract State Machine Theorem states that every classical algorithm is behaviorally equivalent to an abstract state machine. This theorem presupposes three natural postulates about algorithmic computation. Here, we show that augmenting those postulates with an additional requirement regarding basic operations gives a natural axiomatization of computability and a proof of Church's (...) Thesis, as Gödel and others suggested may be possible. In a similar way, but with a different set of basic operations, one can prove Turing's Thesis, characterizing the effective string functions, and--in particular--the effectively-computable functions on string representations of numbers. (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)

Many philosophical accounts of scientific models fail to distinguish between a simulation model and other forms of models. This failure is unfortunate because there are important differences pertaining to their methodology and epistemology that favor their philosophical understanding. The core claim presented here is that simulation models are rich and complex units of analysis in their own right, that they depart from known forms of scientific models in significant ways, and that a proper understanding of the type of model simulations (...) are fundamental for their philosophical assessment. I argue that simulation models can be distinguished from other forms of models by the many algorithmic structures, representation relations, and new semantic connections involved in their architecture. In this article, I reconstruct a general architecture for a simulation model, one that faithfully captures the complexities involved in most scientific research with computer simulations. Furthermore, I submit that a new methodology capable of conforming such architecture into a fully functional, computationally tractable computer simulation must be in place. I discuss this methodology—what I call recasting—and argue for its philosophical novelty. If these efforts are heading towards the right interpretation of simulation models, then one can show that computer simulations shed new light on the philosophy of science. To illustrate the potential of my interpretation of simulation models, I briefly discuss simulation-based explanations as a novel approach to questions about scientific explanation. (shrink)

This article is a methodological discussion of formal approaches to the question of identity of proofs from a philosophical standpoint. First, an introduction to the question of identity of proofs itself is given, followed by a brief reconstruction of the so-called normalisation thesis, proposed by Dag Prawitz in 1971, in which some of its core mathematical and conceptual traits are presented. After that, a comparison between the normalisation thesis and the more well-known Church-Turing thesis on computability is carried out in (...) three main parts: the first dedicated to highlighting some of the analogies between them; the second, their most remarkable differences; and the third, to the possible relations of dependence between the two. Based on these considerations, some concluding remarks concerning the potential of the normalisation thesis and similar approaches to the question of identity of proofs are made in the last section. (shrink)

Una imagen muy generalizada a la hora de entender el software de computador es la que lo representa como una “caja negra”: no importa realmente saber qué partes lo componen internamente, sino qué resultados se obtienen de él según ciertos valores de entrada. Al hacer esto, muchos problemas filosóficos son ocultados, negados o simplemente mal entendidos. Este artículo discute tres unidades de análisis del software de computador, esto es, las especificaciones, los algoritmos y los procesos computacionales. El objetivo central es (...) entender las prácticas cientficas e ingenieriles detrás de cada unidad de software, así como analizar su metodología, ontología y epistemología. (shrink)