The long‐standing issue of Wittgenstein's controversial remarks on Gödel's Theorem has recently heated up in a number of different and interesting directions [,, ]. In their, Juliet Floyd and Hilary Putnam purport to argue that Wittgenstein's‘notorious’ “Contains a philosophical claim of great interest,” namely, “if one assumed. that →P is provable in Russell's system one should… give up the “translation” of P by the English sentence ‘P is not provable’,” because if ωP is provable in PM, PM is ω ‐inconsistent, (...) and if PM is ω‐inconsistent, we cannot translate ‘P’as ’P is not provable in PM’because the predicate‘NaturalNo.’in ‘P’“cannot be…interpreted” as “x is a natural number.” Though Floyd and Putnam do not clearly distinguish the two tasks, they also argue for “The Floyd‐Putnam Thesis,” namely, that in the 1930's Wittgenstein had a particular understanding of Gödel's First Incompleteness Theorem. In this paper, I endeavour to show, first, that the most natural and most defensible interpretation of Wittgenstein's and the rest of is incompatible with the Floyd‐Putnam attribution and, second, that evidence from Wittgenstein's Nachla strongly indicates that the Floyd‐ Putnam attribution and the Floyd‐Putnam Thesis are false. By way of this examination, we shall see that despite a failure to properly understand Gödel's proof—perhaps because, as Kreisel says, Wittgenstein did not read Gödel's 1931 paper prior to 1942‐Wittgenstein's 1937–38, 1941 and 1944 remarks indicate that Gödel's result makes no sense from Wittgenstein's own perspective. (shrink)

The long‐standing issue of Wittgenstein's controversial remarks on Gödel's Theorem has recently heated up in a number of different and interesting directions [, , ]. In their , Juliet Floyd and Hilary Putnam purport to argue that Wittgenstein's‘notorious’ “Contains a philosophical claim of great interest,” namely, “if one assumed. that →P is provable in Russell's system one should… give up the “translation” of P by the English sentence ‘P is not provable’,” because if ωP is provable in PM, PM is (...) ω ‐inconsistent, and if PM is ω‐inconsistent, we cannot translate ‘P’as ’P is not provable in PM’because the predicate‘NaturalNo.’in ‘P’“cannot be…interpreted” as “x is a natural number.” Though Floyd and Putnam do not clearly distinguish the two tasks, they also argue for “The Floyd‐Putnam Thesis,” namely, that in the 1930's Wittgenstein had a particular understanding of Gödel's First Incompleteness Theorem. In this paper, I endeavour to show, first, that the most natural and most defensible interpretation of Wittgenstein's and the rest of is incompatible with the Floyd‐Putnam attribution and, second, that evidence from Wittgenstein's Nachla strongly indicates that the Floyd‐ Putnam attribution and the Floyd‐Putnam Thesis are false. By way of this examination, we shall see that despite a failure to properly understand Gödel's proof—perhaps because, as Kreisel says, Wittgenstein did not read Gödel's 1931 paper prior to 1942‐Wittgenstein's 1937–38, 1941 and 1944 remarks indicate that Gödel's result makes no sense from Wittgenstein's own perspective. (shrink)

Although molecular biology has meant different things at different times, the term is often associated with a tendency to view cellular causation as conforming to simple linear schemas in which macro-scale effects are specified by micro-scale structures. The early achievements of molecular biologists were important for the formation of such an outlook, one to which the discovery of recombinant DNA techniques, and a number of other findings, gave new life even after the complexity of genotype–phenotype
relations had become apparent. Against this (...) background we outline how a range of scientific developments and conceptual considerations can be regarded as enabling and perhaps necessitating contemporary systems approaches. We suggest that philosophical ideas have a valuable part to play in making sense of complex scientific and disciplinary issues. (shrink)

In the 1950s, Alan Turing proposed his influential test for machine intelligence, which involved a teletyped dialogue between a human player, a machine, and an interrogator. Two readings of Turing's rules for the test have been given. According to the standard reading of Turing's words, the goal of the interrogator was to discover which was the human being and which was the machine, while the goal of the machine was to be indistinguishable from a human being. According to the literal (...) reading, the goal of the machine was to simulate a man imitating a woman, while the interrogator – unaware of the real purpose of the test – was attempting to determine which of the two contestants was the woman and which was the man. The present work offers a study of Turing's rules for the test in the context of his advocated purpose and his other texts. The conclusion is that there are several independent and mutually reinforcing lines of evidence that support the standard reading, while fitting the literal reading in Turing's work faces severe interpretative difficulties. So, the controversy over Turing's rules should be settled in favor of the standard reading. (shrink)

The Second World War was a watershed in history in many ways. I focus on the World War II discontinuity as it relates to the intersection of scientific and military enterprise. I am interested in how we should conceptualize that intersection and in offering a preliminary tracing of the “World War II regime” that has grown out of it—a regime that includes new forms of scientific and military practice but that has invaded and transformed many other cultural spaces, including—my primary (...) example here—the industrial workplace. I exploit the figure of the cyborg to thematize the social, material, and conceptual heterogeneity of the developments at issue; specify a distinct range of cyborg objects and sciences that emerged from the World War II matrix; and exemplify a historiographical approach that escapes the traditional master-narrative structures of science studies. (shrink)

This paper concerns Alan Turing’s ideas about machines, mathematical methods of proof, and intelligence. By the late 1930s, Kurt Gödel and other logicians, including Turing himself, had shown that no finite set of rules could be used to generate all true mathematical statements. Yet according to Turing, there was no upper bound to the number of mathematical truths provable by intelligent human beings, for they could invent new rules and methods of proof. So, the output of a human mathematician, for (...) Turing, was not a computable sequence (i.e., one that could be generated by a Turing machine). Since computers only contained a finite number of instructions (or programs), one might argue, they could not reproduce human intelligence. Turing called this the “mathematical
objection” to his view that machines can think. Logico-mathematical reasons, stemming from his own work, helped to convince Turing that it should be possible to reproduce human intelligence, and eventually compete with it, by developing the appropriate kind of digital computer. He felt it
should be possible to program a computer so that it could learn or discover new rules, overcoming the limitations imposed by the incompleteness and undecidability results in the same way that human
mathematicians presumably do. (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)

In 1972, we proposed a theory of biological pattern formation in which concentration maxima of pattern forming substances are generated through local self- enhancement in conjunction with long range inhibition. Since then, much evidence in various developmental systems has confirmed the importance of autocatalytic feedback loops combined with inhibitory interaction. Examples are found in the formation of embryonal organizing regions, in segmentation, in the polarization of individual cells, and in gene activation. By computer simulations, we have shown that the theory (...) accounts for much of the regulatory phenomena observed, including signalling to regenerate removed parts. These self- regulatory features contribute to making development robust and error-tolerant. Furthermore, the resulting pattern is, to a large extent, independent of the details provided by initial conditions and inducing signals. (shrink)

This paper is dedicated to Alonzo Church, who died in August 1995 after a long life devoted to logic. To Church we owe lambda calculus, the thesis bearing his name and the solution to the Entscheidungsproblem.His well-known book Introduction to Mathematical LogicI, defined the subject matter of mathematical logic, the approach to be taken and the basic topics addressed. Church was the creator of the Journal of Symbolic Logicthe best-known journal of the area, which he edited for several decades This (...) paper is in three sections. The first is written in journalistic style:the story of the life of AlonzoChurch is told, including some of the many anecdotes I have collected from different sources. The secondpart is devoted to his work, but is far from being exhaustive. The last part is more original; in it I attempto show that Church’s great discovery was lambda calculus and that his remaining contributions weremainly inspired afterthoughts in the sense that most of his contributions as well as some of his pupils derivefrom that initial achievement. Included are Kleene’s Recursion Theory and the completeness proof ofHenkin. I have added an appendix in which is presented the typed lambda calculus and a proof of theundecidability of first-order logic. (shrink)

A. M. Turing has bequeathed us a conceptulary including 'Turing, or Turing-Church, thesis', 'Turing machine', 'universal Turing machine', 'Turing test' and 'Turing structures', plus other unnamed achievements. These include a proof that any formal language adequate to express arithmetic contains undecidable formulas, as well as achievements in computer science, artificial intelligence, mathematics, biology, and cognitive science. Here it is argued that these achievements hang together and have prospered well in the 50 years since Turing's death.

In recent decades, there has been a proliferation among the scientific community of works that focus on Alan Turing’s contributions to the design and development of the modern computer. However, there are significant discrepancies among these studies, to such a point that some of them cast serious doubts on Alan Turing’s work with respect to today’s computer, and there are others that staunchly defend his leading role, as well as other studies that set out more well-balanced opinions. Faced with this (...) situation, the aim of this paper is to analyse the evidence existing today in order to be able to draw a conclusion about whether or not Turing anticipated the trivialisation of the modern computer memory and, likewise, if his universal a-machine is the precursor of the general-purpose computer so omnipresent today. As a result of our research, the authors conclude that Turing did indeed play a leading role in the appearance of the modern computer, although he was not the only one or the first in the field of Computing Science, albeit he was the most influential, both in scope and in depth. (shrink)

A. N. Turing’s 1936 concept of computability, computing machines, and computable binary digital sequences, is subject to Turing’s Cardinality Paradox. The paradox conjoins two opposed but comparably powerful lines of argument, supporting the propositions that the cardinality of dedicated Turing machines outputting all and only the computable binary digital sequences can only be denumerable, and yet must also be nondenumerable. Turing’s objections to a similar kind of diagonalization are answered, and the implications of the paradox for the concept of a (...) Turing machine, computability, computable sequences, and Turing’s effort to prove the unsolvability of the Entscheidungsproblem, are explained in light of the paradox. A solution to Turing’s Cardinality Paradox is proposed, positing a higher geometrical dimensionality of machine symbol-editing information processing and storage media than is available to canonical Turing machine tapes. The suggestion is to add volume to Turing’s discrete two-dimensional machine tape squares, considering them instead as similarly ideally connected massive three-dimensional machine information cells. Three-dimensional computing machine symbol-editing information processing cells, as opposed to Turing’s two-dimensional machine tape squares, can take advantage of a denumerably infinite potential for parallel digital sequence computing, by which to accommodate denumerably infinitely many computable diagonalizations. A three-dimensional model of machine information storage and processing cells is recommended on independent grounds as better representing the biological realities of digital information processing isomorphisms in the three-dimensional neural networks of living computers. (shrink)

Cognitive technology is an umbrella term sometimes used to designate the realm of technologies that assist, augment or simulate cognitive processes or that can be used for the achievement of cognitive aims. This technological macro-domain encompasses both devices that directly interface the human brain as well as external systems that use artificial intelligence to simulate or assist (aspects of) human cognition. As they hold the promise of assisting and augmenting human cognitive capabilities both individually and collectively, cognitive technologies could produce, (...) in the next decades, a significant effect on human cultural evolution. At the same time, due to their dual-use potential, they are vulnerable to being coopted by State and non-State actors for non-benign purposes (e.g. cyberterrorism, cyberwarfare and mass surveillance) or in manners that violate democratic values and principles. Therefore, it is the responsibility of technology governance bodies to align the future of cognitive technology with democratic principles such as individual freedom, avoidance of centralized, equality of opportunity and open development. This paper provides a preliminary description of an approach to the democratization of cognitive technologies based on six normative ethical principles: avoidance of centralized control, openness, transparency, inclusiveness, user-centeredness and convergence. This approach is designed to universalize and evenly distribute the potential benefits of cognitive technology and mitigate the risk that such emerging technological trend could be coopted by State or non-State actors in ways that are inconsistent with the principles of liberal democracy or detrimental to individuals and groups. (shrink)

This paper explores the question of whether or not the law is a computable number in the sense described by Alan Turing in his 1937 paper ‘On computable numbers with an application to the Entscheidungsproblem.’ Drawing upon the legal, social, and political context of Alan Turing’s own involvement with the law following his arrest in 1952 for the criminal offence of gross indecency, the article explores the parameters of computability within the law and analyses the applicability of Turing’s computability thesis (...) within the context of legal decision-making. (shrink)

Turing tersely mentioned a notion of ``cultural search'' while otherwise deeply engaged in the design and operations of one of the earliest computers. His idea situated the individual squarely within a collaborative intellectual environment, but did he mean to suggest this in the form of a general information system? In the same writing Turing forecast mechanizations of proofs and outlined genetical searches, much later implemented in cellular automata. The conjecture explores the networked data-information-knowledge continuum as the subject of Turing's notions (...) of search and intelligence, using analogous models from library systems theory. Floridi's philosophy of information is posed as a potential guide to applied information services design of the Turing type. The initial problem is to identify a minimal set of assumptions from Turing's essay beyond the general context of computing. This set will form a bridge to an analogous set of principles in library systems models by eliciting supporting evidence in the literature relating the two. Finally it will be shown how Floridi's philosophy of information more fully encompasses Turing's insight in view of the conjecture. (shrink)

John Searle's Chinese room argument is perhaps the most influential andwidely cited argument against artificial intelligence (AI). Understood astargeting AI proper – claims that computers can think or do think– Searle's argument, despite its rhetorical flash, is logically andscientifically a dud. Advertised as effective against AI proper, theargument, in its main outlines, is an ignoratio elenchi. It musterspersuasive force fallaciously by indirection fostered by equivocaldeployment of the phrase "strong AI" and reinforced by equivocation on thephrase "causal powers" (at least) equal (...) to those of brains." On a morecarefully crafted understanding – understood just to targetmetaphysical identification of thought with computation ("Functionalism"or "Computationalism") and not AI proper the argument is still unsound,though more interestingly so. It's unsound in ways difficult for high church– "someday my prince of an AI program will come" – believersin AI to acknowledge without undermining their high church beliefs. The adhominem bite of Searle's argument against the high church persuasions of somany cognitive scientists, I suggest, largely explains the undeserved reputethis really quite disreputable argument enjoys among them. (shrink)

The aim of this paper is to grasp the relevant distinctions between various ways in which models and simulations in Artificial Intelligence (AI) relate to cognitive phenomena. In order to get a systematic picture, a taxonomy is developed that is based on the coordinates of formal versus material analogies and theory-guided versus pre-theoretic models in science. These distinctions have parallels in the computational versus mimetic aspects and in analytic versus exploratory types of computer simulation. The proposed taxonomy cuts across the (...) traditional dichotomies between symbolic and embodied AI, general intelligence and symbol and intelligence and cognitive simulation and human/non-human-like AI. -/- According to the taxonomy proposed here, one can distinguish between four distinct general approaches that figured prominently in early and classical AI, and that have partly developed into distinct research programs: first, phenomenal simulations (e.g., Turing’s “imitation game”); second, simulations that explore general-level formal isomorphisms in pursuit of a general theory of intelligence (e.g., logic-based AI); third, simulations as exploratory material models that serve to develop theoretical accounts of cognitive processes (e.g., Marr’s stages of visual processing and classical connectionism); and fourth, simulations as strictly formal models of a theory of computation that postulates cognitive processes to be isomorphic with computational processes (strong symbolic AI). -/- In continuation of pragmatic views of the modes of modeling and simulating world affairs, this taxonomy of approaches to modeling in AI helps to elucidate how available computational concepts and simulational resources contribute to the modes of representation and theory development in AI research—and what made that research program uniquely dependent on them. (shrink)

-/- The aim of this paper is to grasp the relevant distinctions between various ways in which models and simulations in Artificial Intelligence (AI) relate to cognitive phenomena. In order to get a systematic picture, a taxonomy is developed that is based on the coordinates of formal versus material analogies and theory-guided versus pre-theoretic models in science. These distinctions have parallels in the computational versus mimetic aspects and in analytic versus exploratory types of computer simulation. The proposed taxonomy cuts across (...) the traditional dichotomies between symbolic and embodied AI, general intelligence and symbol and intelligence and cognitive simulation and human/non-human-like AI. -/- According to the taxonomy proposed here, one can distinguish between four distinct general approaches that figured prominently in early and classical AI, and that have partly developed into distinct research programs: first, phenomenal simulations (e.g., Turing’s “imitation game”); second, simulations that explore general-level formal isomorphisms in pursuit of a general theory of intelligence (e.g., logic-based AI); third, simulations as exploratory material models that serve to develop theoretical accounts of cognitive processes (e.g., Marr’s stages of visual processing and classical connectionism); and fourth, simulations as strictly formal models of a theory of computation that postulates cognitive processes to be isomorphic with computational processes (strong symbolic AI). -/- In continuation of pragmatic views of the modes of modeling and simulating world affairs, this taxonomy of approaches to modeling in AI helps to elucidate how available computational concepts and simulational resources contribute to the modes of representation and theory development in AI research—and what made that research program uniquely dependent on them. (shrink)

The Turing test has been studied and run as a controlled experiment and found to be underspecified and poorly designed. On the other hand, it has been defended and still attracts interest as a test for true artificial intelligence (AI). Scientists and philosophers regret the test’s current status, acknowledging that the situation is at odds with the intellectual standards of Turing’s works. This article refers to this as the Turing Test Dilemma, following the observation that the test has been under (...) discussion for over seventy years and still is widely seen as either too bad or too good to be a valuable experiment for AI. An argument that solves the dilemma is presented, which relies on reconstructing the Turing test as a thought experiment in the modern scientific tradition. It is argued that Turing’s exposition of the imitation game satisfies Mach’s characterization of the basic method of thought experiments and that Turing’s uses of his test satisfy Popper’s conception of the critical and heuristic uses of thought experiments and Kuhn’s association of thought experiments to conceptual change. It is emphasized how Turing methodically varied the imitation game design to address specific challenges posed to him by other thinkers and how his test illustrates a property of the phenomenon of intelligence and suggests a hypothesis on machine learning. This reconstruction of the Turing test provides a rapprochement to the conflicting views on its value in the literature. (shrink)

Turing made strong statements about the future of machines in society. This article asks how they can be interpreted to advance our understanding of Turing’s philosophy. His irony has been largely caricatured or minimized by historians, philosophers, scientists, and others. Turing is often portrayed as an irresponsible scientist, or associated with childlike manners and polite humor. While these representations of Turing have been widely disseminated, another image suggested by one of his contemporaries, that of a nonconformist, utopian, and radically progressive (...) thinker reminiscent of the English Romantic poet Percy B. Shelley, has remained largely underexplored. Following this image, I will reconstruct the argument underlying what Turing called (but denied being guilty of) his “Promethean irreverence” (1947–1951) as a utopian satire directed against chauvinists of all kinds, especially intellectuals who might sacrifice independent thought to maintain their power. These, Turing hoped, would eventually be rivaled and surpassed by intelligent machines and transformed into ordinary people, as work once considered “intellectual” would be transformed into non-intellectual, “mechanical” work. I study Turing’s irony in its historical context and follow the internal logic of his arguments to their limit. I suggest that Turing genuinely believed that the possibilities of the machines he envisioned were not utopian dreams, and yet he conceived them from a utopian frame of mind, aspiring to a different society. His ever-learning child machines, whose intelligence would grow out of their own individual experiences, would help distribute power. (shrink)

In 1950, Alan Turing proposed his iconic imitation game, calling it a ‘test’, an ‘experiment’, and the ‘the only really satisfactory support’ for his view that machines can think. Following Turing’s rhetoric, the ‘Turing test’ has been widely received as a kind of crucial experiment to determine machine intelligence. In later sources, however, Turing showed a milder attitude towards what he called his ‘imitation tests’. In 1948, Turing referred to the persuasive power of ‘the actual production of machines’ rather than (...) that of a controlled experiment. Observing this, I propose to distinguish the logical structure from the rhetoric of Turing’s argument. I argue that Turing’s proposal of a crucial experiment may have been a concession to meet the standards of his interlocutors more than his own, while his construction of machine intelligence rather reveals a method of successive idealizations and exploratory experiments. I will draw a parallel with Galileo’s construction of idealized fall in a void and the historiographical controversies over the role of experiment in Galilean science. I suggest that Turing, like Galileo, relied on certain kinds of experiment, but also on rhetoric and propaganda to inspire further research that could lead to convincing scientific and technological progress. (shrink)

The presence of intelligence and rationality in Artificial Intelligence and the Internet requires a new context of analysis in which Herbert Simon’s approach to the sciences of the artificial is surpassed in order to grasp the role of information in our contemporary setting. This new framework requires taking into account some relevant aspects. In the historical endeavor of building up AI and the Internet, minds and machines have interacted over the years and in many ways through the interrelation between scientific (...) creativity and technological innovation. Philosophically, minds and machines can have epistemological, methodological and ontological differences, which are based on the distinct configuration of human intelligence and artificial intelligence. Their comparison with rationality and its various forms is particularly relevant. Scientifically, AI and the Internet belong to the sciences of the artificial, because they work on designs that search for specific aims, following selected processes in order to achieve expected results. Technologically, AI and the Internet require the support of information and communication technologies. These have an instrumental role regarding the existence of AI and the Internet. Also ICT shape their diverse forms of configuration over the years.Within this framework, this paper offers a new context of analysis that goes beyond Simon’s and follows four main steps: the interaction between scientific creativity and technological innovation as the philosophico-methodological setting for Artificial Intelligence and the Internet; artificial intelligence and human intelligence as epistemological basis for machines and minds, where the differences between artificial intelligence and human intelligence are made explicit and the analysis of minds and machines is made from the perspective of rationality ; intention and its difference with design of machine learning are considered to distinguish human intelligence from artificial intelligence; and the internal and external aspects of artificial designs in contemporary society are considered through the perspective of rationality, which leads to the transition from intelligence to rationality in the Internet as well as to the historicity of information. (shrink)

Este artículo analiza el Test de Turing, uno de los métodos más famosos y controvertidos para evaluar la existencia de vida mental en la Filosofía de la Mente, revelando dos mitos filosóficos comúnmente aceptados y criticando su dogma. En primer lugar, se muestra por qué Turing nunca propuso una definición de inteligencia. En segundo lugar, se refuta que el Test de Turing involucre condiciones necesarias o suficientes para la inteligencia. En tercer lugar, teniendo presente el objetivo y el tipo de (...) evidencia que recopila, se considera si el Test de Turing cuenta como un experimento científico a la luz de la concepción de Fodor. Finalmente, se argumenta que Turing simpatiza con una forma de Conductismo, confundiendo la simulación -un proceso epistémico que, gobernado por la verosimilitud, es eficaz cuando alguien es causado a creer que el computador es inteligente- con la duplicación de la inteligencia en cuanto propiedad, lo que ocurre a nivel ontológico. Tal confusión implica un dogma y explica por qué, a pesar de haber sido propuesto como una solución final a la problemática de si las máquinas programadas piensan, el Test de Turing ha tenido precisamente el efecto contrario en más de cinco décadas, estimulando el debate filosófico en torno a la naturaleza de lo mental. (shrink)

An evaluation of the 2008 Loebner contest.