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8 pages, 239 KiB

Open AccessArticle

Effective Procedures

by Nathan Salmon

Philosophies 2023, 8(2), 27; https://doi.org/10.3390/philosophies8020027 - 16 Mar 2023

Viewed by 1472

The “somewhat vague, intuitive” notion from computability theory of an effective procedure (method) or algorithm can be fairly precisely defined, even if it does not have a purely mathematical definition—and even if (as many have asserted) for that reason, the Church–Turing thesis (that [...] Read more.

The “somewhat vague, intuitive” notion from computability theory of an effective procedure (method) or algorithm can be fairly precisely defined, even if it does not have a purely mathematical definition—and even if (as many have asserted) for that reason, the Church–Turing thesis (that the effectively calculable functions on natural numbers are exactly the general recursive functions), cannot be proved. However, it is logically provable from the notion of an effective procedure, without reliance on any (partially) mathematical thesis or conjecture concerning effective procedures, such as the Church–Turing thesis, that the class of effective procedures is undecidable, i.e., that there is no effective procedure for ascertaining whether a given procedure is effective. The proof does not even appeal to a precise definition of ‘effective procedure’. Instead, it relies solely and entirely on a basic grasp of the intuitive notion of such a procedure. Though the result itself is not surprising, it is also not without significance. It has the consequence, for example, that the solution to a decision problem, if it is to be complete, must be accompanied by a separate argument that the proposed ascertainment procedure is, in fact, a decision procedure, i.e., effective—for example, that it invariably terminates with the correct verdict. Full article

(This article belongs to the Special Issue Turing the Philosopher: Established Debates and New Developments)

30 pages, 1737 KiB

Open AccessArticle

Turing and Von Neumann: From Logic to the Computer

by B. Jack Copeland and Zhao Fan

Philosophies 2023, 8(2), 22; https://doi.org/10.3390/philosophies8020022 - 9 Mar 2023

Viewed by 5240

Abstract

This article provides a detailed analysis of the transfer of a key cluster of ideas from mathematical logic to computing. We demonstrate the impact of certain of Turing’s logico-philosophical concepts from the mid-1930s on the emergence of the modern electronic computer—and so, in [...] Read more.

This article provides a detailed analysis of the transfer of a key cluster of ideas from mathematical logic to computing. We demonstrate the impact of certain of Turing’s logico-philosophical concepts from the mid-1930s on the emergence of the modern electronic computer—and so, in consequence, Turing’s impact on the direction of modern philosophy, via the computational turn. We explain why both Turing and von Neumann saw the problem of developing the electronic computer as a problem in logic, and we describe their joint journey from logic to electronic computation. While much has been written about Turing’s and von Neumann’s individual contributions to the development of the computer, this article investigates less well-known terrain: their interactions and mutual influences. Along the way we argue against ‘logic skeptics’ and ‘Turing skeptics’, who claim that neither logic nor Turing played any significant role in the creation of the modern computer. Full article

(This article belongs to the Special Issue Turing the Philosopher: Established Debates and New Developments)

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20 pages, 331 KiB

Open AccessArticle

Turing’s Biological Philosophy: Morphogenesis, Mechanisms and Organicism

by Hajo Greif, Adam Kubiak and Paweł Stacewicz

Philosophies 2023, 8(1), 8; https://doi.org/10.3390/philosophies8010008 - 13 Jan 2023

Cited by 1 | Viewed by 2850

Abstract

Alan M. Turing’s last published work and some posthumously published manuscripts were dedicated to the development of his theory of organic pattern formation. In “The Chemical Basis of Morphogenesis” (1952), he provided an elaborated mathematical formulation of the theory of the origins [...] Read more.

Alan M. Turing’s last published work and some posthumously published manuscripts were dedicated to the development of his theory of organic pattern formation. In “The Chemical Basis of Morphogenesis” (1952), he provided an elaborated mathematical formulation of the theory of the origins of biological form that had been first proposed by Sir D’Arcy Wendworth Thompson in On Growth and Form (1917/1942). While arguably his most mathematically detailed and his systematically most ambitious effort, Turing’s morphogenetical writings also form the most thematically self-contained and least philosophically explored part of his work. We dedicate our inquiry to the reasons and the implications of Turing’s choice of biological topic and viewpoint. We will probe for possible factors in Turing’s choice that go beyond availability and acquaintance with On Growth and Form. On these grounds, we will explore how and to what extent his theory of morphogenesis actually ties in with his concept of mechanistic computation. Notably, Thompson’s pioneering work in biological ‘structuralism’ was organicist in outlook and explicitly critical of the Darwinian approaches that were popular with Turing’s cyberneticist contemporaries—and partly used by Turing himself in his proto-connectionist models of learning. Resolving this apparent dichotomy, we demonstrate how Turing’s quest for mechanistic explanations of how organisation emerges in nature leaves room for a non-mechanist view of nature. Full article

(This article belongs to the Special Issue Turing the Philosopher: Established Debates and New Developments)

24 pages, 413 KiB

Open AccessArticle

“Surveyability” in Hilbert, Wittgenstein and Turing

by Juliet Floyd

Philosophies 2023, 8(1), 6; https://doi.org/10.3390/philosophies8010006 - 11 Jan 2023

Cited by 1 | Viewed by 2753

Abstract

An investigation of the concept of “surveyability” as traced through the thought of Hilbert, Wittgenstein, and Turing. The communicability and reproducibility of proof, with certainty, are seen as earmarked by the “surveyability” of symbols, sequences, and structures of proof in all these thinkers. [...] Read more.

An investigation of the concept of “surveyability” as traced through the thought of Hilbert, Wittgenstein, and Turing. The communicability and reproducibility of proof, with certainty, are seen as earmarked by the “surveyability” of symbols, sequences, and structures of proof in all these thinkers. Hilbert initiated the idea within his metamathematics, Wittgenstein took up a kind of game formalism in the 1920s and early 1930s in response. Turing carried Hilbert’s conception of the “surveyability” of proof in metamathematics through into his analysis of what a formal system (what a step in a computation) is in “On computable numbers, with an application to the Entscheidungsproblem” (1936). Wittgenstein’s 1939 investigations of the significance of surveyability to the concept of “proof “in Principia Mathematica were influenced, both by Turing’s remarkable everyday analysis of the Hilbertian idea, and by conversations with Turing. Although Turing does not use the word “surveyability” explicitly, it is clear that the Hilbertian idea plays a recurrent role in his work, refracted through his engagement with Wittgenstein’s idea of a “language-game”. This is evinced in some of his later writings, where the “reform” of mathematical notation for the sake of human surveyability (1944/45) may be seen to draw out the Hilbertian idea. For Turing, as for Wittgenstein, the need for “surveyability” earmarks the evolving culture of humans located in an evolving social and scientific world, just as it had for Hilbert. Full article

(This article belongs to the Special Issue Turing the Philosopher: Established Debates and New Developments)

13 pages, 239 KiB

Open AccessArticle

Gödel, Turing and the Iconic/Performative Axis

by Juliette Cara Kennedy

Philosophies 2022, 7(6), 141; https://doi.org/10.3390/philosophies7060141 - 12 Dec 2022

Viewed by 1748

Abstract

1936 was a watershed year for computability. Debates among Gödel, Church and others over the correct analysis of the intuitive concept “human effectively computable”, an analysis at the heart of the Incompleteness Theorems, the Entscheidungsproblem, the question of what a finite computation is, [...] Read more.

1936 was a watershed year for computability. Debates among Gödel, Church and others over the correct analysis of the intuitive concept “human effectively computable”, an analysis at the heart of the Incompleteness Theorems, the Entscheidungsproblem, the question of what a finite computation is, and most urgently—for Gödel—the generality of the Incompleteness Theorems, were definitively set to rest with the appearance, in that year, of the Turing Machine. The question I explore here is, do the mathematical facts exhaust what is to be said about the thinking behind the “confluence of ideas in 1936”? I will argue for a cultural role in Gödel’s, and, by extension, the larger logical community’s absorption of Turing’s 1936 model. As scaffolding I employ a conceptual framework due to the critic Leo Marx of the technological sublime; I also make use of the distinction within the technological sublime due to Caroline Jones, between its iconic and performative modes—a distinction operating within the conceptual art of the 1960s, but serving the history of computability equally well. Full article

(This article belongs to the Special Issue Turing the Philosopher: Established Debates and New Developments)

15 pages, 293 KiB

Open AccessArticle

An Analysis of Turing’s Criterion for ‘Thinking’

by Diane Proudfoot

Philosophies 2022, 7(6), 124; https://doi.org/10.3390/philosophies7060124 - 3 Nov 2022

Cited by 5 | Viewed by 3281

Abstract

In this paper I argue that Turing proposed a new approach to the concept of thinking, based on his claim that intelligence is an ‘emotional concept’; and that the response-dependence interpretation of Turing’s ‘criterion for “thinking”’ is a better fit with his writings [...] Read more.

In this paper I argue that Turing proposed a new approach to the concept of thinking, based on his claim that intelligence is an ‘emotional concept’; and that the response-dependence interpretation of Turing’s ‘criterion for “thinking”’ is a better fit with his writings than orthodox interpretations. The aim of this paper is to clarify the response-dependence interpretation, by addressing such questions as: What did Turing mean by the expression ‘emotional’? Is Turing’s criterion subjective? Are ‘emotional’ judgements decided by social consensus? Turing’s take on these issues impacts current philosophical debates on response-dependent concepts and on the nature of artificial intelligence. Full article

(This article belongs to the Special Issue Turing the Philosopher: Established Debates and New Developments)

21 pages, 362 KiB

Open AccessArticle

Not All Computational Methods Are Effective Methods

by Mark Sprevak

Philosophies 2022, 7(5), 113; https://doi.org/10.3390/philosophies7050113 - 10 Oct 2022

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Abstract

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 [...] Read more.

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. Full article

(This article belongs to the Special Issue Turing the Philosopher: Established Debates and New Developments)

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14 pages, 278 KiB

Open AccessArticle

The Accidental Philosopher and One of the Hardest Problems in the World

by Sonje Finnestad and Eric Neufeld

Philosophies 2022, 7(4), 76; https://doi.org/10.3390/philosophies7040076 - 4 Jul 2022

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Abstract

Given the difficulties of defining “machine” and “think”, Turing proposed to replace the question “Can machines think?” with a proxy: how well can an agent engage in sustained conversation with a human? Though Turing neither described himself as a philosopher nor published much [...] Read more.

Given the difficulties of defining “machine” and “think”, Turing proposed to replace the question “Can machines think?” with a proxy: how well can an agent engage in sustained conversation with a human? Though Turing neither described himself as a philosopher nor published much on philosophical matters, his Imitation Game has stood the test of time. Most understood at that time that success would not come easy, but few would have guessed just how difficult engaging in ordinary conversation would turn out to be. Despite the proliferation of language processing tools, we have seen little progress towards doing well at the Imitation Game. Had Turing instead suggested ability at games or even translation as a proxy for intelligence, his paper might have been forgotten. We argue that these and related problems are amenable to mechanical, though sophisticated, formal techniques. Turing appears to have taken care to select sustained, productive conversation and that alone as his proxy. Even simple conversation challenges a machine to engage in the rich practice of human discourse in all its generality and variety. Full article

(This article belongs to the Special Issue Turing the Philosopher: Established Debates and New Developments)

20 pages, 3226 KiB

Open AccessArticle

Turing’s Conceptual Engineering

by Marcin Miłkowski

Philosophies 2022, 7(3), 69; https://doi.org/10.3390/philosophies7030069 - 20 Jun 2022

Viewed by 2763

Abstract

Alan Turing’s influence on subsequent research in artificial intelligence is undeniable. His proposed test for intelligence remains influential. In this paper, I propose to analyze his conception of intelligence by relying on traditional close reading and language technology. The Turing test is interpreted [...] Read more.

Alan Turing’s influence on subsequent research in artificial intelligence is undeniable. His proposed test for intelligence remains influential. In this paper, I propose to analyze his conception of intelligence by relying on traditional close reading and language technology. The Turing test is interpreted as an instance of conceptual engineering that rejects the role of the previous linguistic usage, but appeals to intuition pumps instead. Even though many conceive his proposal as a prime case of operationalism, it is more plausibly viewed as a stepping stone toward a future theoretical construal of intelligence in mechanical terms. To complete this picture, his own conceptual network is analyzed through the lens of distributional semantics over the corpus of his written work. As it turns out, Turing’s conceptual engineering of the notion of intelligence is indeed quite similar to providing a precising definition with the aim of revising the usage of the concept. However, that is not its ultimate aim: Turing is after a rich theoretical understanding of thinking in mechanical, i.e., computational, terms. Full article

(This article belongs to the Special Issue Turing the Philosopher: Established Debates and New Developments)

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8 pages, 211 KiB

Open AccessArticle

From Turing to Conscious Machines

by Igor Aleksander

Philosophies 2022, 7(3), 57; https://doi.org/10.3390/philosophies7030057 - 29 May 2022

Cited by 2 | Viewed by 2936

Abstract

In the period between Turing’s 1950 “Computing Machinery and Intelligence” and the current considerable public exposure to the term “artificial intelligence (AI)”, Turing’s question “Can a machine think?” has become a topic of daily debate in the media, the home, and, indeed, the [...] Read more.

In the period between Turing’s 1950 “Computing Machinery and Intelligence” and the current considerable public exposure to the term “artificial intelligence (AI)”, Turing’s question “Can a machine think?” has become a topic of daily debate in the media, the home, and, indeed, the pub. However, “Can a machine think?” is sliding towards a more controversial issue: “Can a machine be conscious?” Of course, the two issues are linked. It is held here that consciousness is a pre-requisite to thought. In Turing’s imitation game, a conscious human player is replaced by a machine, which, in the first place, is assumed not to be conscious, and which may fool an interlocutor, as consciousness cannot be perceived from an individual’s speech or action. Here, the developing paradigm of machine consciousness is examined and combined with an extant analysis of living consciousness to argue that a conscious machine is feasible, and capable of thinking. The route to this utilizes learning in a “neural state machine”, which brings into play Turing’s view of neural “unorganized” machines. The conclusion is that a machine of the “unorganized” kind could have an artificial form of consciousness that resembles the natural form and that throws some light on its nature. Full article

(This article belongs to the Special Issue Turing the Philosopher: Established Debates and New Developments)

10 pages, 224 KiB

Open AccessArticle

Intuition and Ingenuity: Gödel on Turing’s “Philosophical Error”

by Long Chen

Philosophies 2022, 7(2), 33; https://doi.org/10.3390/philosophies7020033 - 18 Mar 2022

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Abstract

Despite his unreserved appreciation of Turing’s analysis for being a “precise and unquestionably adequate definition” of formal system or mechanical computability, Gödel nevertheless published a short note in 1972 claiming to have found a “philosophical error” in Turing’s argument with regard to the [...] Read more.

Despite his unreserved appreciation of Turing’s analysis for being a “precise and unquestionably adequate definition” of formal system or mechanical computability, Gödel nevertheless published a short note in 1972 claiming to have found a “philosophical error” in Turing’s argument with regard to the finite nature of mental states and memory. A natural question arises: how could Gödel enjoy the generality conferred on his results by Turing’s work, despite the error of its ways? Previous interpretative strategies by Feferman, Shagrir and others have mainly tried to resolve the disparity by distinguishing different types of arguments in Turing and taking Gödel to approve only some of them. By a more integral examination of their ideas, especially Turing’s response to the “mathematical objection” based on Gödel’s incompleteness theorem and Gödel’s own conception of finite yet non-mechanical procedures, and taking some of the main ideas of current developments in machine learning into consideration, I will try to present a new explanation for the apparent disparity, arguing that there is no “error” on Turing’s side and the seemingly conflicting views held by Turing and Gödel should best be seen as complementary, keeping intuition and ingenuity together. Full article

(This article belongs to the Special Issue Turing the Philosopher: Established Debates and New Developments)

10 pages, 243 KiB

Open AccessArticle

Computability, Notation, and de re Knowledge of Numbers

by Stewart Shapiro, Eric Snyder and Richard Samuels

Philosophies 2022, 7(1), 20; https://doi.org/10.3390/philosophies7010020 - 18 Feb 2022

Cited by 2 | Viewed by 2489

Abstract

Saul Kripke once noted that there is a tight connection between computation and de re knowledge of whatever the computation acts upon. For example, the Euclidean algorithm can produce knowledge of which number is the greatest common divisor of two numbers. Arguably, algorithms [...] Read more.

Saul Kripke once noted that there is a tight connection between computation and de re knowledge of whatever the computation acts upon. For example, the Euclidean algorithm can produce knowledge of which number is the greatest common divisor of two numbers. Arguably, algorithms operate directly on syntactic items, such as strings, and on numbers and the like only via how the numbers are represented. So we broach matters of notation. The purpose of this article is to explore the relationship between the notations acceptable for computation, the usual idealizations involved in theories of computability, flowing from Alan Turing’s monumental work, and de re propositional attitudes toward numbers and other mathematical objects. Full article

(This article belongs to the Special Issue Turing the Philosopher: Established Debates and New Developments)

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