B. Jack Copeland

It is not widely realised that Turing was probably the first person to consider building computing machines out of simple, neuron-like elements connected together into networks in a largely random manner. Turing called his networks ‘unorganised machines’. By the application of what he described as ‘appropriate interference, mimicking education’ an unorganised machine can be trained to perform any task that a Turing machine can carry out, provided the number of ‘neurons’ is sufficient. Turing proposed simulating both the behaviour of the network and the training process by means of a computer program. We outline Turing's connectionist project of 1948.

Presupposing no familiarity with the technical concepts of either philosophy or computing, this clear introduction reviews the progress made in AI since the inception of the field in 1956. Copeland goes on to analyze what those working in AI must achieve before they can claim to have built a thinking machine and appraises their prospects of succeeding. There are clear introductions to connectionism and to the language of thought hypothesis which weave together material from philosophy, artificial intelligence and neuroscience. John Searle's attacks on AI and cognitive science are countered and close attention is given to foundational issues, including the nature of computation, Turing Machines, the Church-Turing Thesis and the difference between classical symbol processing and parallel distributed processing. The book also explores the possibility of machines having free will and consciousness and concludes with a discussion of in what sense the human brain may be a computer.

Church's Thesis (CT) was first published by Alonzo Church in 1935. CT is a proposition that identifies two notions: an intuitive notion of an effectively computable function defined in natural numbers with the notion of a recursive function. Despite the many efforts of prominent scientists, Church's Thesis has never been disproven. There exists a vast literature concerning the thesis. The aim of this book is to provide a one volume summary of the state of research on Church's Thesis. These include the following: different formulations of CT, CT and intuitionism, CT and intensional mathematics, CT and physics, the epistemic status of CT, CT and philosophy of mind, provability of CT and CT and functional programming. Adam Olszewski, is assistant professor of the philosophy of mathematics and mathematical logic at the Department of Philosophy of Pontifical Academy of Theology, Cracow (Poland). Jan Wolenski is professor of philosophy, Institute of Philosphy, Jagiellonian University, Cracow (Poland). He is one of the most distinguished logicians in Poland. Robert Janusz is assistant professor in the Department of Philosophy of Ignatius College, Cracow (Poland).

Alan Turing anticipated many areas of current research incomputer and cognitive science. This article outlines his contributionsto Artificial Intelligence, connectionism, hypercomputation, andArtificial Life, and also describes Turing's pioneering role in thedevelopment of electronic stored-program digital computers. It locatesthe origins of Artificial Intelligence in postwar Britain. It examinesthe intellectual connections between the work of Turing and ofWittgenstein in respect of their views on cognition, on machineintelligence, and on the relation between provability and truth. Wecriticise widespread and influential misunderstandings of theChurch–Turing thesis and of the halting theorem. We also explore theidea of hypercomputation, outlining a number of notional machines that“compute the uncomputable.”

The story of Turing’s pioneering work in creating the first computer-generated musical notes in Manchester in 1948–1949 is told, as well as the story of Christopher Strachey ’s work (later Oxford’s first professor of computing), who extended Turing’s note-playing routines to create computer-generated melodies. Recordings were made in Turing’s Computing Machine Laboratory by the British Broadcasting Corporation (BBC) in 1951: by analyzing Turing’s programming manual for the Manchester machine—the first ever written for a stored-program computer—and utilizing retrospective computer analysis of the recordings, a kind of “digital archaeology” is employed in order to reconstruct the Turing-style routines that were used to play the music recorded by the BBC. These techniques have also enabled us to restore the recordings. We establish Turing’s leading role in the history of computer music.

Respected scholars regard pre-Buddhist philosopher Sañjaya Belaṭṭhiputta as originator of the catuṣkoṭi and catuṣkoṭi vinirmukta. We argue that the early texts do not support this view; the question of the origin of these argument-forms is open. While the Sāmaññaphala Sutta and some of its parallels portray Sañjaya as deploying the catuṣkoṭi, nothing in these passages suggests he was its originator. The situation concerning the catuṣkoṭi vinirmukta is even more surprising: There is nothing in the early Pāli texts and their parallels—nor in Buddhagosa's famous commentary on the early texts—to show that Sañjaya even deployed the catuṣkoṭi vinirmukta, let alone originated it. Our investigations also call into question the standard portrayal of Sañjaya as an obfuscator and prevaricator. He may have been a more interesting and able philosopher than the Sāmaññaphala Sutta, and modern accounts based on it, maintain.

Respected modern scholars regard the pre-Buddhist philosopher Sañjaya Belaṭṭhiputta—a significant figure in the Buddhist canon—as the originator of the important classical argument- forms known as the catuṣkoṭi and catuṣkoṭi vinirmukta. We argue that the early Buddhist texts do not in fact support this view of the origin of these argument-forms; the question of their origin is open. While it is certainly true that the Pāli Sāmaññaphala Sutta and some of its parallels portray Sañjaya as deploying the catuṣkoṭi, there is nothing in these passages to suggest that he was its originator. The situation concerning the catuṣkoṭi vinirmukta is perhaps even more surprising: There is nothing in the early Pāli texts and their parallels—nor in Buddhagosa’s famous Pāli commentary on the early texts—to show that Sañjaya even deployed the catuṣkoṭi vinirmukta let alone originated it. Further, our investigations also call into question the standard portrayal of Sañjaya as an obfuscator and prevaricator. It appears he may have been a more interesting and able philosopher than the Sāmaññaphala Sutta—and modern accounts based on it—maintain.

Do the dynamics of a physical system determine what function the system computes? Except in special cases, the answer is no: it is often indeterminate what function a given physical system computes. Accordingly, care should be taken when the question ‘What does a particular neuronal system do?’ is answered by hypothesising that the system computes a particular function. The phenomenon of the indeterminacy of computation has important implications for the development of computational explanations of biological systems. Additionally, the phenomenon lends some support to the idea that a single neuronal structure may perform multiple cognitive functions, each subserved by a different computation. We provide an overarching conceptual framework in order to further the philosophical debate on the nature of computational indeterminacy and computational explanation.