The simulation hypothesis has recently excited renewed interest, especially in the physics and philosophy communities. However, the hypothesis specifically concerns {computers} that simulate physical universes, which means that to properly investigate it we need to couple computer science theory with physics. Here I do this by exploiting the physical Church-Turing thesis. This allows me to introduce a preliminary investigation of some of the computer science theoretic aspects of the simulation hypothesis. In particular, building on Kleene's second recursion theorem, I prove (...) that it is mathematically possible for us to be in a simulation that is being run on a computer \textit{by us}. In such a case, there would be two identical instances of us; the question of which of those is ``really us'' is meaningless. I also show how Rice's theorem provides some interesting impossibility results concerning simulation and self-simulation; briefly describe the philosophical implications of fully homomorphic encryption for (self-)simulation; briefly investigate the graphical structure of universes simulating universes simulating universes, among other issues. I end by describing some of the possible avenues for future research that this preliminary investigation reveals. (shrink)

Between inventing the concept of a universal computer in 1936 and breaking the German Enigma code during World War II, Alan Turing, the British founder of computer science and artificial intelligence, came to Princeton University to study mathematical logic. Some of the greatest logicians in the world--including Alonzo Church, Kurt Gödel, John von Neumann, and Stephen Kleene--were at Princeton in the 1930s, and they were working on ideas that would lay the groundwork for what would become known as computer (...) science. Though less well known than his other work, Turing's 1938 Princeton PhD thesis, "Systems of Logic Based on Ordinals," which includes his notion of an oracle machine, has had a lasting influence on computer science and mathematics. This book presents a facsimile of the original typescript of the thesis along with essays by Andrew Appel and Solomon Feferman that explain its still-unfolding significance. A work of philosophy as well as mathematics, Turing's thesis envisions a practical goal--a logical system to formalize mathematical proofs so they can be checked mechanically. If every step of a theorem could be verified mechanically, the burden on intuition would be limited to the axioms. Turing's point, as Appel writes, is that "mathematical reasoning can be done, and should be done, in mechanizable formal logic." Turing's vision of "constructive systems of logic for practical use" has become reality: in the twenty-first century, automated "formal methods" are now routine. Presented here in its original form, this fascinating thesis is one of the key documents in the history of mathematics and computer science. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable propositions, (...) and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter 2 argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal cognitivism and modal expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic epistemic two-dimensional hyperintensional semantics. Chapter 3 provides an abstraction principle for epistemic (hyper-)intensions. Chapter 4 advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter 5 applies the fixed points of the modal μ-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal μ-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal μ-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter 6 advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter 7 provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters 2 and 4 are availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. Chapters 8-12 provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter 8 examines the interaction between my hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of Ω-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter 9 examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest, too, that observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter 10 examines the philosophical significance of hyperintensional Ω-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter 11 provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter 12 avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between the interpretational and objective modalities and truthmakers thereof. This yields the first hyperintensional category theory in the literature. I invent a new mathematical trick in which first order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals while bypassing the category of Set in category theory. Chapter 13 examines modal responses to the alethic paradoxes. Chapter 14 examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable propositions, (...) and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal cognitivism and modal expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic two-dimensional semantics. Chapter \textbf{3} provides an abstraction principle for epistemic (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} are availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between my hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest, too, that observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between the interpretational and objective modalities and truthmakers thereof. This yields the first hyperintensional category theory in the literature. I invent a new mathematical trick in which first order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals while bypassing the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

I propose to consider the question, "Can machines think?" This should begin with definitions of the meaning of the terms "machine" and "think." The definitions might be framed so as to reflect so far as possible the normal use of the words, but this attitude is dangerous, If the meaning of the words "machine" and "think" are to be found by examining how they are commonly used it is difficult to escape the conclusion that the meaning and the answer to (...) the question, "Can machines think?" is to be sought in a statistical survey such as a Gallup poll. But this is absurd. Instead of attempting such a definition I shall replace the question by another, which is closely related to it and is expressed in relatively unambiguous words. The new form of the problem can be described in terms of a game which we call the 'imitation game." It is played with three people, a man (A), a woman (B), and an interrogator (C) who may be of either sex. The interrogator stays in a room apart front the other two. The object of the game for the interrogator is to determine which of the other two is the man and which is the woman. He knows them by labels X and Y, and at the end of the game he says either "X is A and Y is B" or "X is B and Y is A." The interrogator is allowed to put questions to A and B. We now ask the question, "What will happen when a machine takes the part of A in this game?" Will the interrogator decide wrongly as often when the game is played like this as he does when the game is played between a man and a woman? These questions replace our original, "Can machines think?". (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable propositions, (...) and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal cognitivism and modal expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic two-dimensional semantics. Chapter \textbf{3} provides an abstraction principle for epistemic (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} are availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between my hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest, too, that observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between the interpretational and objective modalities and truthmakers thereof. This yields the first hyperintensional category theory in the literature. I invent a new mathematical trick in which first order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals while bypassing the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

More than a decade ago, philosopher John Searle started a long-running controversy with his paper “Minds, Brains, and Programs” (Searle, 1980a), an attack on the ambitious claims of artificial intelligence (AI). With his now famous _Chinese Room_ argument, Searle claimed to show that despite the best efforts of AI researchers, a computer could never recreate such vital properties of human mentality as intentionality, subjectivity, and understanding. The AI research program is based on the underlying assumption that all important aspects of (...) human cognition may in principle be captured in a computational model. This assumption stems from the belief that beyond a certain level, implementational details are irrelevant to cognition. According to this belief, neurons, and biological wetware in general, have no preferred status as the substrate for a mind. As it happens, the best examples of minds we have at present have arisen from a carbon-based substrate, but this is due to constraints of evolution and possibly historical accidents, rather than to an absolute metaphysical necessity. As a result of this belief, many cognitive scientists have chosen to focus not on the biological substrate of the mind, but instead on the abstract causal structure_ _that the mind embodies (at an appropriate level of abstraction). The view that it is abstract causal structure that is essential to mentality has been an implicit assumption of the AI research program since Turing (1950), but was first articulated explicitly, in various forms, by Putnam (1960), Armstrong (1970) and Lewis (1970), and has become known as _functionalism_. From here, it is a very short step to _computationalism_, the view that computational structure is what is important in capturing the essence of mentality. This step follows from a belief that any abstract causal structure can be captured computationally: a belief made plausible by the Church–Turing Thesis, which articulates the power. (shrink)

This is the first of two papers that use off-training set (OTS) error to investigate the assumption-free relationship between learning algorithms. This first paper discusses the senses in which there are no a priori distinctions between learning algorithms. (The second paper discusses the senses in which there are such distinctions.) In this first paper it is shown, loosely speaking, that for any two algorithms A and B, there are “as many” targets (or priors over targets) for which A has lower (...) expected OTS error than B as vice versa, for loss functions like zero-one loss. In particular, this is true if A is cross-validation and B is “anti-cross-validation” (choose the learning algorithm with largest cross-validation error). This paper ends with a discussion of the implications of these results for computational learning theory. It is shown that one cannot say: if empirical misclassification rate is low, the Vapnik-Chervonenkis dimension of your generalizer is small, and the training set is large, then with high probability your OTS error is small. Other implications for “membership queries” algorithms and “punting” algorithms are also discussed. (shrink)

The epistemic arrow of time is the fact that our knowledge of the past seems to be both of a different kind and more detailed than our knowledge of the future. Just like with the other arrows of time, it has often been speculated that the epistemic arrow arises due to the second law of thermodynamics. In this paper, we investigate the epistemic arrow of time using a fully formal framework. We begin by defining a memory system as any physical (...) system whose present state can provide information about the state of the external world at some time other than the present. We then identify two types of memory systems in our universe, along with an important special case of the first type, which we distinguish as a third type of memory system. We show that two of these types of memory systems are time-symmetric, able to provide knowledge about both the past and the future. However, the third type of memory systems exploits the second law of thermodynamics, at least in all of its instances in our universe that we are aware of. The result is that in our universe, this type of memory system only ever provides information about the past. We also argue that human memory is of this third type, completing the argument. We end by scrutinizing the basis of the second law itself. This uncovers a previously unappreciated formal problem for common arguments that try to derive the second law from the “Past Hypothesis”, i.e., from the claim that the very early universe was in a state of extremely low entropy. Our analysis is indebted to prior work by one of us but expands and improves upon this work in several respects. (shrink)

La Teoría de la Computación es un campo especialmente rico para la indagación filosófica. EI debate sobre el mecanicismo y la discusión en torno a los fundamentos de la matemática son tópicos que estan directamente asociados a la Teoria de la Computación desde su misma creación como disciplina independiente. La Tesis de Turing-Church constituye uno de los resultados mas característicos en este campo estando, además, lleno de consecuencias filosóficas. En este ensayo se ofrece una guía de referencia útil a aquellos (...) que desean prestar alguna atención a estos asuntos y carecen de la base técnica o histórica que se precisa. En primer lugar se ofrece un resurnen de los principales problemas relacionados con la Tesis de Turing-Church para ofrecer a continuación información sobre sus aspectos más controvertidos. Se proponen algunos problemas no resueltos y se analiza su relevancia filosófica.Computer Science is a field specially rich for philosophical inquiry. Mechanism and the discussion around foundations of mathematics are topics directly asociated to Computer Science for its very constitution as an independent discipline. Church-Turing Thesis is one of the most characteristic results in this field and is plenty of philosophical consequences. In this article I offer a referenee guide useful for those who are willing to pay some attention to these matters and ignore the technical and historical basis needed for this task. I resume the main topics related to Church-Turing Thesis and give some informationabout the most controversial aspects of this subject. Some open questions are settled for further investigation paying special attention to their philosophical importance. (shrink)

La Teoría de la Computación es un campo especialmente rico para la indagación filosófica. EI debate sobre el mecanicismo y la discusión en torno a los fundamentos de la matemática son tópicos que estan directamente asociados a la Teoria de la Computación desde su misma creación como disciplina independiente. La Tesis de Turing-Church constituye uno de los resultados mas característicos en este campo estando, además, lleno de consecuencias filosóficas. En este ensayo se ofrece una guía de referencia útil a aquellos (...) que desean prestar alguna atención a estos asuntos y carecen de la base técnica o histórica que se precisa. En primer lugar se ofrece un resurnen de los principales problemas relacionados con la Tesis de Turing-Church para ofrecer a continuación información sobre sus aspectos más controvertidos. Se proponen algunos problemas no resueltos y se analiza su relevancia filosófica.Computer Science is a field specially rich for philosophical inquiry. Mechanism and the discussion around foundations of mathematics are topics directly asociated to Computer Science for its very constitution as an independent discipline. Church-Turing Thesis is one of the most characteristic results in this field and is plenty of philosophical consequences. In this article I offer a referenee guide useful for those who are willing to pay some attention to these matters and ignore the technical and historical basis needed for this task. I resume the main topics related to Church-Turing Thesis and give some informationabout the most controversial aspects of this subject. Some open questions are settled for further investigation paying special attention to their philosophical importance. (shrink)

Writings, including articles, letters, and unpublished work, by one of the twentieth century's most influential figures in mathematical logic and philosophy. Alonzo Church's long and distinguished career in mathematics and philosophy can be traced through his influential and wide-ranging writings. Church published his first article as an undergraduate at Princeton in 1924 and his last shortly before his death in 1995. This volume collects all of his published articles, many of his reviews, his monograph The Calculi of Lambda-Conversion, the introduction (...) to his important and authoritative textbook Introduction to Mathematical Logic, a substantial amount of previously unpublished work (including chapters for the unfinished second volume of Introduction to Mathematical Logic), and a selection of letters to such correspondents as Rudolf Carnap and W. V. O. Quine. With the exception of the reviews, letters, and unpublished work, these appear in chronological order, for the most part in the format in which they were originally published. Church's work in calculability, especially the monograph on the lambda-calculus, helped lay the foundation for theoretical computer science; it attracted the interest of Alan Turing, who later completed his PhD under Church's supervision. (Church coined the term “Turing machine” in a review.) Church's influential textbook, still in print, defined the field of mathematical logic for a generation of logicians. In addition, his close connection with the Association for Symbolic Logic and his many years as review editor for the Journal of Symbolic Logic are documented in the reviews included here. (shrink)

There are four types of information an agent can have concerning the state of the universe: information acquired via observation, via control, via prediction, or via retrodiction, i.e., memory. Each of these four types of information appear to rely on a different kind of physical device. However it turns out that there is some mathematical structure that is common to those four types of devices. Any device that possesses that structure is known as an “inference device”. Here I review (...) some of the properties of IDs, including their relation with Turing machines, and quantum mechanics. I also review the bounds on the joint information about the physical universe that can be held by any set of IDs. These bounds constrain the possible mathematical structure of any universe that contains agents with information concerning that universe in which they are embedded. (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)

We propose a reflection on the construction of scientific knowledge and in so doing an image of this knowledge. This will allow us to develop a comparative analysis of some of the main principles underpinning the constitution of the different sciences. We will highlight the role of critical thought in science, or even “negative results,” which pose limits and hence open new trajectories. In particular, we will address a misleading point of view, based on some informal concepts taken from (...) computer science, which dominates the biological imaginary. An “ethics of knowledge” will follow, as a critical and open perspective, capable of taking on the well-intentioned responsibility of proposing universal, though not absolute, principles of knowledge. (shrink)

The Way of Ideas died an ignoble death, committed to the flames by behaviorist empiricists. Ideas, pictures in the head, perished with the Way. By the time those empiricists were supplanted at the helm by functionalists and causal theorists, a revolution had taken place in linguistics and the last thing anyone wanted to do was revive images as the medium of thought. Currently, some but not all cognitive scientists think that there probably are mental images - experiments in cognitive psychology (...) (e.g. Shepard and Metzler 1971) have shown it to be plausible to posit mental images. Even so, the phenomenon of mental imagery has been largely regarded as peripheral in cognition, perhaps even epiphenomenal. Images cannot fix the content of thought (intentions, rules), the Wittgenstein story went. The central processes of thought, so the post-Wittgenstein story goes, require a propositional representation system, a language of thought, universal and modeled on the machine languages of computers. The language of thought is compositional, productive, and, leading advocates argue, has a causal semantics. Images lack all of these essential qualities and so are hopeless as key players in thinking. (shrink)

We describe a strategy for integration of data that is based on the idea of semantic enhancement. The strategy promises a number of benefits: it can be applied incrementally; it creates minimal barriers to the incorporation of new data into the semantically enhanced system; it preserves the existing data (including any existing data-semantics) in their original form (thus all provenance information is retained, and no heavy preprocessing is required); and it embraces the full spectrum of data sources, types, models, and (...) modalities (including text, images, audio, and signals). The result of applying this strategy to a given body of data is an evolving Dataspace that allows the application of a variety of integration and analytic processes to diverse data contents. We conceive semantic enhancement (SE) as a lightweight and flexible process that leverages the richness of the structured contents of the Dataspace without adding storage and processing burdens to what, in the intelligence domain, will be an already storage- and processing-heavy starting point. SE works not by changing the data to which it is applied, but rather by adding an extra semantic layer to this data. We sketch how the semantic enhancement approach can be applied consistently and in cumulative fashion to new data and data-models that enter the Dataspace. (shrink)

The Way of Ideas died an ignoble death, committed to the flames by behaviorist empiricists. Ideas, pictures in the head, perished with the Way. By the time those empiricists were supplanted at the helm by functionalists and causal theorists, a revolution had taken place in linguistics and the last thing anyone wanted to do was revive images as the medium of thought. Currently, some but not all cognitive scientists think that there probably are mental images - experiments in cognitive psychology (...) (e.g. Shepard and Metzler 1971) have shown it to be plausible to posit mental images. Even so, the phenomenon of mental imagery has been largely regarded as peripheral in cognition, perhaps even epiphenomenal. Images cannot fix the content of thought (intentions, rules), the Wittgenstein story went. The central processes of thought, so the post-Wittgenstein story goes, require a propositional representation system, a language of thought, universal and modeled on the machine languages of computers. The language of thought is compositional, productive, and, leading advocates argue, has a causal semantics. Images lack all of these essential qualities and so are hopeless as key players in thinking. (shrink)

I came to philosophy as a refugee from mathematics and statistics. I was impressed by their power at codifying and precisifying antecedently understood but rather nebulous concepts, and at clarifying and exploring their interrelations. I enjoyed learning many of the great theorems of probability theory—equations rich in ‘P’s of this and of that. But I wondered what is this ‘P’? What do statements of probability mean? When I asked one of my professors, he looked at me like I needed medication. (...) That medication was provided by philosophy, and I found it first during my Masters at the University of Western Ontario, working with Bill Harper, and then during my Ph.D. at Princeton, working with Bas van Fraassen, David Lewis, and Richard Jeffrey—all deft practitioners of formal methods. I found that philosophers had been asking my question about ‘P’ since about 1650, but they were still struggling to find definitive answers. I was also introduced to a host of other philosophical problems, and it became clear to me within nanoseconds of arriving at U.W.O. that I wanted to spend my life pursuing some of them. But I kept being drawn back to the formal methods of mathematics, and in particular of probability theory. It may be worthwhile to pause for a moment and to ask “What are formal methods?” Of course, it’s easy to come up with examples: the use of various logical systems, computational algorithms, causal graphs, information theory, probability theory and mathematics more generally. What do they have in common? They are all abstract representational systems. Sometimes the systems are studied in their own.. (shrink)

Computational complexity theory is a branch of computer science dedicated to classifying computational problems in terms of their difficulty. While computability theory tells us what we can compute in principle, complexity theory informs us regarding our practical limits. In this chapter I argue that the science of \emph{quantum computing} illuminates complexity theory by emphasising that its fundamental concepts are not model-independent, but that this does not, as some suggest, force us to radically revise the foundations of the theory. For (...) model-independence never has been essential to those foundations. The fundamental aim of complexity theory is to describe what is achievable in practice under various models of computation for our various practical purposes. Reflecting on quantum computing illuminates complexity theory by reminding us of this, too often under-emphasised, fact. (shrink)

This peer-reviewed book is a concise introduction to key philosophical questions in artificial intelligence that have long been debated by many of the great minds in computer science, cognitive science and philosophy, from Gottfried Leibniz to Alan Turing to Hubert Dreyfus. Topics include the limits of and problems in trying to create artificial general intelligence, if a computer can really think and have human-like sentience, how to identify intelligence in a computer, ethical and danger issues, and if human-like (...) consciousness and sentience are required to create artificial general intelligence. (shrink)

This volume examines two main questions: What is linguistics about? And how do the results of linguistic theorizing bear on inquiry in related fields, particularly in psychology? The book develops views that depart from received wisdom in both philosophy and linguistics. With regard to questions concerning the subject matter, methodological goals, and ontological commitments of formal syntactic theorizing, it argues that the cognitive conception adopted by most linguists and philosophers is not the only acceptable view, and that the arguments in (...) its favor collapse under scrutiny. Nevertheless, as the book shows, a detailed examination of the relevant psycholinguistic results and computational models does support the claim that the theoretical constructs of formal linguistics are operative in real-time language comprehension. These constructs fall into two categories: mental phrase markers and mental syntactic principles. Both are indeed psychologically real, but in importantly different ways. The book concludes by drawing attention to the importance of the often-elided distinction between personal and subpersonal psychological states and processes, as well as the logical character of dispositional and occurrent states. By clarifying these concepts, particularly by reference to up-and-running psychological and computational models, the book yields a richer and more satisfying perspective on the psychological reality of language. (shrink)

Legally blind participants were able to identify a visual stimulus attribute in the absence of consciously identifying its presence. Specifically, participants—with their corrective lenses removed—correctly guessed the hour-hand position above chance on a clockface shown on a computer screen. This occurred both when presented in a 1-clockface display , as well as when shown a display containing 4 clockfaces , in which only 1 face contained a hand. Even more striking, hand identification accuracy in the 4-clockface condition was comparable whether (...) the clockface containing the hand was or was not correctly identified. That legally blind individuals are capable of identifying stimulus attributes without conscious awareness provides an additional vehicle for exploring implicit perception. Consistent with previous research, the visualsystem can apparently cope with degraded visual input through information available through a secondary pathway via the superior colliculi. (shrink)

Since the announcement and establishment of the Oversight Board (OB) by the technology company Meta as an independent institution reviewing Facebook and Instagram’s content moderation decisions, the OB has been subjected to scholarly scrutiny ranging from praise to criticism. However, there is currently no overarching framework for understanding the OB’s various strengths and weaknesses. Consequently, this article analyses, organises, and supplements academic literature, news articles, and Meta and OB documents to understand the OB’s strengths and weaknesses and how it can (...) be improved. Significant strengths include its ability to enhance the transparency of content moderation decisions and processes, to effect reform indirectly through policy recommendations, and its assertiveness in interpreting its jurisdiction and overruling Meta. Significant weaknesses include its limited jurisdiction, limited impact, Meta’s control over the OB’s precedent, and its lack of diversity. The analysis of a recent OB case in Ethiopia shows these strengths and weaknesses in practice. The OB’s relationship with Meta and governments will lead to challenges and opportunities shaping its future development. Reforms to the OB should improve the OB’s control over its precedent, apply OB precedent to currently disputed cases, and clarify the standards for invoking OB precedent. Finally, these reforms provide the foundation for an additional improvement to address the OB’s institutional weaknesses, by involving users in determining whether the OB’s precedent should be applied to decide current content moderation disputes. (shrink)

This volume began as a remembrance of Alonzo Church while he was still with us and is now finally complete. It contains papers by many well-known scholars, most of whom have been directly influenced by Church's own work. Often the emphasis is on foundational issues in logic, mathematics, computation, and philosophy - as was the case with Church's contributions, now universally recognized as having been of profound fundamental significance in those areas. The volume will be of interest to logicians, computer (...) scientists, philosophers, and linguists. The contributions concern classical first-order logic, higher-order logic, non-classical theories of implication, set theories with universal sets, the logical and semantical paradoxes, the lambda-calculus, especially as it is used in computation, philosophical issues about meaning and ontology in the abstract sciences and in natural language, and much else. The material will be accessible to specialists in these areas and to advanced graduate students in the respective fields. (shrink)

Current fears of a “reproducibility crisis” have led researchers, sources of scientific funding, and the public to question both the efficacy and trustworthiness of science. Suggested policy changes have been focused on statistical problems, such as p-hacking, and issues of experimental design and execution. However, “reproducibility” is a broad concept that includes a number of issues. Furthermore, reproducibility failures occur even in fields such as mathematics or computer science that do not have statistical problems or issues with experimental design. Most (...) importantly, these proposed policy changes ignore a core feature of the process of scientific inquiry that occurs after reproducibility failures: the integration of conflicting observations and ideas into a coherent theory. (shrink)

Against Nature – Chapter Abstracts Chapter 1. A Transdisciplinary Approach. In this short book you will find philosophy – metaphysical and political - economics, critical theory, complexity theory, ecology, sociology, journalism, and much else besides, along with the signposts and reference texts of the Information Systems field. Such transdisciplinarity is a challenge for both author and reader. Such books are often problematic: sections that are just old hat to one audience are by contrast completely new and difficult to another. My (...) hope is that in the interconnections, arguments and thrust of this polemic, readers will discover both interest and insight, alongside a range of new avenues to explore. This introductory chapter sets the scene – today’s digital world of Tech Giants and Fake News, its roots in the philosophical arguments of the 1920s, and the book’s key claims: (i) that the early 20th century philosophical grounding of today’s digital revolution is culpable in digital’s (growing) contribution to the ecological catastrophe unfolding in the 21st century; (ii) that process philosophy offers a new way to rethink that philosophical grounding, and reshape the digital revolution to support strategies to counter that catastrophe. Chapter 2. The Problem with Digital. This chapter begins with a brief overview of the research approaches in information systems as an academic field, before turning to the deeper roots of its malaise, in individualism, and its looming consequences. The three branches of Information Systems research, in academia, prove to be a useful lens through which to understand the field: Positivism, Interpretivism, and the Critical stance taken by this book. The ‘scientism’ at the root of positivism is examined, and the positivism in Information Systems critiqued as a historically contingent response to the ascendancy of a new brand of economics in Business Schools after the Second World War. But the computational market-fundamentalist form of economics sponsored in the 1950s (and applied by governments since the 1970s) centred around notions of the individual rational actor as an information processor. The philosophical underpinning of methodological and possessive individualism in this approach is exposed, and its influence upon the development – long before computing – of the science of ecology, and our notion of ecosystems, introduced. Chapter 3. The Future Does Not Exist. The philosophical core of the book, this chapter introduces process philosophy. Through an examination of the irreversible reality of subjectivity, Bergson’s famous notion of the durée reélle, and Whitehead’s critique of the bifurcation of subject and object, are introduced. The causally closed ‘time’ of positive science determines existence from the beginning to the end of the universe, be it three seconds or three trillion years. But the reality, of course, is that the future does not exist: our choices are real, and only one of myriad potential futures comes into being at each moment. As Bergson insists, durational succession exists, I am conscious of it; it is a fact. Bergson’s star – once the brightest of any living philosopher in the world – faded almost as quickly as it rose, under the onslaught from the logical positivists whose verificationism insisted that any proposition has no factual meaning if no evidence of observation can count for or against it: all ethics, aesthetics, romance, and metaphysics – and the very subjectivity with which duration is experienced - were thus closed down and dismissed. In this chapter it is reintroduced, to a new audience. Chapter 4. The World in a New Light. Many fundamental problems in the world can be seen as resulting from the false philosophy of bifurcation, fixity, and the reification of abstractions critiqued by process philosophy. Being – with all the isolation and focus upon the individual that it entails – must, if we are to address these problems, be seen as secondary to Becoming, with all the connection, interrelatedness, and complex collectivity that it implies. Choices become clearer, between positivism and interpretivism, between accents upon individualism or collectivism, between reductionist and complex adaptive systems approaches. The systemic individualism in Anglo-American societies can be regarded as actually harmful: the Tech Giants severing ties and bonds rather than connecting us; algebraic ecological models actually breaking the co-dependencies and co-requisites upon which real – complex - ecological health depends. Positivism, built as it is upon methodological individualism, seen in the light of process philosophy, becomes a danger to personal psychological balance – cutting us off from one another; a danger to the social fabric – undermining and impoverishing our civic life; and a danger to the ecological health of the planet – ignoring the immense (eco)systemic impact of our activities over the last centuries upon everything around us in the natural world. Chapter 5. A Theoretical Manifesto for Green IT. We are not islands, and in a process-relational social organisation much must be held in common. We are individuals, but we cannot survive alone. Four different perspectives on individualism show it to be little more than greed. An ecological economics reintegrating the household, the social, the supportive State, and – crucially – the life-giving earth into our polities is introduced and promoted. I introduce the concept of ‘Infomateriality’ – a non-bifurcated digital world where the physical bodies of people - fingers touching keyboards and eyes scanning screens - are as much ‘hardware’ as cabling, circuitboards and haptic interfaces, and the social practices, power relations, and embedded politics within IT artefacts define all such techné as fundamentally social. Abstract divisions are false, and whole, socially embedded systems should be the focus of IS, and from a philosophically and sociologically much deeper perspective. ‘Tech for Good’ is held up as movement in the right direction. My hope is that this book will help promote action, in the field of information systems, toward a better world, where Green Tech for Good is deployed for Nature, rather than against it. (shrink)

In this paper, I argue for a modified version of what Devitt calls the Representational Thesis. According to RT, syntactic rules or principles are psychologically real, in the sense that they are represented in the mind/brain of every linguistically competent speaker/hearer. I present a range of behavioral and neurophysiological evidence for the claim that the human sentence processing mechanism constructs mental representations of the syntactic properties of linguistic stimuli. I then survey a range of psychologically plausible computational models of comprehension (...) and show that they are all committed to RT. I go on to sketch a framework for thinking about the nature of the representations involved in sentence processing. My claim is that these are best characterized not as propositional attitudes but, rather, as subpersonal states whose representational properties are determined by their functional role. Finally, I distinguish between explicit and implicit representations and argue that the latter can be drawn on as data by the algorithms that constitute our sentence processing routines. I conclude that skepticism concerning the psychological reality of grammars cannot be sustained. (shrink)

In the field of computability and algorithmicity, there have recently been two essays that are of great interest: Peter Slezak's "Descartes's Diagonal Deduction," and David Deutsch's "Quantum Theory, the Church-Turing Principle and the Universal Quantum Computer." In brief, the former shows that Descartes' Cogito argument is structurally similar to Godel's proof that there are statements true but cannot be proven within a formal system such as Principia Mathematica, while Deutsch provides strong arguments for believing that the universe can (...) be represented as a Turing machine. King contends that the conjoining of Slezak's analysis with Deutsch's provides a perspective from which it is possible to argue that a scientific theology can be taken a little more seriously at present than in the past. , , , , In the field of computability and algorithmicity, there have recently been two essays that are of great interest: Peter Slezak's "Descartes's Diagonal Deduction," and David Deutsch's "Quantum Theory, the Church-Turing Principle and the Universal Quantum Computer." In brief, the former shows that Descartes' Cogito argument is structurally similar to Godel's proof that there are statements true but cannot be proven within a formal system such as Principia Mathematica, while Deutsch provides strong arguments for believing that the universe can be represented as a Turing machine. King contends that the conjoining of Slezak's analysis with Deutsch's provides a perspective from which it is possible to argue that a scientific theology can be taken a little more seriously at present than in the past. (shrink)

1. The Physical Church-Turing Thesis. Physicists often interpret the Church-Turing Thesis as saying something about the scope and limitations of physical computing machines. Although this was not the intention of Church or Turing, the Physical Church Turing thesis is interesting in its own right. Consider, for example, Wolfram’s formulation: One can expect in fact that universal computers are as powerful in their computational capabilities as any physically realizable system can be, that they can simulate any physical system . . . (...) No physically implementable procedure could then shortcut a computationally irreducible process. (Wolfram 1985) Wolfram’s thesis consists of two parts: (a) Any physical system can be simulated (to any degree of approximation) by a universal Turing machine (b) Complexity bounds on Turing machine simulations have physical significance. For example, suppose that the computation of the minimum energy of some system of n particles takes at least exponentially (in n) many steps. Then the relaxation time of the actual physical system to its minimum energy state will also take exponential time. (shrink)

Turing was an exceptional mathematician with a peculiar and fascinating personality and yet he remains largely unknown. In fact, he might be considered the father of the von Neumann architecture computer and the pioneer of Artificial Intelligence. And all thanks to his machines; both those that Church called “Turing machines” and the a-, c-, o-, unorganized- and p-machines, which gave rise to evolutionary computations and genetic programming as well as connectionism and learning. This paper looks at all of these and (...) at why he is such an often overlooked and misunderstood figure. (shrink)

The phenomenon of ‘Deep Learning,’ which has given us such science-fiction-like innovations as self-driving cars, as well as visual search tools in photographic applications, is a new form, and subset, of ‘Machine Learning’ made possible by very recent innovations in computing. Machine Learning itself has been around for some decades – essentially pattern-recognition software that requires very substantial computing resources, which were, until recently, mostly theoretical and hard to come by. Machine Learning was one avenue of the field of Artificial (...) Intelligence known as Narrow A.I. – the kind of ‘artificial intelligence’ that was strictly limited in scope as a first-steps starting point of what came, as a result, to be known as General A.I. General A.I., known then as simply, ‘Artificial Intelligence’, was the 1950s dream that brought us such things as Robbie the Robot, and more recently C3PO, and The Terminator: the kind of science fiction characters that remain the only manifestations of General Artificial Intelligence. -/- ‘Deep Learning’ also continues engineering’s 1940s trend of using language in a way that I will contest in this paper: a co-opting of words that have been used, in the past, to describe human activities, using them instead to describe what engineers have managed to make machines do. These co-optations reduce the richness of the word, making its referent an algorithm: a flow diagram that represents the bare essentials of what an engineer can understand and reproduce of a human activity; not the human activity itself. This diagram of the ‘engineering possible’ over-simplifies the human activity it tries to depict. With continued usage, the meaning of the word for us today has all-too-often become reduced to what the engineer has newly defined it to mean: something much less than it once was. -/- In this paper I attempt to roll back some of these co-optations, and to re-introduce some of the richness of the words that have been taken by engineering. I examine Turing’s seminal paper on the notion of a thinking machine. I use the philosophical insights of Henri Bergson, especially in his book, Matter and Memory, and the discoveries of neuroscience and complexity scientists. I try to show that the answer to Turing’s question, ‘Can machines think?’ remains a resounding, ‘No!’, and that notions such as ‘deep learning’ are in fact not only an inaccurate use of the very human experience of learning, but degrade the latter in using such a term. (shrink)

Though less well known than his other work, Turings 1938 Princeton Thesis, this title which includes his notion of an oracle machine, has had a lasting influence on computer science and mathematics. It presents a facsimile of the original typescript of the thesis along with essays by Appel and Feferman that explain its still-unfolding significance.

Current empirical studies of moral behavior of healthcare professionals are almost entirely focused on self-reports, usually collected under the assumption that an ethical disposition characterizes individuals across various contexts. It is well known, however, that individuals adjust their behavior to what they see being done by those in their peer group. That presents a methodological challenge to traditional research within a community of peers because the behavior of each individual is both the result of norms and a contributor to the (...) norms of others. Computer simulations can be used to address this methodological challenge. A Markov replicator model that runs on an Excel spreadsheet was used to investigate a community with four agent types in the dental community: devious practitioners, ethical practitioners who avoid involvement in the poor ethics of others, ethical practitioners who accept it as part of their professional responsibility to challenge colleagues who act unprofessionally, and those who enforce ethical standards. A panel of leaders in the profession independently estimated parameters for the model and criteria for a possible distribution of agent types in the community. The simulation converged on distributions of the agent types that were very similar to the expectations of the panel. The simulation suggests the following characteristics of such moral communities: The structure of such communities is robust across a wide distribution. It appears that reduction in unethical behavior is more sensitive to the way ethical practitioners interact with each other than to sanctions the enforcement community imposes on unethical practitioners, and that large external interventions will be short lived. (shrink)

The Fairness, Accountability, and Transparency (FAccT) literature tends to focus on bias as a problem that requires ex post solutions (e.g. fairness metrics), rather than addressing the underlying social and technical conditions that (re)produce it. In this article, we propose a complementary strategy that uses genealogy as a constructive, epistemic critique to explain algorithmic bias in terms of the conditions that enable it. We focus on XAI feature attributions (Shapley values) and counterfactual approaches as potential tools to gauge these conditions (...) and offer two main contributions. One is constructive: we develop a theoretical framework to classify these approaches according to their relevance for bias as evidence of social disparities. We draw on Pearl’s ladder of causation (Causality: models, reasoning, and inference. Cambridge University Press, Cambridge, 2000, Causality, 2nd edn. Cambridge University Press, Cambridge, 2009. doi:10.1017/CBO9780511803161) to order these XAI approaches concerning their ability to answer fairness-relevant questions and identify fairness-relevant solutions. The other contribution is critical: we evaluate these approaches in terms of their assumptions about the role of protected characteristics in discriminatory outcomes. We achieve this by building on Kohler-Hausmann’s (Northwest Univ Law Rev 113(5):1163–1227, 2019) constructivist theory of discrimination. We derive three recommendations for XAI practitioners to develop and AI policymakers to regulate tools that address algorithmic bias in its conditions and hence mitigate its future occurrence. (shrink)

Advancements in novel neurotechnologies, such as brain computer interfaces and neuromodulatory devices such as deep brain stimulators, will have profound implications for society and human rights. While these technologies are improving the diagnosis and treatment of mental and neurological diseases, they can also alter individual agency and estrange those using neurotechnologies from their sense of self, challenging basic notions of what it means to be human. As an international coalition of interdisciplinary scholars and practitioners, we examine these challenges and make (...) recommendations to mitigate negative consequences that could arise from the unregulated development or application of novel neurotechnologies. We explore potential ethical challenges in four key areas: identity and agency, privacy, bias, and enhancement. To address them, we propose democratic and inclusive summits to establish globally-coordinated ethical and societal guidelines for neurotechnology development and application, new measures, including “Neurorights,” for data privacy, security, and consent to empower neurotechnology users’ control over their data, new methods of identifying and preventing bias, and the adoption of public guidelines for safe and equitable distribution of neurotechnological devices. (shrink)

Biological evolution provides a creative fount of complex and subtle adaptations, often surprising the scientists who discover them. However, because evolution is an algorithmic process that transcends the substrate in which it occurs, evolution’s creativity is not limited to nature. Indeed, many researchers in the field of digital evolution have observed their evolving algorithms and organisms subverting their intentions, exposing unrecognized bugs in their code, producing unexpected adaptations, or exhibiting outcomes uncannily convergent with ones in nature. Such stories routinely reveal (...) creativity by evolution in these digital worlds, but they rarely fit into the standard scientific narrative. Instead they are often treated as mere obstacles to be overcome, rather than results that warrant study in their own right. The stories themselves are traded among researchers through oral tradition, but that mode of information transmission is inefficient and prone to error and outright loss. Moreover, the fact that these stories tend to be shared only among practitioners means that many natural scientists do not realize how interesting and lifelike digital organisms are and how natural their evolution can be. To our knowledge, no collection of such anecdotes has been published before. This paper is the crowd-sourced product of researchers in the fields of artificial life and evolutionary computation who have provided first-hand accounts of such cases. It thus serves as a written, fact-checked collection of scientifically important and even entertaining stories. In doing so we also present here substantial evidence that the existence and importance of evolutionary surprises extends beyond the natural world, and may indeed be a universal property of all complex evolving systems. (shrink)

In this paper we will discuss the active part played by certain diagonal arguments in the genesis of computability theory. 1 In some cases it is enough to assume the enumerability of Y while in others the effective enumerability is a substantial demand. These enigmatical words by Kleene were our point of departure: When Church proposed this thesis, I sat down to disprove it by diagonalizing out of the class of the λ–definable functions. But, quickly realizing that the diagonalization cannot (...) be done effectively, I became overnight a supporter of the thesis. (1981, p. 59) The title of our paper alludes to this very work, a task on which Kleene claims to have set out after hearing such a remarkable statement from Church, who was his teacher at the time. There are quite a few points made in this extract that may be surprising. First, it talks about a proof by diagonalization in order to test—in fact to try to falsify—a hypothesis that is not strictly formal. Second, it states that such a proof or diagonal construction fails. Third, it seems to use the failure as a support for the thesis. Finally, the episode we have just described took place at a time, autumn 1933, in which many of the results that characterize Computability Theory had not yet materialized. The aim of this paper is to show that Church and Kleene discovered a way to block a very particular instance of a diagonal construction: one that is closely related to the content of Church's thesis. We will start by analysing the logical structure of a diagonal construction. Then we will introduce the historical context in order to analyse the reasons that might have led Kleene to think that the failure of this very specific diagonal proof could support the thesis. This is a joint paper. We have both attempted to add a small piece to an amazing historical jigsaw puzzle at a juncture we feel to be appropiate. In the paper by Manzano 1997 the aforementioned words by Kleene were quoted, and since then several logicians, Enrique Alonso first and foremost, have questioned her on this issue. Here we both submit our reply. (1999, pp. 249--273). (shrink)

What happens when machines become more intelligent than humans? One view is that this event will be followed by an explosion to ever-greater levels of intelligence, as each generation of machines creates more intelligent machines in turn. This intelligence explosion is now often known as the “singularity”. The basic argument here was set out by the statistician I.J. Good in his 1965 article “Speculations Concerning the First Ultraintelligent Machine”: Let an ultraintelligent machine be defined as a machine that can far (...) surpass all the intellectual activities of any man however clever. Since the design of machines is one of these intellectual activities, an ultraintelligent machine could design even better machines; there would then unquestionably be an “intelligence explosion”, and the intelligence of man would be left far behind. Thus the first ultraintelligent machine is the last invention that man need ever make. The key idea is that a machine that is more intelligent than humans will be better than humans at designing machines. So it will be capable of designing a machine more intelligent than the most intelligent machine that humans can design. So if it is itself designed by humans, it will be capable of designing a machine more intelligent than itself. By similar reasoning, this next machine will also be capable of designing a machine more intelligent than itself. If every machine in turn does what it is capable of, we should expect a sequence of ever more intelligent machines. This intelligence explosion is sometimes combined with another idea, which we might call the “speed explosion”. The argument for a speed explosion starts from the familiar observation that computer processing speed doubles at regular intervals. Suppose that speed doubles every two years and will do so indefinitely. Now suppose that we have human-level artificial intelligence 1 designing new processors. Then faster processing will lead to faster designers and an ever-faster design cycle, leading to a limit point soon afterwards. The argument for a speed explosion was set out by the artificial intelligence researcher Ray Solomonoff in his 1985 article “The Time Scale of Artificial Intelligence”.1 Eliezer Yudkowsky gives a succinct version of the argument in his 1996 article “Staring at the Singularity”: “Computing speed doubles every two subjective years of work.. (shrink)

Why study notations, diagrams, or more broadly the variety of nonverbal “representations” or “signs” that are used in mathematical practice? This chapter maps out recent work on the topic by distinguishing three main philosophical motivations for doing so. First, some work (like that on diagrammatic reasoning) studies signs to recover norms of informal or historical mathematical practices that would get lost if the particular signs that these practices rely on were translated away; work in this vein has the potential to (...) broaden our view of the specific normativity of mathematics beyond logical proof. Second, some work focuses on signs to highlight the open-ended and “nonrigorous” aspects of mathematical practice, and the role of these aspects in the historical development of mathematics. The third motivation is based on the following observation: the reason differences in signs matter in mathematics is that humans are finite agents, with cognitive and computational limitations. Accordingly, studying signs can be a way to study how human computational constraints shape the mathematics that we do, and to tackle the topic of mathematical understanding. (shrink)

Artificial intelligence has historically been conceptualized in anthropomorphic terms. Some algorithms deploy biomimetic designs in a deliberate attempt to effect a sort of digital isomorphism of the human brain. Others leverage more general learning strategies that happen to coincide with popular theories of cognitive science and social epistemology. In this paper, I challenge the anthropomorphic credentials of the neural network algorithm, whose similarities to human cognition I argue are vastly overstated and narrowly construed. I submit that three alternative supervised learning (...) methods—namely lasso penalties, bagging, and boosting—offer subtler, more interesting analogies to human reasoning as both an individual and a social phenomenon. Despite the temptation to fall back on anthropomorphic tropes when discussing AI, however, I conclude that such rhetoric is at best misleading and at worst downright dangerous. The impulse to humanize algorithms is an obstacle to properly conceptualizing the ethical challenges posed by emerging technologies. (shrink)

278 non-freshman university students taking a l2-week critical thinking course in a large single-section class, with computer-assisted guided practice as a replacement for small-group discussion, and all testing in machine-scored multiple-choice format, improved their critical thinking skills, as measured by the California Critical Thinking Skills Test, by half a standard deviation, a moderate improvement. The improvement was more than that reported with a traditional format without computer-assisted instruction, but less than that reported with a format using both computer-assisted instruction and (...) essay-type assignments. Further studies are needed to test hypotheses suggested by these results. (shrink)

"A valuable collection both for original source material as well as historical formulations of current problems."-- The Review of Metaphysics "Much more than a mere collection of papers . . . a valuable addition to the literature."-- Mathematics of Computation An anthology of fundamental papers on undecidability and unsolvability by major figures in the field, this classic reference opens with Godel's landmark 1931 paper demonstrating that systems of logic cannot admit proofs of all true assertions of arithmetic. Subsequent papers by (...) Godel, Church, Turing, and Post single out the class of recursive functions as computable by finite algorithms. Additional papers by Church, Turing, and Post cover unsolvable problems from the theory of abstract computing machines, mathematical logic, and algebra, and material by Kleene and Post includes initiation of the classification theory of unsolvable problems. Suitable for graduate and undergraduate courses. 1965 ed. (shrink)

Any attempt to conceptualize, categorize and constraint foundational issues in a living science, such as Computing, is bound to show its limitations and leave a number of open issues. Taking stock with some critical reviews of Primiero (On the foundations of computing, Oxford University Press, Oxford, 2019) published in this Journal, I overview potential new problems to be investigated by a foundational analysis of the science of computing.

A cognitive assessment strategy that is not limited to examining a set of summary test scores may be more helpful for early detection of emergent illness such as Alzheimer’s disease (AD) and may permit a better understanding of cognitive functions and dysfunctions in those with AD and other dementia disorders. A revisit of the work already undertaken by Kaplan and colleagues using the Boston Process-Approach provides a solid basis for identifying new opportunities to capture data on neurocognitive processes, test-taking strategies (...) and response styles. Thus, this critical review will combine traditional process-based assessment strategies with support provided or offered by newer technologies that have the potential to add value to data collection and interpretation. There is now considerable interest in neuropsychological test administration using computer/digital technology, both in research and in clinical settings. To add value, any computerized version of an existing cognitive test should respect the administration procedure for which normative data were obtained, should be time-saving in terms of scoring and interpretation, and should, we argue, facilitate gathering information about the processes and strategies followed in test completion. This article will offer an overview of the steps needed when implementing computerization of neuropsychological tests using a Process-Based Approach (PBA) to these technology-based adaptations and will discuss further developments in this area by linking it to future technological developments that may be possible in the area of neuropsychological assessment. Additionally, an overview of neuropsychological tests that may benefit from computerization will be presented, together with suggestions on the specific processes, strategies and features that may be captured with the aid of such computerization. Finally, hypotheses on how virtual reality could be an asset for the future of the PBA to neuropsychological assessment will also be discussed. (shrink)