This essay discusses Peirce’s appeal to logical machines as an argument against psychologism. It also contends that some of Peirce’s anti-psychologistic remarks on logic contain interesting premonitions arising from his perception of the asymmetry of proof complexity in monadic and relational logical calculi that were only given full formulation and explication in the early twentieth century through Church’s Theorem and Hilbert’s broad-ranging Entscheidungsproblem.

This essay discusses Peirce’s appeal to logical machines as an argument against psychologism. It also contends that some of Peirce’s anti-psychologistic remarks on logic contain interesting premonitions arising from his perception of the asymmetry of proof complexity in monadic and relational logical calculi that were only given full formulation and explication in the early twentieth century through Church’s Theorem and Hilbert’s broad-ranging Entscheidungsproblem.

This hands-on guide offers clear explanations of fuzzy logic along with practical uses and detailed examples. Written by an award-winning engineer and experienced author, Fuzzy Logic: Applications in Artificial Intelligence, Big Data, and Machine Learning is aimed at improving competence and skills in students and professionals alike. Inside, you will discover how to apply fuzzy logic and migrate to a new man-machine relationship in the context of pervasive digitization and big data across emerging technologies. The book lays (...) out real-world applications in intelligent energy systems with demand response, smart homes, electrification of transportation, supply chain efficiencies, smart cities, e-commerce, education, healthcare, and decarbonization. (shrink)

This paper starts by summarizing work that philosophers have done in the fields of inductive logic since 1950s and truth approximation since 1970s. It then proceeds to interpret and critically evaluate the studies on machine learning within artificial intelligence since 1980s. Parallels are drawn between identifiability results within formal learning theory and convergence results within Hintikka’s inductive logic. Another comparison is made between the PAC-learning of concepts and the notion of probable approximate truth.

Wittgenstein’s “machines-as-symbols” are considered with respect to their historical sources and their symbolic and logical nature. Among these sources and precursors, along with Leonardo’s drawings of machines, there are illustrated “machine books”, a kind of book published in the period from the 16th to the 18th centuries which consist of pictures and descriptions of a variety of mechanical devices. Most probably, these books were one of Wittgenstein’s inspirations for his view of machines as components of language-games. The (...) picture of homo volans in Vrančić’s machine book possessed by Wittgenstein is taken as an example. In particular, homo volans is shown to contain patterns of logical laws and rules and to be abstractly interpretable as a logical symbol. A machine, taken as a symbol, is shown to be a precondition of a meaningful “overview” of a mechanical work that exceeds the limits of decidability, and to possess causal features if causality is understood teleologically and in a deeper sense of a “binding” life. (shrink)

Providing more human-like concept learning in machines has always been one of the most significant goals of machine learning paradigms and of human-machine interaction techniques. This article attempts to provide a logical specification of conceptual mappings from humans’ minds into machines’ knowledge bases. We will focus on the representation of the mappings (transformations) relying on First-Order Predicate Logic. Additionally, the structure of concepts in the common ground between humans and machines will be analysed. It seems quite (...) necessary to pay attention to the philosophy of constructivism and constructivist models of knowing. This research constructs a conceptual ground for expressing and analysing concepts in the common ground between humanistic and informatics sciences and in the context of human-machine interplays. (shrink)

I use modal logic and transfinite set-theory to define metaphysical foundations for a general theory of computation. A possible universe is a certain kind of situation; a situation is a set of facts. An algorithm is a certain kind of inductively defined property. A machine is a series of situations that instantiates an algorithm in a certain way. There are finite as well as transfinite algorithms and machines of any degree of complexity (e.g., Turing and super-Turing machines (...) and more). There are physically and metaphysically possible machines. There is an iterative hierarchy of logically possible machines in the iterative hierarchy of sets. Some algorithms are such that machines that instantiate them are minds. So there is an iterative hierarchy of finitely and transfinitely complex minds. (shrink)

This volume brings together a collection of papers covering a wide range of topics in computer and cognitive science. Topics included are: the foundational relevance of logic to computer science, with particular reference to tense logic, constructive logic, and Horn clause logic; logic as the theoretical underpinnings of the engineering discipline of expert systems; a discussion of the evolution of computational linguistics into functionally distinct task levels; and current issues in the implementation of speech act (...) theory. (shrink)

One important problem in the philosophy of science is whether there can be a normative theory of discovery, as opposed to a normative theory of justification. Although the possibility of developing a logic of scientific discovery has been often doubted by philosophers, it is particularly interesting to consider how the basic insights of a normative theory of discovery have been turned into an effective research program in computer science, namely the research field of machine learning. In this paper, I (...) introduce some current research on statistical models to a philosophical audience. In particular, I will stress those features of statistical models that make them plausible computational counterparts of scientific theories. After noticing how these models allow for the main kinds of inference that are a trademark of scientific theories, I will focus on the problem of learning statistical models from data. The analysis will show how machine learning is casting new light on traditional problems in the philosophy of science. More precisely, I will explore the implications of some results in statistical learning with respect to the role of simplicity in theory choice and to the role of scalability (as a formal property of induction) in making scientific discovery effective. (shrink)

We can imagine a human operator playing a game of one-upmanship against a programmed computer. If the program is Fn, the human operator can print the theorem Gn, which the programmed computer, or, if you prefer, the program, would never print, if it is consistent. This is true for each whole number n, but the victory is a hollow one since a second computer, loaded with program C, could put the human operator out of a job.... It is useless for (...) the `mentalist' to argue that any given program can always be improves since the process for improving programs can presumably be programmed also; certainly this can be done if the mentalist describes how the improvement is to be made. If he does give such a description, then he has not made a case. (shrink)

§1. Mathematics and the physical world. Genuine scientific knowledge cannot be certain, nor can it be justified a priori. Instead, it must be conjectured, and then tested by experiment, and this requires it to be expressed in a language appropriate for making precise, empirically testable predictions. That language is mathematics.This in turn constitutes a statement about what the physical world must be like if science, thus conceived, is to be possible. As Galileo put it, “the universe is written in the (...) language of mathematics”. Galileo's introduction of mathematically formulated, testable theories into physics marked the transition from the Aristotelian conception of physics, resting on supposedly necessary a priori principles, to its modern status as a theoretical, conjectural and empirical science. Instead of seeking an infallible universal mathematical design, Galilean science usesmathematics to express quantitative descriptions of an objective physical reality. Thus mathematics became the language in which we express our knowledge of the physical world — a language that is not only extraordinarily powerful and precise, but also effective in practice. Eugene Wigner referred to “the unreasonable effectiveness of mathematics in the physical sciences”. But is this effectiveness really unreasonable or miraculous?Numbers, sets, groups and algebras have an autonomous reality quite independent of what the laws of physics decree, and the properties of these mathematical structures can be just as objective as Plato believed they were. (shrink)

We argued [Since this argument appeared in other journals, I am reprising it here, almost verbatim.] (Fulda in J Law Info Sci 2:230–232, 1991/AI & Soc 8(4):357–359, 1994) that the paradox of the preface suggests a reason why machines cannot, will not, and should not be allowed to judge criminal cases. The argument merely shows that they cannot now and will not soon or easily be so allowed. The author, in fact, now believes that when—and only when—they are ready (...) they actually should be so allowed, in the interests of justice. Both the original argument applied and this detailed reconsideration applies exclusively to trial courts, and both specifically exclude(d) sentencing. The argument highlights some key relevant differences between minds and machines and attempts, also, to explain why automation is of far greater import for the first-level justice system (trial courts) than for higher courts. A final section discusses why sentencing was, is, and should be excluded. (shrink)

Machine learning systems have shown great potential for performing or supporting inferential reasoning through analyzing large data sets, thereby potentially facilitating more informed decision-making. However, a hindrance to such use of ML systems is that the predictive models created through ML are often complex, opaque, and poorly understood, even if the programs “learning” the models are simple, transparent, and well understood. ML models become difficult to trust, since lay-people, specialists, and even researchers have difficulties gauging the reasonableness, correctness, and reliability (...) of the inferences performed. In this article, we argue that bridging this gap in the understanding of ML models and their reasonableness requires a focus on developing an improved methodology for their creation. This process has been likened to “alchemy” and criticized for involving a large degree of “black art,” owing to its reliance on poorly understood “best practices”. We soften this critique and argue that the seeming arbitrariness often is the result of a lack of explicit hypothesizing stemming from an empiricist and myopic focus on optimizing for predictive performance rather than from an occult or mystical process. We present some of the problems resulting from the excessive focus on optimizing generalization performance at the cost of hypothesizing about the selection of data and biases. We suggest embedding ML in a general logic of scientific discovery similar to the one presented by Charles Sanders Peirce, and present a recontextualized version of Peirce’s scientific hypothesis adjusted to ML. (shrink)

Source: "This book addresses the fundamentals of machine ethics. It discusses abilities required for ethical machine reasoning and the programming features that enable them. It connects ethics, psychological ethical processes, and machine implemented procedures. From a technical point of view, the book uses logic programming and evolutionary game theory to model and link the individual and collective moral realms. It also reports on the results of experiments performed using several model implementations. Opening specific and promising inroads into the terra (...) incognita of machine ethics, the authors define here new tools and describe a variety of program-tested moral applications and implemented systems. In addition, they provide alternative readings paths, allowing readers to best focus on their specific interests and to explore the concepts at different levels of detail. Mainly written for researchers in cognitive science, artificial intelligence, robotics, philosophy of technology and engineering of ethics, the book will also be of general interest to other academics, undergraduates in search of research topics, science journalists as well as science and society forums, legislators and military organizations concerned with machine ethics.". (shrink)

In this paper, I set out some basic elements of a deontic logic with an implementation appropriate for handling conflicting legal obligations for purposes of programming autonomous machine agents. Kantian justice demands that the prescriptive system of enforceable public laws be consistent, yet statutes or case holdings may often describe legal obligations that contradict; moreover, even fundamental constitutional rights may come into conflict. I argue that a deontic logic of the law should not try to work around such (...) conflicts but, instead, identify and expose them so that the rights and duties that generate inconsistencies in public law can be explicitly qualified and the conflicts resolved. I then argue that a credulous, non-monotonic deontic logic can describe inconsistent legal obligations while meeting Kant’s demand for consistency in the prescriptive system of public law. Finally, I propose an implementation of this logic via a modified form of “answer set programming,” which I demonstrate with some simple examples. (shrink)

This article critically examines one of the most prevalent metaphors in modern biology, namely the machine conception of the organism (MCO). Although the fundamental differences between organisms and machines make the MCO an inadequate metaphor for conceptualizing living systems, many biologists and philosophers continue to draw upon the MCO or tacitly accept it as the standard model of the organism. This paper analyses the specific difficulties that arise when the MCO is invoked in the study of development and evolution. (...) In developmental biology the MCO underlies a logically incoherent model of ontogeny, the genetic program, which serves to legitimate three problematic theses about development: genetic animism, neo-preformationism, and developmental computability. In evolutionary biology the MCO is responsible for grounding unwarranted theoretical appeals to the concept of design as well as to the interpretation of natural selection as an engineer, which promote a distorted understanding of the process and products of evolutionary change. Overall, it is argued that, despite its heuristic value, the MCO today is impeding rather than enabling further progress in our comprehension of living systems. (shrink)

Machines were introduced as calculating devices to simulate operations carried out by human computers following fixed algorithms. The mathematical study of (paper) machines is the topic of our essay. The first three sections provide necessary logical background, examine the analyses of effective calculability given in the thirties, and describe results that are central to recursion theory, reinforcing the conceptual analyses. In the final section we pursue our investigation in a quite different way and focus on principles that govern (...) the operations of physically realizable machines. (shrink)

In the propositional modal treatment of two-variable first-order logic equality is modelled by a ‘diagonal’ constant, interpreted in square products of universal frames as the identity relation. Here we study the decision problem of products of two arbitrary modal logics equipped with such a diagonal. As the presence or absence of equality in two-variable first-order logic does not influence the complexity of its satisfiability problem, one might expect that adding a diagonal to product logics in general is similarly (...) harmless. We show that this is far from being the case, and there can be quite a big jump in complexity, even from decidable to the highly undecidable. Our undecidable logics can also be viewed as new fragments of first-order logic where adding equality changes a decidable fragment to undecidable. We prove our results by a novel application of counter machine problems. While our formalism apparently cannot force reliable counter machine computations directly, the presence of a unique diagonal in the models makes it possible to encode both lossy and insertion-error computations, for the same sequence of instructions. We show that, given such a pair of faulty computations, it is then possible to reconstruct a reliable run from them. (shrink)

According to Karl Popper, the evolution of science, logically, methodologically, and even psychologically, is an involved interplay of acute conjectures and blunt refutations. Like biological evolution, it is an endless round of blind variation and selective retention. But unlike biological evolution, it incorporates, at the stage of selection, the use of reason. Part I of this two-part paper begins by repudiating the common beliefs that Hume’s problem of induction, which compellingly confutes the thesis that science is rational in the way (...) that most people think that it is rational, can be solved by assuming that science is rational, or by assuming that Hume was irrational (that is, by ignoring his argument). The problem of induction can be solved only by a non-authoritarian theory of rationality. It is shown also that because hypotheses cannot be distilled directly from experience, all knowledge is eventually dependent on blind conjecture, and therefore itself conjectural. In particular, the use of rules of inference, or of good or bad rules for generating conjectures, is conjectural. Part II of the paper expounds a form of Popper’s critical rationalism that locates the rationality of science entirely in the deductive processes by which conjectures are criticized and improved. But extreme forms of deductivism are rejected. The paper concludes with a sharp dismissal of the view that work in artificial intelligence, including the JSM method cultivated extensively by Victor Finn, does anything to upset critical rationalism. Machine learning sheds little light on either the problem of induction or on the role that logic plays in the development of scientific knowledge. (shrink)

In this paper, I set out a new Kantian approach to resolving conflicts between moral obligations for highly autonomous machine agents. First, I argue that efforts to build explicitly moral autonomous machine agents should focus on what Kant refers to as duties of right, which are duties that everyone could accept, rather than on duties of virtue (or “ethics”), which are subject to dispute in particular cases. “Moral” machines must first be rightful machines, I argue. I then show (...) how this shift in focus from ethics to a standard of public right resolves the conflicts in what is known as the "trolley problem" for autonomous ma-chine agents. Finally, I consider how a deontic logic suitable for capturing duties of right might meet Kant’s requirement that rightfully enforceable obligations be consistent in a system of equal freedom under universal law. (shrink)

The dynamic development of technology, as well as of AI’s, raises the fundamental question: can machines think? At the beginning of the 20th Century the Austrian philosopher wonders about this problem and analyses it from a logical-philosophical conception which conveys the need to recognize all the elements comprised in the thought-language relationship. An ethical-religious dimension is revealed in certain uses of language. This dimension, which shows the human’s attitude to the world, stems from the human tendency to search for (...) explanations. This attitude does not extend to machines. (shrink)

Wants, preferences, and cares are physical things or events, not ideas or propositions, and therefore no chain of pure logic can conclude with a want, preference, or care. It follows that no pure-logic machine will ever want, prefer, or care. And its behavior will never be driven in the way that deliberate human behavior is driven, in other words, it will not be motivated or goal directed. Therefore, if we want to simulate human-style interactions with the world, we (...) will need to first understand the physical structure of goal-directed systems. I argue that all such systems share a common nested structure, consisting of a smaller entity that moves within and is driven by a larger field that contains it. In such systems, the smaller contained entity is directed by the field, but also moves to some degree independently of it, allowing the entity to deviate and return, to show the plasticity and persistence that is characteristic of goal direction. If all this is right, then human want-driven behavior probably involves a behavior-generating mechanism that is contained within a neural field of some kind. In principle, for goal directedness generally, the containment can be virtual, raising the possibility that want-driven behavior could be simulated in standard computational systems. But there are also reasons to believe that goal-direction works better when containment is also physical, suggesting that a new kind of hardware may be necessary. (shrink)

Recent years have seen a growing consensus in the philosophical community that the grandfather paradox and similar logical puzzles do not preclude the possibility of time travel scenarios that utilize spacetimes containing closed timelike curves. At the same time, physicists, who for half a century acknowledged that the general theory of relativity is compatible with such spacetimes, have intensely studied the question whether the operation of a time machine would be admissible in the context of the same theory and of (...) its quantum cousins. A time machine is a device which brings about closed timelike curves—and thus enables time travel—where none would have existed otherwise. The physics literature contains various no-go theorems for time machines, i.e., theorems which purport to establish that, under physically plausible assumptions, the operation of a time machine is impossible. We conclude that for the time being there exists no conclusive no-go theorem against time machines. The character of the material covered in this article makes it inevitable that its content is of a rather technical nature. We contend, however, that philosophers should nevertheless be interested in this literature for at least two reasons. First, the topic of time machines leads to a number of interesting foundations issues in classical and quantum theories of gravity; and second, philosophers can contribute to the topic by clarifying what it means for a device to count as a time machine, by relating the debate to other concerns such as Penrose's cosmic censorship conjecture and the fate of determinism in general relativity theory, and by eliminating a number of confusions regarding the status of the paradoxes of time travel. The present article addresses these ambitions in as non-technical a manner as possible, and the reader is referred to the relevant physics literature for details. (shrink)

We construct a machine that knows its own code, at the price of not knowing its own factivity.

In philosophical logic and metaphysics there is a long-standing debate around the most appropriate structures to represent indeterministic scenarios concerning the future. We reconstruct here such a debate in a computational setting, focusing on the fundamental difference between moment-based and history-based structures. Our presentation is centered around two versions of an indeterministic scenario in which a programmer wants a machine to perform a given task at some point after a specified time. One of the two versions includes an assumption (...) about the future behaviour of the machine that cannot be encoded in any programming instruction; such version has models over history-based structures but no model over a moment-based structure. Therefore, our work adds a new stance to the debate: moment-based structures can be said to rule out certain indeterministic scenarios that are computationally unfeasible. (shrink)