This volume examines the limitations of mathematical logic and proposes a new approach to logic intended to overcome them. To this end, the book compares mathematical logic with earlier views of logic, both in the ancient and in the modern age, including those of Plato, Aristotle, Bacon, Descartes, Leibniz, and Kant. From the comparison it is apparent that a basic limitation of mathematical logic is that it narrows down the scope of logic confining it to the study of deduction, without (...) providing tools for discovering anything new. As a result, mathematical logic has had little impact on scientific practice. Therefore, this volume proposes a view of logic according to which logic is intended, first of all, to provide rules of discovery, that is, non-deductive rules for finding hypotheses to solve problems. This is essential if logic is to play any relevant role in mathematics, science and even philosophy. To comply with this view of logic, this volume formulates several rules of discovery, such as induction, analogy, generalization, specialization, metaphor, metonymy, definition, and diagrams. A logic based on such rules is basically a logic of discovery, and involves a new view of the relation of logic to evolution, language, reason, method and knowledge, particularly mathematical knowledge. It also involves a new view of the relation of philosophy to knowledge. This book puts forward such new views, trying to open again many doors that the founding fathers of mathematical logic had closed historically. (shrink)

The book’s core argument is that an artificial intelligence that could equal or exceed human intelligence—sometimes called artificial general intelligence (AGI)—is for mathematical reasons impossible. It offers two specific reasons for this claim: Human intelligence is a capability of a complex dynamic system—the human brain and central nervous system. Systems of this sort cannot be modelled mathematically in a way that allows them to operate inside a computer. In supporting their claim, the authors, Jobst Landgrebe and Barry Smith, marshal evidence (...) from mathematics, physics, computer science, philosophy, linguistics, and biology, setting up their book around three central questions: What are the essential marks of human intelligence? What is it that researchers try to do when they attempt to achieve "artificial intelligence" (AI)? And why, after more than 50 years, are our most common interactions with AI, for example with our bank’s computers, still so unsatisfactory? Landgrebe and Smith show how a widespread fear about AI’s potential to bring about radical changes in the nature of human beings and in the human social order is founded on an error. There is still, as they demonstrate in a final chapter, a great deal that AI can achieve which will benefit humanity. But these benefits will be achieved without the aid of systems that are more powerful than humans, which are as impossible as AI systems that are intrinsically "evil" or able to "will" a takeover of human society. (shrink)

Whether abduction is treated as an argument or as an inference, the mainstream view presupposes a tight connection between abduction and inference to the best explanation. This paper critically evaluates this link and supports a narrower view on abduction. Our main thesis is that merely the hypothesis-generative aspect, but not the evaluative aspect, is properly abductive in the sense introduced by C. S. Peirce. We show why equating abduction with IBE unnecessarily complicates argument evaluation by levelling the status of abduction (...) as a third reasoning mode. We also propose a scheme for abductive argument along with critical questions, and suggest retaining abduction alongside IBE as related but distinct categories. (shrink)

“Scientific research faces up with an open and unknown world”Within the work of C. S. Peirce, the most fundamental and contentious form of inference is that of abduction. According to Peirce, abduction is the only type of inference from which new ideas are created (CP 5.171, 1903). He wrote, “every single item of scientific theory which stands established today has been due to Abduction” (CP 5.172, 1903). Similarly, “All that makes knowledge applicable comes to us viâ abduction. […] Not the (...) smallest advance can be made in knowledge beyond the stage of vacant staring, without making an abduction at every step” (HP 2:899–900, 1901). It is little wonder that so much attention has been paid to this particular type of.. (shrink)

Scientific Realism (SR) has three crucial aspects: 1) the centrality of the concept of truth, 2) the idea that success is a reliable indicator of truth, and 3) the idea that the Inference to the Best Explanation is a reliable inference rule. It will be outlined how some realists try to overcome the difficulties which arise in justifying such crucial aspects relying on an adaptationist view of evolutionism, and why such attempts are inadequate. Finally, we will briefly sketch some of (...) the main difficulties the realist has to face in defending those crucial aspects, and how such difficulties are deeply related: they derive from the inability of SR to satisfyingly avoid the sceptical challenge of the criterion of truth. Indeed, SR seems not to be able to fill the so-called ‘epistemic gap’ (Sankey 2008). In fact, the epistemic gap cannot be filled in no way other than obtaining a criterion of truth, but such a criterion cannot be obtained if the epistemic gap obtains. (shrink)

We distinguish three aspects of medical diagnosis: generating new diagnostic hypotheses, selecting hypotheses for further pursuit, and evaluating their probability in light of the available evidence. Drawing on Peirce’s account of abduction, we argue that hypothesis generation is amenable to normative analysis: physicians need to make good decisions about when and how to generate new diagnostic hypothesis as well as when to stop. The intertwining relationship between the generation and selection of diagnostic hypotheses is illustrated through the analysis of a (...) detailed clinical case study. This interaction is not adequately captured by the existing probabilistic, decision-theoretic models of the threshold approach to clinical decision-making. Instead, we propose to conceptualize medical diagnosis in terms of strategic reasoning. (shrink)

I respond to the bad lot argument in the context of biological systematics. The response relies on the historical nature of biological systematics and on the availability of pattern explanations. The basic assumption of common descent enables systematic methodology to naturally generate candidate explanatory hypotheses. However, systematists face a related challenge in the issue of character analysis. Character analysis is the central problem for contemporary systematics, yet the general problem of which it is a case—what counts as evidence?—has not been (...) adequately discussed by proponents of inference to the best explanation. Facing this problem is the price of adopting abductive methods. I sketch an account of how systematists approach the problem of evidence. (shrink)

Debates concerning the character, scope, and warrant of abductive inference have been active since Peirce first proposed that there was a third form of inference, distinct from induction and deduction. Abductive reasoning has been dubbed weak, incoherent, and even nonexistent. Part, at least, of the problem of articulating a clear sense of abductive inference is due to difficulty in interpreting Peirce. Part of the fault must lie with his critics, however. While this article will argue that Peirce indeed left a (...) number of puzzles for interpreters, it will also contend that interpreters should be careful to distinguish discussion of the formal and strictly epistemic question of whether and how abduction is a sound form of inference from discussions of the practical goals of abduction, as Peirce understood them. This article will trace a history of critics and defenders of Peirce’s notion of abduction and discuss how Peirce both fueled the confusion and in fact anticipated and responded to several recurring objections. (shrink)

Inspired by Bermúdez’s notion of proto-logic, I would like to fathom what the true proto-logic could be like. But this will be approached only in a negative way of figuring out what it could not be. I shall argue that it could not be purely deductive by exploiting the recent researches in logic of maps. This will allow us to reorient the search for proto-logic, starting with animal abduction. I will also suggest that proto-logic won’t get off the ground without (...) proto-geometry. These negative results will shed some lights on some further conceptual and historical issues around the language of thought hypothesis to arrive at the true proto-logic. (shrink)

This paper details how ghost hunting, as a set of learning activities, can be used to enhance critical thinking and philosophy of science classes. We describe in some detail our own work with ghost hunting, and reflect on both intended and unintended consequences of this pedagogical choice. This choice was partly motivated by students’ lack of familiarity with science and philosophic questions about it. We offer reflections on our three different implementations of the ghost hunting activities. In addition, we discuss (...) the practical nuances of implementing these activities, as well the relation of ghost hunting to our course content, including informal fallacies and some models for scientific inference. We conclude that employing ghost hunting along-side traditional activities and content of critical thinking and philosophy of science offers a number of benefits, including being fun, increasing student attendance, enhancing student learning, and providing a platform for campus wide dialogues about philosophy. (shrink)

Essential to Peirce's distinction among three kinds of reasoning, deduction, induction and abduction, is the claim that each is correlated to a unique species of validity irreducible to that of the others. In particular, abductive validity cannot be analyzed in either deductive or inductive terms, a consequence of considerable importance for the logical and epistemological scrutiny of scientific methods. But when the full structure of abductive argumentation — as viewed by the mature Peirce — is clarified, every inferential step in (...) the process can be seen to dissolve into familiar forms of deductive and inductive reasoning. Specifically, the final stage is a special type of practical inference which, if correct, is deductively valid, while the creative phase, surprisingly, is not inferential at all. In neither is abduction a type of inference to the best explanation. The result is a major reassessment of the relevance of Peirce's views to contemporary methodological studies. (shrink)

Despite their centrality to the scientific enterprise, both the nature of scientific variables and their relation to inductive inference remain obscure. I suggest that scientific variables should be viewed as equivalence classes of sets of physical states mapped to representations (often real numbers) in a structure preserving fashion, and argue that most scientific variables introduced to expand the degrees of freedom in terms of which we describe the world can be seen as products of an algorithmic inductive inference first identified (...) by William W. Rozeboom. This inference algorithm depends upon a notion of natural kind previously left unexplicated. By appealing to dynamical kinds—equivalence classes of causal system characterized by the interventions which commute with their time evolution—to fill this gap, we attain a complete algorithm. I demonstrate the efficacy of this algorithm in a series of experiments involving the percolation of water through granular soils that result in the induction of three novel variables. Finally, I argue that variables obtained through this sort of inductive inference are guaranteed to satisfy a variety of norms that in turn suit them for use in further scientific inferences. (shrink)

Abductive reasoning takes place in forming``hypotheses'''' in order to explain ``facts.'''' Thus, theconcept of abduction promises an understanding ofcreativity in science and learning. It raises,however, also a lot of problems. Some of them will bediscussed in this paper. After analyzing thedifference between induction and abduction (1), Ishall discuss Peirce''s claim that there is a ``logic''''of abduction (2). The thesis is that this claim can beunderstood, if we make a clear distinction between inferential elements and perceptive elements of abductive reasoning. For (...) Peirce, the creative act offorming explanatory hypotheses and the emergence of``new ideas'''' belongs exclusively to the perceptive side of abduction. Thus, it is necessary to study the roleof perception in abductive reasoning (3). A furtherproblem is the question whether there is arelationship between abduction and Peirce''s concept of``theorematic reasoning'''' in mathematics (4). Both forms of reasoning could be connected, because both arebased on perception. The last problem concerns therole of instincts in explaining the success ofabductive reasoning in science, and the question whether the concept of instinct might be replaced bymethods of inquiry (5). (shrink)

“What is abduction?” asks Jaakko Hintikka in the title to his 1998 article on C. S. Peirce’s concept. The answer to Hintikka’s question is problematic on several counts. There is, to begin with, a difference between Peirce’s own views on abduction and later interpretations of abduction as “inference to the best explanation” (Minnameier 2004; Paavola 2006). There are, furthermore, tensions within Peirce’s own account of abduction, for instance, a tension between “inferential” and “instinctual” aspects of abduction (Fann 1970; Anderson 1986; (...) Kapitan 1990; Paavola 2005; Paavola and Hakkarainen 2005). These tensions are exacerbated by two factors. First, there are several terminological variants of the word.. (shrink)

The view that the subject matter of epistemology is the concept of knowledge is faced with the problem that all attempts so far to define that concept are subject to counterexamples. As an alternative, this article argues that the subject matter of epistemology is knowledge itself rather than the concept of knowledge. Moreover, knowledge is not merely a state of mind but rather a certain kind of response to the environment that is essential for survival. In this perspective, the article (...) outlines an answer to four basic questions about knowledge: What is the role of knowledge in human life? What is the relation between knowledge and reality? How is knowledge acquired? Is there any a priori knowledge? (shrink)

I argue against the tendency in the philosophy of science literature to link abduction to the inference to the best explanation (IBE), and in particular, to claim that Peireean abduction is a conceptual predecessor to IBE. This is not to discount either abduction or IBE. Rather the purpose of this paper is to clarify the relation between Peireean abduction and IBE in accounting for ampliative inference in science. This paper aims at a proper classification—not justification—of types of scientific reasoning. In (...) particular, I claim that Peireean abduction is an in-depth account of the process of generating explanatory hypotheses, while IBE, at least in Peter Lipton's thorough treatment, is a more encompassing account of the processes both of generating and of evaluating scientific hypotheses. There is then a two-fold problem with the claim that abduction is IBE. On the one hand, it conflates abduction and induction, which are two distinct forms of logical inference, with two distinct aims, as shown by Charles S. Peirce; on the other hand it lacks a clear sense of the full scope of IBE as an account of scientific inference. (shrink)

Reverse inference is a crucial inferential strategy used in cognitive neuroscience to derive conclusions about the engagement of cognitive processes from patterns of brain activation. While widely employed in experimental studies, it is now viewed with increasing scepticism within the neuroscience community. One problem with reverse inference is that it is logically invalid, being an instance of abduction in Peirce’s sense. In this paper, we offer the first systematic analysis of reverse inference as a form of abductive reasoning and highlight (...) some relevant implications for the current debate. We start by formalising an important distinction that has been entirely neglected in the literature, namely the distinction between weak and strong reverse inference. Then, we rely on case studies from recent neuroscientific research to systematically discuss the role and limits of both strong and weak reverse inference; in particular, we offer the first exploration of weak reverse inference as a discovery strategy within cognitive neuroscience. (shrink)

Computer simulations are involved in numerous branches of modern science, and science would not be the same without them. Yet the question of how they can explain real-world processes remains an issue of considerable debate. In this context, a range of authors have highlighted the inferences back to the world that computer simulations allow us to draw. I will first characterize the precise relation between computer and target of a simulation that allows us to draw such inferences. I then argue (...) that in a range of scientifically interesting cases they are particular abductions and defend this claim by appeal to two case studies. (shrink)

Abstract In Peirce's and Hanson's characterization of abductive inference, the abducted hypothesis (but not others) is present in the premises, so that the inference can hardly be taken as ampliative. Abduction has consequently been treated as part of the process whereby already generated hypotheses are judged in terms of their plausibility, simplicity, etc. I propose an interpretation of abduction which supports an ampliative view. It relies on a distinction between two logical stages in the generation of hypotheses, one ?factual? and (...) one ?explanatory?. I also indicate how we may reconstruct Peirce's and Hanson's original inference in an ampliative form. (shrink)

We propose a logic of abduction that (i) provides an appropriate formalization of the explanatory conditional, and that (ii) captures the defeasible nature of abductive inference. For (i), we argue that explanatory conditionals are non-classical, and rely on Brian Chellas’s work on conditional logics for providing an alternative formalization of the explanatory conditional. For (ii), we make use of the adaptive logics framework for modeling defeasible reasoning. We show how our proposal allows for a more natural reading of explanatory relations, (...) and how it overcomes problems faced by other systems in the literature. (shrink)

One of the least explored areas of C.S. Peirce's wide range of work is his contributions to psychology and the philosophy of mind. This dissertation examines the corpus of this work, especially as it relates to the subjects of mind, habit, instinct, sentiment, emotion, perception, consciousness, cognition, and community. The argument is that Peirce's contributions to these areas of investigation were both highly original and heavily influenced by the main intellectual currents of his time. An effort has been made to (...) present Peirce's philosophy without apology, within the conceptual framework and idiom of its time, and without appeal to a comprehensive view that Peirce never articulated. Nevertheless, as several noted interpreters have argued, much of this work can be viewed through the lens of Peirce's innovative theory of signs and the notion of the semiotic triad as its central unifying feature, despite the fact that the general theory was itself under continuous refinement and remained incomplete at the time of his death. Another hermeneutical device employed is William James' better known and more accessible work which, when juxtaposed with Peirce's ideas, serves to bring them into sharper relief. While general and historical in the presentation of material, this study seeks, at the same time, to engage the criticism of contemporary Peirce scholars in an attempt to account for several of the conundrums inherent in Peirce's work. Among the problems with implications for his philosophy of mind and theory of inquiry are the limitations of his theory of continuity, his negative view of the self, his somewhat ambiguous position on the relation of psychology to logic, and the metaethical puzzle arising from application of his theory of probable inference to truly fateful decisions. These problems provide an interesting perspective and lend balance to the truly insightful contributions Peirce made to the discovery of the mind. (shrink)

According to C. S. Peirce, abduction is a rational attempt to locate an explanation for a puzzling phenomenon, where this is a process that includes both generating explanatory hypotheses and selecting certain hypotheses for further scrutiny. Since inference is a controlled process that can be subjected to normative standards, essential to his view of abductive rasoning is that it is correlated to a unique species of correctness that cannot be reduced to deductive validity or inductive strength. This irreducibility claim is (...) of considerable importance for the logical and epistemological scrutiny of scientific methods, but it is not clear that Peirce produced a convicing argument for it. To the contrary, when the full structure of abductive argumentation is clarified, especially as presented in Peirce’s later writings on the topic, a good case can be made for viewing every inferential step in the abductive process as dissolving into familiar forms of deductive and inductive reasoning. Specifically, hypothesis-selection is a special type of practical inference that, if correct, is deductively valid, while the creative phase, hypothesis-generation, is not inferential at all. Once this is understood, it emerges that the familiar descriptions of abduction as “inference to the best explanation” or as a process of “belief revision” are, at best, misleading. (shrink)

The question is what are the preconditions for being able to rephrase visual objects in propositional form and consequently in argumentational terms. The idea is to identify the fundamentals of a linguistic-semiotic analysis of visual objects, which rest on philosophical notions in logic, linguistics and aesthetics.

In order for visual objects to be fully integrated in argumentation studies, we should be able to show how some visual objects can be part of a rational communication process and be analyzed as part of rational activity, where audiences reason their way to intentions and beliefs via their recognition of the arguer's intention to produce such results. This paper will focus on the way to enable the embedment of some visual objects in argumentation theory.