Theorems in automated theorem proving are usually proved by formal logical proofs. However, there is a subset of problems which humans can prove by the use of geometric operations on diagrams, so called diagrammatic proofs. Insight is often more clearly perceived in these proofs than in the corresponding algebraic proofs; they capture an intuitive notion of truthfulness that humans find easy to see and understand. We are investigating and automating such diagrammatic reasoning about mathematical theorems. Concrete, rather than general diagrams (...) are used to prove particular concrete instances of the universally quantified theorem. The diagrammatic proof is captured by the use of geometric operations on the diagram. These operations are the inference steps of the proof. An abstracted schematic proof of the universally quantified theorem is induced from these proof instances. The constructive -rule provides the mathematical basis for this step from schematic proofs to theoremhood. In this way we avoid the difficulty of treating a general case in a diagram. One method of confirming that the abstraction of the schematic proof from the proof instances is sound is proving the correctness of schematic proofs in the meta-theory of diagrams. These ideas have been implemented in the system, called Diamond, which is presented here. (shrink)

The concept of virtual machine allows us to combine the dynamical and computational hypotheses in an investigation of cognition. Van Gelder explicitly rejects this approach, but not only does it allow us to use the modelling technique most appropriate to the task, it also opens up a new range of phenomena where these techniques interact.

Reflecting Alan Robinson's fundamental contribution to computational logic, this book brings together seminal papers in inference, equality theories, and logic programming. It is an exceptional collection that ranges from surveys of major areas to new results in more specialized topics. Alan Robinson is currently the University Professor at Syracuse University. Jean-Louis Lassez is a Research Scientist at the IBM Thomas J. Watson Research Center. Gordon Plotkin is Professor of Computer Science at the University of Edinburgh. Contents: Inference. Subsumption, (...) A Sometimes Undervalued Procedure, Larry Wos, Ross Overbeek, and Ewing Lusk. The Markgraf Karl Refutation Procedure, Hans Jurgen Ohlbach and Jorg H. Siekmann. Modal Logic Should Say More than it Does, Melvin Fitting. Interactive Proof Presentation, W. W. Bledsoe. Intelligent Backtracking Revisited, Maurice Bruynooghe. A Science of Reasoning, Alan Bundy. Inductive Inference of Theories from Facts, Ehud Y. Shapiro. Equality. Solving Equations in Abstract Algebras: A Rule-based Survey of Unification, Jean-Pierre Jouannaud and Claude Kirchner. Disunification: A Survey, Hubert Comon. A Case Study of the Completion Procedure: Proving Ring Commutativity Problems, Deepak Kapur and Hantao Zhang. Computations in Regular Rewriting Systems I and II, Girard Huet and JeanJacques Levy. Unification and ML Type Reconstruction, Paris Kanellakis, Harry Mairson, and John Mitchell. Automatic Dimensional Analysis, Mitchell Wand. Logic Programming. Logic Programming Schemes and Their Implementations, Keith Clark. A Near-Horn Prolog for Compilation, Donald Loveland and David Reed. Unfold/Fold Transformations of Logic Programs, P. A. Gardner and J. C. Shepherdson. An Algebraic Representation of Logic Program Computations, Andrea Corradini and Ugo Montanari. Theory of Disjunctive Logic Programs, Jack Minker, Arcot Rajasekar, and Jorge Lobo. Bottom-Up Evaluation of Logic Programs, Jeffrey Naughton and Raghu Ramakrishnan. Absys, the First Logic Programming Language: A View of the Inevitability of Logic Programming, E. W. Elcock. (shrink)

In practice, mathematical proofs are most often the result of careful planning by the agents who produced them. As a consequence, each mathematical proof inherits a plan in virtue of the way it is produced, a plan which underlies its “architecture” or “unity”. This paper provides an account of plans and planning in the context of mathematical proofs. The approach adopted here consists in looking for these notions not in mathematical proofs themselves, but in the agents who produced them. The (...) starting point is to recognize that to each mathematical proof corresponds a proof activity which consists of a sequence of deductive inferences—i.e., a sequence of epistemic actions—and that any written mathematical proof is only a report of its corresponding proof activity. The main idea to be developed is that the plan of a mathematical proof is to be conceived and analyzed as the plan of the agent(s) who carried out the corresponding proof activity. The core of the paper is thus devoted to the development of an account of plans and planning in the context of proof activities. The account is based on the theory of planning agency developed by Michael Bratman in the philosophy of action. It is fleshed out by providing an analysis of the notions of intention—the elementary components of plans—and practical reasoning—the process by which plans are constructed—in the context of proof activities. These two notions are then used to offer a precise characterization of the desired notion of plan for proof activities. A fruitful connection can then be established between the resulting framework and the recent theme of modularity in mathematics introduced by Jeremy Avigad. This connection is exploited to yield the concept of modular presentations of mathematical proofs which has direct implications for how to write and present mathematical proofs so as to deliver various epistemic benefits. The account is finally compared to the technique of proof planning developed by Alan Bundy and colleagues in the field of automated theorem proving. The paper concludes with some remarks on how the framework can be used to provide an analysis of understanding and explanation in the context of mathematical proofs. (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)

In this book, Alan Wertheimer seeks to identify when a transaction or relationship can be properly regarded as exploitative--and not oppressive, manipulative, or morally deficient in some other way--and explores the moral weight of taking ...

Whose Keeper? is a profound and creative treatise on modernity and its challenge to social science. Alan Wolfe argues that modern liberal democracies, such as the United States and Scandinavia, have broken with traditional sources of mortality and instead have relied upon economic and political frameworks to define their obligations to one another. Wolfe calls for reinvigorating a sense of community and thus a sense of obligation to the larger society.

Rowlands defends environmentalism, that is, the conjunction of the ontological claim that cognitive processes are not located exclusively inside the skin of cognizing organisms and the epistemological claim that it is not possible to understand the nature of cognitive processes by focusing exclusively on what is occurring inside the skin of cognizing organisms. Chapter 3 is devoted to explaining how environmentalism differs from other forms of externalism about the mental. The crucial points are that the arguments to be presented for (...) the ontological claim do not turn on considerations about the content of mental states, that environmentalism implies a strong form of externalism, and that standard arguments for externalism, based on considerations about content, do not establish the strong form. (shrink)

There is a tendency in current philosophical thought to treat sensory experiences as a peculiar species of propositional attitude. Alan Millar argues against this view. While allowing that experiences may in some sense bear propositional content, he presents a view of sensory experiences asa species of psychological state. He applies the resulting analytical framework to a discussion of justified belief, dealing, firstly, with how beliefs may derive justification from other beliefs, and secondly, with how current sensory experiences may contribute (...) to the justification of a person'sbeliefs. A key theme in his general approach is that justified belief results from the competent exercise of conceptual capacities, some of which involve an ability to respond appropriately to current experience. In working out this approach the author develops a view of concepts and theirmastery, explores the role of groundless beliefs drawing on suggestions of Wittgenstein, illuminates aspects of the thought of Locke, Hume, Quine, and Goldman, and finally offers a response to a sophisticated variety of scepticism. (shrink)

Using undergraduate students from the Waikato University in New Zealand as a sample, this study compared the ethical positions of students of different field of study and demographic characteristics. It was found that the ethical standard of business students are not significantly different from that of non-business students. The findings also suggest that female students are more ethical than male students, and senior students are more ethical than junior students.Besides sex and year of study, other variables studied were parents' occupation, (...) religiosity and household income of the students. All these variables were found to have no significant impact on the ethical position of the students. Furthermore, all the interaction effects between the variables studied and the students' major field of study were nonsignificant. (shrink)

There is a traditional conception of sensory experience on which the experiences one has looking at, say, a cat could be had by someone merely hallucinating a cat. Disjunctivists take issue with this conception on the grounds that it does not enable us to understand how perceptual knowledge is possible. In particular, they think, it does not explain how it can be that experiences gained in perception enable us to be in ‘cognitive contact’ with objects and facts. I develop this (...) chal- lenge to the traditional conception and then show that it is possible to accommo- date an adequate account of cognitive contact in keeping with the traditional conception. One upshot of the discussion is that experiences do not bear the explanatory burden placed upon them by disjunctivists. (shrink)

First published in 1991. Routledge is an imprint of Taylor & Francis, an informa company.

This paper defends the traditional view that the laws of nature are contingent, or, if some of them are necessary, this is due to analytic principles for the individuation of the law-governed properties. Fundamentally, I argue that the supposed explanatory purposes served by taking the laws to be necessary --showing how laws support counterfactuals, how properties are individuated, or how we have knowledge of properties--are in fact undermined by the continued possibility of the imagined scenarios--this time, described neutrally--which seemed to (...) disprove the claim to necessity in the first place. I speculate that this will be true for any proposed necessary a posteriori truths, and is a basis for rejecting their supposed metaphysical significance. (shrink)

In this reinterpretation and reconstruction of Spinoza's thought, Donagan (humanities, Caltech) demonstrates that it was Spinoza's unique usage of traditional philosophical vocabulary that resulted in the history of misunderstanding that is his continuing fate. Annotation copyrighted by Book News, Inc., Portland, OR.

The goal of this paper is to encourage a reconfiguration of the discussion about typology in biology away from the metaphysics of essentialism and toward the epistemology of classifying natural phenomena for the purposes of empirical inquiry. First, I briefly review arguments concerning ‘typological thinking’, essentialism, species, and natural kinds, highlighting their predominantly metaphysical nature. Second, I use a distinction between the aims, strategies, and tactics of science to suggest how a shift from metaphysics to epistemology might be accomplished. Typological (...) thinking can be understood as a scientific tactic that involves representing natural phenomena using idealizations and approximations, which facilitates explanation, investigation, and theorizing via abstraction and generalization. Third, a variety of typologies from different areas of biology are introduced to emphasize the diversity of this representational reasoning. One particular example is used to examine how there can be epistemological conflict between typology and evolutionary analysis. This demonstrates that alternative strategies of typological thinking arise due to the divergent explanatory goals of researchers working in different disciplines with disparate methodologies. I conclude with several research questions that emerge from an epistemological reconfiguration of typology. (shrink)

This volume explores questions about conceptual change from both scientific and philosophical viewpoints by analyzing the recent history of evolutionary developmental biology. It features revised papers that originated from the workshop "Conceptual Change in Biological Science: Evolutionary Developmental Biology, 1981-2011" held at the Max Planck Institute for the History of Science in Berlin in July 2010. The Preface has been written by Ron Amundson. In these papers, philosophers and biologists compare and contrast key concepts in evolutionary developmental biology and their (...) development since the original, seminal Dahlem conference on evolution and development held in Berlin in 1981. Many of the original scientific participants from the 1981 conference are also contributors to this new volume and, in conjunction with other expert biologists and philosophers specializing on these topics, provide an authoritative, comprehensive view on the subject. Taken together, the papers supply novel perspectives on how and why the conceptual landscape has shifted and stabilized in particular ways, yielding insights into the dynamic epistemic changes that have occurred over the past three decades. This volume will appeal to philosophers of biology studying conceptual change, evolutionary developmental biologists focused on comprehending the genesis of their field and evaluating its future directions, and historians of biology examining this period when the intersection of evolution and development rose again to prominence in biological science. (shrink)

This book, first published in 1987, investigates what distinguishes the part of human behaviour that is action from the part that is not. The distinction was clearly drawn by Socrates, and developed by Aristotle and the medievals, but key elements of their work became obscured in modern philosophy, and were not fully recovered when, under Wittgenstein’s influence, the theory of action was revived in analytical philosophy. This study aims to recover those elements, and to analyse them in terms of a (...) defensible semantics on Fregean lines. Among its conclusions: that actions are bodily or mental events that are causally explained by their doers’ propositional attitudes, especially by their choices or fully specific intentions; that choice cannot be reduced to desire and belief, and hence that the traditional concept of will as intellectual appetite must be revived. (shrink)

Applies a philosophical analysis of the natural sciences to the social sciences.

There is a traditional conception of sensory experience on which the experiences one has looking at, say, a cat could be had by someone merely hallucinating a cat. Disjunctivists take issue with this conception on the grounds that it does not enable us to understand how perceptual knowledge is possible. In particular, they think, it does not explain how it can be that experiences gained in perception enable us to be in ‘cognitive contact’ with objects and facts. I develop this (...) challenge to the traditional conception and then show that it is possible to accommodate an adequate account of cognitive contact in keeping with the traditional conception. One upshot of the discussion is that experiences do not bear the explanatory burden placed upon them by disjunctivists. (shrink)