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  1. Commitment in Dialogue: Basic Concepts of Interpersonal Reasoning.Douglas Neil Walton & Erik C. W. Krabbe - 1995 - Albany, NY, USA: State University of New York Press.
    Develops a logical analysis of dialogue in which two or more parties attempt to advance their own interests. It includes a classification of the major types of dialogues and a discussion of several important informal fallacies.
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  • (5 other versions)What is Cantor's Continuum Problem?Kurt Gödel - 1947 - The American Mathematical Monthly 54 (9):515--525.
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  • What is Mathematical Truth?Hilary Putnam - 1979 - In Philosophical Papers: Volume 1, Mathematics, Matter and Method. New York: Cambridge University Press. pp. 60--78.
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  • (1 other version)Mathematics and plausible reasoning.George Pólya - 1968 - Princeton, N.J.,: Princeton University Press.
    2014 Reprint of 1954 American Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. This two volume classic comprises two titles: "Patterns of Plausible Inference" and "Induction and Analogy in Mathematics." This is a guide to the practical art of plausible reasoning, particularly in mathematics, but also in every field of human activity. Using mathematics as the example par excellence, Polya shows how even the most rigorous deductive discipline is heavily dependent on techniques of guessing, inductive (...)
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  • (1 other version)Elementary logic.Benson Mates - 1972 - New York,: Oxford University Press.
    The present text book is intended as an introduction to elementary logic. Its content, structure, and manner have been determined in large measure - perhaps 'caused' is the better word- by certain desiderata about which the reader should be informed at the outset. The leading idea is that even an introductory treatment of logic may profitably be fashioned around a rigorous framework.
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  • (3 other versions)Introduction to Logic.Irving M. Copi - manuscript
    There are obvious benefits to be gained from the study of logic: heightened ability to express ideas clearly and concisely, increased skill in defining one's terms, enlarged capacity to formulate arguments rigorously and to analyze them critically. But the greatest benefit, in my judgment, is the recognition that reason can be applied in every aspect of human affairs.
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  • Realism in mathematics.Penelope Maddy - 1990 - New York: Oxford University Prress.
    Mathematicians tend to think of themselves as scientists investigating the features of real mathematical things, and the wildly successful application of mathematics in the physical sciences reinforces this picture of mathematics as an objective study. For philosophers, however, this realism about mathematics raises serious questions: What are mathematical things? Where are they? How do we know about them? Offering a scrupulously fair treatment of both mathematical and philosophical concerns, Penelope Maddy here delineates and defends a novel version of mathematical realism. (...)
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  • (1 other version)Mathematics and Plausible Reasoning: Induction and analogy in mathematics.George Pólya - 1954 - Princeton, NJ, USA: Princeton University Press.
    Here the author of How to Solve It explains how to become a "good guesser." Marked by G. Polya's simple, energetic prose and use of clever examples from a wide range of human activities, this two-volume work explores techniques of guessing, inductive reasoning, and reasoning by analogy, and the role they play in the most rigorous of deductive disciplines.
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  • The four-color problem and its philosophical significance.Thomas Tymoczko - 1979 - Journal of Philosophy 76 (2):57-83.
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  • Non-deductive logic in mathematics.James Franklin - 1987 - British Journal for the Philosophy of Science 38 (1):1-18.
    Mathematicians often speak of conjectures as being confirmed by evidence that falls short of proof. For their own conjectures, evidence justifies further work in looking for a proof. Those conjectures of mathematics that have long resisted proof, such as Fermat's Last Theorem and the Riemann Hypothesis, have had to be considered in terms of the evidence for and against them. It is argued here that it is not adequate to describe the relation of evidence to hypothesis as `subjective', `heuristic' or (...)
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  • Poincaré vs. Russell on the rôle of logic in mathematicst.Michael Detlefsen - 1993 - Philosophia Mathematica 1 (1):24-49.
    In the early years of this century, Poincaré and Russell engaged in a debate concerning the nature of mathematical reasoning. Siding with Kant, Poincaré argued that mathematical reasoning is characteristically non-logical in character. Russell urged the contrary view, maintaining that (i) the plausibility originally enjoyed by Kant's view was due primarily to the underdeveloped state of logic in his (i.e., Kant's) time, and that (ii) with the aid of recent developments in logic, it is possible to demonstrate its falsity. This (...)
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  • The derivation-indicator view of mathematical practice.Jody Azzouni - 2004 - Philosophia Mathematica 12 (2):81-106.
    The form of nominalism known as 'mathematical fictionalism' is examined and found wanting, mainly on grounds that go back to an early antinominalist work of Rudolf Carnap that has unfortunately not been paid sufficient attention by more recent writers.
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  • A Systematic Theory of Argumentation: The Pragma-Dialectical Approach.Frans Hendrik van Eemeren & Rob Grootendorst - 2003 - Cambridge, England: Cambridge University Press.
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  • (1 other version)Why Do We Prove Theorems?Yehuda Rav - 1999 - Philosophia Mathematica 7 (1):5-41.
    Ordinary mathematical proofs—to be distinguished from formal derivations—are the locus of mathematical knowledge. Their epistemic content goes way beyond what is summarised in the form of theorems. Objections are raised against the formalist thesis that every mainstream informal proof can be formalised in some first-order formal system. Foundationalism is at the heart of Hilbert's program and calls for methods of formal logic to prove consistency. On the other hand, ‘systemic cohesiveness’, as proposed here, seeks to explicate why mathematical knowledge is (...)
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  • (1 other version)Why Do We Prove Theorems?Yehuda Rav - 1998 - Philosophia Mathematica 6 (3):5-41.
    Ordinary mathematical proofs—to be distinguished from formal derivations—are the locus of mathematical knowledge. Their epistemic content goes way beyond what is summarised in the form of theorems. Objections are raised against the formalist thesis that every mainstream informal proof can be formalised in some first-order formal system. Foundationalism is at the heart of Hilbert's program and calls for methods of formal logic to prove consistency. On the other hand, ‘systemic cohesiveness’, as proposed here, seeks to explicate why mathematical knowledge is (...)
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  • (3 other versions)Introduction to Logic.Irving M. Copi - 1956 - Philosophy of Science 23 (3):267-268.
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  • Reasoning.Michael Scriven - 1976 - New York: McGraw-Hill Companies.
    The Aims of the Book -/- 1. To improve your skill in analyzing and evaluating arguments and presentations of the kind you find in everyday discourse (news media, discussions, advertisements), textbooks, and lectures. 2. To improve your skill in presenting arguments, reports and instructions clearly and persuasively. 3. To improve your critical instincts, that is, your immediate judgments of your attitudes toward the communications and behavior of others and yourself, so that you consistently approach them with the standards of reason (...)
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  • Tracking Reason: Proof, Consequence, and Truth.Jody Azzouni - 2005 - Oxford, England: Oup Usa.
    When ordinary people - mathematicians among them - take something to follow from something else, they are exposing the backbone of our self-ascribed ability to reason. Jody Azzouni investigates the connection between that ordinary notion of consequence and the formal analogues invented by logicians. One claim of the book is that, despite our apparent intuitive grasp of consequence, we do not introspect rules by which we reason, nor do we grasp the scope and range of the domain, as it were, (...)
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  • Fallacies in Mathematics.E. A. Maxwell - 2006 - University Press.
    "Enjoyment as well as enlightenment is provided by trying to detect the fallacies, or at least by reading the solutions given by the author of this lovely little work." Science.
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  • A Systematic Theory of Argumentation: The Pragma-Dialectical Approach.Frans H. Van Eemeren & Rob Grootendorst - 2003 - Cambridge University Press.
    In this book two of the leading figures in argumentation theory present a view of argumentation as a means of resolving differences of opinion by testing the acceptability of the disputed positions. Their model of a 'critical discussion' serves as a theoretical tool for analysing, evaluating and producing argumentative discourse. They develop a method for the reconstruction of argumentative discourse that takes into account all aspects that are relevant to a critical assessment. They also propose a practical code of behaviour (...)
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  • The Uses of Argument in Mathematics.Andrew Aberdein - 2005 - Argumentation 19 (3):287-301.
    Stephen Toulmin once observed that ”it has never been customary for philosophers to pay much attention to the rhetoric of mathematical debate’ [Toulmin et al., 1979, An Introduction to Reasoning, Macmillan, London, p. 89]. Might the application of Toulmin’s layout of arguments to mathematics remedy this oversight? Toulmin’s critics fault the layout as requiring so much abstraction as to permit incompatible reconstructions. Mathematical proofs may indeed be represented by fundamentally distinct layouts. However, cases of genuine conflict characteristically reflect an underlying (...)
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  • (5 other versions)What is Cantor's Continuum Problem?Kurt Gödel - 1983 - In Paul Benacerraf & Hilary Putnam (eds.), Philosophy of Mathematics: Selected Readings (2nd Edition). Cambridge University Press. pp. 470-485.
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  • (1 other version)Proofs and Refutations.Imre Lakatos - 1980 - Noûs 14 (3):474-478.
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  • Critical Thinking, Critical Reasoning, and Methodological Reflection.Maurice Finocchiaro - 1996 - Inquiry: Critical Thinking Across the Disciplines 15 (4):66-79.
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  • Fundamentals of Critical Argumentation.Douglas N. Walton - 2005 - New York: Cambridge University Press.
    Fundamentals of Critical Argumentation presents the basic tools for the identification, analysis, and evaluation of common arguments for beginners. The book teaches by using examples of arguments in dialogues, both in the text itself and in the exercises. Examples of controversial legal, political, and ethical arguments are analyzed. Illustrating the most common kinds of arguments, the book also explains how to evaluate each kind by critical questioning. Douglas Walton shows how arguments can be reasonable under the right dialogue conditions by (...)
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  • Reducibility Among Combinatorial Problems.Richard M. Karp, Raymond E. Miller & James W. Thatcher - 1975 - Journal of Symbolic Logic 40 (4):618-619.
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  • Three Recalcitrant Problems of Argument Identification.Michael E. Malone - 2003 - Informal Logic 23 (3):237-261.
    Logicians disagree on (1) criteria for the presence of an argument, (2) criteria for adding implicit premises and (3) criteria for linking premises. I attempt to resolve all three problems, and in the process to remove the main obstacles to teaching diagramming. The first problem is resolved by working with real discourse that students find on their own, rather than the artificial examples and problems found in logic texts; it is further reduced by examining the different uses of argument and (...)
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  • The Applicability of Mathematics as a Philosophical Problem.Mark Steiner - 1998 - Harvard University Press.
    This book analyzes the different ways mathematics is applicable in the physical sciences, and presents a startling thesis--the success of mathematical physics ...
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  • The four-color theorem and mathematical proof.Michael Detlefsen & Mark Luker - 1980 - Journal of Philosophy 77 (12):803-820.
    I criticize a recent paper by Thomas Tymoczko in which he attributes fundamental philosophical significance and novelty to the lately-published computer-assisted proof of the four color theorem (4CT). Using reasoning precisely analogous to that employed by Tymoczko, I argue that much of traditional mathematical proof must be seen as resting on what Tymoczko must take as being "empirical" evidence. The new proof of the 4CT, with its use of what Tymoczko calls "empirical" evidence is therefore not so novel as he (...)
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  • The informal logic of mathematical proof.Andrew Aberdein - 2006 - In Reuben Hersh (ed.), 18 Unconventional Essays on the Nature of Mathematics. Springer. pp. 56-70.
    Informal logic is a method of argument analysis which is complementary to that of formal logic, providing for the pragmatic treatment of features of argumentation which cannot be reduced to logical form. The central claim of this paper is that a more nuanced understanding of mathematical proof and discovery may be achieved by paying attention to the aspects of mathematical argumentation which can be captured by informal, rather than formal, logic. Two accounts of argumentation are considered: the pioneering work of (...)
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  • The Applicability of Mathematics as a Philosophical Problem.Mark Steiner - 2000 - Mind 109 (434):390-394.
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  • Intentional gaps in mathematical proofs.Don Fallis - 2003 - Synthese 134 (1-2):45 - 69.
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  • Proofs and refutations (IV).I. Lakatos - 1963 - British Journal for the Philosophy of Science 14 (56):296-342.
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  • (3 other versions)Introduction to Logic.Irving M. Copi - 1954 - Philosophy 29 (110):271-271.
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  • Believing the axioms. II.Penelope Maddy - 1988 - Journal of Symbolic Logic 53 (3):736-764.
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  • Poincaré against the logicians.Michael Detlefsen - 1992 - Synthese 90 (3):349 - 378.
    Poincaré was a persistent critic of logicism. Unlike most critics of logicism, however, he did not focus his attention on the basic laws of the logicists or the question of their genuinely logical status. Instead, he directed his remarks against the place accorded to logical inference in the logicist's conception of mathematical proof. Following Leibniz, traditional logicist dogma (and this is explicit in Frege) has held that reasoning or inference is everywhere the same — that there are no principles of (...)
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  • The Epistemic Status of Probabilistic Proof.Don Fallis - 1997 - Journal of Philosophy 94 (4):165-186.
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  • Manifest Rationality: A Pragmatic Theory of Argument.Ralph H. Johnson - 2000 - Lawrence Earlbaum Associates.
    He further argues that it is necessary to rethink traditional conceptions of argument, and to find a position that avoids the limitations of both the highly abstract approach of formal logic and the highly contextualized approaches of rhetoric and communication theory.".
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  • Physical-mathematical reasoning: Galileo on the extruding power of terrestrial rotation.Maurice A. Finocchiaro - 2003 - Synthese 134 (1-2):217 - 244.
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  • Mathematical Proof and the Reliability of DNA Evidence.Don Fallis - 1996 - The American Mathematical Monthly 103 (6):491-497.
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