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Logic and Philosophy of Logic, General Works

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  1. P. B. Andrews (2002). An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof. Kluwer Academic Publishers.
    This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs (...)
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  2. G. E. M. Anscombe & Roger Teichmann (2000). Logic, Cause & Action: Essays in Honour of Elizabeth Anscombe. Cambridge University Press.
    Elizabeth Anscombe is among the most distinguished and original philosophers alive today. Her work has ranged over many areas of philosophy, including metaphysics, ethics, the philosophy of mind and action, and the philosophy of religion. In each of these areas she has made seminal contributions. The essays in this book reflect the breadth of her interests and the esteem in which she is held by her colleagues. The distinguished contributors include Michael Dunnett, Nancy Cartwright, Peter Geach and Philippa Foot; and (...)
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  3. Jack Arnold & Stewart Shapiro (2007). Where in the (World Wide) Web of Belief is the Law of Non-Contradiction? Noûs 41 (2):276–297.
    It is sometimes said that there are two, competing versions of W. V. O. Quine’s unrelenting empiricism, perhaps divided according to temporal periods of his career. According to one, logic is exempt from, or lies outside the scope of, the attack on the analytic-synthetic distinction. This logic-friendly Quine holds that logical truths and, presumably, logical inferences are analytic in the traditional sense. Logical truths are knowable a priori, and, importantly, they are incorrigible, and so immune from revision. The other, radical (...)
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  4. Jon Barwise, William Ladusaw, Alice ter Meulen, Richard Oehrle & Richmond Thomason (1992). Logic and Linguistics Meeting: Santa Cruz, 1991. Journal of Symbolic Logic 57 (4):1498-1499.
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  5. J. C. Beall (2010). Logic: The Basics. Routledge.
    Background ideas -- Consequences -- Relations of support -- Logical consequence : the basic recipe -- Valid arguments and truth -- Language, form, and logical theories -- Language -- Atoms, connectives, and molecules -- Connectives and form -- Validity and form -- Language and formal languages -- Logical theories : rivalry -- Set-theoretic tools -- Sets -- Ordered sets : pairs and n-tuples -- Relations -- Functions -- Sets as tools -- Basic connectives -- Classical theory -- Cases : complete (...)
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  6. Sandy Berkovski, Formal Logic.
    of Γ, {X, Y } is simultaneously satisfiable. 2. Given that Γ and ∆ are simultaneously satisfiable, would Π = Γ ∩ ∆ be simultaneously satisfiable? 3. Prove the following results: (a) {A ⊃ B, ¬A ⊃ B} B. (b) A ∨ B B ∨ A. (c) ¬(A ∧ ¬A). 4. Find a disjunctive normal form for the formula (B ∧ C) ⊃ (A ↔ (¬B ∨ C)). 5. Show that the formula:    Ai..
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  7. Francesco Berto (2007). How to Sell a Contradiction. College Publications.
    There is a principle in things, about which we cannot be deceived, but must always, on the contrary, recognize the truth – viz. that the same thing cannot at one and the same time be and not be": with these words of the Metaphysics, Aristotle introduced the Law of Non-Contradiction, which was to become the most authoritative principle in the history of Western thought. However, things have recently changed, and nowadays various philosophers, called dialetheists, claim that this Law does not (...)
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  8. Jean-Yves Beziau, What is “Formal Logic”?
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  9. Jean-Yves Béziau & Décio Krause (2007). New Trends in the Foundations of Science. Synthese 154 (3):345 - 347.
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  10. Andrew Brennan, Necessary and Sufficient Conditions. Stanford Encyclopedia of Philosophy.
    Describes the received theory of necessary and sufficient conditions, explains some standard objections to it, and lays out alternative ways of thinking about conditions and conditionals.
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  11. Joseph E. Brenner (2008). Logic in Reality. Springer.
    The work is the presentation of a logical theory - Logic in Reality (LIR) - and of applications of that theory in natural science and philosophy, including ...
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  12. Walter A. Carnielli (2004). Book Review: Yves Nievergelt, Foundations of Logic and Mathematics: Applications to Computer Science and Cryptography, Birkäuser Verlag, Boston, 2002, €90, Pp. 480, ISBN 0-8176-4249-8, Hardcover. Dimensions (in Inches): 1.00 × 9.96 × 7.36. Studia Logica 78 (3).
    Book review r A. (2004). "Book review: Yves nievergelt, foundations of ...
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  13. Leigh S. Cauman (1998). First-Order Logic: An Introduction. Walter De Gruyter.
    Introduction This is an elementary logic book designed for people who have no technical familiarity with modern logic but who have been reasoning, ...
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  14. Ian Chiswell (2007). Mathematical Logic. Oxford University Press.
    Assuming no previous study in logic, this informal yet rigorous text covers the material of a standard undergraduate first course in mathematical logic, using natural deduction and leading up to the completeness theorem for first-order logic. At each stage of the text, the reader is given an intuition based on standard mathematical practice, which is subsequently developed with clean formal mathematics. Alongside the practical examples, readers learn what can and can't be calculated; for example the correctness of a derivation proving (...)
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  15. Alonzo Church (1944). Introduction to Mathematical Logic. London, H. Milford, Oxford University Press.
    This book is intended to be used as a textbook by students of mathematics, and also within limitations as a reference work.
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  16. Alonzo Church, C. Anthony Anderson & Michael Zelëny (2001). Logic, Meaning, and Computation: Essays in Memory of Alonzo Church. Kluwer Academic Publishers.
    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 (...)
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  17. Nino B. Cocchiarella (1988). Predication Versus Membership in the Distinction Between Logic as Language and Logic as Calculus. Synthese 77 (1):37 - 72.
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  18. Marcelo E. Coniglio (2007). Recovering a Logic From its Fragments by Meta-Fibring. Logica Universalis 1 (2):377-416.
    . In this paper we address the question of recovering a logic system by combining two or more fragments of it. We show that, in general, by fibring two or more fragments of a given logic the resulting logic is weaker than the original one, because some meta-properties of the connectives are lost after the combination process. In order to overcome this problem, the categories Mcon and Seq of multiple-conclusion consequence relations and sequent calculi, respectively, are introduced. The main feature (...)
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  19. John Corcoran (1980). Categoricity. History and Philosophy of Logic 1 (1):187-207.
    After a short preface, the first of the three sections of this paper is devoted to historical and philosophic aspects of categoricity. The second section is a self-contained exposition, including detailed definitions, of a proof that every mathematical system whose domain is the closure of its set of distinguished individuals under its distinguished functions is categorically characterized by its induction principle together with its true atoms (atomic sentences and negations of atomic sentences). The third section deals with applications especially those (...)
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  20. Gabbay Dm & Guenthner F. (2002). Handbook of Philosophical Logic. History and Philosophy of Logic 23 (4):289-291.
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  21. Burton Dreben & Juliet Floyd (1991). Tautology: How Not to Use a Word. Synthese 87 (1):23 - 49.
  22. Michael Durrant & Charles Sayward (1967). Austin On Whether Every Proposition Has A Contradictory. Analysis 27 (April):167-170.
    Austin rejects the contention that every proposition has a contradictory. This paper finds problems with the case Austin makes for rejecting the contention in question.
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  23. Antony Eagle, Elements of Deductive Logic.
    A textbook for an 'advanced introductory' logic class (I used it as a textbook for mathematically capable introductory logic students). The book uses the tableau method, and includes standard results up to a proof of the soundness of predicate logic. Its slightly unusual features include a slightly greater emphasis on decidability than is usual, and more obviously, the presentation of a free logic as standard, alongside a classical alternative. A change of syllabus here means this is no longer under active (...)
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  24. Heinz-Dieter Ebbinghaus (1996). Mathematical Logic. Springer.
    This junior/senior level text is devoted to a study of first-order logic and its role in the foundations of mathematics: What is a proof? How can a proof be justified? To what extent can a proof be made a purely mechanical procedure? How much faith can we have in a proof that is so complex that no one can follow it through in a lifetime? The first substantial answers to these questions have only been obtained in this century. The most (...)
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  25. M. R. Haight (1999). The Snake and the Fox: An Introduction to Logic. Routledge.
    The Snake and the Fox offers students a new and exciting way to look at and understand logic. Mary Haight uses graphics to tell the story of how logic works, and why it works the way it does. This introductory text uses easy to understand language for the student who has no prior understanding of logic or philosophy. The author includes some discussion on the philosophical theory underlying the logic: not just how to do it, but why it takes the (...)
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  26. Wilfrid Hodges (1977). Logic. Penguin.
    From this starting point, and assuming no previous knowledge of logic, Wilfrid Hodges takes the reader through the whole gamut of logical expressions in a ...
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  27. Colin Howson (1997). Logic with Trees: An Introduction to Symbolic Logic. Routledge.
    Logic With Trees is a new and original introduction to modern formal logic. It contains discussions on philosophical issues such as truth, conditionals and modal logic, presenting the formal material with clarity, and preferring informal explanations and arguments to intimidatingly rigorous development. Worked examples and exercises guide beginners through the book, with answers to selected exercises enabling readers to check their progress. Logic With Trees equips students with: a complete and clear account of the truth-tree system for first order logic; (...)
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  28. Philip Hugly & Charles Sayward (2000). Frege on Identities. History and Philosophy of Logic 21 (3):195-205.
    The idea underlying the Begriffsschrift account of identities was that the content of a sentence is a function of the things it is about. If so, then if an identity a=b is about the content of its contained terms and is true, then a=a and a=b have the same content. But they do not have the same content; so, Frege concluded, identities are not about the contents of their contained terms. The way Frege regarded the matter is that in an (...)
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  29. Philip Hugly & Charles Sayward (1977). Prior’s Theory of Propositions. Analysis 37 (3):104-112.
    Prior propounded a theory that, if correct, explains how it is possible for a statement about propositions to be true even if there are no propositions. The major feature of his theory is his treatment of sentence letters as bindable variables in non-referential positions. His theory, however, does not include a semantical account of the resulting quantification. The paper tries to fill that gap.
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  30. Patrick J. Hurley (2000). A Concise Introduction to Logic. Wadsworth Pub..
    Preface The most immediate benefit derived from the study of logic is the skill needed to construct sound arguments of one's own and to evaluate the ...
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  31. James Ladyman, Oystein Linnebo & Richard Pettigrew (forthcoming). Identity and Discernibility in Philosophy and Logic. Review of Symbolic Logic.
    There has been much debate in philosophy about the relation between identity and distinctness on the one hand, and various forms of discernibility on the other. For instance, philosophers have debated the truth of the Principle of the Identity of Indiscernibles (PII), which is naturally formulated using a second-order quantifier ranging over some class of properties of particular philosophical significance.
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  32. Ernest LePore (2000). Meaning and Argument: An Introduction to Logic Through Language. Blackwell.
    Meaning and Argument shifts introductory logic from the traditional emphasis on proofs to the symbolization of arguments. Another distinctive feature of this book is that it shows how the need for expressive power and for drawing distinctions forces formal language development. This revised edition includes expanded sections, additional exercises, and an updated bibliography. Updated and revised edition includes extended sections, additional exercises, and an updated bibliography. Distinctive approach in that this text is a philosophical, rather than mathematical introduction to logic. (...)
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  33. Per Lindström, First-Order Logic.
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  34. J. R. Lucas, Chapter 9a What is Logic?
    Thus far the logic out of which mathematics has developed has been First-order Predicate Calculus with Identity, that is the logic of the sentential functors, ¬, →, ∧, ∨, etc., together with identity and the existential and universal quotifiers restricted to quotify- ing only over individuals, and not anything else, such as qualities or quotities themselves. Some philosophers—among them Quine— have held that this, First-order Logic, as it is often called, con- stitutes the whole of logic. But that is a (...)
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  35. Ofra Magidor (forthcoming). Strict Finitism and the Happy Sorites. Journal of Philosophical Logic.
    Call an argument a ‘happy sorites’ if it is a sorites argument with true premises and a false conclusion. It is a striking fact that although most philosophers working on the sorites paradox find it at prima facie highly compelling that the premises of the sorites paradox are true and its conclusion false, few (if any) of the standard theories on the issue ultimately allow for happy sorites arguments. There is one philosophical view, however, that appears to allow for at (...)
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  36. David Miller, Word Games for Formal Logic.
    Some students in the humanities take fright when introduced to the formal manipulations characteristic of elementary sentential & predicate logic. One way to lessen the pain of initiation is to start with word games, of which Lewis Carroll’s Doublets (section 1) is a familiar example. The paper presents some other games that successively introduce more of the..
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  37. Terence Parsons (1996). What is an Argument? Journal of Philosophy 93 (4):164-185.
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  38. Erich Rast, Logic: A Primer.
    This text is a short introduction to logic that was primarily used for accompanying an introductory course in Logic for Linguists held at the New University of Lisbon (UNL) in fall 2010. The main idea of this course was to give students the formal background and skills in order to later assess literature in logic, semantics, and related fields and perhaps even use logic on their own for the purpose of doing truth-conditional semantics. This course in logic does not replace (...)
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  39. Stephen Read (1994). Formal and Material Consequence. Journal of Philosophical Logic 23 (3):247 - 265.
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  40. Charles Sayward (1987). Prior’s Theory of Truth. Analysis 47 (2):83-87.
    This paper is a critical exposition of Prior’s theory of truth as expressed by the following truth locutions: (1) ‘it is true that’ prefixed to sentences; (2) ‘true proposition’; (3) true belief’, ‘true assertion’, ‘true statement’, etc.; (4) ‘true sentence’.
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  41. Charles Sayward (1972). True Propositions: A Reply to C.J.F. Williams. Analysis 32 (3):101-106.
    This paper replies to points Williams makes to his reply to Sayward’s criticism of Williams’s proposal of ‘for some p ___ states that p & p’ as an analysis of ‘___ is true’.
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  42. Charles Sayward (1970). Williams’ Definition of ‘X is True’. Analysis 30 (3):95-97.
    C. J. F, Williams proposed ‘for some p ___ states that p & p’ as a satisfactory analysis of ‘___ is true’. This paper takes issue with this claim.
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  43. Uwe Schöning (1989). Logic for Computer Scientists. Birkhäuser.
    This book introduces the notions and methods of formal logic from a computer science standpoint, covering propositional logic, predicate logic, and foundations ...
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  44. Peter Smith (2003). An Introduction to Formal Logic. Cambridge University Press.
    Formal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this highly accessible book, Peter Smith presents a guide to the fundamental aims and basic elements of formal logic. He introduces the reader to the languages of propositional and predicate logic, and then develops formal systems for evaluating arguments translated into these languages, (...)
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  45. Patrick Suppes (1957/1999). Introduction to Logic. Dover Publications.
    Coherent, well organized text familiarizes readers with complete theory of logical inference and its applications to math and the empirical sciences. Part I deals with formal principles of inference and definition; Part II explores elementary intuitive set theory, with separate chapters on sets, relations, and functions. Last section introduces numerous examples of axiomatically formulated theories in both discussion and exercises. Ideal for undergraduates; no background in math or philosophy required.
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  46. Clinton Tolley (forthcoming). Kant on the Generality of Logic. In Proceedings of the 11th International Kant Congress. De Gruyter.
  47. Clinton Tolley (2006). Kant on the Nature of Logical Laws. Philosophical Topics 34 (1/2):371-407.
  48. Paul Tomassi (1999). Logic. Routledge.
    Logic brings elementary logic out of the academic darkness into the light of day. Paul Tomassi makes logic fully accessible for anyone trying to come to grips with the complexities of this challenging subject. This book is written in a patient and user-friendly way which makes both the nature and value of formal logic crystal clear. This textbook proceeds from a frank, informal introduction to fundamental logical notions to a system of formal logic rooted in the best of our natural (...)
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  49. Crispin Wright, On Quantifying Into Predicate Position: Steps Towards a New(Tralist) Perspective.
    In the Begriffschrift Frege drew no distinction—or anyway signalled no importance to the distinction—between quantifying into positions occupied by what he called eigennamen—singular terms—in a sentence and quantification into predicate position or, more generally, quantification into open sentences—into what remains of a sentence when one or more occurrences of singular terms are removed. He seems to have conceived of both alike as perfectly legitimate forms of generalisation, each properly belonging to logic. More accurately: he seems to have conceived of quantification (...)
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