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Summary Predicate logic is the more complicated of the two modern classical logics.  It does not consider atomic propositions as indivisible, notwithstanding the etymology, but also considers the structure within propositions. In its treatment of the general, as opposed to the singular, propositions, it achieves the aims of Aristotelian logic in combination with the aims of propositional logic.  In the classification structure chosen by the general editors, second-order and higher-order logics are separate categories, and are therefore not classified as (ordinary) predicate calculus. This may seem a curiosity; it is exlpored in Eklund 1996. In its treatment of singular propositions, relations are permitted, too, as is the special predicate, identity. In classical predicate logic, molecular or compound propositions are built up from atomic propositions by means of the connectives, whose meaning is given by their truth tables.  Likewise, one way of understanding the meaning of the two classical quantifiers, existential and universal, is by taking them to be expanded disjunctions and conjunctions, respectively, over the universe of discourse.  The principle by which the meaning or truth conditions of compound propositions can be recovered by this "building up" process is known as compositionality.  Aside from an appropriate way to understand the meaning of the quantifiers, there is the additional issue of existential import. This leaf node is a sub-category of classical logic.  As such, non-standard predicate logics are not generally classified in this category—unless a comparison between classical logic and another logic is being drawn or one is reduced to the other—although restrictions of predicate logic in which nothing not a theorem in ordinary predicate logic is a theorem in the restriction do fit here.  Also appropriate are modest extensions of predicate logic, excluding higher-order logics as noted above, provided that Boole's three laws of thought are not violated, viz. a proposition is either true or false, not neither, and not both. Meta-theoretical results for predicate logic are generally also classified as "proof theory," "model theory," "mathematical logic," etc.
Key works See below.
Introductions Because of the age of predicate logic there are literally hundreds of introductions to logic which cover this subject reasonably well.  Instructors will have their own favorites.  In selecting a book for classroom use, I recommend checking two things: (1) The correctness and clarity of the restrictions on universal generalization and existential instantiation; (2) how much meta-theory is included, so that the book is neither below nor above the level students can handle.
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  1. added 2020-02-05
    Traits essentiels d'une formalisation adéquate.Gheorghe-Ilie Farte - 2020 - Argumentum. Journal of the Seminar of Discursive Logic, Argumentation Theory and Rhetoric 18 (1):163-174.
    In order to decide whether a discursive product of human reason corresponds or not to the logical order, one must analyze it in terms of syntactic correctness, consistency, and validity. The first step in logical analysis is formalization, that is, the process by which logical forms of thoughts are represented in different formal languages or logical systems. Although each thought can be properly formalized in different ways, the formalization variants are not equally adequate. The adequacy of formalization seems to depend (...)
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  2. added 2020-01-11
    The Accident of Logical Constants.Tristan Grøtvedt Haze - 2020 - Thought: A Journal of Philosophy 9 (1):34-42.
    Work on the nature and scope of formal logic has focused unduly on the distinction between logical and extra-logical vocabulary; which argument forms a logical theory countenances depends not only on its stock of logical terms, but also on its range of grammatical categories and modes of composition. Furthermore, there is a sense in which logical terms are unnecessary. Alexandra Zinke has recently pointed out that propositional logic can be done without logical terms. By defining a logical-term-free language with the (...)
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  3. added 2019-08-21
    Edgar Morscher: Die wissenschaftliche Definition. [REVIEW]Moritz Cordes - 2018 - Zeitschrift für Philosophische Forschung 72:443-446.
  4. added 2019-06-07
    A variant of the proof of completeness of first order functional calculus.J. Slupecki - 1961 - Studia Logica 12:125.
  5. added 2019-06-06
    Introduction to Symbolic Logic. [REVIEW]E. McMullin - 1956 - Philosophical Studies (Dublin) 6:238-239.
    This is a useful little book. Within a surprisingly short space it manages to cover most of the fundamentals of symbolic logic in a clear and accurate way. The development is step-by-step, and each new term is carefully explained at its first mention. The main topics covered are the logic of sentences, the axiomatic method, and an elementary form of the logic of predicates. In the final chapter and appendix a number of more difficult problems are briefly touched upon: higher-order (...)
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  6. added 2019-06-06
    Formal Logic. Prior - 1955 - Oxford University Press.
    This book was designed primarily as a textbook; though the author hopes that it will prove to be of interests to others beside logic students. Part I of this book covers the fundamentals of the subject the propositional calculus and the theory of quantification. Part II deals with the traditional formal logic and with the developments which have taken that as their starting-point. Part III deals with modal, three-valued, and extensional systems.
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  7. added 2019-06-06
    Symbolic Logic.Irving Copi - 1954 - New York: Macmillan.
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  8. added 2019-06-05
    Symbolic Logic. Clarence Irving Lewis, Cooper Harold Landford.Henry Bradford Smith - 1934 - Philosophy of Science 1 (2):239-246.
  9. added 2019-06-04
    The Truth Assignments That Differentiate Human Reasoning From Mechanistic Reasoning: The Evidence-Based Argument for Lucas' Goedelian Thesis.Bhupinder Singh Anand - 2016 - Cognitive Systems Research 40:35-45.
    We consider the argument that Tarski's classic definitions permit an intelligence---whether human or mechanistic---to admit finitary evidence-based definitions of the satisfaction and truth of the atomic formulas of the first-order Peano Arithmetic PA over the domain N of the natural numbers in two, hitherto unsuspected and essentially different, ways: (1) in terms of classical algorithmic verifiabilty; and (2) in terms of finitary algorithmic computability. We then show that the two definitions correspond to two distinctly different assignments of satisfaction and truth (...)
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  10. added 2019-03-24
    Two-Sided Trees for Sentential Logic, Predicate Logic, and Sentential Modal Logic.Jesse Fitts & David Beisecker - 2019 - Teaching Philosophy 42 (1):41-56.
    This paper will present two contributions to teaching introductory logic. The first contribution is an alternative tree proof method that differs from the traditional one-sided tree method. The second contribution combines this tree system with an index system to produce a user-friendly tree method for sentential modal logic.
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  11. added 2019-03-09
    An Arithmetization of Logical Oppositions.Fabien Schang - 2016 - In Jean-Yves Beziau & Gianfranco Basti (eds.), The Square of Opposition: A Cornerstone of Thought. Bâle, Suisse: pp. 215-237.
    An arithmetic theory of oppositions is devised by comparing expressions, Boolean bitstrings, and integers. This leads to a set of correspondences between three domains of investigation, namely: logic, geometry, and arithmetic. The structural properties of each area are investigated in turn, before justifying the procedure as a whole. Io finish, I show how this helps to improve the logical calculus of oppositions, through the consideration of corresponding operations between integers.
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  12. added 2018-11-21
    On the Concept of a Notational Variant.Alexander W. Kocurek - 2017 - In Alexandru Baltag, Jeremy Seligman & Tomoyuki Yamada (eds.), Logic, Rationality, and Interaction (LORI 2017, Sapporo, Japan). pp. 284-298.
    In the study of modal and nonclassical logics, translations have frequently been employed as a way of measuring the inferential capabilities of a logic. It is sometimes claimed that two logics are “notational variants” if they are translationally equivalent. However, we will show that this cannot be quite right, since first-order logic and propositional logic are translationally equivalent. Others have claimed that for two logics to be notational variants, they must at least be compositionally intertranslatable. The definition of compositionality these (...)
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  13. added 2018-08-06
    Categories of First-Order Quantifiers.Urszula Wybraniec-Skardowska - 2018 - In Urszula Wybraniec-Skardowska & Ángel Garrido (eds.), The Lvov-Warsaw School. Past and Present. Basel, Switzerland: pp. 575-597.
    One well known problem regarding quantifiers, in particular the 1storder quantifiers, is connected with their syntactic categories and denotations. The unsatisfactory efforts to establish the syntactic and ontological categories of quantifiers in formalized first-order languages can be solved by means of the so called principle of categorial compatibility formulated by Roman Suszko, referring to some innovative ideas of Gottlob Frege and visible in syntactic and semantic compatibility of language expressions. In the paper the principle is introduced for categorial languages generated (...)
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  14. added 2018-06-29
    Gödel's Slingshot Revisited: Does Russell's Theory of Descriptions Really Evade the Slingshot.João Daniel Dantas - 2016 - Dissertation, UFRN
    “Slingshot Arguments” are a family of arguments underlying the Fregean view that if sentences have reference at all, their references are their truth-values. Usually seen as a kind of collapsing argument, the slingshot consists in proving that, once you suppose that there are some items that are references of sentences (as facts or situations, for example), these items collapse into just two items: The True and The False. This dissertation treats of the slingshot dubbed “Gödel’s slingshot”. Gödel argued that there (...)
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  15. added 2018-05-31
    Introducción a la lógica moderna, 2a edición.Andrés Páez - 2010 - Bogotá: Ediciones Uniandes.
    The book is an undergraduate-level introduction to first-order logic and proposi­tional modal logic. The book presents symbolic logic in a way that is pedagogi­cally attractive and formally rigorous. The main concepts are formally defined, in­formally explained, and illustrated with several examples. The book is aimed at philosophy majors and it includes discussions of several problems in the philosophy of logic.
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  16. added 2018-04-20
    Classes and Theories of Trees Associated with a Class of Linear Orders.Valentin Goranko & Ruaan Kellerman - 2011 - Logic Journal of the IGPL 19 (1):217-232.
    Given a class of linear order types C, we identify and study several different classes of trees, naturally associated with C in terms of how the paths in those trees are related to the order types belonging to C. We investigate and completely determine the set-theoretic relationships between these classes of trees and between their corresponding first-order theories. We then obtain some general results about the axiomatization of the first-order theories of some of these classes of trees in terms of (...)
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  17. added 2018-02-16
    The Proper Treatment of Variables in Predicate Logic.Kai Wehmeier - 2018 - Linguistics and Philosophy 41 (2):209-249.
    In §93 of The Principles of Mathematics, Bertrand Russell observes that “the variable is a very complicated logical entity, by no means easy to analyze correctly”. This assessment is borne out by the fact that even now we have no fully satisfactory understanding of the role of variables in a compositional semantics for first-order logic. In standard Tarskian semantics, variables are treated as meaning-bearing entities; moreover, they serve as the basic building blocks of all meanings, which are constructed out of (...)
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  18. added 2017-10-14
    Rigid and Flexible Quantification in Plural Predicate Logic.Lucas Champollion, Justin Bledin & Haoze Li - forthcoming - Semantics and Linguistic Theory 27.
    Noun phrases with overt determiners, such as <i>some apples</i> or <i>a quantity of milk</i>, differ from bare noun phrases like <i>apples</i> or <i>milk</i> in their contribution to aspectual composition. While this has been attributed to syntactic or algebraic properties of these noun phrases, such accounts have explanatory shortcomings. We suggest instead that the relevant property that distinguishes between the two classes of noun phrases derives from two modes of existential quantification, one of which holds the values of a variable fixed (...)
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  19. added 2017-10-12
    The Epsilon Calculus.Jeremy Avigad & Richard Zach - 2008 - In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. The Metaphysics Research Lab, Center for the Study of Language and Information, Stanford University.
    The epsilon calculus is a logical formalism developed by David Hilbert in the service of his program in the foundations of mathematics. The epsilon operator is a term-forming operator which replaces quantifiers in ordinary predicate logic. Specifically, in the calculus, a term εx A denotes some x satisfying A(x), if there is one. In Hilbert's Program, the epsilon terms play the role of ideal elements; the aim of Hilbert's finitistic consistency proofs is to give a procedure which removes such terms (...)
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  20. added 2017-07-31
    Disquotation and Infinite Conjunctions.Lavinia Picollo & Thomas Schindler - 2017 - Erkenntnis (5):1-30.
    One of the main logical functions of the truth predicate is to enable us to express so-called ‘infinite conjunctions’. Several authors claim that the truth predicate can serve this function only if it is fully disquotational, which leads to triviality in classical logic. As a consequence, many have concluded that classical logic should be rejected. The purpose of this paper is threefold. First, we consider two accounts available in the literature of what it means to express infinite conjunctions with a (...)
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  21. added 2017-07-28
    Semantics and Proof Theory of the Epsilon Calculus.Richard Zach - 2017 - In Sujata Ghosh & Sanjiva Prasad (eds.), Logic and Its Applications. ICLA 2017. Berlin, Heidelberg: Springer. pp. 27-47.
    The epsilon operator is a term-forming operator which replaces quantifiers in ordinary predicate logic. The application of this undervalued formalism has been hampered by the absence of well-behaved proof systems on the one hand, and accessible presentations of its theory on the other. One significant early result for the original axiomatic proof system for the epsilon-calculus is the first epsilon theorem, for which a proof is sketched. The system itself is discussed, also relative to possible semantic interpretations. The problems facing (...)
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  22. added 2017-05-20
    A Technique for Determing Closure in Semantic Tableaux.Steven James Bartlett - 1983 - Methodology and Science: Interdisciplinary Journal for the Empirical Study of the Foundations of Science and Their Methodology 16 (1):1-16.
    The author considers the model-theoretic character of proofs and disproofs by means of attempted counterexample constructions, distinguishes this proof format from formal derivations, then contrasts two approaches to semantic tableaux proposed by Beth and Lambert-van Fraassen. It is noted that Beth's original approach has not as yet been provided with a precisely formulated rule of closure for detecting tableau sequences terminating in contradiction. To remedy this deficiency, a technique is proposed to clarify tableau operations.
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  23. added 2016-12-08
    The Logic of Failures of the Cinematic Imagination: Two Case Studies – and a Logical Puzzle and Solution in Just One.Joseph S. Fulda - 2013 - Pragmatics and Society 4 (1):105-111.
    This piece is intended to explicate - by providing a precising definition of - the common cinematic figure which I term “the failure of the cinematic imagination,“ while presenting a logical puzzle and its solution within a simple Gricean framework. -/- It should be noted that this is neither fully accurate nor fully precise, because of the audience; one should examine the remaining articles in the issue to understand what I mean.
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  24. added 2016-12-08
    Schönfinkel-Type Operators for Classical Logic.Katalin Bimbó - 2010 - Studia Logica 95 (3):355-378.
    We briefly overview some of the historical landmarks on the path leading to the reduction of the number of logical connectives in classical logic. Relying on the duality inherent in Boolean algebras, we introduce a new operator ( Nallor ) that is the dual of Schönfinkel’s operator. We outline the proof that this operator by itself is sufficient to define all the connectives and operators of classical first-order logic ( Fol ). Having scrutinized the proof, we pinpoint the theorems of (...)
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  25. added 2016-12-08
    Tableaux and Dual Tableaux: Transformation of Proofs.Joanna Golińska-Pilarek & Ewa Orłowska - 2007 - Studia Logica 85 (3):283-302.
    We present two proof systems for first-order logic with identity and without function symbols. The first one is an extension of the Rasiowa-Sikorski system with the rules for identity. This system is a validity checker. The rules of this system preserve and reflect validity of disjunctions of their premises and conclusions. The other is a Tableau system, which is an unsatisfiability checker. Its rules preserve and reflect unsatisfiability of conjunctions of their premises and conclusions. We show that the two systems (...)
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  26. added 2016-12-08
    Cut Elimination Inside a Deep Inference System for Classical Predicate Logic.Kai Brünnler - 2006 - Studia Logica 82 (1):51-71.
    Deep inference is a natural generalisation of the one-sided sequent calculus where rules are allowed to apply deeply inside formulas, much like rewrite rules in term rewriting. This freedom in applying inference rules allows to express logical systems that are difficult or impossible to express in the cut-free sequent calculus and it also allows for a more fine-grained analysis of derivations than the sequent calculus. However, the same freedom also makes it harder to carry out this analysis, in particular it (...)
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  27. added 2016-12-08
    Symbolic Logic. [REVIEW]E. J. A. - 1966 - Review of Metaphysics 19 (4):808-808.
    Among the more important changes in this revised edition: the incompleteness of the first set of natural deduction rules is proved; many proofs are shortened and simplified, especially in the development of the first-order functional calculus; there is a more lucid exposition of the quantification rules; more exercises are provided, with answers given for a number of them. The changes are all improvements, but none of them are of a sufficiently radical nature to be likely to alter anyone's original opinion (...)
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  28. added 2016-12-08
    Fundamentals of Symbolic Logic. [REVIEW]D. J. - 1963 - Review of Metaphysics 16 (3):579-579.
    A revised edition of the author's 1948 introductory text, the present version differs only in minor points from the original work. Truth functions are discussed in some detail, and a propositional calculus derived from the five axioms of Principia Mathematica is presented. Quantification, however, is less extensively treated. The "traditional Aristotelian" interpretation of categorical propositions is contrasted with the non-existential interpretation of modern logic; a theory of the syllogism is offered; and various methods for evaluating the validity of syllogisms are (...)
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  29. added 2016-12-08
    Introduction to Symbolic Logic and Its Applications. [REVIEW]P. R. - 1959 - Review of Metaphysics 12 (4):662-662.
    An accelerated introductory text in symbolic logic, this work is a translation and revision of Carnap's 1954 Einführung.... The latter portion of the book is devoted to semantics and to axiom systems in areas as diverse as geometry and biology.--R. P.
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  30. added 2016-12-05
    On the Interpretations of Aristotelian Categorical Propositions in the Predicate Calculus.Stanisław Jaśkowski - 1969 - Studia Logica 24 (1):161-172.
  31. added 2016-12-05
    Exercises in Introductory Symbolic Logic. [REVIEW]T. E. - 1956 - Review of Metaphysics 10 (1):180-180.
    Offers the logical tyro a varied diet, from Aristotle to Lewis Carroll, including the "neglected" forms of argument as well as examples from the logic of classes and relations. To avoid translation among systems, the examples are all in "English." Copious explanatory footnotes and references recommend it to the self-taught.--E. T.
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  32. added 2016-05-14
    The Benefits of Realism: A Realist Logic with Applications.Barry Smith - 2008 - In Katherine Munn & Barry Smith (eds.), Applied Ontology: An Introduction. Ontos. pp. 109-124.
    We propose a formalization of a realist ontology using first order logic with identity and allowing quantification over terms representing both individuals and universals. In addition to identity, the ontology includes also relational predicates such as subtype, instantiation, parthood, location, and inherence. Inspired in part by Davidson’s treatment of events, the ontology includes also various relations linking events to their participants and to the times at which they occur.
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  33. added 2016-02-26
    Reference variables and the empty universe.H. G. Callaway - 1979 - Logique Et Analyse 22 (85):85.
    In this early paper I set out an argument in favor of the standard semantics of first-order logic, to the effect that (Vx)(Ey)x=y. Though my arguments from the paper have since been revised in details, The conclusion of the paper seems still viable and acceptable.
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  34. added 2016-02-08
    1983 Review in Mathematical Reviews 83e:03005 Of: Cocchiarella, Nino “The Development of the Theory of Logical Types and the Notion of a Logical Subject in Russell's Early Philosophy: Bertrand Russell's Early Philosophy, Part I”. Synthese 45 (1980), No. 1, 71-115.John Corcoran - 1983 - MATHEMATICAL REVIEWS 83:03005.
    CORCORAN RECOMMENDS COCCHIARELLA ON TYPE THEORY. The 1983 review in Mathematical Reviews 83e:03005 of: Cocchiarella, Nino “The development of the theory of logical types and the notion of a logical subject in Russell's early philosophy: Bertrand Russell's early philosophy, Part I”. Synthese 45 (1980), no. 1, 71-115 .
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  35. added 2015-12-30
    Introducción a la lógica moderna.Andrés Páez - 2007 - Ediciones Uniandes.
    Introducción a la lógica moderna es un libro de texto dedicado al estudio de la lógica simbólica elemental. No presupone familiaridad alguna con la lógica, las matemáticas o la filosofía, y se ha hecho un esfuerzo deliberado por adaptarlo a los intereses de estudiantes provenientes de las más diversas disciplinas. Al mismo tiempo, los conceptos centrales son expuestos de una manera precisa y rigurosa, sin ocultar los detalles y problemas técnicos y filosóficos que hacen de la lógica un área de (...)
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  36. added 2015-09-20
    Information Recovery Problems.John Corcoran - 1995 - Theoria 10 (3):55-78.
    An information recovery problem is the problem of constructing a proposition containing the information dropped in going from a given premise to a given conclusion that folIows. The proposition(s) to beconstructed can be required to satisfy other conditions as well, e.g. being independent of the conclusion, or being “informationally unconnected” with the conclusion, or some other condition dictated by the context. This paper discusses various types of such problems, it presents techniques and principles useful in solving them, and it develops (...)
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  37. added 2015-07-09
    An Alternative Approach for Quasi-Truth.Marcelo E. Coniglio & Luiz H. Da Cruz Silvestrini - 2014 - Logic Journal of the IGPL 22 (2):387-410.
    In 1986, Mikenberg et al. introduced the semantic notion of quasi-truth defined by means of partial structures. In such structures, the predicates are seen as triples of pairwise disjoint sets: the set of tuples which satisfies, does not satisfy and can satisfy or not the predicate, respectively. The syntactical counterpart of the logic of partial truth is a rather complicated first-order modal logic. In the present article, the notion of predicates as triples is recursively extended, in a natural way, to (...)
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  38. added 2015-06-05
    Complete Enumerative Inductions.John Corcoran - 2006 - Bulletin of Symbolic Logic 12:465-6.
    Consider the following. The first is a one-premise argument; the second has two premises. The question sign marks the conclusions as such. -/- Matthew, Mark, Luke, and John wrote Greek. ? Every evangelist wrote Greek. -/- Matthew, Mark, Luke, and John wrote Greek. Every evangelist is Matthew, Mark, Luke, or John. ? Every evangelist wrote Greek. -/- The above pair of premise-conclusion arguments is of a sort familiar to logicians and philosophers of science. In each case the first premise is (...)
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  39. added 2015-05-26
    Commentary On: Jesse Bohl's "What Are We to Do About Traditional Logic?".Gilbert Plumer - 2000 - In Christopher W. Tindale, Hans V. Hansen & Elmar Sveda (eds.), Argumentation at the Century's Turn [CD-ROM]. Ontario Society for the Study of Argumentation. pp. 1-4.
  40. added 2015-04-19
    “Truth-Preserving and Consequence-Preserving Deduction Rules”,.John Corcoran - 2014 - Bulletin of Symbolic Logic 20 (1):130-1.
    A truth-preservation fallacy is using the concept of truth-preservation where some other concept is needed. For example, in certain contexts saying that consequences can be deduced from premises using truth-preserving deduction rules is a fallacy if it suggests that all truth-preserving rules are consequence-preserving. The arithmetic additive-associativity rule that yields 6 = (3 + (2 + 1)) from 6 = ((3 + 2) + 1) is truth-preserving but not consequence-preserving. As noted in James Gasser’s dissertation, Leibniz has been criticized for (...)
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  41. added 2015-04-13
    Forms of Thought, by E. J. Lowe. [REVIEW]Brian Ball - 2014 - Mind 123 (492):1205-1208.
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  42. added 2015-03-12
    Counterfactuals Revisited.Joseph Fulda - 1996 - Sorites 5:35-38.
    This paper presents an ontologically leaner, mathematically cleaner, and logically keener explication of counterfactuals and possible worlds than the standard Lewis-Stalnaker account.
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  43. added 2015-03-12
    Denied Conditionals Are Not Negated Conditionals.Joseph Fulda - 1995 - Sorites 2:45-45.
    This note addresses the problems that arise from denying conditionals in classical logic and concludes that such problems result from using propositional logic where predicate logic with quantification over cases is indicated.
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  44. added 2015-02-17
    Logic: The Drill.Nicholas J. J. Smith & John Cusbert - 2012 - Princeton University Press.
    Contains exercises and solutions to accompany Logic: The Laws of Truth by Nicholas J. J. Smith (Princeton University Press, 2012).
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  45. added 2015-02-17
    Logic: The Laws of Truth.Nicholas J. J. Smith - 2012 - Princeton University Press.
    Logic is essential to correct reasoning and also has important theoretical applications in philosophy, computer science, linguistics, and mathematics. This book provides an exceptionally clear introduction to classical logic, with a unique approach that emphasizes both the hows and whys of logic. Here Nicholas Smith thoroughly covers the formal tools and techniques of logic while also imparting a deeper understanding of their underlying rationales and broader philosophical significance. In addition, this is the only introduction to logic available today that presents (...)
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  46. added 2015-01-12
    Aristotle's Many-Sorted Logic.J. Corcoran - 2008 - Bulletin of Symbolic Logic 14 (1):155-156.
    As noted in 1962 by Timothy Smiley, if Aristotle’s logic is faithfully translated into modern symbolic logic, the fit is exact. If categorical sentences are translated into many-sorted logic MSL according to Smiley’s method or the two other methods presented here, an argument with arbitrarily many premises is valid according to Aristotle’s system if and only if its translation is valid according to modern standard many-sorted logic. As William Parry observed in 1973, this result can be proved using my 1972 (...)
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  47. added 2014-11-07
    Existential Import Today: New Metatheorems; Historical, Philosophical, and Pedagogical Misconceptions.John Corcoran & Hassan Masoud - 2015 - History and Philosophy of Logic 36 (1):39-61.
    Contrary to common misconceptions, today's logic is not devoid of existential import: the universalized conditional ∀ x [S→ P] implies its corresponding existentialized conjunction ∃ x [S & P], not in all cases, but in some. We characterize the proexamples by proving the Existential-Import Equivalence: The antecedent S of the universalized conditional alone determines whether the universalized conditional has existential import, i.e. whether it implies its corresponding existentialized conjunction.A predicate is an open formula having only x free. An existential-import predicate (...)
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  48. added 2014-09-20
    Ein Redehandlungskalkül: Folgern in einer Sprache.Moritz Cordes & Friedrich Reinmuth - 2011 - XXII. Deutscher Kongress Für Philosophie.
    Wir stellen einen pragmatisierten Kalkül des natürlichen Schließens vor, der sich dadurch auszeichnet, dass Ableitungen reine Folgen objektsprachlicher Sätze sind und ohne graphische oder andere Kommentarmittel auskommen.
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  49. added 2014-04-02
    The First-Order Syntax of Variadic Functions.Samuel Alexander - 2013 - Notre Dame Journal of Formal Logic 54 (1):47-59.
    We extend first-order logic to include variadic function symbols, and prove a substitution lemma. Two applications are given: one to bounded quantifier elimination and one to the definability of certain Borel sets.
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  50. added 2014-04-02
    The Translation of First Order Logic Into Modal Predicate Logic.Beomin Kim - 2008 - Proceedings of the Xxii World Congress of Philosophy 13:65-69.
    This paper deals with the translation of first order formulas to predicate S5 formulas. This translation does not bring the first order formula itself to a modal system, but modal interpretation of the first order formula can be given by the translation. Every formula can be translated, and the additional condition such as formula's having only one variable, or having both world domain and individual domain is not required. I introduce an indexical predicate 'E' for the translation. The meaning that (...)
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