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Elementary logic

New York,: Oxford University Press (1972)

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  1. Names.Sam Cumming - 2009 - Stanford Encyclopedia of Philosophy.
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  • In search of an integrated logic of conviction and intention.Prof Dr B. Sharon Byrd, Prof Dr Joachim Hruschka & Prof Dr Jan C. Joerden - 2004 - Philosophical Explorations.
    According to a two-level criterion for combination tests in the field of ordinary language, moral 'ought'-sentences may be taken to imply 'I intend'-sentences partly semantically and partly pragmatically. If so, a trenchant linguistic analysis of the concept of moral obligation cannot do without a non-classical logic which allows to model these important kinds of ordinary-language implications by means of purely syntactical derivations. For this purpose, an integrated logic of conviction and intention has been tentatively devised by way of a doxastically, (...)
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  • (1 other version)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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  • (2 other versions)Frege and semantics.Richard G. Heck - 2007 - Grazer Philosophische Studien 75 (1):27-63.
    In recent work on Frege, one of the most salient issues has been whether he was prepared to make serious use of semantical notions such as reference and truth. I argue here Frege did make very serious use of semantical concepts. I argue, first, that Frege had reason to be interested in the question how the axioms and rules of his formal theory might be justified and, second, that he explicitly commits himself to offering a justification that appeals to the (...)
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  • Self-reference and validity.Stephen Read - 1979 - Synthese 42 (2):265 - 274.
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  • The punctuational sources of the truth-functional 'or'.R. E. Jennings - 1986 - Philosophical Studies 50 (2):237-259.
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  • (1 other version)The Logical Structure of Spinoza's Ethics, Part I.Charles Jarrett - 1978 - Synthese 37 (1):15 - 65.
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  • Intensionality and the gödel theorems.David D. Auerbach - 1985 - Philosophical Studies 48 (3):337--51.
    Philosophers of language have drawn on metamathematical results in varied ways. Extensionalist philosophers have been particularly impressed with two, not unrelated, facts: the existence, due to Frege/Tarski, of a certain sort of semantics, and the seeming absence of intensional contexts from mathematical discourse. The philosophical import of these facts is at best murky. Extensionalists will emphasize the success and clarity of the model theoretic semantics; others will emphasize the relative poverty of the mathematical idiom; still others will question the aptness (...)
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  • Logic and the autonomy of ethics.Charles R. Pigden - 1989 - Australasian Journal of Philosophy 67 (2):127 – 151.
    My first paper on the Is/Ought issue. The young Arthur Prior endorsed the Autonomy of Ethics, in the form of Hume’s No-Ought-From-Is (NOFI) but the later Prior developed a seemingly devastating counter-argument. I defend Prior's earlier logical thesis (albeit in a modified form) against his later self. However it is important to distinguish between three versions of the Autonomy of Ethics: Ontological, Semantic and Ontological. Ontological Autonomy is the thesis that moral judgments, to be true, must answer to a realm (...)
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  • A simple type theory without platonic domains.Charles S. Chihara - 1984 - Journal of Philosophical Logic 13 (3):249 - 283.
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  • Sobre la naturaleza multiple de las constantes lógicas.Axel Barcelo - 2007 - In Orayen: De la Forma Lógica al Significado. México: IIFs UNAM. pp. 61-82.
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  • The Logicality of Equality.Andrzej Indrzejczak - 2024 - In Thomas Piecha & Kai F. Wehmeier (eds.), Peter Schroeder-Heister on Proof-Theoretic Semantics. Springer. pp. 211-238.
    The status of the equality predicate as a logical constant is problematic. In the paper we look at the problem from the proof-theoretic standpoint and survey several ways of treating equality in formal systems of different sorts. In particular, we focus on the framework of sequent calculus and examine equality in the light of criteria of logicality proposed by Hacking and Došen. Both attempts were formulated in terms of sequent calculus rules, although in the case of Došen it has a (...)
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  • (1 other version)Inferential Quantification and the ω-rule.Constantin C. Brîncuş - 2024 - In Antonio Piccolomini D'Aragona (ed.), Perspectives on Deduction: Contemporary Studies in the Philosophy, History and Formal Theories of Deduction. Springer Verlag. pp. 345--372.
    Logical inferentialism maintains that the formal rules of inference fix the meanings of the logical terms. The categoricity problem points out to the fact that the standard formalizations of classical logic do not uniquely determine the intended meanings of its logical terms, i.e., these formalizations are not categorical. This means that there are different interpretations of the logical terms that are consistent with the relation of logical derivability in a logical calculus. In the case of the quantificational logic, the categoricity (...)
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  • The Subject Matter of Logic: Explaining what logic is about.Elizabeth Olsen - 2021 - Dissertation, Victoria University of Wellington
    Logicians disagree about how validity—the very heart of logic—should be understood. Many different formal systems have been born due to this disagreement. This thesis examines how teachers explain the subject matter of logic to students in introductory logic textbooks, and demonstrates the different explanations teachers use. These differences help explain why logicians have different intuitions about validity.
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  • Against Fregean Quantification.Bryan Pickel & Brian Rabern - 2023 - Ergo: An Open Access Journal of Philosophy 9 (37):971-1007.
    There are two dominant approaches to quantification: the Fregean and the Tarskian. While the Tarskian approach is standard and familiar, deep conceptual objections have been pressed against its employment of variables as genuine syntactic and semantic units. Because they do not explicitly rely on variables, Fregean approaches are held to avoid these worries. The apparent result is that the Fregean can deliver something that the Tarskian is unable to, namely a compositional semantic treatment of quantification centered on truth and reference. (...)
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  • Handbook of Argumentation Theory.Frans H. van Eemeren, Bart Garssen, Erik C. W. Krabbe, A. Francisca Snoeck Henkemans, Bart Verheij & Jean H. M. Wagemans - 2014 - Dordrecht, Netherland: Springer.
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  • Shadows of Syntax: Revitalizing Logical and Mathematical Conventionalism.Jared Warren - 2020 - New York, USA: Oxford University Press.
    What is the source of logical and mathematical truth? This book revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. Shadows of Syntax is the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. It (...)
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  • Single-domain free logic and the problem of compositionality.Dolf Rami - 2020 - Synthese 198 (10):9479-9523.
    In this paper, I will defend a new compositional semantics for single-domain free logic. This semantics makes use of a distinction between the semantic value of a singular term and its semantic referent. The semantic value of a singular term is conceived of as a set that either contains the semantic referent or no element at all. The semantic referent is the object that the term designates. Before I will introduce this new semantics for single-domain predicate and an S5-type modal (...)
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  • Enciclopédia de Termos Lógico-Filosóficos.João Miguel Biscaia Branquinho, Desidério Murcho & Nelson Gonçalves Gomes (eds.) - 2006 - São Paulo, SP, Brasil: Martins Fontes.
    Esta enciclopédia abrange, de uma forma introdutória mas desejavelmente rigorosa, uma diversidade de conceitos, temas, problemas, argumentos e teorias localizados numa área relativamente recente de estudos, os quais tem sido habitual qualificar como «estudos lógico-filosóficos». De uma forma apropriadamente genérica, e apesar de o território teórico abrangido ser extenso e de contornos por vezes difusos, podemos dizer que na área se investiga um conjunto de questões fundamentais acerca da natureza da linguagem, da mente, da cognição e do raciocínio humanos, bem (...)
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  • A Cláusula Final da Definição Geral do Silogismo e suas funções na silogística e nos Primeiros Analíticos I de Aristóteles.Felipe Weinmann - 2014 - Dissertation, University of Campinas
    Aristotle's General Definition of the Syllogism may be taken as consisting of two parts: the Inferential Conditions and the Final Clause. Although this distinction is well known, traditional interpretations neglect the Final Clause and its influence on syllogistic. Instead, the aforementioned tradition focuses on the Inferential Conditions only. We intend to show that this neglect has severe consequences not just on syllogistic but on the whole exegesis of Aristotle's Prior Analytics I. Due to these consequences, our objective is to analyse (...)
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  • Fred Sommers’ Contributions to Formal Logic.George Englebretsen - 2016 - History and Philosophy of Logic 37 (3):269-291.
    Fred Sommers passed away in October of 2014 in his 92nd year. Having begun his teaching at Columbia University, he eventually became the Harry A. Wolfson Chair in Philosophy at Brandeis University, where he taught from 1963 to 1993. During his long and productive career, Sommers authored or co-authored over 50 books, articles, reviews, etc., presenting his ideas on numerous occasions throughout North America and Europe. His work was characterized by a commitment to the preservation and application of historical insights (...)
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  • A measure of inferential-role preservation.A. C. Paseau - 2019 - Synthese 196 (7):2621-2642.
    The point of formalisation is to model various aspects of natural language. Perhaps the main use to which formalisation is put is to model and explain inferential relations between different sentences. Judged solely by this objective, a formalisation is successful in modelling the inferential network of natural language sentences to the extent that it mirrors this network. There is surprisingly little literature on the criteria of good formalisation, and even less on the question of what it is for a formalisation (...)
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  • 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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  • Gentzen and Jaśkowski Natural Deduction: Fundamentally Similar but Importantly Different.Allen P. Hazen & Francis Jeffry Pelletier - 2014 - Studia Logica 102 (6):1103-1142.
    Gentzen’s and Jaśkowski’s formulations of natural deduction are logically equivalent in the normal sense of those words. However, Gentzen’s formulation more straightforwardly lends itself both to a normalization theorem and to a theory of “meaning” for connectives . The present paper investigates cases where Jaskowski’s formulation seems better suited. These cases range from the phenomenology and epistemology of proof construction to the ways to incorporate novel logical connectives into the language. We close with a demonstration of this latter aspect by (...)
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  • Non-deductive Logic in Mathematics: The Probability of Conjectures.James Franklin - 2013 - In Andrew Aberdein & Ian J. Dove (eds.), The Argument of Mathematics. Dordrecht, Netherland: Springer. pp. 11--29.
    Mathematicians often speak of conjectures, yet unproved, as probable or well-confirmed by evidence. The Riemann Hypothesis, for example, is widely believed to be almost certainly true. There seems no initial reason to distinguish such probability from the same notion in empirical science. Yet it is hard to see how there could be probabilistic relations between the necessary truths of pure mathematics. The existence of such logical relations, short of certainty, is defended using the theory of logical probability (or objective Bayesianism (...)
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  • (1 other version)Bayesian Informal Logic and Fallacy.Kevin Korb - 2004 - Informal Logic 24 (1):41-70.
    Bayesian reasoning has been applied formally to statistical inference, machine learning and analysing scientific method. Here I apply it informally to more common forms of inference, namely natural language arguments. I analyse a variety of traditional fallacies, deductive, inductive and causal, and find more merit in them than is generally acknowledged. Bayesian principles provide a framework for understanding ordinary arguments which is well worth developing.
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  • The Port-Royal Logic's Theory of Argument.Maurice A. Finocchiaro - 1997 - Argumentation 11 (4):393-410.
    This is a critical examination of Antoine Arnauld's Logic or the Art of Thinking (1662), commonly known as the Port-Royal Logic. Rather than reading this work from the viewpoint of post-Fregean formal logic or the viewpoint of seventeenth-century intellectual history, I approach it with the aim of exploring its relationship to that contemporary field which may be labeled informal logic and/or argumentation theory. It turns out that the Port-Royal Logic is a precursor of this current field, or conversely, that this (...)
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  • Zero-place operations and functional completeness, and the definition of new connectives.I. L. Humberstone - 1993 - History and Philosophy of Logic 14 (1):39-66.
    Tarski 1968 makes a move in the course of providing an account of ?definitionally equivalent? classes of algebras with a businesslike lack of fanfare and commentary, the significance of which may accordingly be lost on the casual reader. In ?1 we present this move as a response to a certain difficulty in the received account of what it is to define a function symbol (or ?operation symbol?). This difficulty, which presents itself as a minor technicality needing to be got around (...)
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  • (1 other version)Towards a theory of mathematical argument.Ian J. Dove - 2009 - Foundations of Science 14 (1-2):136-152.
    In this paper, I assume, perhaps controversially, that translation into a language of formal logic is not the method by which mathematicians assess mathematical reasoning. Instead, I argue that the actual practice of analyzing, evaluating and critiquing mathematical reasoning resembles, and perhaps equates with, the practice of informal logic or argumentation theory. It doesn’t matter whether the reasoning is a full-fledged mathematical proof or merely some non-deductive mathematical justification: in either case, the methodology of assessment overlaps to a large extent (...)
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  • Logical constants.John MacFarlane - 2008 - Mind.
    Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and semantic (...)
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  • ‘That’-Clauses and Non-nominal Quantification.Tobias Rosefeldt - 2008 - Philosophical Studies 137 (3):301 - 333.
    This paper argues that ‘that’-clauses are not singular terms (without denying that their semantical values are propositions). In its first part, three arguments are presented to support the thesis, two of which are defended against recent criticism. The two good arguments are based on the observation that substitution of ‘the proposition that p’ for ‘that p’ may result in ungrammaticality. The second part of the paper is devoted to a refutation of the main argument for the claim that ‘that’-clauses are (...)
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  • Peter Schroeder-Heister on Proof-Theoretic Semantics.Thomas Piecha & Kai F. Wehmeier (eds.) - 2024 - Springer.
    This open access book is a superb collection of some fifteen chapters inspired by Schroeder-Heister's groundbreaking work, written by leading experts in the field, plus an extensive autobiography and comments on the various contributions by Schroeder-Heister himself. For several decades, Peter Schroeder-Heister has been a central figure in proof-theoretic semantics, a field of study situated at the interface of logic, theoretical computer science, natural-language semantics, and the philosophy of language. -/- The chapters of which this book is composed discuss the (...)
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  • Non-metric Propositional Similarity.A. C. Paseau - 2022 - Erkenntnis 87 (5):2307-2328.
    The idea that sentences can be closer or further apart in meaning is highly intuitive. Not only that, it is also a pillar of logic, semantic theory and the philosophy of science, and follows from other commitments about similarity. The present paper proposes a novel way of comparing the ‘distance’ between two pairs of propositions. We define ‘\ is closer in meaning to \ than \ is to \’ and thereby give a precise account of comparative propositional similarity facts. Notably, (...)
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  • Newman’s Objection is Dead; Long Live Newman’s Objection!Sebastian Lutz - manuscript
    There are two ways of reading Newman’s objection to Russell’s structuralism. One assumes that according to Russell, our knowledge of a theory about the external world is captured by an existential generalization on all non-logical symbols of the theory. Under this reading, our knowledge amounts to a cardinality claim. Another reading assumes that our knowledge singles out a structure in Russell’s (and Newman’s) sense: a model theoretic structure that is determined up to isomorphism. Under this reading, our knowledge is far (...)
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  • Quantifier Variance and Indefinite Extensibility.Jared Warren - 2017 - Philosophical Review 126 (1):81-122.
    This essay clarifies quantifier variance and uses it to provide a theory of indefinite extensibility that I call the variance theory of indefinite extensibility. The indefinite extensibility response to the set-theoretic paradoxes sees each argument for paradox as a demonstration that we have come to a different and more expansive understanding of ‘all sets’. But indefinite extensibility is philosophically puzzling: extant accounts are either metasemantically suspect in requiring mysterious mechanisms of domain expansion, or metaphysically suspect in requiring nonstandard assumptions about (...)
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  • (1 other version)Towards a theory of mathematical argument.Ian J. Dove - 2013 - In Andrew Aberdein & Ian J. Dove (eds.), The Argument of Mathematics. Dordrecht, Netherland: Springer. pp. 291--308.
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  • Neutralism within the Semantic Tradition.Robert Trueman - 2012 - Thought: A Journal of Philosophy 1 (3):246-251.
    A neutralist framework is an account of the second-order quantifiers which does not by itself tell us what the ontological commitments of second-order quantification are, but which does tell us that those commitments cannot exceed those of predication. Recently, Wright has suggested that an inferentialist account of the second-order quantifiers is an adequate neutralist framework. I show that we do not have to become inferentialists in the pursuit of a neutralist framework: such a framework can be established within the semantic (...)
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  • Newcomb's many solutions.Ellery Eells - 1984 - Theory and Decision 16 (1):59-105.
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  • Busting a Myth about Leśniewski and Definitions.Rafal Urbaniak & K. Severi Hämäri - 2012 - History and Philosophy of Logic 33 (2):159-189.
    A theory of definitions which places the eliminability and conservativeness requirements on definitions is usually called the standard theory. We examine a persistent myth which credits this theory to Leśniewski, a Polish logician. After a brief survey of its origins, we show that the myth is highly dubious. First, no place in Leśniewski's published or unpublished work is known where the standard conditions are discussed. Second, Leśniewski's own logical theories allow for creative definitions. Third, Leśniewski's celebrated ‘rules of definition’ lay (...)
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  • Can There be a Proof that an Unprovable Sentence of Arithmetic is True?Philip Hugly & Charles Sayward - 1989 - Dialectica 43 (43):289-292.
    Various authors of logic texts are cited who either suggest or explicitly state that the Gödel incompleteness result shows that some unprovable sentence of arithmetic is true. Against this, the paper argues that the matter is one of philosophical controversy, that it is not a mathematical or logical issue.
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  • Nominalistic systems.Rolf A. Eberle - 1970 - Dordrecht,: Reidel.
    1. 1. PROGRAM It will be our aim to reconstruct, with precision, certain views which have been traditionally associated with nominalism and to investigate problems arising from these views in the construction of interpreted formal systems. Several such systems are developed in accordance with the demand that the sentences of a system which is acceptable to a nominalist must not imply the existence of any entities other than individuals. Emphasis will be placed on the constructionist method of philosophical analysis. To (...)
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  • Aspects of the logic of history-of-science explanation.Maurice A. Finocchiaro - 1985 - Synthese 62 (3):429 - 454.
    The topic of history-of-science explanation is first briefly introduced as a generally important one for the light it may shed on action theory, on the logic of discovery, and on philosophy''s relations with historiography of science, intellectual history, and the sociology of knowledge. Then some problems and some conclusions are formulated by reference to some recent relevant literature: a critical analysis of Laudan''s views on the role of normative evaluations in rational explanations occasions the result that one must make aconceptual (...)
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  • Linguistics and psychology.Scott Soames - 1984 - Linguistics and Philosophy 7 (2):155 - 179.
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  • The Hintikka-Kripke problem.S. K. Lehmann - 1978 - Philosophia 8 (1):59-70.
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  • On being called something.Geoff Georgi - 2017 - Linguistics and Philosophy 40 (6):595-619.
    Building on recent work by Delia Graff Fara and Ora Matushansky on appellative constructions like ‘Mirka called Roger handsome’, I argue that if Millianism about proper names is true, then the quantifier ‘something’ in ‘Mirka called Roger something’ is best understood as a kind of substitutional quantifier. Any adequate semantics for such quantifiers must explain both the logical behavior of ‘Mirka called Roger something’ and the acceptability of ‘so’-anaphora in ‘Mirka called Roger something, and everyone so called is handsome’. Millianism (...)
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  • The Logic and Meaning of Plurals. Part I.Byeong-Uk Yi - 2005 - Journal of Philosophical Logic 34 (5-6):459-506.
    Contemporary accounts of logic and language cannot give proper treatments of plural constructions of natural languages. They assume that plural constructions are redundant devices used to abbreviate singular constructions. This paper and its sequel, "The logic and meaning of plurals, II", aim to develop an account of logic and language that acknowledges limitations of singular constructions and recognizes plural constructions as their peers. To do so, the papers present natural accounts of the logic and meaning of plural constructions that result (...)
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  • (1 other version)Can There Be A Proof That Some Unprovable Arithmetic Sentence Is True?Philip Hugly & Charles Sayward - 1989 - Dialectica 43 (3):289-292.
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  • Leśniewski's Systems of Logic and Foundations of Mathematics.Rafal Urbaniak - 2013 - Cham, Switzerland: Springer.
    With material on his early philosophical views, his contributions to set theory and his work on nominalism and higher-order quantification, this book offers a uniquely expansive critical commentary on one of analytical philosophy’s great ...
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  • A Brief History of Natural Deduction.Francis Jeffry Pelletier - 1999 - History and Philosophy of Logic 20 (1):1-31.
    Natural deduction is the type of logic most familiar to current philosophers, and indeed is all that many modern philosophers know about logic. Yet natural deduction is a fairly recent innovation in logic, dating from Gentzen and Jaśkowski in 1934. This article traces the development of natural deduction from the view that these founders embraced to the widespread acceptance of the method in the 1960s. I focus especially on the different choices made by writers of elementary textbooks—the standard conduits of (...)
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  • Negation and Quantification in Aristotle.Michael V. Wedin - 1990 - History and Philosophy of Logic 11 (2):131-150.
    Two main claims are defended. The first is that negative categorical statements are not to be accorded existential import insofar as they figure in the square of opposition. Against Kneale and others, it is argued that Aristotle formulates his o statements, for example, precisely to avoid existential commitment. This frees Aristotle's square from a recent charge of inconsistency. The second claim is that the logic proper provides much thinner evidence than has been supposed for what appears to be the received (...)
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