Results for 'natural deduction'

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  1. Aristotle's Natural Deduction System.John Corcoran - 1974 - In Ancient Logic and its Modern Interpretations. Boston: Reidel. pp. 85--131.
    This presentation of Aristotle's natural deduction system supplements earlier presentations and gives more historical evidence. Some fine-tunings resulted from conversations with Timothy Smiley, Charles Kahn, Josiah Gould, John Kearns,John Glanvillle, and William Parry.The criticism of Aristotle's theory of propositions found at the end of this 1974 presentation was retracted in Corcoran's 2009 HPL article "Aristotle's demonstrative logic".
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  2.  72
    Commentary and Illocutionary Expressions in Linear Calculi of Natural Deduction.Moritz Cordes & Friedrich Reinmuth - 2017 - Logic and Logical Philosophy 26 (2).
    We argue that the need for commentary in commonly used linear calculi of natural deduction is connected to the “deletion” of illocutionary expressions that express the role of propositions as reasons, assumptions, or inferred propositions. We first analyze the formalization of an informal proof in some common calculi which do not formalize natural language illocutionary expressions, and show that in these calculi the formalizations of the example proof rely on commentary devices that have no counterpart in the (...)
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  3. A Speech Act Calculus. A Pragmatised Natural Deduction Calculus and its Meta-Theory.Moritz Cordes & Friedrich Reinmuth - manuscript
    Building on the work of Peter Hinst and Geo Siegwart, we develop a pragmatised natural deduction calculus, i.e. a natural deduction calculus that incorporates illocutionary operators at the formal level, and prove its adequacy. In contrast to other linear calculi of natural deduction, derivations in this calculus are sequences of object-language sentences which do not require graphical or other means of commentary in order to keep track of assumptions or to indicate subproofs. (Translation of (...)
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  4. Natural Deduction for Diagonal Operators.Fabio Lampert - 2017 - In Maria Zack & Dirk Schlimm (eds.), Research in History and Philosophy of Mathematics: The CSHPM 2016 Annual Meeting in Calgary, Alberta. Cham: Birkhäuser. pp. 39-51.
    We present a sound and complete Fitch-style natural deduction system for an S5 modal logic containing an actuality operator, a diagonal necessity operator, and a diagonal possibility operator. The logic is two-dimensional, where we evaluate sentences with respect to both an actual world (first dimension) and a world of evaluation (second dimension). The diagonal necessity operator behaves as a quantifier over every point on the diagonal between actual worlds and worlds of evaluation, while the diagonal possibility quantifies over (...)
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  5. Natural Deduction for the Sheffer Stroke and Peirce’s Arrow (and Any Other Truth-Functional Connective).Richard Zach - 2016 - Journal of Philosophical Logic 45 (2):183-197.
    Methods available for the axiomatization of arbitrary finite-valued logics can be applied to obtain sound and complete intelim rules for all truth-functional connectives of classical logic including the Sheffer stroke and Peirce’s arrow. The restriction to a single conclusion in standard systems of natural deduction requires the introduction of additional rules to make the resulting systems complete; these rules are nevertheless still simple and correspond straightforwardly to the classical absurdity rule. Omitting these rules results in systems for intuitionistic (...)
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  6. Natural Deduction for Modal Logic with a Backtracking Operator.Jonathan Payne - 2015 - Journal of Philosophical Logic 44 (3):237-258.
    Harold Hodes in [1] introduces an extension of first-order modal logic featuring a backtracking operator, and provides a possible worlds semantics, according to which the operator is a kind of device for ‘world travel’; he does not provide a proof theory. In this paper, I provide a natural deduction system for modal logic featuring this operator, and argue that the system can be motivated in terms of a reading of the backtracking operator whereby it serves to indicate modal (...)
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  7.  40
    Teaching the PARC System of Natural Deduction.Daryl Close - 2015 - American Association of Philosophy Teachers Studies in Pedagogy 1:201-218.
    PARC is an "appended numeral" system of natural deduction that I learned as an undergraduate and have taught for many years. Despite its considerable pedagogical strengths, PARC appears to have never been published. The system features explicit "tracking" of premises and assumptions throughout a derivation, the collapsing of indirect proofs into conditional proofs, and a very simple set of quantificational rules without the long list of exceptions that bedevil students learning existential instantiation and universal generalization. The system can (...)
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  8.  74
    A Binary Quantifier for Definite Descriptions in Intuitionist Negative Free Logic: Natural Deduction and Normalisation.Nils Kürbis - 2019 - Bulletin of the Section of Logic 48 (2):81-97.
    This paper presents a way of formalising definite descriptions with a binary quantifier ι, where ιx[F, G] is read as ‘The F is G’. Introduction and elimination rules for ι in a system of intuitionist negative free logic are formulated. Procedures for removing maximal formulas of the form ιx[F, G] are given, and it is shown that deductions in the system can be brought into normal form.
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  9. Natural Deduction for Three-Valued Regular Logics.Yaroslav Petrukhin - 2017 - Logic and Logical Philosophy 26 (2):197–206.
    In this paper, I consider a family of three-valued regular logics: the well-known strong and weak S.C. Kleene’s logics and two intermedi- ate logics, where one was discovered by M. Fitting and the other one by E. Komendantskaya. All these systems were originally presented in the semantical way and based on the theory of recursion. However, the proof theory of them still is not fully developed. Thus, natural deduction sys- tems are built only for strong Kleene’s logic both (...)
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  10. Logics of Rejection: Two Systems of Natural Deduction.Allard Tamminga - 1994 - Logique Et Analyse 146:169-208.
    This paper presents two systems of natural deduction for the rejection of non-tautologies of classical propositional logic. The first system is sound and complete with respect to the body of all non-tautologies, the second system is sound and complete with respect to the body of all contradictions. The second system is a subsystem of the first. Starting with Jan Łukasiewicz's work, we describe the historical development of theories of rejection for classical propositional logic. Subsequently, we present the two (...)
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  11. Wordmorph!: A Word Game to Introduce Natural Deduction.Ian Stoner - 2018 - Teaching Philosophy 41 (2):199-204.
    Some logic students falter at the transition from the mechanical method of truth tables to the less-mechanical method of natural deduction. This short paper introduces a word game intended to ease that transition.
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  12. Systematic Construction of Natural Deduction Systems for Many-Valued Logics.Matthias Baaz, Christian G. Fermüller & Richard Zach - 1993 - In Proceedings of The Twenty-Third International Symposium on Multiple-Valued Logic, 1993. Los Alamitos, CA: IEEE Press. pp. 208-213.
    A construction principle for natural deduction systems for arbitrary, finitely-many-valued first order logics is exhibited. These systems are systematically obtained from sequent calculi, which in turn can be automatically extracted from the truth tables of the logics under consideration. Soundness and cut-free completeness of these sequent calculi translate into soundness, completeness, and normal-form theorems for natural deduction systems.
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  13. A Natural Deduction Relevance Logic.Fred Johnson - 1977 - The Bulletin of the Section of Logic 6 (4):164-168.
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  14.  84
    Application of Natural Deduction in Renaissance Geometry.Mirek Ryszard - 2014 - Argument: Biannual Philosophical Journal 4 (2):425-438.
    my goal here is to provide a detailed analysis of the methods of inference that are employed in De prospectiva pingendi. For this purpose, a method of natural deduction is proposed. the treatise by Piero della Francesca is a manifestation of a union between the ne arts and the mathematical sciences of arithmetic and geometry. He de nes painting as a part of perspective and, speaking precisely, as a branch of geometry, which is why we nd advanced geometrical (...)
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  15.  79
    Future Logic: Categorical and Conditional Deduction and Induction of the Natural, Temporal, Extensional, and Logical Modalities.Avi Sion - 1990,1996 - Geneva, Switzerland: CreateSpace & Kindle; Lulu..
    Future Logic is an original, and wide-ranging treatise of formal logic. It deals with deduction and induction, of categorical and conditional propositions, involving the natural, temporal, extensional, and logical modalities. Traditional and Modern logic have covered in detail only formal deduction from actual categoricals, or from logical conditionals (conjunctives, hypotheticals, and disjunctives). Deduction from modal categoricals has also been considered, though very vaguely and roughly; whereas deduction from natural, temporal and extensional forms of conditioning (...)
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  16. Natural Philosophy, Deduction, and Geometry in the Hobbes-Boyle Debate.Marcus P. Adams - 2017 - Hobbes Studies 30 (1):83-107.
    This paper examines Hobbes’s criticisms of Robert Boyle’s air-pump experiments in light of Hobbes’s account in _De Corpore_ and _De Homine_ of the relationship of natural philosophy to geometry. I argue that Hobbes’s criticisms rely upon his understanding of what counts as “true physics.” Instead of seeing Hobbes as defending natural philosophy as “a causal enterprise … [that] as such, secured total and irrevocable assent,” 1 I argue that, in his disagreement with Boyle, Hobbes relied upon his understanding (...)
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  17. A Note on Harmony.Nissim Francez & Roy Dyckhoff - 2012 - Journal of Philosophical Logic 41 (3):613-628.
    In the proof-theoretic semantics approach to meaning, harmony , requiring a balance between introduction-rules (I-rules) and elimination rules (E-rules) within a meaning conferring natural-deduction proof-system, is a central notion. In this paper, we consider two notions of harmony that were proposed in the literature: 1. GE-harmony , requiring a certain form of the E-rules, given the form of the I-rules. 2. Local intrinsic harmony : imposes the existence of certain transformations of derivations, known as reduction and expansion . (...)
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  18. Completeness of an Ancient Logic.John Corcoran - 1972 - Journal of Symbolic Logic 37 (4):696-702.
    In previous articles, it has been shown that the deductive system developed by Aristotle in his "second logic" is a natural deduction system and not an axiomatic system as previously had been thought. It was also stated that Aristotle's logic is self-sufficient in two senses: First, that it presupposed no other logical concepts, not even those of propositional logic; second, that it is (strongly) complete in the sense that every valid argument expressible in the language of the system (...)
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  19. SEPTEMBER 2015 UPDATE CORCORAN ARISTOTLE BIBLIOGRAPHY.John Corcoran - forthcoming - Aporia 5.
    This presentation includes a complete bibliography of John Corcoran’s publications relevant on Aristotle’s logic. The Sections I, II, III, and IV list respectively 23 articles, 44 abstracts, 3 books, and 11 reviews. Section I starts with two watershed articles published in 1972: the Philosophy & Phenomenological Research article—from Corcoran’s Philadelphia period that antedates his discovery of Aristotle’s natural deduction system—and the Journal of Symbolic Logic article—from his Buffalo period first reporting his original results. It ends with works published (...)
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  20. Ein Redehandlungskalkül. Ein pragmatisierter Kalkül des natürlichen Schließens nebst Metatheorie.Moritz Cordes & Friedrich Reinmuth - manuscript
    Building on the work of Peter Hinst and Geo Siegwart, we develop a pragmatised natural deduction calculus, i.e., a natural deduction calculus that incorporates illocutionary operators at the formal level, and prove its adequacy. In contrast to other linear calculi of natural deduction, derivations in this calculus are sequences of object-language sentences which do not require graphical or other means of commentary in order to keep track of assumptions or to indicate subproofs.
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  21.  38
    Proof Theory of Finite-Valued Logics.Richard Zach - 1993 - Dissertation, Technische Universität Wien
    The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of finite-valued (...)
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  22. Proofs Are Programs: 19th Century Logic and 21st Century Computing.Philip Wadler - manuscript
    As the 19th century drew to a close, logicians formalized an ideal notion of proof. They were driven by nothing other than an abiding interest in truth, and their proofs were as ethereal as the mind of God. Yet within decades these mathematical abstractions were realized by the hand of man, in the digital stored-program computer. How it came to be recognized that proofs and programs are the same thing is a story that spans a century, a chase with as (...)
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  23. Biological Essentialism and the Tidal Change of Natural Kinds.John S. Wilkins - 2013 - Science & Education 22 (2):221-240.
    The vision of natural kinds that is most common in the modern philosophy of biology, particularly with respect to the question whether species and other taxa are natural kinds, is based on a revision of the notion by Mill in A System of Logic. However, there was another conception that Whewell had previously captured well, which taxonomists have always employed, of kinds as being types that need not have necessary and sufficient characters and properties, or essences. These competing (...)
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  24.  93
    Identity Logics.John Corcoran & Stanley Ziewacz - 1979 - Notre Dame Journal of Formal Logic 20 (4):777-784.
    In this paper we prove the completeness of three logical systems I LI, IL2 and IL3. IL1 deals solely with identities {a = b), and its deductions are the direct deductions constructed with the three traditional rules: (T) from a = b and b = c infer a = c, (S) from a = b infer b = a and (A) infer a = a(from anything). IL2 deals solely with identities and inidentities {a ± b) and its deductions include both (...)
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  25. Aristotle's Theory of the Assertoric Syllogism.Stephen Read - manuscript
    Although the theory of the assertoric syllogism was Aristotle's great invention, one which dominated logical theory for the succeeding two millenia, accounts of the syllogism evolved and changed over that time. Indeed, in the twentieth century, doctrines were attributed to Aristotle which lost sight of what Aristotle intended. One of these mistaken doctrines was the very form of the syllogism: that a syllogism consists of three propositions containing three terms arranged in four figures. Yet another was that a syllogism is (...)
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  26. Aristotle's Prior Analytics and Boole's Laws of Thought.John Corcoran - 2003 - History and Philosophy of Logic. 24 (4):261-288.
    Prior Analytics by the Greek philosopher Aristotle (384 – 322 BCE) and Laws of Thought by the English mathematician George Boole (1815 – 1864) are the two most important surviving original logical works from before the advent of modern logic. This article has a single goal: to compare Aristotle’s system with the system that Boole constructed over twenty-two centuries later intending to extend and perfect what Aristotle had started. This comparison merits an article itself. Accordingly, this article does not discuss (...)
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  27. JUNE 2015 UPDATE: A BIBLIOGRAPHY: JOHN CORCORAN's PUBLICATIONS ON ARISTOTLE 1972–2015.John Corcoran - manuscript
    JUNE 2015 UPDATE: A BIBLIOGRAPHY: JOHN CORCORAN’S PUBLICATIONS ON ARISTOTLE 1972–2015 By John Corcoran -/- This presentation includes a complete bibliography of John Corcoran’s publications relevant to his research on Aristotle’s logic. Sections I, II, III, and IV list 21 articles, 44 abstracts, 3 books, and 11 reviews. It starts with two watershed articles published in 1972: the Philosophy & Phenomenological Research article from Corcoran’s Philadelphia period that antedates his Aristotle studies and the Journal of Symbolic Logic article from his (...)
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  28. Stable Harmony.Nils Kurbis - 2008 - In Peliš Michal (ed.), Logica Yearbook 2007.
    In this paper, I'll present a general way of "reading off" introduction/elimination rules from elimination/introduction rules, and define notions of harmony and stability on the basis of it.
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  29. Teaching Logic to Blind Students.Patrick Girard & Jonathan McKeown-Green - manuscript
    This paper is about teaching elementary logic to blind or visually impaired students. The targeted audience are teachers who all of sudden have a blind or visually impaired student in their introduction to logic class, find limited help from disability centers in their institution, and have no idea what to do. We provide simple techniques that allow direct communication between a teacher and a visually impaired student. We show how the use of what is known as Polish notation simplifies communication, (...)
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  30. A BIBLIOGRAPHY: JOHN CORCORAN's PUBLICATIONS ON ARISTOTLE 1972–2015.John Corcoran - manuscript
    This presentation includes a complete bibliography of John Corcoran’s publications devoted at least in part to Aristotle’s logic. Sections I–IV list 20 articles, 43 abstracts, 3 books, and 10 reviews. It starts with two watershed articles published in 1972: the Philosophy & Phenomenological Research article that antedates Corcoran’s Aristotle’s studies and the Journal of Symbolic Logic article first reporting his original results; it ends with works published in 2015. A few of the items are annotated with endnotes connecting them with (...)
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  31. Discourse Grammars and the Structure of Mathematical Reasoning II: The Nature of a Correct Theory of Proof and Its Value.John Corcoran - 1971 - Journal of Structural Learning 3 (2):1-16.
    1971. Discourse Grammars and the Structure of Mathematical Reasoning II: The Nature of a Correct Theory of Proof and Its Value, Journal of Structural Learning 3, #2, 1–16. REPRINTED 1976. Structural Learning II Issues and Approaches, ed. J. Scandura, Gordon & Breach Science Publishers, New York, MR56#15263. -/- This is the second of a series of three articles dealing with application of linguistics and logic to the study of mathematical reasoning, especially in the setting of a concern for improvement of (...)
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  32. Review of Striker Translation of Aristotle's PRIOR ANALYTICS. [REVIEW]John Corcoran - 2010 - Notre Dame Philosophical Reviews:1-13.
    This review places this translation and commentary on Book A of Prior Analytics in historical, logical, and philosophical perspective. In particular, it details the author’s positions on current controversies. The author of this translation and commentary is a prolific and respected scholar, a leading figure in a large and still rapidly growing area of scholarship: Prior Analytics studies PAS. PAS treats many aspects of Aristotle’s Prior Analytics: historical context, previous writings that influenced it, preservation and transmission of its manuscripts, editions (...)
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  33. Ancient Logic and its Modern Interpretations Proceedings of the Buffalo Symposium on Modernist Interpretations of Ancient Logic, 21 and 22 April, 1972. [REVIEW]John Corcoran (ed.) - 1974 - Reidel.
    Articles by Ian Mueller, Ronald Zirin, Norman Kretzmann, John Corcoran, John Mulhern, Mary Mulhern,Josiah Gould, and others. Topics: Aristotle's Syllogistic, Stoic Logic, Modern Research in Ancient Logic.
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  34. The Theory of a Natural Afterlife: A Newfound, Real Possibility for What Awaits Us at Death.Bryon K. Ehlmann - 2016 - Journal of Consciousness Exploration & Research 7 (11):931-950.
    For centuries humans have considered just two main possibilities for what awaits us at death: a “nothingness” like that of our before-life or some type of supernatural afterlife. The theory of a natural afterlife defines a vastly different, real possibility. The natural afterlife embodies all of the sensory perceptions, thoughts, and emotions present in the final moment of a near-death, dreamlike experience. With death this moment becomes timeless and everlasting to the dying person—essentially, a never-ending experience. The relativeness (...)
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  35. The Prolegomena and the Critiques of Pure Reason.Gary Hatfield - 2001 - In Volker Gerhardt, Rolf-Peter Horstmann & Ralph Schumacher (eds.), Kant Und Die Berliner Aufklärung: Akten des IX Internationalen Kant-Kongresses. Walter de Gruyter. pp. 185-208.
    This chapter considers Kant's relation to Hume as Kant himself understood it when he wrote the Critique of Pure Reason and the Prolegomena. It first seeks to refine the question of Kant's relation to Hume's skepticism, and it then considers the evidence for Kant's attitude toward Hume in three works: the A Critique, Prolegomena, and B Critique. It argues that in the A Critique Kant viewed skepticism positively, as a necessary reaction to dogmatism and a spur toward critique. In his (...)
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  36.  42
    The Logic of Causation: Definition, Induction and Deduction of Deterministic Causality.Avi Sion - 1999-2000, 2003- - Geneva, Switzerland: CreateSpace & Kindle; Lulu..
    The Logic of Causation: Definition, Induction and Deduction of Deterministic Causality is a treatise of formal logic and of aetiology. It is an original and wide-ranging investigation of the definition of causation (deterministic causality) in all its forms, and of the deduction and induction of such forms. The work was carried out in three phases over a dozen years (1998-2010), each phase introducing more sophisticated methods than the previous to solve outstanding problems. This study was intended as part (...)
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  37.  51
    Aristotelian Assertoric Syllogistic.Mohamed A. Amer - manuscript
    Abstract. Aristotelian assertoric syllogistic, which is currently of growing interest, has attracted the attention of the founders of modern logic, who approached it in several (semantical and syntactical) ways. Further approaches were introduced later on. These approaches (with few exceptions) are here discussed, developed and interrelated. Among other things, di-erent facets of soundness, completeness, decidability and independence are investigated. Speci/cally arithmetization (Leibniz), algebraization (Leibniz and Boole), and Venn models (Euler and Venn) are closely examined. All proofs are simple. In particular (...)
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  38.  68
    Strong Normalization via Natural Ordinal.Daniel Durante Pereira Alves - 1999 - Dissertation,
    The main objective of this PhD Thesis is to present a method of obtaining strong normalization via natural ordinal, which is applicable to natural deduction systems and typed lambda calculus. The method includes (a) the definition of a numerical assignment that associates each derivation (or lambda term) to a natural number and (b) the proof that this assignment decreases with reductions of maximal formulas (or redex). Besides, because the numerical assignment used coincide with the length of (...)
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  39.  90
    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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  40.  93
    Discourse Grammars and the Structure of Mathematical Reasoning III: Two Theories of Proof,.John Corcoran - 1971 - Journal of Structural Learning 3 (3):1-24.
    ABSTRACT This part of the series has a dual purpose. In the first place we will discuss two kinds of theories of proof. The first kind will be called a theory of linear proof. The second has been called a theory of suppositional proof. The term "natural deduction" has often and correctly been used to refer to the second kind of theory, but I shall not do so here because many of the theories so-called are not of the (...)
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  41.  83
    Disbelief Logic Complements Belief Logic.John Corcoran & Wagner Sanz - 2008 - Bulletin of Symbolic Logic 14 (3):436.
    JOHN CORCORAN AND WAGNER SANZ, Disbelief Logic Complements Belief Logic. Philosophy, University at Buffalo, Buffalo, NY 14260-4150 USA E-mail: corcoran@buffalo.edu Filosofia, Universidade Federal de Goiás, Goiás, GO 74001-970 Brazil E-mail: sanz@fchf.ufg.br -/- Consider two doxastic states belief and disbelief. Belief is taking a proposition to be true and disbelief taking it to be false. Judging also dichotomizes: accepting a proposition results in belief and rejecting in disbelief. Stating follows suit: asserting a proposition conveys belief and denying conveys disbelief. Traditional logic (...)
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  42.  30
    Sistema Experto en Deducción Natural.Gabriel Garduño-Soto, David René Thierry García, Rafael Vidal Uribe & Hugo Padilla Chacón - manuscript
    Proceeding on the Automatic Deduction System developped at the Philosophy Faculty of the UNAM at Mexico City. (Deduktor Mexican Group of Logics work under the direction of the professor Hugo Padilla Chacón). Conference presented at the mexican City of Guadalajara at the Universidad de Guadalajara, Jalisco, by invitation of the latinoamerican association of philosophy SOPHIA. Early stage of the deductional systems at 2-valued logic. This work embodies the implementation of the first whole and standalone arithmetization of bivalent Logic, the (...)
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  43. Putting Modal Metaphysics First.Antonella Mallozzi - 2018 - Synthese:1-20.
    I propose that we approach the epistemology of modality by putting modal metaphysics first and, specifically, by investigating the metaphysics of essence. Following a prominent Neo-Aristotelian view, I hold that metaphysical necessity depends on the nature of things, namely their essences. I further clarify that essences are core properties having distinctive superexplanatory powers. In the case of natural kinds, which is my focus in the paper, superexplanatoriness is due to the fact that the essence of a kind is what (...)
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  44. The Founding of Logic.John Corcoran - 1994 - Ancient Philosophy 14 (Special Issue):9-24.
    Since the time of Aristotle's students, interpreters have considered Prior Analytics to be a treatise about deductive reasoning, more generally, about methods of determining the validity and invalidity of premise-conclusion arguments. People studied Prior Analytics in order to learn more about deductive reasoning and to improve their own reasoning skills. These interpreters understood Aristotle to be focusing on two epistemic processes: first, the process of establishing knowledge that a conclusion follows necessarily from a set of premises (that is, on the (...)
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  45. Jakob Friedrich Fries (1773-1843): Eine Philosophie der Exakten Wissenschaften.Kay Herrmann - 1994 - Tabula Rasa. Jenenser Zeitschrift Für Kritisches Denken (6).
    Jakob Friedrich Fries (1773-1843): A Philosophy of the Exact Sciences -/- Shortened version of the article of the same name in: Tabula Rasa. Jenenser magazine for critical thinking. 6th of November 1994 edition -/- 1. Biography -/- Jakob Friedrich Fries was born on the 23rd of August, 1773 in Barby on the Elbe. Because Fries' father had little time, on account of his journeying, he gave up both his sons, of whom Jakob Friedrich was the elder, to the Herrnhut Teaching (...)
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  46. A Mathematical Model of Aristotle’s Syllogistic.John Corcoran - 1973 - Archiv für Geschichte der Philosophie 55 (2):191-219.
    In the present article we attempt to show that Aristotle's syllogistic is an underlying logiC which includes a natural deductive system and that it isn't an axiomatic theory as had previously been thought. We construct a mathematical model which reflects certain structural aspects of Aristotle's logic. We examine the relation of the model to the system of logic envisaged in scattered parts of Prior and Posterior Analytics. Our interpretation restores Aristotle's reputation as a logician of consummate imagination and skill. (...)
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  47. Logical Consequence in Modal Logic II: Some Semantic Systems for S4.George Weaver - 1974 - Notre Dame Journal of Formal Logic 15:370.
    ABSTRACT: This 1974 paper builds on our 1969 paper (Corcoran-Weaver [2]). Here we present three (modal, sentential) logics which may be thought of as partial systematizations of the semantic and deductive properties of a sentence operator which expresses certain kinds of necessity. The logical truths [sc. tautologies] of these three logics coincide with one another and with those of standard formalizations of Lewis's S5. These logics, when regarded as logistic systems (cf. Corcoran [1], p. 154), are seen to be equivalent; (...)
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  48. Proof-Theoretic Semantics for Subsentential Phrases.Nissim Francez, Roy Dyckhoff & Gilad Ben-Avi - 2010 - Studia Logica 94 (3):381-401.
    The paper briefly surveys the sentential proof-theoretic semantics for fragment of English. Then, appealing to a version of Frege’s context-principle (specified to fit type-logical grammar), a method is presented for deriving proof-theoretic meanings for sub-sentential phrases, down to lexical units (words). The sentential meaning is decomposed according to the function-argument structure as determined by the type-logical grammar. In doing so, the paper presents a novel proof-theoretic interpretation of simple type, replacing Montague’s model-theoretic type interpretation (in arbitrary Henkin models). The domains (...)
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  49.  84
    Forall X: Calgary. An Introduction to Formal Logic.P. D. Magnus, Tim Button, Aaron Thomas-Bolduc, Richard Zach & Robert Trueman - 2019
    forall x: Calgary is a full-featured textbook on formal logic. It covers key notions of logic such as consequence and validity of arguments, the syntax of truth-functional propositional logic TFL and truth-table semantics, the syntax of first-order (predicate) logic FOL with identity (first-order interpretations), translating (formalizing) English in TFL and FOL, and Fitch-style natural deduction proof systems for both TFL and FOL. It also deals with some advanced topics such as truth-functional completeness and modal logic. Exercises with solutions (...)
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  50. Proof-Theoretic Semantics, a Problem with Negation and Prospects for Modality.Nils Kürbis - 2015 - Journal of Philosophical Logic 44 (6):713-727.
    This paper discusses proof-theoretic semantics, the project of specifying the meanings of the logical constants in terms of rules of inference governing them. I concentrate on Michael Dummett’s and Dag Prawitz’ philosophical motivations and give precise characterisations of the crucial notions of harmony and stability, placed in the context of proving normalisation results in systems of natural deduction. I point out a problem for defining the meaning of negation in this framework and prospects for an account of the (...)
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