Switch to: References

Add citations

You must login to add citations.
  1. Eigenlogic in the Spirit of George Boole.Zeno Toffano - 2020 - Logica Universalis 14 (2):175-207.
    This work presents an operational and geometric approach to logic. It starts from the multilinear elective decomposition of binary logical functions in the original form introduced by George Boole. A justification on historical grounds is presented bridging Boole’s theory and the use of his arithmetical logical functions with the axioms of Boolean algebra using sets and quantum logic. It is shown that this algebraic polynomial formulation can be naturally extended to operators in finite vector spaces. Logical operators will appear as (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Aristotle's Demonstrative Logic.John Corcoran - 2009 - History and Philosophy of Logic 30 (1):1-20.
    Demonstrative logic, the study of demonstration as opposed to persuasion, is the subject of Aristotle's two-volume Analytics. Many examples are geometrical. Demonstration produces knowledge (of the truth of propositions). Persuasion merely produces opinion. Aristotle presented a general truth-and-consequence conception of demonstration meant to apply to all demonstrations. According to him, a demonstration, which normally proves a conclusion not previously known to be true, is an extended argumentation beginning with premises known to be truths and containing a chain of reasoning showing (...)
    Download  
     
    Export citation  
     
    Bookmark   11 citations  
  • LOGIC TEACHING IN THE 21ST CENTURY.John Corcoran - 2016 - Quadripartita Ratio: Revista de Argumentación y Retórica 1 (1):1-34.
    We are much better equipped to let the facts reveal themselves to us instead of blinding ourselves to them or stubbornly trying to force them into preconceived molds. We no longer embarrass ourselves in front of our students, for example, by insisting that “Some Xs are Y” means the same as “Some X is Y”, and lamely adding “for purposes of logic” whenever there is pushback. Logic teaching in this century can exploit the new spirit of objectivity, humility, clarity, observationalism, (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • The Absence of Multiple Universes of Discourse in the 1936 Tarski Consequence-Definition Paper.John Corcoran & José Miguel Sagüillo - 2011 - History and Philosophy of Logic 32 (4):359 - 374.
    This paper discusses the history of the confusion and controversies over whether the definition of consequence presented in the 11-page 1936 Tarski consequence-definition paper is based on a monistic fixed-universe framework?like Begriffsschrift and Principia Mathematica. Monistic fixed-universe frameworks, common in pre-WWII logic, keep the range of the individual variables fixed as the class of all individuals. The contrary alternative is that the definition is predicated on a pluralistic multiple-universe framework?like the 1931 Gödel incompleteness paper. A pluralistic multiple-universe framework recognizes multiple (...)
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  • Lewis Carroll's Visual Logic.Francine F. Abeles - 2007 - History and Philosophy of Logic 28 (1):1-17.
    John Venn and Charles L. Dodgson (Lewis Carroll) created systems of logic diagrams capable of representing classes (sets) and their relations in the form of propositions. Each is a proof method for syllogisms, and Carroll's is a sound and complete system. For a large number of sets, Carroll diagrams are easier to draw because of their self-similarity and algorithmic construction. This regularity makes it easier to locate and thereby to erase cells corresponding with classes destroyed by the premises of an (...)
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  • I Can't Get No Satisfaction: A Reply to Barrett Et Al.Robert King - 2016 - Frontiers in Psychology 7.
    Download  
     
    Export citation  
     
    Bookmark  
  • Methodological Practice and Complementary Concepts of Logical Consequence: Tarski's Model-Theoretic Consequence and Corcoran's Information-Theoretic Consequence.José M. Sagüillo - 2009 - History and Philosophy of Logic 30 (1):21-48.
    This article discusses two coextensive concepts of logical consequence that are implicit in the two fundamental logical practices of establishing validity and invalidity for premise-conclusion arguments. The premises and conclusion of an argument have information content (they ?say? something), and they have subject matter (they are ?about? something). The asymmetry between establishing validity and establishing invalidity has long been noted: validity is established through an information-processing procedure exhibiting a step-by-step deduction of the conclusion from the premise-set. Invalidity is established by (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Bi-Facial Truth: A Case for Generalized Truth Values.Dmitry Zaitsev & Yaroslav Shramko - 2013 - Studia Logica 101 (6):1299-1318.
    We explore a possibility of generalization of classical truth values by distinguishing between their ontological and epistemic aspects and combining these aspects within a joint semantical framework. The outcome is four generalized classical truth values implemented by Cartesian product of two sets of classical truth values, where each generalized value comprises both ontological and epistemic components. This allows one to define two unary twin connectives that can be called “semi-classical negations”. Each of these negations deals only with one of the (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • Validity, the Squeezing Argument and Alternative Semantic Systems: The Case of Aristotelian Syllogistic. [REVIEW]Catarina Dutilh Novaes & Edgar Andrade-Lotero - 2012 - Journal of Philosophical Logic 41 (2):387 - 418.
    We investigate the philosophical significance of the existence of different semantic systems with respect to which a given deductive system is sound and complete. Our case study will be Corcoran's deductive system D for Aristotelian syllogistic and some of the different semantic systems for syllogistic that have been proposed in the literature. We shall prove that they are not equivalent, in spite of D being sound and complete with respect to each of them. Beyond the specific case of syllogistic, the (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • Review: Frank Markham Brown’s Boolean Reasoning: The Logic Of Boolean Equations. [REVIEW]Kari Saukkonen - 2005 - Australasian Journal of Logic 3:67-75.
    Brown, Frank Markham: Boolean Reasoning: The Logic of Boolean Equations. Second edition, New York: Dover, 2003; i–xii, 291 pp. USD$16.95. ISBN: 0486427854.
    Download  
     
    Export citation  
     
    Bookmark  
  • What's in Your File Folder?Roger E. Bissell - 2014 - Journal of Ayn Rand Studies 14 (2):171.
    Download  
     
    Export citation  
     
    Bookmark  
  • History and Philosophy of Logic.Risto Vilkko - 2005 - Bulletin of Symbolic Logic 11 (1):89-91.
    Download  
     
    Export citation  
     
    Bookmark  
  • Giving Wings to Logic: Mary Everest Boole's Propagation and Fulfilment of a Legacy.K. G. Valente - 2010 - British Journal for the History of Science 43 (1):49-74.
    In his influential Laws of Thought , the mathematician George Boole presented a formulation of logic using algebraic expressions and manipulations. His widow, Mary Everest Boole, undertook an ambitious project of disseminating his ideas by introducing lay audiences to the law of pulsation, a prescription for correct reasoning that incorporates two of his fundamental insights. Contemporary scholarship presents a fragmented picture of Mary Boole, regarding her largely as a source of information on the religio-psychological impetus for her husband's contributions to (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Aristotle’s Prototype Rule-Based Underlying Logic.John Corcoran - 2018 - Logica Universalis 12 (1-2):9-35.
    This expository paper on Aristotle’s prototype underlying logic is intended for a broad audience that includes non-specialists. It requires as background a discussion of Aristotle’s demonstrative logic. Demonstrative logic or apodictics is the study of demonstration as opposed to persuasion. It is the subject of Aristotle’s two-volume Analytics, as its first sentence says. Many of Aristotle’s examples are geometrical. A typical geometrical demonstration requires a theorem that is to be demonstrated, known premises from which the theorem is to be deduced, (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation