Benítez, Juan Manuel Campos (Author)
History and Philosophy of Logic
Volume: 35, no. 4
Issue: 4
Pages: 354-368
Publication date: 2014
Language: English
Edition Details: Part of a Series: “The Square of Opposition”
The traditional Square of Opposition consists of four sentence types. Two are universal and two particular; two are affirmative and two negative. Examples, where `S' and `P' designate the subject and the predicate, are: `every S is P', `no S is P', `some S is P' and `some S is not P'. Taking the usual sentences of the square of opposition, quantifying over their predicates exhibits non-standard sentence forms. These sentences may be combined into non-standard Squares of Opposition (an Octagon in this case), and they reveal a new relationship not found in the usual Square. Medieval logicians termed `disparatae' pairs of sentences like `every S is some P' and `some S is every P', which are neither subaltern nor contrary, neither contradictory nor subcontrary. Walter Redmond has designed a special language L to express the logical form of these sentences in a precise way. I will use this language to show how Squares of Opposition, standard and non-standard, form a complex network of relations which bring to light the subtleties contained in this traditional doctrine.
...MoreArticle Beziau, Jean-Yves; Read, Stephen (2014) Square of Opposition: A Diagram and a Theory in Historical Perspective. History and Philosophy of Logic (pp. 315-316).
Similar Citations
Article
Moretti, Alessio;
(2014)
Was Lewis Carroll an Amazing Oppositional Geometer?
Article
Chatt, Saloua;
(2014)
Avicenna on Possibility and Necessity
Chapter
Verboon, Annemieke R.;
(2008)
Einen alten Baum verpflanzt man nicht. Die Metapher des Porphyrianischen Baums im Mittelalter
Book
Turing, Alan Mathison;
Appel, Andrew W.;
Feferman, Solomon;
(2012)
Alan Turing's Systems of Logic: The Princeton Thesis
Article
Claudia Cristalli;
Ahti-Veikko Pietarinen;
(2021)
Abstraction and Generalization in the Logic of Science: Cases from Nineteenth-Century Scientific Practice
Chapter
Hon, Giora;
(2009)
Living Extremely Flat: The Life of an Automaton; John von Neumann's Conception of Error of (in)Animate Systems
Book
Magnani, Lorenzo;
Nersessian, Nancy J.;
(2002)
Model Based Reasoning: Science, Technology, Values
Article
Mutanen, Arto;
(2015)
Hintikka's Interrogative Model and a Logic of Discovery and Justification
Chapter
Morgan, Mary S.;
(2007)
The Curious Case of the Prisoner's Dilemma: Model Situation? Exemplary Narrative?
Article
Dupré, Sven;
(2012)
Kepler's Optics without Hypotheses
Article
Basak, Subhash C.;
(2013)
Philosophy of Mathematical Chemistry: A Personal Perspective
Article
Shell-Gellasch, Amy;
(2003)
The Olivier String Models at West Point
Article
Cerroni, Cinzia;
(2004)
Non-Desarguian Geometries and the Foundations of Geometry from David Hilbert to Ruth Moufang
Article
Glas, Eduard;
(2000)
Model-based reasoning and mathematical discovery: The Case of Felix Klein
Article
June Barrow-Green;
(2021)
“Knowledge gained by experience”: Olaus Henrici—engineer, geometer and maker of mathematical models
Article
Yavetz, Ido;
(2001)
A New Role for the Hippopede of Eudoxus
Article
Pantalony, David;
(2001)
H. S. M. Coxeter's Unusual Collection of Geometric Models
Chapter
Rich, Mike;
(2006)
Representing Euclid in the Eighteenth Century
Article
Christián C. Carman;
(2023)
A Ptolemaic lunar model of the 17th century: François Viète and his first lunar model
Article
Johns, Chris;
(2014)
Leibniz and the Square: A Deontic Logic for the Vir Bonus
Be the first to comment!