The Mathematical Analysis of Logic. George Boole

1949 ◽  
Vol 16 (1) ◽  
pp. 88-88
Author(s):  
C. West Churchman
Keyword(s):  
Mathematical Analysis ◽  
George Boole

Reviews - A. E. Heath. Preface. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 7–8. - R. Rhees. Note in editing. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 9–43. - George Boole. The mathematical analysis of logic, being an essay towards a calculus of deductive reasoning. A reprint of 191. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 45–119. - George Boole. Later notes (to the foregoing). Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 119–124. (Taken from manuscript in the Library of the Royal Society.) - George Boole. The calculus of logic. A reprint of 192. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 125–140. - George Boole. Sketch of a theory and method of probabilities founded upon the calculus of logic. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 141–166. (From manuscripts in the Royal Society Library, probably before 1851.) - George Boole. Of propositions numerically definite. A reprint of 194. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 167–186. - George Boole. The claims of science, especially as founded in its relation to human nature. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 187–210. (Lecture published in London, 1851.) - George Boole. Logic and reasoning. Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 211–229. (From Royal Society manuscripts, after 1855.) - George Boole. Extracts from a paper entitled “On the mathematical theory of logic and on the philosophical interpretation of its methods and processes.”Studies in logic and probability, by George Boole, Watts & Co., London1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, pp. 230–246. (From Royal Society manuscripts, later than 1855.)

1959 ◽  
Vol 24 (3) ◽  
pp. 203-209 ◽  
Author(s):  
Michael Dummett
Keyword(s):  
Mathematical Analysis ◽  
Royal Society ◽  
Mathematical Theory ◽  
Deductive Reasoning ◽  
Publishing Company ◽  
Philosophical Interpretation ◽  
Open Court ◽  
Court Publishing ◽  
George Boole ◽  
Nature Studies

scholarly journals A new presentation of categorical syllogisms

2018 ◽  
Author(s):  
Dan Constantin Radulescu
Keyword(s):  
Mathematical Analysis ◽  
Venn Diagram ◽  
Inference Rules ◽  
George Boole ◽  
Clear Presentation

One proposes two simple schemes - a graphical and a tree like one - for finding logical conclusions (LCs) from any pair of categorical premises (PCP), via using a set model for the syllogistic terms S,P,M, non-S (S'), non-P (P'), non-M (M'). In this model, any universal, (resp. particular), premise empties, (resp. lays set elements into), two subsets out of the 8-subset partition of the universal set U which models the categorical statements: U=MSP+MS'P+MSP' +MS'P'+M'SP+M'S'P+M'SP' +M'S'P', (where the union of disjoints sets is denoted by a plus sign, S',P',M' are the complementary sets in U of the S,P,M terms respectively, and MSP:= M∩S∩P, etc.). A cylindrical Venn diagram replaces the 8 “irregularly shaped” subsets from the usual 3-circle Venn diagram of U by rectangular shapes drawn on a cylinder and provides a very clear presentation of the two LCs finding schemes. One shows, (without using syllogistic moods and figures, syllogistic axioms and inference rules, nor valid syllogism rules and syllogism reduction), that any LC refers to just one of the 8 subsets of U and that any PCP entailing an LC, (called valid syllogistic argument (VCA), may be recast as, e.g., one of the Barbara, Darapti or Darii valid syllogisms (VSs). The recasting is done via set relabelings instead of the syllogism reduction (used, e.g., by Aristotle and J. Lukasiewicz). One may say that this paper approaches categorical syllogisms in the same spirit as George Boole approached them in The Mathematical Analysis of Logic – but instead of Boole's equations one uses graphic and tree like methods for finding the LCs.

scholarly journals Film and the Digital

2001 ◽  
Author(s):  
Rod Stoneman
Keyword(s):  
Decision Making ◽  
Mathematical Logic ◽  
19Th Century ◽  
Mathematical Analysis ◽  
Short History ◽  
Digital History ◽  
Digital World ◽  
George Boole

RECYCLED ELECTRONS: FILM AND THE DIGITAL I - Algebra in CorkTo begin with a digression from digital history, which is a short history - the prehistory to the development of the digital world that we now inhabit is rarely in focus. It was a 19th century Irish mathematician, George Boole, who created a novel mathematical logic, describing a new algebra which sketched the structure of choice and created a paradigm for human, and now electronic, decision making. He wrote The Mathematical Analysis of Logic in 1847 and The Investigation of the Laws of Thought in 1854. He lived, thought and is buried in Cork. His work showed chains of information and choice categorised into the two logic states of true or false: "Shall I go out and not stay in? Is it raining or has it stopped? If I go out and it's raining should I wear this...

The Algebraic Tradition of Logic

2017 ◽  
Author(s):  
Jan von Plato
Keyword(s):  
Mathematical Analysis ◽  
Propositional Logic ◽  
Deductive Reasoning ◽  
Algebraic Logic ◽  
Logical Reasoning ◽  
Syllogistic Reasoning ◽  
Algebraic Equations ◽  
Classical Propositional Logic ◽  
George Boole

This chapter explores how algebraic logic began in 1847 when George Boole presented his “calculus of deductive reasoning” in a short book titled The Mathematical Analysis of Logic. His calculus reduced known ways of logical reasoning into the solution of algebraic equations. The known ways of logical reasoning were not just accounted for but were extended to full classical propositional logic. Boole reduced Aristotelian syllogistic reasoning to calculation, which was a wonderful achievement. Encouraged by the success, he wrote a book with the bold title An Investigation of the Laws of Thought (1854). However, his logic was not able to treat relations but just one-place predicates.

Density waves in disk galaxies

1967 ◽  
Vol 31 ◽  
pp. 313-317 ◽  
Author(s):  
C. C. Lin ◽  
F. H. Shu
Keyword(s):  
Mathematical Analysis ◽  
Spiral Structure ◽  
Stellar System ◽  
Collective Modes ◽  
Disk Galaxies ◽  
Spiral Pattern ◽  
Density Waves ◽  
The Galaxy ◽  
Detailed Mathematical Analysis

Density waves in the nature of those proposed by B. Lindblad are described by detailed mathematical analysis of collective modes in a disk-like stellar system. The treatment is centered around a hypothesis of quasi-stationary spiral structure. We examine (a) the mechanism for the maintenance of this spiral pattern, and (b) its consequences on the observable features of the galaxy.

Computing cell tractions from particle displacements on silicone rubber substrata

1994 ◽  
Vol 52 ◽  
pp. 162-163
Author(s):  
Tim Oliver ◽  
Akira Ishihara ◽  
Ken Jacobsen ◽  
Micah Dembo
Keyword(s):  
Plane Stress ◽  
Linear Elasticity ◽  
Silicone Rubber ◽  
Mathematical Analysis ◽  
Elastic Recovery ◽  
Video Images ◽  
Cell Traction Forces ◽  
Latex Beads ◽  
Cell Traction ◽  
Better Than

In order to better understand the distribution of cell traction forces generated by rapidly locomoting cells, we have applied a mathematical analysis to our modified silicone rubber traction assay, based on the plane stress Green’s function of linear elasticity. To achieve this, we made crosslinked silicone rubber films into which we incorporated many more latex beads than previously possible (Figs. 1 and 6), using a modified airbrush. These films could be deformed by fish keratocytes, were virtually drift-free, and showed better than a 90% elastic recovery to micromanipulation (data not shown). Video images of cells locomoting on these films were recorded. From a pair of images representing the undisturbed and stressed states of the film, we recorded the cell’s outline and the associated displacements of bead centroids using Image-1 (Fig. 1). Next, using our own software, a mesh of quadrilaterals was plotted (Fig. 2) to represent the cell outline and to superimpose on the outline a traction density distribution. The net displacement of each bead in the film was calculated from centroid data and displayed with the mesh outline (Fig. 3).

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