scholarly journals The Development of Symbolic Logic: A Critical-Historical Study of the Logical Calculus.

1907 ◽  
Vol 4 (18) ◽  
pp. 494
Author(s):  
Walter T. Marvin ◽  
A. T. Shearman
Keyword(s):  
Historical Study ◽  
Symbolic Logic ◽  
Logical Calculus

An emendation of the axiom system of Hilbert and Ackermann for the restricted calculus of predicates

1962 ◽  
Vol 27 (2) ◽  
pp. 131-138 ◽  
Author(s):  
David Pager
Keyword(s):  
Axiom System ◽  
The Other ◽  
Symbolic Logic ◽  
Standard Formulation ◽  
Logical Calculus ◽  
Finite Set ◽  
Original Approach

The fundamental role of the restricted calculus of predicates in applications of symbolic logic, and particularly in Hubert's Beweistheorie as summed up by Hilbert and Bernays, makes it important that this logical calculus should be accurately defined. The first standard formulation of the calculus was that of Hilbert and Ackermann's Grundzüge der theoretischen Logik. This employed (in the first three editions) a finite set of axioms and rules of derivation, with rules of substitution included. A reaction by Hilbert and Ackermann's successors to persistent difficulty encountered with the rules of substitution has been to omit these rules, and instead enlarge the set of axioms and the other rules of derivation so as to encompass all possible substitutions. Such an enlargement seems to me to be undesirable. As an alternative, this note is designed to put the original approach of Hilbert and Ackermann for once and for all on a sound basis.

Leibniz's interpretation of his logical calculi

1954 ◽  
Vol 19 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Nicholas Rescher
Keyword(s):  
Formal Logic ◽  
Point Of View ◽  
Symbolic Logic ◽  
Logical Calculus ◽  
Formal Systems ◽  
Logical Calculi

The historical researches of Louis Couturat saved the logical work of Leibniz from the oblivion of neglect and forgetfulness. They revealed that Leibniz developed in succession several versions of a “logical calculus” (calculus ratiocinator or calculus universalis). In consequence of Couturat's investigations it has become well known that Leibniz's development of these logical calculi adumbrated the notion of a logistic system; and for these foreshadowings of the logistic treatment of formal logic Leibniz is rightly regarded as the father of symbolic logic.It is clear from what has been said that it is scarcely possible to overestimate the debt which the contemporary student of Leibniz's logic owes to Couturat. This gratitude must, however, be accompanied by the realization that Couturat's own theory of logic is gravely defective. Couturat was persuaded that the extensional point of view in logic is the only one which is correct, an opinion now quite antiquated, and shared by no one. This prejudice of Couturat's marred his exposition of Leibniz's logic. It led him to battle with windmills: he viewed the logic of Leibniz as rife with shortcomings stemming from an intensional approach.The task of this paper is a re-examination of Leibniz's logic. It will consider without prejudgment how Leibniz conceived of the major formal systems he developed as logical calculi – that is, these systems will be studied with a view to the interpretation or interpretations which Leibniz himself intends for them. The aim is to undo some of the damage which Couturat's preconception has done to the just understanding of Leibniz's logic and to the proper evaluation of his contribution.

Liberty, Property and Popular Politics

2016 ◽  
Keyword(s):  
Eighteenth Century ◽  
Intellectual History ◽  
French Revolution ◽  
British History ◽  
Historical Study ◽  
Thomas Paine ◽  
Parliamentary History ◽  
Long Eighteenth Century ◽  
Scottish History ◽  
The University

Few scholars can claim to have shaped the historical study of the long eighteenth century more profoundly than Professor H. T. Dickinson, who, until his retirement in 2006, held the Sir Richard Lodge Chair of British History at the University of Edinburgh. This volume, based on contributions from Dickinson's students, friends and colleagues from around the world, offers a range of perspectives on eighteenth-century Britain and provides a tribute to a remarkable scholarly career. Dickinson's work and career provides the ideal lens through which to take a detailed snapshot of current research in a number of areas. The book includes contributions from scholars working in intellectual history, political and parliamentary history, ecclesiastical and naval history; discussions of major themes such as Jacobitism, the French Revolution, popular radicalism and conservatism; and essays on prominent individuals in English and Scottish history, including Edmund Burke, Thomas Muir, Thomas Paine and Thomas Spence. The result is a uniquely rich and detailed collection with an impressive breadth of coverage.

Migration and Modernities

2019 ◽  
Keyword(s):  
Native Americans ◽  
Literary History ◽  
Historical Study ◽  
Racial Categories ◽  
Geographic Boundaries ◽  
The Us ◽  
Technological Developments ◽  
History Of ◽  
The Aesthetic ◽  
Eighteenth And Nineteenth Centuries

Migration and Modernities recovers a comparative literary history of migration by bringing together scholars from the US and Europe to explore the connections between migrant experiences and the uneven emergence of modernity. The collection initiates transnational, transcultural and interdisciplinary conversations about migration in the eighteenth and nineteenth centuries, demonstrating how mobility unsettles the geographic boundaries, temporal periodization, and racial categories we often use to organize literary and historical study. Migrants are by definition liminal, and many have existed historically in the spaces between nations, regions or ethnicities. In exploring these spaces, Migration and Modernities also investigates the origins of current debates about belonging, rights, and citizenship. Its chapters traverse the globe, revealing the experiences — real or imagined — of eighteenth- and nineteenth-century migrants, from dispossessed Native Americans to soldiers in South America, Turkish refugees to Scottish settlers. They explore the aesthetic and rhetorical frameworks used to represent migrant experiences during a time when imperial expansion and technological developments made the fortunes of some migrants and made exiles out of others. These frameworks continue to influence the narratives we tell ourselves about migration today and were crucial in producing a distinctively modern subjectivity in which mobility and rootlessness have become normative.

Language and Meaning in the Age of Modernism

2018 ◽  
Author(s):  
James McElvenny
Keyword(s):  
Philosophy Of Language ◽  
Vienna Circle ◽  
Bertrand Russell ◽  
Historical Study ◽  
Personal Connection ◽  
International Language ◽  
Academic Philosophy ◽  
Significant Figures ◽  
Basic English ◽  
And Linguistics

This book is a historical study of influential currents in the philosophy of language and linguistics of the first half of the twentieth century, explored from the perspective of the English scholar C. K. Ogden (1889–1957). Although no ‘Great Man’ in his own right, Ogden had a personal connection, reflected in his work, to several of the most significant figures of the age. The background to the ideas espoused in Ogden’s book The Meaning of Meaning, co-authored with I.A. Richards (1893–1979), is examined in detail, along with the application of these ideas in his international language project Basic English. A richly interlaced network of connections is revealed between early analytic philosophy, semiotics and linguistics, all inevitably shaped by the contemporary cultural and political environment. In particular, significant interaction is shown between Ogden’s ideas, the varying versions of ‘logical atomism’ of Bertrand Russell (1872–1970) and Ludwig Wittgensten (1889–1951), Victoria Lady Welby’s (1837–1912) ‘significs’, and the philosophy and political activism of Otto Neurath (1882–1945) and Rudolf Carnap (1891–1970) of the Vienna Circle. Amid these interactions emerges a previously little known mutual exchange between the academic philosophy and linguistics of the period and the practically oriented efforts of the international language movement.

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