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Irving H. Anellis - One of the best experts on this subject based on the ideXlab platform.
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Peirce’s Role in the History of Logic: Lingua Universalis and Calculus Ratiocinator
Studies in Universal Logic, 2015Co-Authors: Irving H. AnellisAbstract:This chapter discusses central issues of Peirce’s conception of logic, comparing his work with the works of other logicians of the time, in particular Boole, Venn, Schroder, and Frege. It presents a detailed analysis of Peirce’s approach to notation, including pasigraphy and Peirce’s claw.
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peirce s role in the history of logic lingua universalis and Calculus Ratiocinator
2015Co-Authors: Irving H. AnellisAbstract:This chapter discusses central issues of Peirce’s conception of logic, comparing his work with the works of other logicians of the time, in particular Boole, Venn, Schroder, and Frege. It presents a detailed analysis of Peirce’s approach to notation, including pasigraphy and Peirce’s claw.
Volker Peckhaus - One of the best experts on this subject based on the ideXlab platform.
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Calculus Ratiocinator versus characteristica universalis the two traditions in logic revisited
History and Philosophy of Logic, 2004Co-Authors: Volker PeckhausAbstract:It is a commonplace that in the development of modern logic towards its actual shape at least two directions or traditions have to be distinguished. These traditions may be called, following the mo...
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Calculus Ratiocinator versus characteristica universalis? The two traditions in logic, revisited
History and Philosophy of Logic, 2004Co-Authors: Volker PeckhausAbstract:It is a commonplace that in the development of modern logic towards its actual shape at least two directions or traditions have to be distinguished. These traditions may be called, following the model of Ivor Grattan-Guinness (1988 ), the tradition of the algebra of logic and the tradition of mathematical logic. They are represented by the developments going back to the British algebraist George Boole with his The Mathematical Analysis of Logic (1847 ), and, independently, to the German mathematician Gottlob Frege with his Begriffsschrift (1879 ) Closely connected to this distinction is a comparative evaluation of the respective logical systems, culminating in the question who parented modern logic. Some interpreters, among them Boole’s biographer Desmond MacHale (1985, 71–72) or P. L. Heath (in Prior, ed., 1967, 542) have seen Boole as the father of modern logic. Others, like Robert Feys (1957 ) call his work the origin of modern logic. A few, like Bertrand Russell (1951, 74), even regarded him as the discoverer of pure mathematics (i. e., according to Russell’s logicism, mathematical logic). (Those who like Wolfgang Lenzen plead for exchanging Boole with Leibniz (1984, 203) will not concern us here.) Most influential, however, have been those who did not deny that the continuous debate about questions relevant for modern logic started with Boole in the middle of the 19th century, but who questioned the scientific value of the algebraic tradition for the actual shape of logic. Arthur Prior may be named
Potrč Matjaž - One of the best experts on this subject based on the ideXlab platform.
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LEIBNIZOVSKA TRADICIJA IN FREGEJEV POJMOVNI ZAPIS
ZRC SAZU Založba ZRC, 2016Co-Authors: Potrč MatjažAbstract:Afin de pouvoir donner une appréciation adéquate de la contribution de Frege à la constitution de la logique moderne (Begriffsschrift, 1879), l'auteur remonte dans son analyse jusqu'à la lingua characteristica de Leibniz. Les parallèles entre les deux approches sont en effet évidents: suppression de l'ambiguïté dans le langage et, sur cette base, construction d'une langue univoque, ainsi que possibilité d'étendre la faculté cognitive au moyen du calcul. C'est se dernier point qui différencie la tradition de Leibniz de celle de Descartes. Le sol commun des deux théories, c'est le même conflit entre le discours scientifique et le langage alors que leur différence réside dans la manière dont le passage à 1'écrit réalise l'idéal du Calculus Ratiocinator. Les différentes manières de combiner les éléments de ce conflit peuvent fournir une base pour l'appréciation de la dimension sociale spécifique de deux façons d'aborder la question.Da bi ocenil Fregejev prispevek k utemeljitvi moderne logike (Pojmovni zapis, 1879) se je avtor v svojem prispevku vrnil v preteklost, do Leibnizove lingua characteristica. Vzporednic ni težko najti: odprava dvoumja v govorici in zgradba enoznačnega jezika na tej osnovi, možnost razrešitve spoznavne moči s kalkulom, kar ločuje leibnizoviko tradicijo od kartezijanske. Srž obeh teorij je en in isti boj znanstvenega govora z govorico, razlika pa je v načinu, kako prehod k zapisu udejani ideal Calculus Ratiocinator. Različni načini, kako so elementi tega boja med seboj povezani, lahko nudijo tudi osnove za premero specifike družbene razsežnosti obeh pristopov
Inna Semetsky - One of the best experts on this subject based on the ideXlab platform.
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Silent Discourse: The Language of Signs and "Becoming-Woman"
SubStance, 2010Co-Authors: Inna SemetskyAbstract:Since time immemorial, humankind has searched for a universal language in the quest for the perfect means of communication that would transcend prevailing cultural, religious, and language barriers. The hero of a poetic tale, in his quest for the language once understood by everybody yet now forgotten, arrived at the understanding that it’s all written there. Medieval symbolism considered the World as a book of God written in a codex vivus, to be deciphered. Leibniz conceived of a lingua characteristica as a universal pictographic or ideographic alphabet of human thought, complemented by Calculus Ratiocinator and reflecting ratio embedded in Nature. The corollary is that, ultimately, the correspondence between primitive signs and the complex ideas for which they stand is natural, and not simply arbitrary or conventional. Yet the contemporary transference of Leibniz’s dream into AI research or analytic philosophy of language has not brought us closer to realizing his project, even when the urgency of understanding the other is paramount for our survival in a global climate permeated by diverse beliefs, disparate values and cultural conflicts
Venancio, Rafael Duarte Oliveira - One of the best experts on this subject based on the ideXlab platform.
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Peirce between Frege and Boole: on the search for possible dialogues with Wittgenstein
Universidade de São Paulo Faculdade de Filosofia Letras e Ciências Humanas, 2012Co-Authors: Venancio, Rafael Duarte OliveiraAbstract:O presente artigo busca debater a posição de Charles Sanders Peirce e dos primeiros estudantespeirceanos de Lógica (Christine Ladd e O. H. Mitchell nos Studies in Logic, 1883) dentro do debate inspiradorda visão da linguagem dentro da Filosofia Analítica, conhecido como “Lingua Universalis contra CalculusRatiocinator”, cujos primórdios podem ser traçados desde a filosofia de Gottfried Leibniz. Para isso, comparamosesse campo do pensamento peirceano com o debate crucial entre a conceitografia de Gottlob Frege (Begriffsschrift,1879) e a lógica algébrica de George Boole (An investigation of the Laws of Thought on which are founded themathematical theories of Logic and Probabilities, 1854). O nosso objetivo principal é observar que esse momento dafilosofia peirceana pode ser comparado com o pensamento wittgensteiniano, especialmente em sua nova vertente,chamada New Wittgenstein, que tenta superar a tradicional divisão entre Tractatus Logico-Philosophicus eInvestigações Filosóficas. Pela comparação entre pensadores influenciados por C. S. Peirce e a filosofia de LudwigWittgenstein, pretendemos abrir caminhos na compreensão do conceito de jogo de linguagem, especialmente emsua gramática e em seus operadores simbólicos, através da observação das funções de verdade [truth functions]e as tabelas de verdade [truth tables] enquanto lógica algébrica.This article seeks to discuss the position of Charles Sanders Peirce and his first students of Logic (Christine Ladd and O. H. Mitchell in “Studies in Logic”, 1883) in the debate which inspired the vision of language in Analytic Philosophy known as “Lingua Universalis vs. Calculus Ratiocinator”, whose origins can be traced back to the philosophy of Gottfried Leibniz. To do so, we will compare this field of the Peircean thought with the crucial debate between Gottlob Frege’s concept-script (Begriffsschrift, 1879) and George Boole’s algebraic logic (An investigation of the Laws of Thought on which are founded the mathematical theories of Logic and Probabilities, 1854). Our main goal is to see that this moment of Peircean philosophy can be compared with the Wittgensteinian thought, especially in its new interpretation, called “New Wittgenstein”, which tries to overcome the traditional division between “Tractatus Logico-Philosophicus” and “Philosophical Investigations”. Through this comparison between thinkers influenced by C. S. Peirce and the philosophy of Ludwig Wittgenstein, we will be able to open our search for ways to understand the concept of language-game, especially in its grammar and its symbolic operators, through the observation of the truth functions and truth tables as algebraic logic
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Peirce entre Frege e Boole: sobre a busca de diálogos possíveis com Wittgenstein
2012Co-Authors: Venancio, Rafael Duarte OliveiraAbstract:O presente artigo busca debater a posição de Charles Sanders Peirce e dos primeiros estudantes peirceanos de Lógica (Christine Ladd e O. H. Mitchell nos Studies in Logic, 1883) dentro do debate inspirador da visão da linguagem dentro da Filosofia Analítica, conhecido como “Lingua Universalis contra Calculus Ratiocinator”, cujos primórdios podem ser traçados desde a filosofia de Gottfried Leibniz. Para isso, comparamos esse campo do pensamento peirceano com o debate crucial entre a conceitografia de Gottlob Frege (Begriffsschrift, 1879) e a lógica algébrica de George Boole (An investigation of the Laws of Thought on which are founded the mathematical theories of Logic and Probabilities, 1854). O nosso objetivo principal é observar que esse momento da filosofia peirceana pode ser comparado com o pensamento wittgensteiniano, especialmente em sua nova vertente, chamada New Wittgenstein, que tenta superar a tradicional divisão entre Tractatus Logico-Philosophicus e Investigações Filosóficas. Pela comparação entre pensadores influenciados por C. S. Peirce e a filosofia de Ludwig Wittgenstein, pretendemos abrir caminhos na compreensão do conceito de jogo de linguagem, especialmente em sua gramática e em seus operadores simbólicos, através da observação das funções de verdade [truth functions] e as tabelas de verdade [truth tables] enquanto lógica algébrica
