Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Frege, Peano and the Interplay between Logic and Mathematics
View through CrossRef
In contemporary historical studies, Peano is usually included in the logical tradition pioneered by Frege. In this paper, I shall first demonstrate that Frege and Peano independently developed a similar way of using logic for the rigorous expression and proof of mathematical laws. However, I shall then suggest that Peano also used his mathematical logic in such a way that anticipated a formalisation of mathematical theories which was incompatible with Frege’s conception of logic.
Title: Frege, Peano and the Interplay between Logic and Mathematics
Description:
In contemporary historical studies, Peano is usually included in the logical tradition pioneered by Frege.
In this paper, I shall first demonstrate that Frege and Peano independently developed a similar way of using logic for the rigorous expression and proof of mathematical laws.
However, I shall then suggest that Peano also used his mathematical logic in such a way that anticipated a formalisation of mathematical theories which was incompatible with Frege’s conception of logic.
Related Results
Reflections Of Zoltan P. Dienes On Mathematics Education
Reflections Of Zoltan P. Dienes On Mathematics Education
The name of Zoltan P. Dienes (1916- ) stands with those ofJean Piaget, Jerome Bruner, Edward Begle, and Robert Davis as legendary figures whose work left a lasting impression on th...
What is Analytic Philosophy
What is Analytic Philosophy
Special Issue: What is Analytic PhilosophyReferencesHaaparantaG. P. Baker and P. M. S. Hacker. Frege: Logical Excavations. Oxford, Blackwell, 1984.M. Dummett. The Interpretation of...
Frege, Gottlob (1848–1925)
Frege, Gottlob (1848–1925)
A German philosopher-mathematician, Gottlob Frege was primarily interested in understanding both the nature of mathematical truths and the means whereby they are ultimately to be j...
COUNTABLE SPACES WITH PEANO PROPERTY
COUNTABLE SPACES WITH PEANO PROPERTY
In 1890, Giuseppe Peano published an example of a continuous curve passing through every point of the square $[0,1]^2$. A curve with such properties is called a Peano curve. In fa...
An Exploratory Study of Mathematics Anxiety in Caribbean Preservice Teachers
An Exploratory Study of Mathematics Anxiety in Caribbean Preservice Teachers
The Problem Correlational studies suggest that gender, attitudes to mathematics, mathematics performance, the number of college mathematics courses taken, and mathematics teacher ...
Logic in the early 20th century
Logic in the early 20th century
The creation of modern logic is one of the most stunning achievements of mathematics and philosophy in the twentieth century. Modern logic – sometimes called logistic, symbolic log...
Frege’s platonism and mathematical creation: some new perspectives
Frege’s platonism and mathematical creation: some new perspectives
Abstract
In this three-part essay, I investigate Frege’s platonist and anti-creationist position in Grundgesetze der Arithmetik and to some extent also in Die Grundlagen ...
Wittgenstein and Frege
Wittgenstein and Frege
AbstractIn the Preface to Tractatus Logico-Philosophicus, Ludwig Wittgenstein acknowledges his debt to ‘the great works of Gottlob Frege’; and even during the years in which he res...