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# The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number

by

*The Foundations of Arithmetic*is undoubtedly the best introduction to Frege's thought; it is here that Frege expounds the central notions of his philosophy, subjecting the views of his predecessors and contemporaries to devastating analysis. The book represents the first philosophically sound discussion of the concept of number in Western civilization. It profoundly ...more

Paperback, 144 pages

Published
December 1st 1980
by Northwestern University Press
(first published 1884)

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Start your review of The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number

Jun 02, 2011
Josie
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I have no recollection of having read this book but I have it on good authority that I did.

Sep 02, 2014
Dr. A
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Discovered and popularized posthumously by Bertrand Russell (see Russell and Alfred North Whitehead'’s

Frege examines the philosophical ...more

*Read this and reviews of other classics in Western Philosophy on the History page of www.BestPhilosophyBooks.org (a thinkPhilosophy*Production).---

Discovered and popularized posthumously by Bertrand Russell (see Russell and Alfred North Whitehead'’s

*Principia Mathematica*), Ludwig Wittgenstein, and others, Gottlob Frege is now known as the father of modern logic and of analytic philosophy, and*The Foundations of Arithmetic*is his most important work.Frege examines the philosophical ...more

Unfortunately, Frege does some hand-waving throughout the book. He is attempting to show that arithmetic is an extension of logic. Critical to his argument is the definition of number as a concept expresssable by second-order classical logic. In showing his definition of number is in fact correct, he isolates number away from the realm of psychology. There are some minor points throughout the text in which he relies on the reader's intuition and some popular beliefs to 'wave ...more

This one contains discussions of Kant and J.S. ...more

-Scharfe Trennung von Psychologischem und Logischem.

-Scharfe Trennung von Subjektivem und Objektivem.

-Die Bedeutung der Wörter ist im Satzzusammenhang zu erfragen.

-Der Unterschied zwischen Begriff und Gegenstand ist wichtig.

In diesem Buch unterscheidet Frege die Wahrheiten in analytische und synthetische und ferner in a priori und a posteriori Wahrheiten.

Was ist ein leerer Begriff?

Bejahung der Existenz als Verneinung der Nullzahl!

...more

Feb 03, 2016
Diogo
added it

A very short, very concise, very dense attempt by Frege to address the business of logically deriving the primitive concepts of Peano. Not an inviting writing. I somewhat feel I'm not yet qualified to rate this work. It is nevertheless very entertaining & instructive to read him addressing the theories of others. Perhaps worthy of the hardship of braving through to the last page.

If you like mathematics, the theory of numbers and topics akin to the like (e.g. logic), then check out the book. If not,

then ignore the mundane review Frege gives to the concept of numbers.

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Friedrich Ludwig Gottlob Frege (German: [ˈɡɔtloːp ˈfreːɡə]) was a German mathematician, logician and philosopher. He is considered to be one of the founders of modern logic and made major contributions to the foundations of mathematics. He is generally considered to be the father of analytic philosophy, for his writings on the philosophy of language and mathematics. While he was mainly ignored by
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