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

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Grundlagen der Arithmetik

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy. See our Privacy Policy and User Agreement for details. Published on Mar 12, The foundations of arithmetic a logico mathematical enquiry into the concept of number. SlideShare Explore Search You. Submit Search. Successfully reported this slideshow.

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We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime. Upcoming SlideShare. Like this document? Why not share! Embed Size px. Start on. Show related SlideShares at end. WordPress Shortcode. Apr 12, Eliot rated it really liked it. Yeah, yeah, his theory of numbers doesn't really make any sense.

But, whatever. You try to define a number. Jun 02, Josie added it. I have no recollection of having read this book but I have it on good authority that I did. Jul 18, Walt rated it really liked it. Russell's paradox be damned!

Catalog Record: The foundations of arithmetic; a | HathiTrust Digital Library

Jun 15, Gavin rated it liked it Shelves: technicalx. Bloody weird to slap a star rating on this, but there you go, welcome to where nothing is not rateable. Aug 13, Simon rated it it was amazing Shelves: philosophy-read. Originally read many years ago. Michael Dummett cites its 62 as the "most pregnant philosophical paragraph ever written"! Jul 19, Gerrit G. A close study of Kant's first critique certainly helps understanding this text which I lack and consequently do not understand some parts fully.

If you come from modern mathematics you'll feel as if you are studying its very inception. Sep 02, Dr. Frege examines the philosophical foundat Read this and reviews of other classics in Western Philosophy on the History page of www. Frege examines the philosophical foundations for mathematics, destroying some earlier theories i. Psychologism, the idea that knowledge of numbers is subjective and proposing a rigorous system that establishes objectivity for mathematics.

In short, he proved how mathematical truths and numbers have properties that are independent of the subjects who think them. Jun 13, Jackie rated it it was amazing. This was a fun read. 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 This was a fun read. There are some minor points throughout the text in which he relies on the reader's intuition and some popular beliefs to 'wave away' a point.

Maybe he's done so because his treatment indirectly expresses how stupid the point in question was. Whatever the reason, the result is a break from rigorous definition. My wish for the content of the book is to see it written in logical formalism. Jul 22, Rick Sam rated it really liked it Shelves: history , philosophy. Dec 26, Salvador rated it really liked it Recommends it for: Philosophy Nerds. Perhaps some the clearest writing I've ever encountered.

Sep 21, Libcrypt rated it it was amazing. Written like a knife, this concise exposition of Frege's philosophy of mathematics still stands up well to scrutiny today.

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Feb 24, William rated it it was amazing Shelves: math. Good work, if you've done mathematics you've probably seen the definition of number laid out a bit more clearly in terms of sets instead of extensions of concepts, but close enough. However the really meaty part of the work is the engagement with philosophers Leibniz, Mill, etc , and the descriptions of the mathematical difficulties faced along the way which create problems for formalists, etc.

A great review of the failures of an older empiricism. Mar 19, Adrien Mogenet rated it liked it. The title is not misleading. Frege revisits a concept as simple as "Number", but this quickly escalates to something extremely hard to formally define. Throughout his set of axioms, he explores multiple angles and highlight the fallacious reasonings.

The Foundations of Arithmetic a Logico Mathematical Enquiry Into the Concept of Number

Sep 19, Joseph Madison rated it it was amazing. Seminal work in the historical development of the logical foundations of mathematics. Frege has a very beautiful logical framework which is described and defended, only to be later dismantled by Russell. Mar 25, Will rated it it was amazing Shelves: central-europe , philosophy , favorites. Agonistic philosophy is rare enough after the Greeks. Frege's bashing of J. Mill ranks right up there with Schopenhauer's sarcastic hostility toward Fichte and Hegel, and Nietzsche making fun of everyone but especially Kant.

Mar 04, Zach Mazlish rated it liked it.

Don't have much to say as yet just because I don't know enough, but hopefully my thoughts will evolve as I learn more about it. May 05, Walid Amoura rated it it was amazing.

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Absolutely brilliant. May 04, Jake Yaniak rated it really liked it. Definitely the kind of book that makes you really think.

  • Frege's Works in English.
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In philosophy it is amazing just how much we take for granted. If you ever thought that 19th century mathematics has gotten far enough with the constructions of real numbers out of rationals and its continuous zeal for the foundations of analysis, you have not read this one. Herr Frege tries to construct natural numbers out of logic. Whatever one thinks of this book or the importance of the project these days, as a philosophical discussion this has one of the greatest forms that I have witnessed in philosophy.

This one contains discussions of Kant and J. Mill still relevant to this day, and especially the destruction of Mill's opinions on arithmetic is quite exciting even today. This book is probably the founding document of modern analytic philosophy. In it all the topics which are foundational for the whole tradition are contained. Philosophy of language, logic, philosophy of mathematics and a certain disdain for a certain kind of epistemology.

It is still written before Sinn und Bedeutung, so you need to be especially careful when Frege talks about Sinn of expressions here, as these thoughts are not so clear at this stage of his thinking. Here also the contextual principle is mentioned for the only time in Frege's philosophy. I must give it 5 stars as a piece of philosophy, as a historical documents and also as a piece of prose. From the academic literature the only exposition that came near was Chomsky's Syntactic Structures.

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! Eigenschaften von Begriffen - Eigenschaften von Dingen. Umfang und Inhalt von Begriffen.

Frege's Logical Revolution: Classical Logic (feat. Graham Priest)

Null as Anzahl, welche dem Begriffe sich selbst ungleich zukommt.