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

4.13  ·  Rating Details ·  569 Ratings  ·  23 Reviews
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 influe ...more
Paperback, 144 pages
Published December 1st 1980 by Northwestern University Press (first published 1884)
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Apr 12, 2007 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, 2011 Josie added it
I have no recollection of having read this book but I have it on good authority that I did.
Jul 18, 2008 Walt rated it really liked it
Russell's paradox be damned!
Aug 12, 2016 باحث rated it really liked it
Shelves: فلسفة

الكتاب يقع في حوالي 119 صفحة
وهو لـ"جوتلوب فريجه" وهو فيلسوف ورياضي

وهذا الكتاب يعد له تأثير كبير في الفلسفة الحديثة والرياضيات والمنطق
وعلى وجه الخصوص الفلسفة التحليلية

والكتاب فيه رد على "كانط" الفيلسوف الألماني صاحب "نقد العقل المحض" الذي جعل
علم الحساب
كـ1+1=2 من "القضايا التركيبية القبلية" أي ما قبل التجربة

فيثبت "فريجه" في كتابه بأنها من "القضايا التحليلية القبلية" وهي أحد الردود الأخرى على "كانط" في نظريته للمعرفة

والكتاب يعرض عدة مواضيع
مجموعة الأعداد الطبيعية
والأعداد اللامتناهية

Reinhard Gobrecht
Frege nennt in diesem Buch die folgenden wichtigen Grundsätze:
-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!
Jul 22, 2016 Gottfried rated it really liked it
Shelves: history, philosophy
*Review coming soon*
Sep 21, 2008 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.
Aug 13, 2012 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"!
Dr. A
Read this and reviews of other classics in Western Philosophy on the History page of (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 foundat
Dec 26, 2007 Salvador rated it really liked it
Recommends it for: Philosophy Nerds
Perhaps some the clearest writing I've ever encountered.
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.
Walid Amourà
May 10, 2016 Walid Amourà rated it really liked it
"To those who feel inclined to criticize my definitions as unnatural, I would suggest that the point here is not whether they are natural, but whether they go to the root of the matter and are logically beyond criticism" -Frege
A good entrance to mathematical philosophy with way too many brain orgasms for one book.
Jun 25, 2015 Dmk rated it really liked it
It's hard to read it becouse of all philosophical nonsenses, but it gives you overall knowledge about understanding of natural numbers and Frege gives an amazing explanation about what he thinks that natural number is. I highly reccomend it but it's possible that you will dislikes some parts from the middle of book.
Alex Jones
Feb 13, 2014 Alex Jones rated it really liked it  ·  review of another edition
Read this for my philosophy of maths course and I really enjoyed it. Not just in an, for an academic book it was pretty readable and not too slow, kinda-way, but in an I'm a massive geek for all things mathematically philosophical or philosophically mathematical and genuinely liked reading it. As the book that led to most modern discussions within the area it is well worth reading, even if the system presented is as wrong as can be, there are still some salient points to be found.
Jun 13, 2013 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
Aug 27, 2015 Logan rated it it was amazing
Highly recommended as the first stop for anyone interested in the Philosophy of Mathematics or interested in understanding the potential relationships between mathematics and concepts.
Porschla Lim
Jul 29, 2016 Porschla Lim rated it really liked it
Not qualified to give a book review.
Steven Dunn
Jun 15, 2013 Steven Dunn rated it really liked it
Shelves: philosophy
I bought the book at a used bookstore for 15$ (sort of ridiculous). But, after reading Anthony Kenny's exposition of Frege, I can say the book was interesting and not that much of a difficult read.

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.
Oct 16, 2008 David rated it really liked it
Just reread this mornings in the bathroom, lovely for clearing my head, not much use otherwise. Still can't understand what those reducing math to logic folks were thinking.
Jun 13, 2012 Vladimir rated it it was amazing
Necessary to understand the core of Ludwig Witggentein's masterpiece "Tractatus logico-philosophicus" who built on this previous, necessary work.
Sep 11, 2008 Courtney rated it it was ok
Can't say I fully absorbed this one the first time around. I'll have to give it a second try again later.
нєνєℓ  ¢ανα
Apr 16, 2013 нєνєℓ ¢ανα rated it it was amazing
Excellent, lucid, wonderful, clever, delightful...
Ray ✡
Jul 17, 2016 Ray ✡ rated it it was ok
This review has been hidden because it contains spoilers. To view it, click here.
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  • Introduction to Mathematical Philosophy
  • From a Logical Point of View: Nine Logico-Philosophical Essays
  • On Formally Undecidable Propositions of Principia Mathematica and Related Systems
  • Proofs and Refutations: The Logic of Mathematical Discovery
  • On the Plurality of Worlds
  • Introduction to Logic: and to the Methodology of Deductive Sciences
  • The Logical Structure of the World and Pseudoproblems in Philosophy
  • Intention
  • Naming and Necessity
  • Philosophy of Mathematics: Selected Readings
  • Remarks on the Foundations of Mathematics
  • Essays on the Theory of Numbers
  • The Concept of Mind
  • Mind and World: With a New Introduction by the Author
  • Sense and Sensibilia: Reconstructed from the Manuscript Notes by C.J. Warnock
  • Inquiries Into Truth and Interpretation
  • Language, Truth, and Logic
  • Studies in the Way of Words
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 ...more
More about Gottlob Frege...

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