Customer Reviews (7)

Inspiring and foundational
I'm a self-directed learner and had been struggling with generating interest in mathematics for some time. I had bought this book in the hopes that it would bridge my love and interest in logic with a new found interest in mathematics. It did exactly that.

Foundations of Arithmetic
This subtitle, "A Logico-mathematical Enquiry into the Concept of Number," indicates very well the nature of the work.The first three quarters of the book are devoted to a critical analysis of the idea of previous writers (Kant, Leibnitz, Grassmann, Mill, Lipschitz, Hankel, Jevons, Cantor, Schröder, Hobbers, Hume, and others) on the subject of number, and Frege does not find the ideas of any of these philosophers and mathematicians entirely satisfactory.His conclusions is "that a statement of a number contains an assertion about a concept," and his definition of number is: The number which belongs to the concept F is the extension of the concept "equal to the concept F."

Frege regards the number zero as belonging to to the "natural" or "counting" numbers, whereas we subscribe to the view that zero is not a counting number at all (the first of the counting numbers being 1) and is only properly used when we regard a number as a "relative-magnitude," zero being the relative-magnitude of two equal counting numbers.

This work of Frege's has considerable historical interest as a forerunner of the work of Whitehead and Russell.The translation is excellent and the printing leaves nothing to be desired.

The first escape from the Elencus...
You know how _frustrating_ it is, reading a platonic dialog? Some question like "What is virtue?" or "What is justice" is asked, and Socretes goes on for pages showing that the so-called "experts" don't have a clue about what it really is?

But what's _really_ frustrating is that you're all expecting, at the end of the dialog, after following a hard line of argument, that you'll be rewarded with THE definitivie definition of 'virtue' or 'justice' or whatever--only to be disapointed.All you get in the end is a new appreciation of your own hopeless ignorance...

...well, imagine a platonic dialog which started the same as any other platonic dialog, but with the question "What is a number?"Only this time, at the end of the dialog, you actually get an answer to the question?

In retrospect, its pretty amazing that Plato didn't write a Socratic dialog concerned with the question "What is number?'After all, Plato considered numbers more real than physical objects, and people like the Pythagorians were going around claiming that everything _was_ made out of numbers.But what the heck _is_ a number, anyways?

Perhaps the reason was that everybody thought they already understood what numbers were.But Frege, like Socretes before him, realized that this so-called knowledge was really just a collective ignorance.So Frege starts out this book with a thorough, merciless review of what his coleages and predicessors were saying about what numbers were, showing that they ranged from cocksure to confused, from pompously-wrongheaded to just plain silly.

But then Frege does something really amazing--for the first time in history, he goes on give a real answer to the question "what are numbers?"Building on the work of Hume, he gives a sustained argument now known as "Frege's theorem" which shows how numbers can be grounded on an understanding of one-to-one correspondence.

Unfortunately, this work had to wait almost a century for the rest of us to really catch up to its significance.Russell found a contradiction in the arguments presented here, and for the next 80 years attention shifted elsewhere.But first Charles Parsons, in 1964, and then Crispen Wright and others in the 80's and 90's begain to realize that Frege's theorem could be reconstructed without the paradox.This sparked a whole flurry of neo-Fregean studies which is one of the most active branches of analytic philosophy today.

This revival means that Frege's importance, and the importance of reading and comming to grips with the arguments presented by Frege in this book, are going to continue to grow.Although tragically Frege didn't live to see the day, we now realize that the line of reasoning he followed in this book was one of those signature moments in human history, every bit as profound as the invention of the wheel or the discovery of the pythagorian theorem--it was the moment where, for the first time ever, the question "what the heck _are_ numbers, anyways?" got a real answer.

Frege, You're Not Supposed To Have...
*The Foundations of Arithmetic*, one of the most durable works of philosophy of mathematics ever produced, is something of a curiosity as presented by J.L. Austin (who translated the work for the use of an Oxford undergraduate course); and perhaps Frege's platonism got the best of Austin, and this work is really just as , well, Kantian as it appears, "a good sight" more Kantian than "standard" Frege is typically allowed to be.Frege's definition of number in terms of equipollence (one-one correspondence of sets) is legendary: that is to say, it is traditionally understood to do a great deal more work than the "thin" version allowed by mathematical logic as reconstructed to avoid Russell's paradox.

But here Frege's work-up of the concept for a general readership is so "genteel" as to suggest that this may not in fact be the case, and that Frege actually partook more heavily of Neo-Kantian bromides than his *theory of arithmetic* suggests; to wit, that this theory was always intended to be situated within a general philosophy of mathematics obeying the strictures of reasoning involving Kantian "intuition" (as is typically said of Frege's last efforts in the field).As such, it would be unfortunate that we cannot effectively read this book (formerly available *en face*, and unfortunately much the worse for the original's omission) in conjunction with its contemporary geometrical counterpart: long out of print, rarely making its way into the philosophical Frege literature, and perhaps in all parts an *anticipatory* if "crochety" rebuke to Hilbertian formalism.

Perhaps Frege was to a certain extent wholly other than the mathematics of his time; perhaps we are not well-served by a Frege "out of time"; we certainly have one of the great prose stylists of English on hand here, and perhaps it would actually do to consider his aptitude for "gold" extraction here as a clue to puzzling out the rest of Frege -- a figure supremely unconcerned with sameness of meaning, and already owing a certain debt to those para-philosophical figures all his work is at cross-purposes with (the German '70s having been quite a time indeed).A great help to understanding number theory, a marvelous thing for a library to have.

Excellent work
His conclusion (p.99e) is that the laws of arithmetic are analytic judgements and consequently a priori.

Note that he is very consistently hard on Mill.

Some interesting quotes: p. 115e #106. "...number is neither a collection of things nor a property of such, yet at the same time is not a subjective product of mental processes either, we concluded that a statement of number asserts something objective of a concept.

... (p. 116e) We next laid down the fundamental principle that we must never try to define the meaning of a word in isolation, but only as it is used in the context of a proposition: only by adhering to this can we, as I believe, avoid a physical view of it.

#107. (p.117e) "A recognition statement must always have a sense." ... Read more

Product Description

Part of the Longman Library of Primary Sources in Philosophy,” this edition ofFrege's Foundations of Arithmetic is framed by a pedagogical structure designed to make this important work of philosophy more accessible and meaningful for readers. A General Introduction includes the work's historical context, a discussion of historical influences, and biographical information on Gottlob Frege.  The conclusion discusses how the work has influenced other philosophers and why it is important today. Annotations and notes from the editor clarify difficult passages for greater understanding, and a bibliography gives the reader additional resources for further study.

Product Description
This is the first single-volume edition and translation of Frege's philosophical writings to include all of his seminal papers as well as substantial selections from all three of his major works.It is intended to provide the essential primary texts for students of logic, philosophical logic, philosophy of language, and philosophy of mathematics. It contains in particular Frege's four papers "Function and Concept", "On Concept and Object", "On Sense and Reference", and "Thought", and new translations of key parts of the Begriffsschrift, The Foundations of Arithmetic, and the Basic Laws of Arithmetic. The editor's substantial introduction provides the reader with an overview of the significance and development of Frege's philosophy, while the footnotes, appendices and glossary facilitate understanding of some of the more difficult elements of Frege's thought. ... Read more

Customer Reviews (3)

Comment on The Frege Reader:
What a great book this is! The Frege Reader is not for everybody, that's for sure. But when/if you get into the "right space" - then please read this book.

I can't remember when I first heard the name "Frege". But I do know how my reading and study began that eventually brought me to stumble across this mathematician, logician, and philosopher. You see I'm a software developer, more specifically a database guy. I have read much of Chris Date and Hugh Darwen's work. They say that programming languages and databases are considered to be "formal systems", that is to say, a formal system of logic. Date and Darwin go on to say that what we are really doing when we call the database to create an answer set is "instantiating the predicate". So, I started on a path to learn what a "predicate" is. It did not take long before the names: Russell, Whitehead, Wittgenstein, and finally, Frege came up.

There are many fine authors who have written about Frege's logic and philosophy. But, until you read his words (and his words are really, really good!) you really don't get a sense for what this man was really trying to say. This book is not just talking about numbers. This book is about everything we can talk about. Using Frege's "perfect language" we learn to distinguish between "objects", and what we say about those "objects".

So, I learned from this book that when I "instantiate my predicate" I am (in Frege's words) finding the content of the concept, saturating the concept, finding its meaning, its "Bedeudung", returning thoughts to my user.

In his book, LOGIC, LOGIC, and LOGIC, George Boolos quotes one of his professors. The professor said that the way to seduce good students to philosophy is to teach them Russell's and Frege's concept of number. Programmers and DBAs can also be "seduced" by reading Frege. So, if you want to be "seduced" to philosophy, then read The Frege Reader.

Stephen A. Wilson
sawilson3@att.com

Nice collection of an important philosopher
This is a nice selection of excerpts and full essays written by Frege.The book is a pleasure to read, however, not only becaues of the selections and the fine introductory section, but because Frege is such a clear writer and thinker himself. I particularly enjoyed Frege's Begriffshrift - you can see modern quantificational logic being born.

All you need and more
The Frege Reader is an excellent collection of Frege's works. The texts are edited carefully and the editor has supplied extremely helpful footnotes throughout. The introduction and appendices are clear resourcesthat the reader will consult often as she works through the text.

Theexcerpts from many of Frege's letters are a great addition as these shedlight on the development of his project. This work will remain for yearsthe standard first place to turn for Frege. ... Read more

Product Description
Gottlob Frege (1848-1925) was unquestionably one of the most important philosophers of all time. He trained as a mathematician, and his work in philosophy started as an attempt to provide an explanation of the truths of arithmetic, but in the course of this attempt he not only founded modern logic but also had to address fundamental questions in the philosophy of language and philosophical logic. Frege is generally seen (along with Russell and Wittgenstein) as one of the fathers of the analytic method, which dominated philosophy in English-speaking countries for most of the twentieth century. His work is studied today not just for its historical importance but also because many of his ideas are still seen as relevant to current debates in the philosophies of logic, language, mathematics and the mind. The Cambridge Companion to Frege provides a route into this lively area of research. ... Read more

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This volume contains all of Frege's extant unpublished writings on philosophy and logic other than his correspondence, written at various stages of his career. (Philosophy) ... Read more

Product Description
Tyler Burge presents a collection of his seminal essays on Gottlob Frege (1848-1925), who has a strong claim to be seen as the founder of modern analytic philosophy, and whose work remains at the centre of philosophical debate today. Truth, Thought, Reason gathers some of Burge's most influential work from the last twenty-five years, and also features important new material, including a substantial introduction and postscripts to four of the ten papers. It will be an essential resource for any historian of modern philosophy, and for anyone working on philosophy of language, epistemology, or philosophical logic. ... Read more

Customer Reviews (1)

A Great Collection
This is a great collection of readings from a great philosopher. Burge offers many insights on Frege's philosophy among other things. ... Read more

Product Description
This analysis of Frege's views on language metaphysics raised in On Sense Reference, (arguably one of the most important philosophical essays of the past hundred years) provides a thorough introduction to the function/argument analysis. It applies Frege's technique to the central notions of predication, identity, existence and truth, and Bertrand Russell's views throughout serve as a foil to Frege. ... Read more

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Gottlob Frege has exerted an enormous influence on the evolution of twentieth-century philosophy, yet the real significance of that influence is still very much a matter of debate. This book provides a completely new and systematic account of Frege's philosophy by focusing on its cornerstone: the theory of sense and reference. This study represents a major reassessment of a seminal figure in the history of philosophy, and will be of particular interest to philosophers concerned with language and epistemology. ... Read more

Product Description
This brief text assists students in understanding Frege's philosophy and thinking so they can more fully engage in useful, intelligent class dialogue and improve their understanding of course content. Part of the Wadsworth Notes Series, (which will eventually consist of approximately 100 titles, each focusing on a single "thinker" from ancient times to the present), ON FREGE is written by a philosopher deeply versed in the philosophy of this key thinker. Like other books in the series, this concise book offers sufficient insight into the thinking of a notable philosopher, better enabling students to engage in reading and to discuss the material in class and on paper. ... Read more

Product Description
Examines Frege's theory of judgement, according to which a judgement is, paradigmatically, the assertion that a particular object falls under a given concept.Throughout the book the aim is to both state Frege's views clearly and concisely, and to defend, modify or reject these where appropriate. ... Read more

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Este libro pone al alcance del lector no especializado la obra cardinal de GottlobFrege, padre de la filosofia analitica. De facillectura y compresion, la pluma de Stepanians nos conduce vivamente por el entramado primordial del significados y sentidos vislumbrados por una de las mentes mas brillantes de la historia del pensamiento y que aun sigue siendo uno de los pensadores menos leidos en lengua castellana. ... Read more

Product Description
This collection brings together recent scholarship on Frege, including new translations of German material, made available to Anglophone scholars for the first time.

Gottlob Frege (1848-1925) has come to be recognized as someone who, in demonstrating the affinity of logic with mathematics, laid the foundations for modern philosophy of language and modern logic. Frege regarded logic as the foundation for philosophy. In so doing he instigated a radical change in the stance of the majority of Western philosophers whose main pre-occupation had been with the nature of logic rather than logic. His influence can be seen in the work of the logical positivists of the early twentieth century and in much of Ludwig Wittgenstein's philosophy. ... Read more

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What is the number one?Does 2 plus 2 always equal 4? These seemingly simple questions have perplexed philosophers for eons, but the ideas of German philosopher Gottlob Frege (1848–1925) transformed the discussion. Frege believed that the truths of arithmetic and of all mathematics are derived from self-evident logical truths. His new way of looking at logic and mathematics was influential and his convictions revolutionized logic and laid the foundation for modern analytic philosophy. Joan Weiner presents an accurate, accessible explanation of Frege's ideas, tracing the development of his thought and making the essential concepts understandable. ... Read more

Customer Reviews (2)

Pre-introduction to Frege.
There's this very good "introduction" to Frege, and then there's the superb Anthony Kenny's "Frege". I read one after the other.

Weiner is easier to read, whereas Kenny is a bit more technical. But for the same reason, Kenny's introduction is unmatched in clarity and precision (and even depth), whereas this one is more general and "philosophical".

Ideally you should read the two, but otherwise I personally recommend Kenny's "Frege" over this one.

At any rate IMHO the clearest, most concise introduction to Frege is Montgomery Furth's introduction to his selective translation of Frege's main opus "Grundesetze der Arithmetik" ("The Basic Laws of Arithmetic", University of California Press, 1964).

I also do recommend "Frege's Lectures on Logic", by Erich H. Reck and Steve Awodey (translation based on the German text by Gottfried Gabriel) for a masterful introduction to Frege's "Begriffsschrift" (conceptual language), also a clear exposition of his system and a rare personal glimpse of Frege at work at Jena in his later years. It includes three lectures by Frege himself taken from Rudolf Carnap's own notebook, two of them introducing the "Begriffsschrift" by means of a simplified version of the system of "Grundesetze", so it's a unique way, led by the hand of the master himself, to gain a thorough ground for a deeper understanding of his theory.

An in-depth examination of Frege's career and legacy
Written by a Professor of Philosophy at Indiana University, Frege Explained: From Arithmetic to Analytic Philosophy is an in-depth examination of Frege's career and legacy. Frege's work was marked by his determination to show that arithmetic is really a part of logic; while that effort ended in failure, in the process Frege revolutionized philosophic understanding of logic and set the foundation for analytic philosophy. Chapters survey Frege's life and character, his "new logic" and definitions of numbers, his logical investigations and speculations upon the foundations of geometry, his impact upon recent and modern philosophy, and much more. Especially for philosophy students and scholars, Frege Explained presents complex concepts in as straightforward a manner as practically possible, and is especially recommended for college library philosophy shelves.
... Read more