Frege, Gottlob

Collected Papers on Mathematics, Logic, and Philosophy

Average customer rating:

Collected Papers on Mathematics, Logic, and Philosophy
Gottlob Frege
Manufacturer: Blackwell Publishers
ProductGroup: Book
Binding: Hardcover

General | Philosophy | Nonfiction | Subjects | Books

Modern | Philosophy | Nonfiction | Subjects | Books

General | Mathematics | Science | Subjects | Books

Look Inside Nonfiction Books | Trip | Specialty Stores | Books

Look Inside Science Books | Trip | Specialty Stores | Books
ASIN: 0631127283

The Varieties of Reference (Clarendon Paperbacks)

Average customer rating:

This dude is haggard!
Basic Concepts in Varieties of Reference

The Varieties of Reference (Clarendon Paperbacks)
Gareth Evans
Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Paperback

Policy & Current Events | Popular Economics | Business & Investing | Subjects | Books

Development & Growth | Economics | Business & Investing | Subjects | Books

Economic Policy & Development | Economics | Business & Investing | Subjects | Books

General | Business & Investing | Subjects | Books

Consciousness & Thought | Philosophy | Nonfiction | Subjects | Books

Epistemology | Philosophy | Nonfiction | Subjects | Books

General | Philosophy | Nonfiction | Subjects | Books

Logic & Language | Philosophy | Nonfiction | Subjects | Books

Look Inside Business Books | Trip | Specialty Stores | Books

Look Inside Nonfiction Books | Trip | Specialty Stores | Books
Similar Items:

Collected Papers
Frege: Philosophy of Language, Second Edition
Individuals
Reference and Description: The Case against Two-Dimensionalism
Beyond Rigidity: The Unfinished Semantic Agenda of Naming and Necessity

ASIN: 0198246862

Book Description

Gareth Evans, one of the most brilliant philosophers of his generation, died in 1980 at the age of thirty-four. He had been working for many years on a book about reference, but did not complete it before his death. The work was edited for publication by John McDowell, who contributes a Preface.

Customer Reviews:

This dude is haggard!.......2003-09-24

I was totaly blown away by the awsomness of this book. the way the guy says things makes you want to scream yeah go ahead! I'm not a expert on reference books or anything, but I think that by the way he writes the book it is just killin' to the reader!!!!!buy this book, light up a big blunt, and chill to the deepness.

Basic Concepts in Varieties of Reference.......2003-08-04

In Varieties of Reference (hereafter, Varieties), Evans sets out a modified Fregean theory of sense for singular terms in language, and their counterpart constituents in thoughts (singular thoughts). Russell's Principle (RP) is an initial formulation of what thinking about an object (grasping its sense) requires. The central thesis of Varieties is that RP applies to all cases of understanding singular reference. Evans distinguishes what counts as satisfying RP for different kinds of objects (e.g., numbers, colors, shapes, spatio-temporal objects). These are the fundamental grounds of difference for those kinds of objects. And there are multiple modes of satisfying RP: demonstrative identification, recognition-based identification, and information-based descriptions. Evans has chapters dedicated to demonstrative and recognition-based modes.

Varieties is dense and difficult material (in the early eighties, Hilary Putnam wrote a surprisingly negative review where he blasts Evans for writing a book that is overly technical; John McDowell wrote several letters responding to Putnam's criticism). But Varieties is packed with awesome thought and is deeply satisfying to read. Also enjoyable are Evans's odd examples, like the coughing sheep, the spinning steel balls, and the hands feeling velvet.

To grasp the motivation for Evans's theory, it is helpful to have some feeling for Dummett's theory of sense, and the attacks on sense made by proponents of the new theory of reference like Kripke. Evans criticizes these positions early in the book, but he also wants to salvage elements of both. Strawson's Individuals and Geach's Mental Acts are also a big influence on Varieties. For example, reading the first couple chapters of Individuals are very helpful for getting a general sense of what is going on when Evans talks about the "fundamental ground of difference" for spatio-temporal objects.

Some of the most important technical concepts in Varieties are the following:

1. Russell's Principle: "The principle is that a subject cannot make a judgment about something unless he knows which object his judgment is about.... In order to make Russell's Principle a substantial principle, I shall suppose that the knowledge which it requires is what might be called discriminating knowledge: the subject must have a capacity to distinguish the object of his judgment from all other things.... We have the idea of certain sufficient conditions for being able to discriminate an object from all other things: for example, when one can perceive it at the present time; when one can recognize it if presented with it; and when one knows distinguishing facts about it" (89).

2. The Generality Constraint: "It seems to me that there must be a sense in which thoughts are structured.... I should prefer to explain the sense in which thoughts are structured, not in terms of their being composed of several distinct elements, but in terms of their being a complex of the exercise of several distinct conceptual abilities.... Thus if a subject can be credited with the thought that a is F, then he must have the conceptual resources for entertaining the thought that a is G, for every property of being G of which he has a conception" (100-104).

3. Idea (capitalized): "I shall speak of the Ideas a subject has, of this or that particular object, on the model of the way we speak of the concepts a subject has, of this or that property". Combined with the Generality Constraint, this yields the notion that "An Idea of an object, then, is something which makes it possible for a subject to think of an object in a series of indefinitely many thoughts, in each of which he will be thinking of the object in the same way" (104).

4. Fundamental Ground of Difference: "An Idea of an object is part of a conception of a world of such objects, distinguished from one another in certain fundamental ways. For every kind of object, there is a general answer to the question, `What makes it the case that there are two objects of this kind rather than one (or three rather than two)?' For example, we may say that shades of color are distinguished from one another by their phenomenal properties, that shapes are distinguished from one another by their geometrical properties, that sets are differentiated from one another by their possessing different members, that numbers are differentiated from one another by their position in an infinite ordering, and that chess positions are distinguished from one another by the positions of pieces upon the board" (106-107).

5. The Fundamental Ground of Difference for Spatio-Temporal Objects: "In the case of temporal objects-objects which exist in time and which change-we must replace the absolute notion of what differentiates an object from others with the notion of what differentiates an object from others at a time.... The answer to the question what differentiates a statue from every other thing at a time is given by citing (i) the position which it occupies at that time and (ii) the fact that it is a statue" (107). The fundamental ground of difference is that which knowledge of suffices to distinguish an object from all other objects (of its kind), that is, knowledge of which satisfies Russell's Principle.

6. Fundamental Idea: "Let us say that one has a fundamental Idea of an object if one thinks of it as the possessor of the fundamental ground of difference which it in fact possesses" (107).

7. Information-based Thought: "An [information-based thought] is governed by a conception of its object which is the result neither of fancy...nor of linguistic stipulation...but rather is the result of a belief about how the world is which the subject has because he has received information (or misinformation) from the object" (121). Information is meant to capture our causal involvement with the world around us.

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

The first escape from the Elencus...

Frege, You're Not Supposed To Have...

Excellent work

great work

A Must for Any Philosopher of Mathematics

The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number
Gottlob Frege
Manufacturer: Northwestern University Press
ProductGroup: Book
Binding: Paperback

General | Philosophy | Nonfiction | Subjects | Books
Logic & Language | Philosophy | Nonfiction | Subjects | Books
General | Science | Subjects | Books
General | Mathematics | Science | Subjects | Books
Arithmetic | Popular & Elementary | Mathematics | Science | Subjects | Books
Mathematics | Professional Science | Professional & Technical | Subjects | Books | Applied | Chaos & Systems | Geometry & Topology | Mathematical Analysis | Mathematical Physics | Number Systems | Pure Mathematics | Transformations | Trigonometry
Look Inside Nonfiction Books | Trip | Specialty Stores | Books
Look Inside Science Books | Trip | Specialty Stores | Books
Qualifying Textbooks - Spring 2007 | Stores | Books
Similar Items:

The Frege Reader (Blackwell Readers)

The Principles of Mathematics

Introduction to Mathematical Philosophy

Tractatus Logico Philosophicus (Routledge Classics)

Contributions to the Founding of the Theory of Transfinite Numbers

ASIN: 0810106051

Book Description

This volume represents the first philosophically sound discussion of the concept of number in Western civilization. (Mathematics)

Customer Reviews:

The first escape from the Elencus..........2005-10-17

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..........2004-03-24

*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.......2003-06-14

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."

great work.......2001-11-28

possibly one of the greatest works in history of philosophy and the founding book of 20th century analytic philosophy... I read it only once and a better appraisal will be coming shortly..I can say right away this is not simply a 'technical' work in philosophy of mathematics but a broad although short philosophical investigation in notions of truth, meaning and identity - although it expressly deals with defining numbers in purely logical terms. continental philosophers who read this work might change some of their negative ideas about where analytic philosophy is coming from.

A Must for Any Philosopher of Mathematics.......2000-09-24

This book written by Gottlob Frege is one of the most influential books of the 20th century philosophy of mathematics. In here Frege establishes the nature of arithmetics as founded in logic, which is his logicist proposal. For that, he refutes the assertion that logic as such is founded on psychology.

Sometimes he distorts a little bit what others say about logic, so he argues against those thinkers more effectively. In here he establishes the anti-psycology difference between concept and object; though he has not made a difference yet between sense and reference. He also refers to a principle called the contextual principle, in which the word makes reference to something depending on the context. Afterwards after he wrote the book, he would reject this principle, because of his doctrine of sense and reference: the sense of the words determine the sense of the sentence; and the reference of the words determine the reference of the sentence.

Book 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.

Customer Reviews:

Comment on The Frege Reader:.......2001-10-03

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.......2001-02-21

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.......2000-06-13

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 resources that the reader will consult often as she works through the text.

The excerpts from many of Frege's letters are a great addition as these shed light on the development of his project. This work will remain for years the standard first place to turn for Frege.

Metaphysicians of Meaning: Russell and Frege on Sense and Denotation (International Library of Philosophy)
Average customer rating:
Metaphysicians of Meaning: Russell and Frege on Sense and Denotation (International Library of Philosophy)
Gideon Makin
Manufacturer: Routledge
ProductGroup: Book
Binding: Paperback

Epistemology | Philosophy | Nonfiction | Subjects | Books
General | Philosophy | Nonfiction | Subjects | Books
Logic & Language | Philosophy | Nonfiction | Subjects | Books
Modern | Philosophy | Nonfiction | Subjects | Books
Similar Items:

Truth, Thought, Reason: Essays on Frege

ASIN: 0415242266

Book Description

Metaphysicians of Meaning is the first book to challenge the accepted understanding of Russell's On Denoting and Frege's On Sense and Reference. Makin compares the work Russell did shortly before his famous essay "On Denoting" with the essay itself and argues that this comparison shows that the traditional view of the problem Russell was trying to solve is untenable. He then examines Frege's classic essay and argues that some of the less well-known views that Frege held have radical implications for our understanding of this essay.

Fixing Frege (Princeton Monographs in Philosophy)

Average customer rating:

Fixing Frege (Princeton Monographs in Philosophy)
John P. Burgess
Manufacturer: Princeton University Press
ProductGroup: Book
Binding: Hardcover

General | Philosophy | Nonfiction | Subjects | Books

Logic & Language | Philosophy | Nonfiction | Subjects | Books

General | Mathematics | Science | Subjects | Books

Qualifying Textbooks - Spring 2007 | Stores | Books
Similar Items:

The Oxford Handbook of Philosophy of Mathematics and Logic (Oxford Handbooks in Philosophy)
Mathematics In Philosophy: Selected Essays
Fictionalism in Metaphysics
Truth and the Absence of Fact
Truth, Thought, Reason: Essays on Frege

ASIN: 0691122318

Book Description

The great logician Gottlob Frege attempted to provide a purely logical foundation for mathematics. His system collapsed when Bertrand Russell discovered a contradiction in it. Thereafter, mathematicians and logicians, beginning with Russell himself, turned in other directions to look for a framework for modern abstract mathematics. Over the past couple of decades, however, logicians and philosophers have discovered that much more is salvageable from the rubble of Frege's system than had previously been assumed. A variety of repaired systems have been proposed, each a consistent theory permitting the development of a significant portion of mathematics. </p>

This book surveys the assortment of methods put forth for fixing Frege's system, in an attempt to determine just how much of mathematics can be reconstructed in each. John Burgess considers every proposed fix, each with its distinctive philosophical advantages and drawbacks. These systems range from those barely able to reconstruct the rudiments of arithmetic to those that go well beyond the generally accepted axioms of set theory into the speculative realm of large cardinals. For the most part, Burgess finds that attempts to fix Frege do less than advertised to revive his system. This book will be the benchmark against which future analyses of the revival of Frege will be measured.</p>

Building on Frege: New Essays about Sense, Content and Concepts
Average customer rating:
Building on Frege: New Essays about Sense, Content and Concepts
Albert Newen , Ulrich Nortmann , and Ranier Stuhlmann-Laeisz
Manufacturer: Center for the Study of Language and Inf
ProductGroup: Book
Binding: Paperback

General | Philosophy | Nonfiction | Subjects | Books
History & Surveys | Philosophy | Nonfiction | Subjects | Books
Logic & Language | Philosophy | Nonfiction | Subjects | Books
Metaphysics | Philosophy | Nonfiction | Subjects | Books
Modern | Philosophy | Nonfiction | Subjects | Books
ASIN: 157586312X

Book Description

An outstanding philosopher-logician, Gottlob Frege's (1848-1924) work has received much attention in recent years. In the pursuit of Frege's main goal to solidify the foundations of mathematics and scientific work, Frege conceived a comprehensive philosophy of language and developed the main thesis of logicism, that mathematics is reducible to logic. This book contains essays covering a large range of issues related to Frege that will be of great interest to philosophers working on these issues. This volume represents an important addition to the study of Frege.

This book contains essays from some of the most important contemporary philosophers investigating Frege's ideas. Treating issues of contemporary interest, this book discusses topics either in a Fregean spirit or in dialogue with Frege's original views. The wide implications of Frege's views are evident in the variety of topics presented in this volume, from the Frege fundamentals to innovative interpretations that break new ground in the study of Frege. Key papers concern the ontological status of propositions and concepts, recent attempts to improve on the semantics of singular terms, the question of how to construe the content of concept-expressions, and other themes within the common grounds in which ontology and philosophical semantics intersect.

From Frege to Wittgenstein: Perspectives on Early Analytic Philosophy

Average customer rating:

From Frege to Wittgenstein: Perspectives on Early Analytic Philosophy

Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Hardcover

General | Philosophy | Nonfiction | Subjects | Books

History & Surveys | Philosophy | Nonfiction | Subjects | Books

Analytic Philosophy | Philosophy | Nonfiction | Subjects | Books

All Amazon Upgrade | Amazon Upgrade | Stores | Books

Nonfiction | Amazon Upgrade | Stores | Books

Qualifying Textbooks - Spring 2007 | Stores | Books
ASIN: 0195133269

Book Description

Analytic philosophy--arguably one of the most important philosophical movements in the twentieth century--has gained a new historical self-consciousness, particularly about its own origins. Between 1880 and 1930, the most important work of its founding figures (Frege, Russell, Moore, Wittgenstein) not only gained attention but flourished. In this collection, fifteen previously unpublished essays explore different facets of this period, with an emphasis on the vital intellectual relationship between Frege and the early Wittgenstein.

Rethinking Identity and Metaphysics: On the Foundations of Analytic Philosophy

Average customer rating:

Excellent Defense of "Intensions" in Philosophy

Rethinking Identity and Metaphysics: On the Foundations of Analytic Philosophy
Claire Ortiz Hill
Manufacturer: Yale University Press
ProductGroup: Book
Binding: Hardcover

General | Philosophy | Nonfiction | Subjects | Books

Logic & Language | Philosophy | Nonfiction | Subjects | Books

Metaphysics | Philosophy | Nonfiction | Subjects | Books

Ontology | Philosophy | Nonfiction | Subjects | Books
ASIN: 0300068379

Customer Reviews:

Excellent Defense of "Intensions" in Philosophy.......2001-08-09

Though Hill never mentions it, this book is based mostly on observations made by Edmund Husserl in his early work "Philosophy of Arithmetic" against some points made to Frege's "The Foundations of Arithmetic". In it Husserl points out, even after his turn to Platonism in his "Logical Investigations", that conceiving numbers as extensions of concepts are unjustified and is scientifically useless. That all Frege's definitions become true and correct propositions when one substitutes extensions of concepts for the concepts, but that then they are absolutely self-evident and without value, and that the results of Frege's endeavors are such as to make one wonder how anyone could believe they were true other than temporarily.

Later Husserl pointed out that one of the main problems proposed by Frege there was his attempt not to distinguish between equality (equivalence) (when two objects share in some properties), and identity (when objects share all properties).

Hill inspired by Husserl's observation, exposes how Frege, after falling in the Zermelo-Russell paradox, traces the problem precisely to the point Husserl was making, without mentioning his name.

And during her entire book, she tries to show that when one philosopher tries to get rid of "intensions" (essences, attributes, senses, meanings, essential properties, concepts, propositions, and universals) to develop Platonist or anti-Platonist extensional treatment of identity, inevitably "intensions" come back again with more force.

From this point of view she looks again at why Frege failed in founding arithmetic on logic, by treating identity and equivalence as the same thing, and in an extensional manner. She uses examples also of Bertrand Russell and W. V. O. Quine to show how this is so.

To illustrate her points she uses examples of the JFK assassination, medicine, politics, you name it.

Philosophers:

Philosophers

Philosophers