The Principia : Mathematical Principles of Natural Philosophy

Book Description

In his monumental 1687 work Philosophiae Naturalis Principia Mathematica, known familiarly as the Principia, Isaac Newton laid out in mathematical terms the principles of time, force, and motion that have guided the development of modern physical science. Even after more than three centuries and the revolutions of Einsteinian relativity and quantum mechanics, Newtonian physics continues to account for many of the phenomena of the observed world, and Newtonian celestial dynamics is used to determine the orbits of our space vehicles.
This completely new translation, the first in 270 years, is based on the third (1726) edition, the final revised version approved by Newton; it includes extracts from the earlier editions, corrects errors found in earlier versions, and replaces archaic English with contemporary prose and up-to-date mathematical forms.
Newton's principles describe acceleration, deceleration, and inertial movement; fluid dynamics; and the motions of the earth, moon, planets, and comets. A great work in itself, the Principia also revolutionized the methods of scientific investigation. It set forth the fundamental three laws of motion and the law of universal gravity, the physical principles that account for the Copernican system of the world as emended by Kepler, thus effectively ending controversy concerning the Copernican planetary system.
The illuminating Guide to the Principia by I. Bernard Cohen, along with his and Anne Whitman's translation, will make this preeminent work truly accessible for today's scientists, scholars, and students.

Customer Reviews:

Excellent translation with helpful apparatus.......2007-06-11

I am writing my dissertation on Newton and have found this translation incredibly helpful and surprisingly readable.

The Principia is one of the most difficult and inaccessible books ever written -- so much so, in fact that even John Locke (himself a pretty smart guy) had to ask Christian Huygens to explain much of it to him. This difficulty was intentional, because Newton did not want people who only understood math a little to try and undermine his arguments. For this reason, he rewrote book three so that only those who had read and understood book 1 could understand its concepts.

People laugh when I tell then that I own a book with a three hundred page introduction, but it's a book that needs a three hundred page intro. In their intro, Cohen and whitman describe the history of the principia, its structure, an explanation of where prior translations have fallen short, and -- most importantly -- note which of the Principia's sections have been most significant during and after Newton's time. This is helpful so that when you get to each section, you are more likely to notice which elements may have seemed most controversial, where he is taking down Descartes' vortices, etc. I'm not saying I agree 100% with cohen and whitman on all of their points, but they have produced a work that does not simply translate the book; it also shares the writers' substantial knowledge about the principia.

This is an essential and monumental translation. If you are at all interested in early modern science, you must own it.

Is Newton come on!.......2006-08-10

What I have to say is Newton.... What else are you lookin for in a Physics book. Ohh yeah the only problem it has that its size is such a college book(huge), and it is not hard cover.

An Engrossing and Time Consuming Masterpiece of Science and Literature.......2005-09-22

Principia explains with great detail some elements of Eucledian geometry, Calculus, Fluid mechanics, Three laws of Gravity and The Method of the Universe. Newtons three hundred year old advice remains true today to read Book One and Three while skipping Book Two altogether. I can honestly say that subject is not too difficult but is guilty of being well conceived but poorly worded. The latter was Newtons own intention to make its reading very exclusive and making him less vunerable to his contemporary critiques. This version has the diagrams illustrated on multiple pages for each Scholium to avoid the constant turning of its pages. I advice a slow read of Book 1 and 3. The last Scholium of Book 3 is the best discussion as to the existance of God that I have read. Long live the spirits of Shakespeare, Newton, Vermeer and Beethoven.

I can't believe people still believe this stuff.......2005-09-20

The Principia is the basis for much of modern science. It is swallowed hook, line and sinker by mathematicians and people in physics as a 'holy grail.' It is a continuation of very old fashioned thinking, hooked on 'cause and effect' relationships, Aristotelian in nature. One would think that modern science could see through this veil of antiquity, but seemingly has not yet had the courage to do so.

It is essential reading, however, so see how far 'science' has not moved for nearly 400 years.

This particular translation is of interest in that half of the book tries to explain and support the original text. Bit too hard of a sell to justify Newton's arguments. Again, it is a must-read for anyone seeking to understand the flaws of modern 'science.'

Wonderful overview, somewhat overwhelming........2004-09-07

This is a wonderful reference, but frankly, it was overwhelming for me. Let's just say that while the first two sections of this book were clear, informative, meticulously and thoroughly footnoted and annotated, the last section-- the actual translation-- proved beyond my abilities. I'd HIGHLY recommend a college-level geometry course before attempting to read the actual translation of Newton's revolutionary work.

Frankly, the combination of archaic verbiage (Cohen kept a number of obsolescent terms in translating from the original Latin), combined with a predominately narrative style (reading in an entire paragraph what can in modern mathematical symbology be articulated in a single line) combined with my lack of working analytic geometry enabled me to follow this seminal work conceptually, but not in detail. Other reviwers have suggested that a working knowledge of calculus and Newtonian physics is required. I disagree. To follow Newton's proofs in detail, it is Euclidean geometry that is required. Newton's Principia CONCEPTUALLY utilizes calculus, but the proofs themselves are Euclidean with the concept of "infinitisimally small" added to the equation. I have single- and multi-variable calculus, linear algebra, differential equations (first-, second-order, and partial), and graduate-level statistics under my belt. Junior high school geometry is insufficient to understand his work. So far, I am studying tensors, differential geometry/exterior calculus with respect to gravitation physics without too much difficuly. Geometry!

Otherwise, this book was wonderful. Section One is a thoroughly researched historical background. Social setting, scientific thought at the time, the controversies of the times, historical perspective, insights into Newton himself. Wonderfully referenced and annotated.

Section Two is a clear "How to Read" section-- discussing section by section of the Principia what the main concepts and issues are, even critiquing Newton's flaws and obvious attempts to fill in gaps or alter data when existing data were insufficient to his theories! Cohen even guides us step-by-step through some of the more important proofs in the Principia-- proofs that for the most part I followed, except for certain geometric assumptions that I had to assume were true.

My fascination has always been relativity... which I am working on understanding now. When finished, I may read a college-level text in analytic geometry, then come back to this. But I was impressed by the sheer breadth of conceptual material Newton covered. Certainly entitling his last book of The Principia "The System of the World" was justified.

Principia Discordia - The Magnum Opiate of Malaclypse the Younger

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The fundamental guide to discord and the goddess
It's magic
Just buy it!
A must read

Principia Discordia - The Magnum Opiate of Malaclypse the Younger
Malaclypse the Younger
Manufacturer: Exposure Publishing
ProductGroup: Book
Binding: Hardcover

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ASIN: 1846856043

Book Description

Here we are in 2007 (or YOLD 3173), forty-eight, or forty-nine years after Mal2 and Omar's Discordian revelations at the hands of the Goddess Eris. Principia Discordia has been republished a number of times over the years, but not since 1976 has it been available to the general public in hardback format. Synaptyclypse Generator is proud to present this special edition of the legendary counter-culture classic, the bible of Discordianism. We have spared no cabbage-power in preparing this wonderful hardback edition for your enjoyment and enlightenment. We have done the best we could have hoped to ensure a quality and cherishable version of Principia Discordia. For this edition, we have included Kerry W. Thornley's introduction to the 1991 Illuminet Press edition and Robert Anton Wilson's Loompanics Unlimited introduction. We include all the material from the last Loompanics printing and any odd bits left over from the Illuminet version. We have closing 'Outroductions' by none other than the Rev.Dr Jon Swabey of Apocrypha Discordia fame and 'crackpot historian,' Adam Gorightly, author of The Prankster and the Conspiracy, The Story of Kerry Thornley and How He Met Oswald and Inspired the Counterculture. It also features the most sumptuously gorgeous cover that any edition has ever had.

Customer Reviews:

The fundamental guide to discord and the goddess.......2007-09-26

The Book is a masterpiece of confusion, philosophy, humor and a religion that only starts out seeming ridiculous, as you read and reread the book you start to find the wisdom that Malaclypse the Younger was trying to convey and yet wrap his own head around at the time. I have owned three copies of this book and evey time i rebuy it and reread it i get somthing new from it. So grab your copy and all hail Eris.

It's magic.......2007-05-02

I recently noticed that I couldn't find my purple version of this book. I have absolutely no idea what happened to it. But if that hadn't happened, I never would have known that there was a hard cover version out. Something mysterious is going on. You should buy this book.

Just buy it!.......2007-04-10

Finally! Principia Discordia in hardback! It's about time too. It seems I've been waiting thirty odd years for this version. I've worn out and given away so many paperback copies I have now gifted myself a permanent version. Just check out all those neat little additions too, like the 'outroductions' and the bit about the...

No, I'm not going to spoil it for you. Just buy it!

A must read.......2007-03-12

It's awesome to finally see what may be one of the most stealthily influential books of the later 20th century in hardback. A definite must have, especially if you're like me and have already destroyed two paperback copies from over reading...

On Formally Undecidable Propositions of Principia Mathematica and Related Systems

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Mathematical Rationalism has limits
The following is a dissenting view
Gödel's proof of the inadequacy of formalism
One of the Best Books You Should Never Read
Unbelievable theorem

On Formally Undecidable Propositions of Principia Mathematica and Related Systems
Kurt Gödel
Manufacturer: Dover Publications
ProductGroup: Book
Binding: Paperback

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ASIN: 0486669807

Book Description

First English translation of revolutionary paper (1931) that established that even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. Introduction by R. B. Braithwaite.

Customer Reviews:

Mathematical Rationalism has limits.......2007-03-17

It is very hard to find faults in what may be the most famous proof of the 20th century.
For those not familiar with the Russell-Whitehead Principia Mathematica notation
this is a very hard book. I had the benefit of the Kac-Ulam explanation.
I did find what might be problems with this proof.
1) One is the reliance on number theory proofs about prime numbers that are assumed true
in the Gödelization of the primes coding of the mathematical axioms.
2) The second is the assumption that the axioms statements represent the minimal
representation of such a system of axioms.
Both are slim if none chances, but ones the Gödel doesn't consider.
Information theory was after this time where we discovered that a system of symbols can indeed at times be more efficiently coded.
The best example of this seems to be Gray code compared to ordinary binary number code ( a number theory code
like Gödel's prime code) where less turns out to be more in information terms.
The theory of primes suffers from the new doctrine of strings that says
that infinite scales don't exist in the "real" world: that a maximum and a minimum
of measure are fixed parts of our reality. This kind of assumption can't be "proved"
but is an axiom of a system of a mathematical sort and is counter to the Euclidean proof of an infinite number of primes.
Primes already discovered by use of computers are much bigger than the numbers of ordinary physics, but
we are already reaching the Turing "stopping" problem in finding new ones.
Some people equate in algorithmic information theory and number theory
the stopping problem with Infinity. That point of view of people like G. J. Chaitin
is itself an unproved assumption. So the metamathematics used in the proof itself may be unprovable propositions.
If so, then the proof based on such propositions can't itself be true.
This argument in no way takes away from the greatness of Gödel and his unique genius
as shown by this line of reasoning.

The following is a dissenting view.......2006-10-25

As indicated in two other reviews of mine here, my comprehension of Goedel's work is opposite to the general one. My marking three stars regardless for this book is motivated by his extensive influence, but also by his fair admission later in life that his thesis could amount to hocus-pocus.

Indeed, I see it as one of the prominent mistakes in logical history, and I shall endeavor to explain as best I can. It should suffice to consider his Section 1, an outline of his proposed proof.

Although that section is brief, it already foreshadows an oppressingly complex logical symbolism for statements that in my view can be made much clearer using ordinary language. The symbolism, to be sure, is intended to establish a formal language, whose meaning is to be decided separately. This will be seen one of the problems.

For now, let me give the principal statement Goedel contended to be true but undecidable (neither provable nor disprovable):

"This statement is unprovable."

He symbolized it (p.40) as: "~Bew[R(n);n]". Font limitations made me slightly change it; the tilde "~" means "not", "Bew" is a German abbreviation for "provable", and within brackets "R(n)" says "Statement n" and "n" stands for the full statement.

Goedel proceeds: "...supposing...~Bew[R(n);n] were provable, it would also be correct; but that means...that...~Bew[R(n);n] would hold good, in contradiction to our initial assumption. If, on the contrary, the negation of ~Bew[R(n);n] were provable, then [its provability] would hold good. ~Bew[R(n);n] would thus be provable [in contradiction to the unprovability it states], which again is impossible." (I corrected some errors within brackets.)

So since both ~Bew[R(n);n] and its negation are unprovable, it is undecidable, and Goedel continues (p.41): "...it follows at once that ~Bew[R(n);n] is correct, since...certainly unprovable (because undecidable). So the proposition which is undecidable in the system...turns out to be decided by metamathematical considerations."

"Metamathematical", in excusing the contradiction, designates the above formal system void of assigned meaning, whereas the statement discussed is to have meaning. Not quite a lucid argument. Overlooked, furthermore, is a contradiction using the same reasoning as in the preceding.

Coupled with the preceding finding that ~Bew[R(n);n] CANNOT be proved unprovable (for if so proved, it would be contradicted), can in contradiction be that it CAN be proved unprovable. For if it were instead provable, it would again be contradicted. The statement in question thus becomes a paradox, rather than true, similar to paradoxes like the "liar", mentioned by Goedel (p.40).

He strangely adds to it the footnote: "Every epistemological [paradox] can likewise be used for a similar undecidability proof." The "liar", however, is, like all paradoxes, not a true statement, as required, but one harboring a contradiction. (I deal in my book with, and offer solutions to, paradoxes more fully, including Goedel's resulting one, without naming him.)

There occurs, further, another huge blunder in the alleged proof. The undecidability is said to apply to some of mathematics; in the above formula, ~Bew[R(n);n], the "n" refers to a number, with this justification by Goedel (p.38): "For metamathematical purposes it is naturally immaterial what objects are taken as basic signs, and we propose to use natural numbers for them." Adding (p.39): "Metamathematical concepts and propositions thereby become concepts and propositions concerning natural numbers..."

How so? In one breath he proposes using natural numbers as immaterial signs, and in the next breath the material concerns natural numbers!

The fallaciousness can indeed be made clear by considering our statement, ~Bew[R(n);n], interpreted as "This statement is unprovable." As noted, in ~Bew[R(n);n] the "n", now a number, is to name the whole statement, inside which it is also used in "Statement n..." But whether or not the statement is named by a number, the point is that the name must refer to the intended content of the statement to correspondingly function, not to the usual number possibly represented. Therefore the statement, or anything else similarly used, has nothing to do with numbers, or mathematics generally.

Gödel's proof of the inadequacy of formalism.......2006-10-16

Gödel proves that a formal system containing arithmetic must be incomplete (i.e. incapable of proving all true statements). The proof consists in creating a statement that says "this statement cannot be proved", for then it follows that either this this statement can be proved and we have proved something false, or it cannot be proved but it is still true. In either case our formal system is flawed. This is in a way an instance of the liar paradox, which was of course well know long before, but no-one had expected it to materialise inside a seemingly sensible formal system. Gödel shows that it does by means of his arithmetisation trick that enables the system to speak about itself. All symbols in the system's alphabet is given a unique number. Then all formulas in the system is assigned the following number: the product of all the factors (n:th prime)^(n:th symbol in the formula). By unique prime factorisation one can recreate the formula from its number. Sequences of formulas---proofs in particular---can be coded by the same method. We can now express the relation "x is a proof of y" inside the formal system. This relation takes two arguments: x*, the Gödel number for the sequence of formulas x, and y*, the Gödel number for the formula y. Inside the formal system it is a perfectly well defined and finite problem to decide whether x is a proof of y, as is quite plausible, although Gödel has to work hard with his recursion theory to prove this strictly. Now that we can express "x is a proof of y" we can also express "x is a proof of y(z)", i.e. a relation that takes three arguments: x*, y*, z*, the Gödel numbers for a sequence x of formulas, a formula y with a free variable, and a formula z. Thus we can also express "there exists no x such that x is a proof of y(z)". In particular, we can send in y* for z, and the statement becomes: "there exists no x such that x is a proof of y(y*)". This expression has one free variable, y. Call it F(y). F(y) is a formula in our formal system, so it has a Gödel number, say F*. Now we can formulate the statement "this statement cannot be proved" inside our formal system as follows: "F(F*)"="there exists no x such that x is a proof of F(F*)"="F(F*) cannot be proved". So if our formal system is consistent (i.e. does not prove false things) then we must accept that it cannot prove F(F*), but then F(F*) is true, so our formal system is incomplete.

One of the Best Books You Should Never Read.......2005-07-24

Godel's incompleteness theorem's are without a doubt genious. However, this day in age, no logician actually reads Godel's original work unless they are only interested in the historical aspect of it. Godel himself is not a very good writer. If you want to study Godel's incompleteness theorems there are other books out there that prove his theorems in a much more refined, shorter, and easier fasion.

Unbelievable theorem.......2004-08-04

Reading through the reviews of self-proclaimed math geniuses (see some of the below unhelpful reviews for examples) is hardly edifying, so I feel compelled to lend a hand. Here are a few comments about this publication:

First, the introduction does a poor job in explicating the theory. I suppose it gives you the basic idea, but this is hardly the first account of the theory one should read. Brathwaite does not connect all of the dots, and it will take a long time to figure out how the proof works from his intro, if you can do it all. (And that's not a challenge or insult; it simply isn't that well written.)

Second, forget about wading through Godel's proof on your own. The reviewer who claimed to do so with two years of algebra and a really good dictionary is simply lying. You do not wade through difficult theorems in mathematical logic without the appropriate tools. And the appropriate tools include having done similar but simpler proofs on your own and having a solid background in mathematical logic. Without this background, it doesn't matter whether you have the ability to be a mathematics professor at Princeton or place top five in the Putnam - you simply will not understand the proof in a rigorous manner. By all means, take a look at it to get a general feel for what's going on, but if you want a semi-technical account read Smullyan's "Godel's Incompleteness Theorems."

Third, as one reviewer pointed out, there are multiple errors in this printing of the proof. This makes what was a tall task virtually impossible.

So what did Godel do that was so interesting?
He proved that there were certain arithmetical statements about whole numbers that were not provable but true. (This was important because it shattered the widely held belief that if you stated a problem in mathematics clearly enough you would be able to determine whether it was true or false. Godel showed this isn't always the case. As an aside, simpler mathematical systems have been shown complete; that is to say, they can answer any well formed question.)
So, how can something be true but unprovable?
The sentence Godel constructed said this, more or less: I am not provable. This statement, if true, is not provable. If it is provable it's false, and correct systems (systems that do not prove false statements) cannot prove false statements. Therefore, it must not be provable. But then it's saying something true, and thus it's true but unprovable. Now, I'm simplifying and being sloppy, and you need to know about the difference between mathematical statements and metamathematical statements, but in a nutshell that's the thrust of his first theorem.

The other interesting aspect of his proof is that he constructed a statement that referred to itself indirectly. Russell, in Principia Mathematica - the work that contains the arithmetical system that served as the model for the arithmetical system in Godel's proof - created a "Theory of Types" which did not allow statements to mention themselves. But the sentence "I am not provable" references itself so it would seem that I've erred. But in fact I haven't; I just didn't fully explain how that sentence worked. (I know you were worried, if for just an instant.) Where was I . . . Godel created a sentence which referred to itself indirectly. The sentenced said, "Sentences with such and such characteristics are unprovable." It so happened that a sentence with such characteristics was itself. Thus, it referred to itself, but only indirectly and not in violation of the "Theory of Types."

All of my blathering, I hope, has impressed on you . . .
1) That this proof is worth understanding.
2) That you shouldn't believe anyone who tells you they worked through and understood the proof without having a signficant background in mathematical logic and the history of the proof. If you don't understand certain basic features of Principia Mathematica you're not going to grasp fully his proof.
3) That you should get an introductory account. Nagle's "Godel's Proof" is excellent and easy to understand. Smullyan's "Godel's Incompleteness Theorems" is more difficult, but not impossible and amounts to what would serve as the textbook of a solid mathematical logic course or two at an elite university.
4) That you shouldn't buy this work if you're hoping to work through his proof, unless of course you have the requisite training. Brain power is not enough.

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Huh?
Nice Version of a Classic
Cornerstone of Modern Ethical Thinking
Modern Ethical Thought Begins With This One!
A Seminal Text in Twentieth-Century Philosophy

Principia Ethica
G. E. Moore
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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ASIN: 0521448484

Amazon.com

It took us thousands of years of struggling with science and ethics before we thought to combine the two. While scientific ethics has advanced only gradually, the science of ethics burst into existence in 1903 with the publication of G.E. Moore's Principia Ethica, which did for the study of morality what Whitehead and Russell's Principia Mathematica did for mathematics--clarify old confusions and define terms that are still with us today. Practically overnight, ethicists turned into meta-ethicists, studying their own terms to establish theoretical ground on which to stand before trying to build any prescriptive edifices.

Moore begins by clearing up some of the most widely spread confusions plaguing moral philosophy, such as the naturalistic fallacy of Bentham, Spencer, and others who insisted on a precise, concrete definition of good. According to Moore, we have to settle for an intuitive assessment of goodness, and his arguments are powerfully compelling. Proceeding to define terms and territory that have lasted a century, he revolutionized philosophy and single-handedly altered the course of ethical studies for generations. While Principia Ethica isn't the easiest book to read (a dictionary of philosophy comes in handy for most of us), it is well worth careful study by anyone interested in the difference between right and wrong. --Rob Lightner

Book Description

Principia Ethica is recognized as the definitive starting point for twentieth-century ethical theory. The text is reprinted here with the previously unpublished preface Moore wrote for a planned, but never completed, second edition. Though unfinished, it sets out clearly Moore's second thoughts about his own work. The volume also includes two important pieces from his later ethical writings, "Free Will" and "The Conception of Intrinsic Value," and a new introduction by Thomas Baldwin.

Customer Reviews:

Huh?.......2007-04-19

this book is a staple among the clever clogs chattering classes, even though he mis-spells the word "shown" at least a hundred times. The prose is terrible and I had no idea what he was talking about.

Verdict: Ivory tower rubbish.

Nice Version of a Classic.......2006-08-02

Originally published in 1903, Principia Ethica by G.E. Moore is a classic of twentieth century philosophy. Aside from being an influential ethical commentator the author is also one of the founding fathers of the modern analytic tradition.

In Principia Ethica Moore consider some of the broadest and most vexing ethical questions. What is the good? What things or actions are good? And how should we live? The book provides a detailed discussion of Moore's so called naturalistic fallacy (the challenge of defining good in any meaningful way).

A brief review of the historic context of a work is often helpful in understanding its focus and objective. In the present case Moore is reacting too the broad speculative philosophy popular at the outset of the last century (stemming in significant part from Hegel and his followers). In regard to background reading the first of Scott Soames' excellent 2-volume Philosophical Analysis in the Twentieth Century has a couple of excellent chapters on Moore that may be helpful.

Much early analytic philosophy has been challenged. Despite their shortcomings, however, we must admire greats like Moore, Russell and Wittgenstein and their attempts to develop comprehensive philosophical models. In our present era of specialization these types of holistic worldviews are extremely rare. Although there is much of worth is Moore's work, perhaps his most his most enduring observation is that philosophic constructs do not trump common sense pre-philosophic views, e.g. the existence of other minds. I agree with Moore that this is an essential consideration to keep in mind when considering some of the more counter-intuitive philosophical theories

Overall, this is a must read for any student. This version is solid, however, the older style print is a minor drawback.

Cornerstone of Modern Ethical Thinking.......2005-12-16

`Principia Ethica' by the very influential Cambridge philosopher, G. E. Moore may easily be one of the very few philosophical works in English written in the 20th century that is widely known outside circles of professional philosophers. The only other works I suspect can fall into this category are Russell and Whitehead's `Principia Mathematica' and Wittgenstein's `Tractatus Logico-Philosophicus' and `Philosophical Investigations'. Oddly enough these last two works were originally written in German; however their influence has been based almost entirely in the English speaking world of intellect.

Moore was very fond of high faultin Latin names for books. This volume was not named after Russell and Whitehead's work, which was published around 1918, but after Isaac Newton's `Principia Mathematica'. Talk about hubris! Being a major influence on Wittgenstein in his early days at Cambridge, he was also the one who suggested the English name for Wittgenstein's first major philosophical work.

What is so nice about approaching this work is that its primary thesis can be boiled down to a relatively simple statement. Moore is claiming that statements about good and bad cannot be reduced to statements about facts in the physical world. Those philosophers who claim that you can do this are committing `the naturalistic fallacy'

The primary object of Moore's argument is the eminent 19th century British philosopher, John Stewart Mill, whose pamphlet, `Utilitarianism' is one of the four or five most important writings on ethical doctrines, along with Kant's `Groundwork...', Thomas Hobbes `Leviathan', and this work by Moore. Mill's doctrine, refining a cruder statement of Utilitarianism by his mentor, Jeremy Bentham, is that all good must be based on observable pleasure. If there is no way that an action can be traced to the pleasure, it cannot be considered `good'. To be sure, Mill, being an exceptionally smart man, put a lot more into his argument than this statement, but you get the idea from this.

Before Moore, Mill's biggest difficulty was the classic dilemma in ethics between `the right and the good'. In many ways, this is the ethical analogue of the dual nature of light, where sometimes it exhibits wave properties and sometimes it exhibits particle behavior. Before Mill, the greatest proponent of a theory of right and wrong was Immanual Kant, who outlined his ideas in his `Groundwork on the Metaphysics of Morals' and laid out the categorical imperative. Looking at Mills' and Kants' basic principles, you would hardly know they were talking about the same thing, as Mill reduces everything to pleasure while Kant reduces everything to the `good will'.

Moore's writings bring him down squarely in the camp opposing Mill, however, his reasoning may not be too familiar to Kant and Hobbes. Moore was one of the founding fathers of what was to become the `ordinary language' movement in Anglo-American philosophy, which was ultimately to be inspired primarily by the later writings of Ludwig Wittgenstein of Cambridge and John Austin of Oxford. Aside from this `Principia Ethica', Moore's most famous philosophical argument was his defense of common sense when he demonstrated the existence of everyday objects by pointing to first his right fist then his left fist as two examples of real physical objects. One can't appreciate the power of this argument until you try it out in a philosophical argument as I once did in a friend's introductory philosophy class.

Moore's naturalistic fallacy says that all statements about good and bad and right and wrong must, when they are reduced to their basic meaning, involve some irreducible statement(s) about duties and right and wrong. There have been philosophers who build whole careers on extrapolating this analysis to fill several books, as in the case of Oxford's R. M. Hare, writing in mid-century under the influence of Austin and Wittgenstein.

If Moore's argument has any problem at all, it is in having been trivialized by so many writers taking the same tact by turning doctrines they don't like into `fallacies'. Simply saying something is a fallacy may have enormous rhetorical impact, but it has no substance to it. Being accused of committing the `ad hominom' fallacy of attacking the person rather than the position can really destroy a position, since this is so universally accepted as a mistake. On the other hand, very smart people have claimed that all questions of value are reducible to questions of pleasure.

Therefore, Moore must put up a fairly detailed argument to show why Utilitarianism, for one, is wrongheaded because it violates this fallacy, thereby showing that it is, indeed a fallacy.

This is a difficult book to read. It is certainly more difficult to read than the average political polemic, but not quite as difficult as Wittgenstein's principle works or of works by European phenomenologists and existentialists after Nietzsche and Kierkegard.

But it is well worth the effort!

Modern Ethical Thought Begins With This One!.......2005-04-04

George Edward Moore has the unfortunate privilege of having spawned one of the most uninformedly invoked ideas of all time - the naturalistic fallacy. Like Thomas Kuhn's "paradigm shift," the naturalistic fallacy is tirelessly invoked by writers to mean any number of things, not many of which agree with the author's original usage. That is perhaps one reason to read G.E. Moore's Principia Ethica. Another, of course, is that it is a classic of twentieth century ethics!

Most of the chapters, of course, deal with Moore's idea about the naturalistic fallacy. Contra those numerous authors that use it to mean simply the fallacy of supposing what is natural to be de facto good (that is one manifestation of it, but not it), the naturalistic fallacy has a much broader meaning. The fallacy, in Moore's view, is to explain what is "The Good" in any way other than to say "it is The Good," - to suppose, that is, that "The Good" is definable in any way. To Moore, "The Good" is simply "The Good" because it is good and that is all we can say. Any attempt to equate "The Good" with something else - pleasure, a metaphysical entity, what is natural, etc. - is a manifestation of the naturalistic fallacy.

Moore uses the first chapter to explain why the naturalistic fallacy is a fallacy. The answer is similar to Hume's is/ought gap. That is that any attempt to say what "The Good" is - i.e., the Good is what causes pleasure; The Good is what exists in the natural order - is nothing other than a criterion for recognizing things that are good; what explanations of this sort are not are actual definitions of the good. (In other words, saying that things which give pleasure tend to be good is much different than saying that "The Good" is constituted by what gives pleasure and that alone.) Another question that the above definitions can always be met with is WHY pleasure (nature, etc.) are good? In which case, the only real answer - owning to "The Good's" ineffability, is "They just are; it is obvious."

The next few chapters (the bulk of the book) is spent trying to prove a negative case - that most ethical theories en vogue suffer from the naturalistic fallacy. Moore spends most of his time on utilitarianism but devotes a good amount also to metaphyiscal theories of the good, also.

After the negative cases are made (I found some more convincing than others), he gives a positive case. Here is where Moore is suprising. While he argues that "Good" and "Bad" in regards to ends are factual matters, he is something of a utilitarian in practical ethics - meaning that he sees right conduct as judged by the consequences of the conduct in question. He is also a certain type of relativist who allows that what is right conduct often varies from time to time and situation to situation, as an act performed at one time in one scenario may well have different consequences as the same act performed in a slightly different situation in another time.

All in all, I found this book exciting to read. Moore is a clear and engaging writer, and with a few exceptions of repitition, the book was easy and fun to digest. I am giving it four stars despite the fact that I disagree with much of it. While I am prepared to say, with Moore, that "Good" may well be essentially indefinable, I did not see him do anything to try and prove that "Good" was a property of the object, rather than a sentiment of the speaker. And if that is so, then we've no reason to suppose "Good" and "Bad" to be ethical facts of the matter, as opposed to sentiments that different speakers with different intuitions are expressing.

Be that as it may, everyone concerned with ethics should read this book. Moore argues strongly for recognition of the naturalistic fallacy and what it means for ethics. Whether you agree or disagree, modern ethics is often a response to this guy.

A Seminal Text in Twentieth-Century Philosophy.......2004-02-21

Moore's Principia Ethica is a central text in twentieth-century meta-ethics. According to the familiar history of the subject, the story of much of twentieth-century meta-ethics can be understood as a series of reactions to this book. In this book Moore argues for non-naturalistic intuitionism. He argues that moral properties are an irreducible part of reality, and that they are sui generis. And he argues that we can acquire knowledge of these sui generis moral properties only through intuition.

The first chapter includes Moore's famous Open Question Argument, his argument that intrinsic goodness is a simple, unanalyzable, non-natural property. There appear to be two strands of the OQA; both of them appeal to our linguistic intuitions. The first focuses on our intuitions about whether certain claims about intrinsic goodness are tautological. Borrowing Moore's own example, suppose someone tries to define 'good' as 'what is pleasant'. All competent users of the language can see that this definition must fail. How? They simply need to ask themselves if "the good is what is pleasant" has the same meaning as "the pleasant is what is pleasant," for these two sentences would be synonymous if 'good' could be correctly defined 'what is pleasant.' And, Moore claims, these sentences clearly aren't synonymous: the claim that "the good is what is pleasant" is not a tautology like "the pleasant is pleasant." This shows that 'good' and 'what is pleasant' have different meanings. Furthermore, Moore argues that thinking about other examples will show that, in principle, we could develop that a structurally similar argument against any other attempted definition of 'good'.

The second strand of the argument draws on our intuitions about what is and is not an open question. If 'what is pleasant' is a correct definition of 'good', then the following should not be an open question: Is what is pleasant good? For, if the proposed definition is correct, then it is true by definition that this what is pleasant is good. But, Moore asserts, competent users of the language don't think it's true by definition that what is pleasant is good; they do, and should, regard this question as an open one. It might be true that what is pleasant is good--but, importantly, it is not true by definition. Again, Moore argues that a similar argument will show that any other attempted definition of 'good' fails.

The conclusions Moore draws from the OQA are that the term 'good' is indefinable, and that goodness is a simple and unanalyzable property. It is somewhat unclear how Moore thinks he can draw any metaphysical conclusion from this argument, but he seems to have reasoned in the following way. If goodness were identical to some natural or metaphysical property, it would be definable in terms of some natural or metaphysical predicate. The OQA shows that it is not definable in this way, and so it shows that goodness is not identical to a property of either of these types. Moore also provides a label for the error made by those who don't understand the nature of intrinsic goodness: they commit "the naturalistic fallacy." The naturalistic fallacy is committed by anyone who identifies intrinsic goodness with some other property, and Moore claims that nearly all previous ethicists have committed this fallacy.

The Preface involves a very brief sketch of Moore's epistemological views, views that he apparently thinks follow from his conclusions about the nature of intrinsic goodness. Moore claims that knowledge of intrinsic goodness can be acquired only through intuitions. There is no non-intuitional evidence for propositions about the intrinsic goodness of things, and they cannot be deduced from any other propositions. How, then, do we come to know these things? We think very carefully about them, ensure that we don't confuse these propositions with other, and then we have an intuition of the proposition's truth or we don't.

The final two chapters are concerned with issues in normative ethics. The substantive moral theory he defends is a form of act-consequentialism. According to Moore, in all situations, the action one ought to perform is the action that will result in the greatest net amount of intrinsic goodness in the world. In the fifth chapter, he discusses what practical conclusions one can draw from this account of right action. He argues for a fairly extreme form of moral conservatism according to which we have good reason to act on the principles constituting conventional morality almost all the time. For we simply don't know enough about the consequences of the possible actions available to us to discover which of them will lead to the greatest amount of net intrinsic goodness. Given our ignorance of these matters, what we ought to do is follow most of the common moral rules in our community. (Moore does allow for exceptions in a limited number of cases, however.)

The sixth and final chapter includes Moore's discussion of which things are intrinsically good. He argues that two things, aesthetic enjoyment and personal affection, are the most intrinsically good of intrinsically good things.

For the most part, this isn't an exciting book. It's filled with the sort of philosophizing one expects from Moore: close reading, lots of subtle distinctions, and patient and careful analysis. His work is slow and painstaking--that's a given. And, to be honest, this book is occasionally dull. But Moore's scrupulous attention to detail doesn't preclude insight and interesting ideas. Nor does it bury them in pages and pages of tedious nit-picking and quibbling.

For students of meta-ethics and anyone interested in the history of twentieth-century ethical thought, this is mandatory reading.

Concerning the revised edition of Principia, edited by Thomas Baldwin. The buyer should know that the text of Principia is unedited in this edition. However, there are reasons to prefer this edition to cheaper alternatives. First, and most importantly, this edition includes the so-called "Preface to the Second Edition," which consists of Moore's later misgivings about the first chapter of Principia. (Moore never published this preface in his lifetime.) He doesn't repudiate his substantial conclusions there, but he raises issues about the statement of those conclusions and the arguments he provided for them. If you're interested in serious study of Principia, knowledge of this preface is crucially important. Second, this edition includes Moore's paper "The Conception of Intrinsic Value," which helps to clarify his views about the nature of intrinsic goodness. Third, Baldwin includes a helpful editor's introduction for this edition.

Average customer rating:

ludicrously quixotic work

A Hallmark in the History of Mathematics and Philosophy.

Principia

If you don't know know this book then you don't need it

Mostly of historical interest

Principia Mathematica to *56 (Cambridge Mathematical Library)
Alfred North Whitehead , and Bertrand Russell
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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ASIN: 0521626064

Amazon.com

Could it be true that Whitehead and Russell's Principia Mathematica is the most influential book written in the 20th century? Ask any mathematician or philosopher--or anyone who understands the impact these fields have had on modern thinking--and you'll get a short answer: yes. Their goal, to set mathematics on a firm logical foundation, was revolutionary, and their tools and rigor continue to influence modern professionals. Using Peano's symbolic logic, they formalized axioms and produced theorems (including the famous "1 + 1 = 2") in orderings, continuous functions, and other areas of mathematics.

Although the Principia is far from comprehensive, Whitehead and Russell's method and program captivate their readers. The audacity to hope to formalize all of mathematics logically was inspirational and helped to give great boosts to math and logical philosophy. Though Gödel proved in 1931 that any such program is doomed to incompleteness, the tools found in and developed from the three volumes helped build the atomic bomb and the Internet. It may not be summer vacation reading (for most), but Principia Mathematica will reward the dedicated student with a deeper understanding of how we got here. --Rob Lightner

Book Description

The great three-volume Principia Mathematica (CUP 1927) is deservedly the most famous work ever written on the foundations of mathematics. Its aim is to deduce all the fundamental propositions of logic and mathematics from a small number of logical premises and primitive ideas, establishing that mathematics is a development of logic. This abridged text of Volume I contains the material that is most relevant to an introductory study of logic and the philosophy of mathematics (more advanced students will of course wish to refer to the complete edition). It contains the whole of the preliminary sections (which present the authors' justification of the philosophical standpoint adopted at the outset of their work); the whole of Part I (in which the logical properties of propositions, propositional functions, classes and relations are established); section A of Part II (dealing with unit classes and couples); and Appendices A and C (which give further developments of the argument on the theory of deduction and truth functions).

Customer Reviews:

ludicrously quixotic work.......2005-03-22

I have not read this book. I tried, having been fascinated by logic and mathematics since high school, but it has absolutely nothing to offer most people. in fact I find it hard to believe anyone has ever read this book. The 4 and 5 star reviews on this page should be taken as evidence there are some people out there with very different taste from mine, and I bet yours. In fact I have difficulty believing they are serious.

I think only a fanatic could enjoy reading this book, certainly not a budding mathematician. If you are attracted by a book that proves 1+1 = 2 somewhere after 100 pages, this is the book for you!

I admit I have been surprized before at what some people find interesting, but the idea that anyone would pay 5 or 6 hundred dollars for the set! the publishers seem to me to be sniffing glue. (I have a PhD in mathematics, a mathematical library costing thousands of dollars, and tried to read this work at Harvard as a young math student.)

To call this book influential, is to me really ridiculous, since I suspect few people have even looked at it in the last half of the 20th century, nor would want to do so at any length, in my opinion.

But don't take my word for it, go to your scientific library and check it out for yourself. You might like it, but I seriously doubt it. I did not intend to review this book, but some of the reviews here really defy belief. I could not let them pass without comment.

One must assume those reviewers here are serious who praise it, but I suggest almost no mathematics student need give it more than a passing look. The review that stated something like "if you do not already know you want this book, then you do not" is pretty accurate.

OK, a quick re reading of reviews here shows many of them say truthfully that this book is only appropriate for a very small group of readers. However I would suggest that group does not even include most mathematicians. The ones who like it are apparently philosophers, and some are the sort who resort to calling people stupid who disagree with them.

A Hallmark in the History of Mathematics and Philosophy........2004-07-22

Much nonsense has been said on the subject of the importance of Principia Mathematica by people ignorant of the history of mathematics and logic. Principia Mathematica together with Frege's Grundgesetze der Arithmetik is the book which gives birth to modern logic. It is absurd to assume that Russell and Whitehead intended their axiomatization of mathematics as a guide to learn the subject, as one reviewer thinks, in fact what they tried to show was that the whole of mathematics could be deduced from a small stock of premises and inference rules and using only notions of first order logic and set theory. In doing this they were following a trend in mathematical thought in the late XIX century, that of introducing more rigour to the subject, they intended to do this by demonstrating that the derivation of mathematics needed only logic (think of Weierstrass, Dedekind, Cantor, Frege). From a philosophical standpoint they also did it to rebut the intuitionist views of Kant and Poincare as well as certain opinions regarding truth coming from British Idealism (think of Bradley). Of course there are much more rigurous treatises on logic, but they would have been impossible without PM because PM was the first thorough treatment of this subject-matter and, indeed, the first book to use the modern day notation. As another reviewer pointed out, Godel's proof would've been impossible without Principia; someone first needed to show that you could reduce mathematics to logic to a great extent (Russell and Whitehead were aware that their treatment used certain axioms unprovable within the system, like the axiom of infinity, but were hopeful a solution would be found, Godel found it, it was a negative solution, there could be no complete system PM like). This book together with Frege's gave birth to modern logic, it gave a tremendous boost to research in set theory, it influenced the presentation of modern mathematics to the extent that every student has to learn about sets at the beginning of a mathematics course, it showed also the scope of the deductive powers of logic and axiomatic systems which made possible the revolution in computers and AI. It developed an influential and responsive philosophy of mathematics, perhaps the most influential of the XX century. In it Russell's superb theory of descriptions, a cornerstone in logic and philosophy, is applied with success. This theory is tremendously important in logic through its use of quantification to break up much more complex expressions revealing their true logical form. In philosophy it provided a theory which would prove immensely useful and important in epistemology, metaphysics and the philosophy of language. Russell's paradox ( regarding those sets of sets which are not members of themselves) is disposed through ramified type-theory, now obsolete in logic (though not in computer science), because, thanks to it, other ways to avoid the paradox were developed, think of Zermelo-Fraenkl or Ramsey's simple type theory. Carnap, Hilbert, Weiner, Ramsey, Quine, Wittgenstein, Turing, Tarski, Godel etc were, as thinkers, tremendously influenced by it. In short, this work is one of the greatest achievements in the history of thought, its importance for mathematics, logic, philosophy (linguistics also) and computer science is first rate, suffice to say that none of these studies would be as advanced as they are now, or as complex, or in the same direction were it not for Russell and Whitehead's groundbreaking scientific work. Of course, like Newton's Philosophia Naturalis Principia Mathematica it is now, because the subjects it initiated are today tremendously advanced, mostly of historical interest, however, for the philosophers at least, Russell's introduction still holds great philosophical interest and rigourous arguments helpful in the contemporary debate in the philosophy of mathematics. For more details, historical background and a well-documented account check out Ivor Grattan Guiness's great works on the history of mathematics, logic and set theory. For an appropiate and easy-going understanding of the scope and purpose of this work read Russell's brilliant "The Principles of Mathematics", his "Introduction to Mathematical Philosophy", or Frank Ramsey's papers on the "Foundations of Mathematics". Even easier is Penrose's account of it in his "The Emperor's New Mind" or his "Shadows of the Mind." If you want to see the direct influence of Russell and Whitehead's work check the works of Quine, Wittgenstein, Godel, Tarski or some of the papers of Turing in Mind (some are available online); van Heijenoort's "From Frege to Godel" is a superb sourcebook on papers which detail the development of mathematical logic.

Considering some statements from mathematicians arguing for the thesis of the irrelevance of the book based on the fact that probably no mathematician of notice has read the work in the last fifty or so years shows the misunderstandings to which people who dislike history are prone, and shows some contempt for the history of mathematics and logic. I am reminded of the comment I heard once, that the theories of the Milesians (all is water, etc) are absurd, a view which I am convinced would only be put forward by someone wholly indifferent to historical context, and who does not consider those theories as the first step towards the current scientific worldview. It is like saying that Bacon's methodology of science is irrelevant because we now have a deeper understanding of how science works, or even like saying that the study of the work of Adam Smith is worthless since for free-market economies we can now consider Hayek's or Milton Friedman's work. This analogy will, hopefully, show the preposterousness of views which do not consider the historical context of such major works. Indeed one does not need to review the proofs in PM (poor by modern standards) that 1 plus 1 equals 2, to understand the important place of this book in contemporary thought. It is only necessary to glance at any contemporary book on logic or set theory, most of the ideas there, the notation, and most developments in both disciplines in the past fifty or so years. Developments which are in debt of the work done by Zermelo, Hilbert, Quine, Turing, Weiner, Tarski, Godel etc, who, as anyone who has studied a bit of their works (as in authored by them) will know, owe their own ideas, developments and work to the study of Principia Mathematica during the first fifty years of the twentieth century. Indeed I would be the first to suggest that no one should read this book from cover to cover if one wants to learn logic (even Russell used to joke he only knew of a couple of poles who had read it and had then perished in WWII), just as I wouldn't suggest anyone interested in contemporary calculus and advanced mathematics to read Newton's Principia, or anyone interested in Set Theory to read Cantor's papers, or again, anyone interested in Einstein's special relativity to read his 1905 papers. In fact I cannot believe anyone would have to stress this point, but I am forced to on account of the various misunderstandings I see here, and by mathematicians, which one would presume would be the most rigurous of thinkers. These days the value of the book is mostly historical (with the introduction, mostly chapters II and III, having philosophical value), but, and I must once again stress this strongly, its tremendously influential and important place in the DEVELOPMENT of logic and set theory (and metatheory with the discovery of Russell's paradox) cannot be doubted, it can indeed be traced, if one takes the time to do so, to the various seminal thinkers it influenced strongly. Its value should be doubted even less by those academics ignorant of the history of their own disciplines not because they disagree with me (I could hardly be that vain) but rather because their misunderstandings are on par with disminishing Darwin's importance to contemporary biology on the grounds that his works are not cited in the bibliography of the most important papers written on the subject nowadays.

Principia.......2003-07-31

I decided to write a review, because, when reading the existing ones,- I realized their incorrectness. Leaving out the "Customer from Christchurch New Zealand", the rest shows an evident shallowness of mind. The reader "La-la land" utilizes an enormous mass of epithets discrediting Russell and Whitehead, which could be valuable in a form, but instead,- he shows a stupid prejudice that must have learned in his Mathematical-logic "polytechnic" course. I will only refute his last thought( which is the base of his "thesis"), because the others refute themselves. He presents Russell as a "Fruitless Mathematician", and even more stupid, compares him with Hilbert, saying: " at least he proved himself worthy.....". Throughout all Mathematics history we have individuals with enormous logic-constructive aptitudes, who although creating fundamentals results, were unable to understand their significance. Two perfect examples are Newton and Leibniz, both creators of the "infinitesimal calculus". One went on to construct the modern mechanistic view of physics in his "Principia". The other, with a much more profound understanding of logic, a superficial "monadic-substantial" and teleological ontology. Newtonian physics was a major episode in modern science, and Leibniz "subject-predicate" logic is the first glance at mathematical-logic.But their incorrect understanding of the infinitesimal calculus made them see, in it, the proof of an omnipotent god: they both conceived a universe with its first cause as god, and the human aptitude is, within it, merely an "algorithmic" one, which could never fully calculate god's creation. Hilbert, also providing fundamental results in constructive knowledge, went on to expose a somewhat "Hegelian" conception of mathematics, giving an almost silly definition of numbers. Both of this errors cause enormous damage, which I don't have space to describe now. Russell's "Principia Mathematica", although written with the wrong "motivation"( that is: to reduce the whole of mathematics into axiomatic form, finding the "universal method"), achieved unquestionable logic-mathematical results: The most valuable and original, the "theory of descriptions". in an abridged explanation, these theory comprehends the next: "algorithmic" function in logic and mathematics. when you say, " this is black", the theory of descriptions shows that you are only saying something about "this", which is a subject-variable(x), and black is an element-predicate, calculable within the conjunct "this". The theory permits mathematical-logic understand algorithmic functions, and is, also, what makes possible via your computer processor to read codified information. The result is more than a "fruit". it gives you the possibility of grasping that, like any other mathematical fruit, men is able of creating it,- and of reading it(calculate it). these means: Mathematical creations are only valuable as a source of human power, not as mystic ontological formulae,- that stupid motivation in all pseudo "Mathematicians".
In terms of actuality, the axiomatic system, the method, has been perfected, simplified, and transcended. If I had to recommend some books on the matter, I would say Tarski's: "Introduction to logic and to the methodology of the deductive sciences", Patrick Suppes:"axiomatic set theory", continued by the reading of the: "Gödel proofs" by Raymond Smullyan, some other text dealing whith "boolean algebra" such as: "logic as algebra" by Halmos. This would give any self-educated person, the basic models he needs to comprehend math-logic, the "method" with which he can possibly contribute to this "powerful trend of modern thought" as described by tarski. Remember that Russell and whitehead say in the introduction that they not claim having the most perfect axiomatic reduction, only that the one presented was enough to reduce mathematics into that form, which was, until godel, true, or at least "thought possible"(completely). Is important to undersatnd that "principia mathematica" made "possible" the incompleteness proofs of Godel: his original paper was named "on formally undecidable propositions of principia mathematica and related systems"(see dover edition), and although he uses mostly the axioms of peano in his system, if someone as Russel had not attempted successfully such axiomatic construction of math, godel would have never found or seen the incompleteness of arithmetic's. Something similar could be said of the later notions of completeness of first order logic, metamathematics, etc. The few works (few only in number) independent from principia may be the ones of: 1) the polish masters: Lukasiewicz, Lesniewski, and the last king Tarski. 2) the forgotten Richard Martin's and Rudolf Carnap's logic-syntaxic-semantic conception of math-logic. The rest walked, continued walking the path of principia. Individual example: Quine. ...

If you don't know know this book then you don't need it.......2003-07-22

Let me try to give a balanced review.

First this is a monumental work and one of the most influential works of the 20th century. I am not giving it five stars: this book earned them. With that said I don't think is the most influential book of the 20th century because such a book doesn't exist. In my opinion that kind of debate is totally misleading.

However the five stars do not suggest that you should buy this book. With the exception of libraries and scholars specializing in Russell or related subjects, I can't see anybody else spending [this amount] on a copy of this work. That is unless they like to collect books. For a math or philosophy student the paperback copy to *56 is all you need.

Unless you are a mathematician, a logician or a philosopher with a strong background in logic and philosophy of mathematics and aware of the issues surrounding the problems in the foundations of mathematics at the beginning of the 20th century then you are not going to benefit from STUDYING this book. The emphasis in studying is important because this book needs to be studied not just read like some reviewers may suggest.

If you are not an expert in this area and you want to learn about the subject then you may want to start with Bertrand Russell's "Introduction to Mathematical Philosophy". It summarizes the major points of this work for the layman and is Russell at its best (he won a Nobel prize mostly due to this book). Read it with a critical mind and then you can continue reading Quine, Putnam, Brower, Heyting and the rest. You can get a good bibliography from Benacerraf and Putnam's "Philosophy of Mathematics".

Finally if you are a mathematician, a logician or a philosopher you already know about this book and you don't need this review. Moreover you know you can borrow a copy from the university library for study...that is unless you like to collect books.

Mostly of historical interest.......2002-10-19

The notation of PM is hard to read by anyone who learned logic post 1960, say. The typesetting is archaic. Hundreds of theorems are proved, but it is not clear where
they all lead. Russell and Whitehead are guilty of a number of major philosophical confusions, such as use and mention, between meta- and object language, and their confused notion of "propositional function." Their choice of axioms can be much improved upon. The PM theory of types and orders is a complicated horror; Chwistek, Ramsey, and others later showed that it could be radically simplified. R & W think they can substitute the intensional for the extensional, and ultimately define sets and relations in logical terms. PM does not have a clue about model theory or metatheory. There is no hint of proofs of consistency, completeness, categoricity, and Loewenheim-Skolem. In this sense, the fathers of modern logic are Skolem, Goedel, Tarski, and Church. And Goedel did indeed prove that there must exist mathematical truths that cannot be proved true using the axioms of PM, or any other finite set of axioms.

But this is still one of the greatest works of mathematics and philosophy of all time. The long prose introduction is a philosophical masterpiece. The collaboration between Russell and Whitehead may be the greatest scientific collaboration in British history. Whitehead, who was trained as a mathematician, went on to become one of the shrewder philosophers of the 20th century, and supervised Quine's PhD thesis. PM's treatment of the algebra of relations (a brilliant generalisation of Boolean algebra that
has not received the study it deserves) is perhaps the most thorough ever.

Book Description

Newton's Philosophiae Naturalis Principia Mathematica provides a coherent and deductive presentation of his discovery of the universal law of gravitation. It is very much more than a demonstration that 'to us it is enough that gravity really does exist and act according to the laws which we have explained and abundantly serves to account for all the motions of the celestial bodies and the sea'. It is important to us as a model of all mathematical physics. Representing a decade's work from a distinguished physicist, this is the first comprehensive analysis of Newton's Principia without recourse to secondary sources. Professor Chandrasekhar analyses some 150 propositions which form a direct chain leading to Newton's formulation of his universal law of gravitation. In each case, Newton's proofs are arranged in a linear sequence of equations and arguments, avoiding the need to unravel the necessarily convoluted style of Newton's connected prose. In almost every case, a modern version of the proofs is given to bring into sharp focus the beauty, clarity, and breath-taking economy of Newton's methods. Subrahmanyan Chandrasekhar is one of the most reknowned scientists of the twentieth century, whose career spanned over 60 years. Born in India, educated at the University of Cambridge in England, he served as Emeritus Morton D. Hull Distinguished Service Professor of Theoretical Astrophysics at the University of Chicago, where he has was based from 1937 until his death in 1996. His early research into the evolution of stars is now a cornerstone of modern astrophysics, and earned him the Nobel Prize for Physics in 1983. Later work into gravitational interactions between stars, the properties of fluids, magnetic fields, equilibrium ellipsoids, and black holes has earned him awards throughout the world, including the Gold Medal from the Royal Astronomical Society in London (1953), the National Medal of Science in the United States (1966), and the Copley Medal from the Royal Society (1984). His many publications include Radiative transfer (1950), Hydrodynamic and hydromagnetic stability (1961), and The mathematical theory of black holes (1983), each being praised for its breadth and clarity. Newton's Principia for the common reader is the result of Professor Chandrasekhar's profound admiration for a scientist whose work he believed is unsurpassed, and unsurpassable.

Customer Reviews:

i'm ordering this book having looked through it.......2007-10-07

perhaps the title "...for the common reader" is the issue here. "the common reader familiar with calculus", perhaps...

there's simply no way anyone without a very solid grounding in mathematics can read this book and understand it. we are talking about the laws of motion & gravity here, etc.

i compared this (a bit dogeared) copy of a book sided by side with a modern copy of principa in a bookshop, and for anyone wishing to tackle this monumentally important work, i cannot think of a better pairing. a modern copy of newton's principia and chandrasekhar's great work for those who wish to see a thorough explanation and working of the equations.

it's like a lot of things; be realistic with your expectations.
someone who is not very competent in mathematics is not going to be able to ever fully comprehend the contents of this book, misleading title notwithstanding.

perhaps the person that gave this book one star would like to let us know what scientific books he has awarded five stars to if he thinks so lowly of this one?

i say all this, because i'm currently self-studying algebra to be able to self-study calculus next year, just so i can try and understand some of this all-important book.

so don't knock the book, just keep putting the time in & struggling (and it's a struggle, alright) with the mathematics that unlock its secrets.

Before you slag this book off, hold on a minute.......2005-01-18

This book was written by the Indian-American Nobel Laureate who proved that the upper limit of white dwarf stars are incapable of being over 1.2 solar masses. Now Chandra(the author of this book), who was amongst the most meticulous of theorists and who worked with bigwigs like Dirac, Bethe, Fermi and Von Neumann amongst the most luminous, wrote this massive treatise on Newton's Principia. This is chandra's take on Newton's work. Don't think its a light read - It isn't. You cannot take it with you to starbucks sipping your cappucino and browse the work. You'll need to be at a table with a straightback chair and concentrate intensely. If you know Chandra's work, then you will know that chandra always said just about what was required and said it in very beautiful English. His English probably has the most beautifully constructed sentences ever among scientific works. So essentially this is about a 20th century giant interpreting the work of THE giant of all time. This is NOT a verbatim reproduction in English of the original latin publication. If you can get this book cheap on e-bay, buy it because it is worth it. It is expensive for a reason. Its beautifully written and bound very beautifully in a red jacket with Newton's bust and handwriting on the jacket. If you bought it, the red cover is attractive enough to make it stand out of your living room book shelf. Most importantly, Chandra tackles each aspect of Newton's principia in a most profoundly original manner. GET IT if you can afford it and if you can't, try a used book place. But get it anyway.

Not What I expected.......2002-10-20

I expected this to be a walkthrough for people like myself who have a knowledge of physics but are far from being experts and are interested in reading the classics of science. This is a guide for the modern Professor of Physics, not a guide for the common reader as it says. If I had known that I wouldn't have bought it. I get the impression that there is certainly a demand for such a walkthrough. I thought this would be it.
A BIG disapointment!

Uncommon price for a book intended for common reader.......2001-06-30

I have not read this book, but would love too. But the price is just too high for a book that is intended for the common reader. It is unaffordable for the common reader.

(NOTE: My stars rating is meaningless because I have not read the book.)

Average customer rating:

The Story of Nothing Minus Everything

I see the fnords

true, false, and meaningless... in some way...

You'll laugh, you'll cry, you might begin to understand

The ULTIMATE post-modern religious text

Principia Discordia, Or, How I Found Goddess and What I Did to Her When I Found Her: The Magnum Opiate of Malaclypse the Younger
Malaclypse , Robert Anton Wilson , and Kerry W. Thornley
Manufacturer: Loompanics Unlimited
ProductGroup: Book
Binding: Paperback

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Principia Discordia: Or How I Found Goddess, and What I Did to Her When I Found Her

ASIN: 1559500409

Customer Reviews:

The Story of Nothing Minus Everything.......2007-08-16

I have read every book ever written except for this one and it is my favorite. I'm not sure how this happened, but it did. As soon as I read it I'll retract this review.

I see the fnords.......2007-03-01

Satire and seriousness, parody and philosophy, reverence and irreverence in approximately equal doses. The only "religion" upon which I am willing to hang my hat. Your mileage may vary. Hail Eris!

true, false, and meaningless... in some way..........2006-08-31

Awesome book, but ya gotta read it at least 5 times to truly understand it... heck, I just ordered my 2nd copy!
gobble gobble, greyfaces!
Saint Virotik, K.S.C., P.O.E.E., Tormenter of Overly-Inebriated Greyfaces

You'll laugh, you'll cry, you might begin to understand.......2006-08-05

This is the most unique religious text I've ever read. A lot of people will ask if it's a joke or if it's serious. If you understand even the most basic points made in this text you will know that it's both.

On the side of this being a really thoughtful religious/philosophicval text, I understood that war and conflict exist because people want to impose order. If everyone accepted chaos, there would be no war.

On the side of this being a big joke, I laughed a lot while reading this, especially at the 3rd commandment. There is some really great absurdist jokes, and hilarious stories.

What you think of this book will depend entirely on how you read it. I think it would be a great gift for anyone with an interest in religion or stoner humor. You never know, they might learn something.

The ULTIMATE post-modern religious text.......2006-01-17

Simultaneously operating as a religion and a parody of religion, the Principia Discordia has acquired a cult following which I was surprised to discover is well-deserved.

The Principia's juxtaposition of seemingly incompatible elements encourages confusion on the part of the reader. For instance, religious anecdotes and revelations are absurd to the point of idiocy; the constant didacticism intentionally contradicts itself; serious concepts are riddled with toilet humor. As a whole, the text seems like a cleverly constructed joke, yet it does contain moments of compelling insight.

In short, I'm still not sure whether to take any of the Principia seriously. Even if it is possible to take seriously, it is impossible to decode.

Regardless of its intentions, the Principia comes across as an ingenious text without so much as a hint of pretentiousness. The text meaningfully addresses complicated ideas while undercutting them with humor and paradox - it's all painfully clever AND a fun read. In this age of shallow post-modern tricks, that alone is a noteworthy achievement.

NOTE: The entire text is available online. If, however, you intend to purchase a copy, buy the black-cover edition published by Steve Jackson Games - it is the most recent and contains additional content not found in the yellow-cover or purple-cover editions.

Principia Discordia: Or How I Found Goddess, and What I Did to Her When I Found Her

Average customer rating:

Um, dude. "Discordianism"?
Do not order this from Amazon if you need it soon
Great fun and thought provoking
Take A Bite, I Won't Fight You
Notes on this edition, my favorite

Principia Discordia: Or How I Found Goddess, and What I Did to Her When I Found Her
Steve Jackson , Jeff Koke , and Derek Pearcy
Manufacturer: Steve Jackson Games
ProductGroup: Book
Binding: Paperback

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ASIN: 1556343205

Customer Reviews:

Um, dude. "Discordianism"?.......2006-10-18

What were you expecting, that this book would materialize in your mailbox on YOUR schedule?

Eris will see to it you get the book when you're READY for it, not when you WANT it.

Do not order this from Amazon if you need it soon, October 5, 2006
Reviewer: Robophonic (Austin, TX USA) - See all my reviews
This is not a review of the book (which I would give 5 stars), but I thought it might be helpful for other customers to know that I purchased this as a gift on July 20 2006, and as of October 5 it still has not arrived. The current delivery estimate is November 7. I would not order this item from Amazon if you need it soon.

I have had good success with Amazon on other items. There seems to be a fulfillment problem with this particular book.

Do not order this from Amazon if you need it soon.......2006-10-06

This is not a review of the book (which I would give 5 stars), but I thought it might be helpful for other customers to know that I purchased this as a gift on July 20 2006, and as of October 5 it still has not arrived. The current delivery estimate is November 7. I would not order this item from Amazon if you need it soon.

I have had good success with Amazon on other items. There seems to be a fulfillment problem with this particular book.

Great fun and thought provoking.......2006-04-28

Give this book another thousand years and it will replace the bible. My gods it is stupid,funny,genius!!!

Take A Bite, I Won't Fight You.......2005-09-29

This is good for all those studying metaphysics
The AISB
The Discordians
And All Those Able Minded People Looking For The Fnords
Bring On The Slack Before BOB
Was His One Time Only Partner
Eris

Notes on this edition, my favorite.......2002-01-15

The original Principia Discordia was very much mish mash of near random pages thrown together, and the pages themselves were changed and modified. I've always felt that it should be a continually evolving book, and with this edition including newly created pages, it hits closest to the spirit of discordianism (at least in my opinion).

The other editions I've seen present it almost as a relic of the past, as something to be looked at, and fondly reminisced over. The purple edition did a great interview with one of the creators (and 3 of his personalities if I remember correctly), which is nice, but too stale for me.

I'm sorry to see it out of print.

In summary: This edition of the Principia is particularly good because it features added material, all in the style and theme of the original.

Book Description

This is the first comprehensive study of the ethics of G. E. Moore, the most important English-speaking ethicist of the 20th century. Moore's ethical project, set out in his seminal text the Principia Ethica is to preserve common moral insight from skepticism and, in effect, persuade his readers to accept the objective character of goodness. Brian Hutchinson explores Moore's arguments in detail, showing Moore's ethical work to be much richer and more sophisticated than his critics have acknowledged.

Download Description

This is the first comprehensive study of the ethics of G. E. Moore, the most important English-speaking ethicist of the twentieth century. Moore's ethical project, set out in his seminal text Principia Ethica, is to preserve common moral insight from skepticism and, in effect, persuade his readers to accept the objective character of goodness. Brian Hutchinson explores Moore's arguments in detail and in the process relates the ethical thought to Moore's anti-skeptical epistemology. Moore was, without perhaps fully realizing it, skeptical about the very enterprise of philosophy itself, and in this regard, as Brian Hutchinson reveals, was much closer in his thinking to Wittgenstein than has been previously realized. This book shows Moore's ethical work to be much richer and more sophisticated than his critics have acknowledged.

Customer Reviews:

An important contribution to the current literature in ethic.......2002-01-13

Hutchinson writes with grace and flair. His judgments of Moore are penetrating and wise, neither adulatory nor inimical. Unlike most writers on Moore, Hutchinson is at home also with Moore's epistemological and metaphysical works. He correctly ties Moore's realism ("objectivism") in ethics to his defense of common sense in epistemology. Moore's "innocence" (Keynes's word) regarding the existence and knowability of values is nicely compared with his much discussed, with derision or admiration, "innocence" regarding the existence and knowability of material objects. Moore thought that both are obvious, and that only intellectual confusion leads to thinking they are not. Hutchinson's book is an important contribution to the current literature in ethics. It would be an excellent "companion" for readers of Moore.

Newton's Principia: The Central Argument

Average customer rating:

Newton's Principia: The Central Argument

Manufacturer: Green Lion Press
ProductGroup: Book
Binding: Hardcover
ASIN: 1888009241

Product Description

Newton's Principia: The Central Argument makes the great adventure of Principia available not only to modern scholars of history of science, but also to nonspecialist undergraduate students of humanities. It moves carefully from Newton's definitions and axioms through the essential propositions, as Newton himself identified them, to the establishment of universal gravitation and elliptical orbits. The guidebook unfolds what is implicit in Newton's words as he himself would have filled in the steps and completes the argument in ways that are authentic and not anachronistic, exactly following Newton's thinking rather than substituting tools of modern calculus or the formulations of modern physics. It is Newton in his own terms, allow