Your rating(Clear)Rate this item

53 people found this helpful

ByMichael Emmett Bradyon May 16, 2005

In this path breaking contribution to the logic of probability,Keynes showed how to adapt the work of George Boole for the purpose of estimating probabilities.Keynes is the first scholar in history to explicitly emphasize the importance of interval estimates in decision making.For Keynes there are only two types of probability estimates,point estimates and interval estimates.Unfortunately,Keynes decided to call interval estimates "non-numerical"probabilities.His reasoning is really quite obvious.A precise estimate of probability used a single numeral for the point estimate.Therefore,an imprecise estimate of probability used two numerals to denote an interval(set).Thus, an interval estimate is not based on a single numeral but two. These types of probabilities are thus "non-numerical"because you are not using a single numeral.In 1922 and 1926,Frank Ramsey reviewed Keynes's book based on his reading of chapters 1-4 plus 3 pages from Part two and 4 pages from Part five.Keynes's discussion of non-numerical probabilities takes place in chapters 5,10,15 and 17.Keynes then applies his new approach to induction and analogy in chapters 20 and 22,using his concept of "finite probability"which applies to both precise numerical probabilities and imprecise non-numerical probabilities.All of Keynes's discoveries ,however,were ignored by the ignorant Ramsey.(To this day(2005)one can regularly read about Keynes's "strange,mysterious,unfathomable,undefined"non-numerical probabilities in literally hundreds of economics and philosophy journal articlesthat are based primarily on Ramsey's reviews.These reviews are still cited as "overwhelming" evidence that Keynes agreed that Ramsey's critique had demolished the entire structure of his logical approach to probability.Nothing could be further from the truth.Ramsey's reviews were so poor that Keynes and Bertrand Russell attempted to downplay their relevance so as to save Ramsey from being embarrassed in the academic community.)Keynes then showed that interval estimates,because they overlap,would very likely also,in many cases,be noncomparable and/or nonrankable if a decision maker used such order preserving operators like"greater than or equal to"or "less than or equal to".While this is quite obvious,it went completely over Ramsey's head. Keynes's second major advance was to create his "conventional coefficient of weight and risk", c=p/(1+q)[2w/(1+w)]. The goal of the decision maker is to Maximize cA,where A is some outcome.This decision rule solves all of the paradoxes and anomalies that plague subjective expected utility theory.A major accomplishment made by Keynes in chapter 26 of the TP was to specify that the weight of the evidence variable,w,was defined on the unit interval [0,1].It would be forty years before Daniel Ellsberg would define his practically identical variable,rho,on the unit interval between 0 and 1 also,where rho measured the degree of confidence in the decision maker's information base.Since these two measures are one to one onto and isomorphic,Keynesian weight(uncertainty in the General Theory) and Ellsbergian ambiguity measure the same thing and are interchangeable.This means that Ellsberg's analysis can be applied when studying the GT and used to buttress Keynes's theory of liquidity preference in the GT.In Part 5 of this book ,Keynes showed how one could use Chebyshev's Inequality as a lower bound to the normal probability distributions overly precise point estimate . Part 5 of the Treatise also includes Keynes's advocacy of the Lexis Q test for stability of a statistical frequency[law of large numbers].It is this part of the TP that forms the basis,along with chapter 17,of Keynes's exchange with Tinbergen over the logical foundations of econometrics in the Economic Journal in 1939-1940.Keynes pointed out that ,in order to justify his assumption of normality,Tinbergen needed to apply the Lexis Q test.Tinbergen never applied either that test or the Chi- Square test for goodness of fit.This will then bring the reader back to Keynes's chapter 8 of the Treatise ,where he presents his own logical frequency interpretation of probability as a special case of his general logical approach to probability.

31 people found this helpful

BySebastianon February 12, 2010

This particular edition (A Treatise on Probability by General Books LLC) of the book seems a ripoff to me and I strongly recommend against buying it.

The small print on the front pages states that the book was created with OCR, to "keep the cost as low as possible".

That's all very well, but readability was kept as low as possible too.

To name a few issues, apart from a stream of spelling errors:

- a table of contents with no titles, just "section 1", "section 2" and so on

- random sections: section 17 starts with "chapter XXI", section 30 with "chapter XXXIII", section 31 appears to be the index

- sections starting in midsentence and, conversely, "chapter XXIX" appearing unceremoniously halfway down a page

- an index which refers to seemingly random pagenumbers

- mathematical formulas that are undecipherable ... supposing these typographical trainwrecks were formulas in the first place

- footnotes strewn through the text, again supposing that the many lines starting with digits are indeed footnotes.

- no layout whatsoever

Please read similar comments on:

[...]

The offer to download the original scan of the book from their website [...] seems meaningless too,

I couldn't find the book by author, title, barcode or ISBN.

The small print on the front pages states that the book was created with OCR, to "keep the cost as low as possible".

That's all very well, but readability was kept as low as possible too.

To name a few issues, apart from a stream of spelling errors:

- a table of contents with no titles, just "section 1", "section 2" and so on

- random sections: section 17 starts with "chapter XXI", section 30 with "chapter XXXIII", section 31 appears to be the index

- sections starting in midsentence and, conversely, "chapter XXIX" appearing unceremoniously halfway down a page

- an index which refers to seemingly random pagenumbers

- mathematical formulas that are undecipherable ... supposing these typographical trainwrecks were formulas in the first place

- footnotes strewn through the text, again supposing that the many lines starting with digits are indeed footnotes.

- no layout whatsoever

Please read similar comments on:

[...]

The offer to download the original scan of the book from their website [...] seems meaningless too,

I couldn't find the book by author, title, barcode or ISBN.

BySebastianon February 12, 2010

This particular edition (A Treatise on Probability by General Books LLC) of the book seems a ripoff to me and I strongly recommend against buying it.

The small print on the front pages states that the book was created with OCR, to "keep the cost as low as possible".

That's all very well, but readability was kept as low as possible too.

To name a few issues, apart from a stream of spelling errors:

- a table of contents with no titles, just "section 1", "section 2" and so on

- random sections: section 17 starts with "chapter XXI", section 30 with "chapter XXXIII", section 31 appears to be the index

- sections starting in midsentence and, conversely, "chapter XXIX" appearing unceremoniously halfway down a page

- an index which refers to seemingly random pagenumbers

- mathematical formulas that are undecipherable ... supposing these typographical trainwrecks were formulas in the first place

- footnotes strewn through the text, again supposing that the many lines starting with digits are indeed footnotes.

- no layout whatsoever

Please read similar comments on:

[...]

The offer to download the original scan of the book from their website [...] seems meaningless too,

I couldn't find the book by author, title, barcode or ISBN.

The small print on the front pages states that the book was created with OCR, to "keep the cost as low as possible".

That's all very well, but readability was kept as low as possible too.

To name a few issues, apart from a stream of spelling errors:

- a table of contents with no titles, just "section 1", "section 2" and so on

- random sections: section 17 starts with "chapter XXI", section 30 with "chapter XXXIII", section 31 appears to be the index

- sections starting in midsentence and, conversely, "chapter XXIX" appearing unceremoniously halfway down a page

- an index which refers to seemingly random pagenumbers

- mathematical formulas that are undecipherable ... supposing these typographical trainwrecks were formulas in the first place

- footnotes strewn through the text, again supposing that the many lines starting with digits are indeed footnotes.

- no layout whatsoever

Please read similar comments on:

[...]

The offer to download the original scan of the book from their website [...] seems meaningless too,

I couldn't find the book by author, title, barcode or ISBN.

ByMichael Emmett Bradyon May 16, 2005

In this path breaking contribution to the logic of probability,Keynes showed how to adapt the work of George Boole for the purpose of estimating probabilities.Keynes is the first scholar in history to explicitly emphasize the importance of interval estimates in decision making.For Keynes there are only two types of probability estimates,point estimates and interval estimates.Unfortunately,Keynes decided to call interval estimates "non-numerical"probabilities.His reasoning is really quite obvious.A precise estimate of probability used a single numeral for the point estimate.Therefore,an imprecise estimate of probability used two numerals to denote an interval(set).Thus, an interval estimate is not based on a single numeral but two. These types of probabilities are thus "non-numerical"because you are not using a single numeral.In 1922 and 1926,Frank Ramsey reviewed Keynes's book based on his reading of chapters 1-4 plus 3 pages from Part two and 4 pages from Part five.Keynes's discussion of non-numerical probabilities takes place in chapters 5,10,15 and 17.Keynes then applies his new approach to induction and analogy in chapters 20 and 22,using his concept of "finite probability"which applies to both precise numerical probabilities and imprecise non-numerical probabilities.All of Keynes's discoveries ,however,were ignored by the ignorant Ramsey.(To this day(2005)one can regularly read about Keynes's "strange,mysterious,unfathomable,undefined"non-numerical probabilities in literally hundreds of economics and philosophy journal articlesthat are based primarily on Ramsey's reviews.These reviews are still cited as "overwhelming" evidence that Keynes agreed that Ramsey's critique had demolished the entire structure of his logical approach to probability.Nothing could be further from the truth.Ramsey's reviews were so poor that Keynes and Bertrand Russell attempted to downplay their relevance so as to save Ramsey from being embarrassed in the academic community.)Keynes then showed that interval estimates,because they overlap,would very likely also,in many cases,be noncomparable and/or nonrankable if a decision maker used such order preserving operators like"greater than or equal to"or "less than or equal to".While this is quite obvious,it went completely over Ramsey's head. Keynes's second major advance was to create his "conventional coefficient of weight and risk", c=p/(1+q)[2w/(1+w)]. The goal of the decision maker is to Maximize cA,where A is some outcome.This decision rule solves all of the paradoxes and anomalies that plague subjective expected utility theory.A major accomplishment made by Keynes in chapter 26 of the TP was to specify that the weight of the evidence variable,w,was defined on the unit interval [0,1].It would be forty years before Daniel Ellsberg would define his practically identical variable,rho,on the unit interval between 0 and 1 also,where rho measured the degree of confidence in the decision maker's information base.Since these two measures are one to one onto and isomorphic,Keynesian weight(uncertainty in the General Theory) and Ellsbergian ambiguity measure the same thing and are interchangeable.This means that Ellsberg's analysis can be applied when studying the GT and used to buttress Keynes's theory of liquidity preference in the GT.In Part 5 of this book ,Keynes showed how one could use Chebyshev's Inequality as a lower bound to the normal probability distributions overly precise point estimate . Part 5 of the Treatise also includes Keynes's advocacy of the Lexis Q test for stability of a statistical frequency[law of large numbers].It is this part of the TP that forms the basis,along with chapter 17,of Keynes's exchange with Tinbergen over the logical foundations of econometrics in the Economic Journal in 1939-1940.Keynes pointed out that ,in order to justify his assumption of normality,Tinbergen needed to apply the Lexis Q test.Tinbergen never applied either that test or the Chi- Square test for goodness of fit.This will then bring the reader back to Keynes's chapter 8 of the Treatise ,where he presents his own logical frequency interpretation of probability as a special case of his general logical approach to probability.

2020 comments*|*53 people found this helpful. Was this review helpful to you?YesNoReport abuse#### There was a problem loading comments right now. Please try again later.

Please write at least one word

You must purchase at least one item from Amazon to post a comment

A problem occurred while submitting your comment. Please try again later.

ByEileen Pon March 8, 2011

Save your $0.99! This is an unreadable edition of a great book. After opening my wirelessly delivered copy, I found the following:

TIIK Hubjtwl mutter of this book was first broached i the brain of Lfibuix, who, in thn dwHortation, written in his twenty-third yiwr, o the woilt .....

And so it continues, page after page. This from a product "optimized for my Kindle"? It reads like a Robert Benchley parody of Old English.

I obviously will not sue Amazon to recover my $0.99, but I will advise others to not buy this edition of Keynes excellent book.

TIIK Hubjtwl mutter of this book was first broached i the brain of Lfibuix, who, in thn dwHortation, written in his twenty-third yiwr, o the woilt .....

And so it continues, page after page. This from a product "optimized for my Kindle"? It reads like a Robert Benchley parody of Old English.

I obviously will not sue Amazon to recover my $0.99, but I will advise others to not buy this edition of Keynes excellent book.

0Comment*|*7 people found this helpful. Was this review helpful to you?YesNoReport abuse#### There was a problem loading comments right now. Please try again later.

Please write at least one word

You must purchase at least one item from Amazon to post a comment

A problem occurred while submitting your comment. Please try again later.

ByMichael Emmett Bradyon June 21, 2004

In this path breaking contribution to the logic of probability,Keynes showed how to adapt the work of George Boole for the purpose of estimating probabilities.For Keynes there are only two types of probability estimates,point estimates and interval estimates.Unfortunately,Keynes decided to call interval estimates "non-numerical"probabilities.His reasoning is really quite obvious.A precise estimate of probability used a single numeral for the point estimate.Therefore,an imprecise estimate of probability used two numerals to denote an interval(set).Thus, an interval estimate is not based on a single numeral but two. These types of probabilities are thus "non-numerical"because you are not using a single numeral.In 1922 and 1926,Frank Ramsey reviewed Keynes's book based on his reading of chapters 1-4 plus 3 pages from Part two and 4 pages from Part five.Keynes's discussion of non-numerical probabilities takes place in chapters 5,10,15 and 17.Keynes then applies his new approach to induction and analogy in chapters 20 and 22,using his concept of "finite probability"which applies to both precise numerical probabilities and imprecise non-numerical probabilities.All of Keynes's discoveries ,however,were ignored by the ignorant Ramsey.To this day(2004)one can regularly read about Keynes's "strange,mysterious,unfathomable,undefined"non-numerical probabilities in literally hundreds of economics and philosophy journal articles based on Ramsey's reviews.Keynes then showed that interval estimates,because they overlap,would very likely also,in many cases,be noncomparable and/or nonrankable if a decision maker used such order preserving operators like"greater than or equal to"or "less than or equal to".While this is quite obvious,it went completely over Ramsey's head. Keynes's second major advance was to create his "conventional coefficient of weight and risk", (...) The goal of the decision maker is to Maximize cA.This decision rule solves all of the paradoxes and anomalies that plague subjective expected utility theory.In Part 5 of his book Keynes showed how one could use Chebyshev's Inequality as a lower bound to the normal probability distributions overly precise point estimate . Part 5 of the Treatise also includes Keynes's advocacy of the Lexis Q test for stability of a statistical frequency[law of large numbers].This will then bring the reader back to Keynes's chapter 8 of the Treatise where he presents his own logical frequency interpretation of probability as a special case of his general logical approach to probability.

66 comments*|*5 people found this helpful. Was this review helpful to you?YesNoReport abuse#### There was a problem loading comments right now. Please try again later.

Please write at least one word

You must purchase at least one item from Amazon to post a comment

A problem occurred while submitting your comment. Please try again later.

ByGunnar Taraldsenon February 19, 2010

This particular edition (A Treatise on Probability by General Books LLC) of the book seems a ripoff to me and I strongly recommend against buying it.

The small print on the front pages states that the book was created with OCR, to "keep the cost as low as possible".

This was not clear from the Amazon web.

This is so bad that I will wait a few years before I buy anything more at Amazon.

Mathematical formulas that are undecipherable ... supposing these typographical trainwrecks were formulas in the first place

To name a few issues, apart from a stream of spelling errors:

- a table of contents with no titles, just "section 1", "section 2" and so on

- random sections: section 17 starts with "chapter XXI", section 30 with "chapter XXXIII", section 31 appears to be the index

- sections starting in midsentence and, conversely, "chapter XXIX" appearing unceremoniously halfway down a page

- an index which refers to seemingly random pagenumbers

- mathematical formulas that are undecipherable ... supposing these typographical trainwrecks were formulas in the first place

- footnotes strewn through the text, again supposing that the many lines starting with digits are indeed footnotes.

- no layout whatsoever

In short: Do not buy this.

The small print on the front pages states that the book was created with OCR, to "keep the cost as low as possible".

This was not clear from the Amazon web.

This is so bad that I will wait a few years before I buy anything more at Amazon.

Mathematical formulas that are undecipherable ... supposing these typographical trainwrecks were formulas in the first place

To name a few issues, apart from a stream of spelling errors:

- a table of contents with no titles, just "section 1", "section 2" and so on

- random sections: section 17 starts with "chapter XXI", section 30 with "chapter XXXIII", section 31 appears to be the index

- sections starting in midsentence and, conversely, "chapter XXIX" appearing unceremoniously halfway down a page

- an index which refers to seemingly random pagenumbers

- mathematical formulas that are undecipherable ... supposing these typographical trainwrecks were formulas in the first place

- footnotes strewn through the text, again supposing that the many lines starting with digits are indeed footnotes.

- no layout whatsoever

In short: Do not buy this.

11 comment*|*7 people found this helpful. Was this review helpful to you?YesNoReport abuse#### There was a problem loading comments right now. Please try again later.

Please write at least one word

You must purchase at least one item from Amazon to post a comment

A problem occurred while submitting your comment. Please try again later.

ByA. K.on April 15, 2016

If you are into statistics and probability, you should study this text. JMK explores both the logic and mathematical structure of probability analysis.

If you are not into statistics, this book will bore you to death. However, the bigger question would be why are you reading reviews of a statistical text?

If you are not into statistics, this book will bore you to death. However, the bigger question would be why are you reading reviews of a statistical text?

0Comment*|*Was this review helpful to you?YesNoReport abuse#### There was a problem loading comments right now. Please try again later.

Please write at least one word

You must purchase at least one item from Amazon to post a comment

A problem occurred while submitting your comment. Please try again later.

ByJonathan Gilliganon December 14, 2013

The kindle edition is so full of typos that it is utterly unreadable. Not just an incorrect letter here and there, but entire sentences reduced to gibberish that looks like randomly swiping one's fingers across a keyboard.

0Comment*|*2 people found this helpful. Was this review helpful to you?YesNoReport abuse#### There was a problem loading comments right now. Please try again later.

Please write at least one word

You must purchase at least one item from Amazon to post a comment

A problem occurred while submitting your comment. Please try again later.

ByKenneth Zimmermanon March 5, 2013

Truly an historical, seminal book. It changed the direction and tone for all human history, including of course economics and history.

0Comment*|*2 people found this helpful. Was this review helpful to you?YesNoReport abuse#### There was a problem loading comments right now. Please try again later.

Please write at least one word

You must purchase at least one item from Amazon to post a comment

A problem occurred while submitting your comment. Please try again later.

ByKaren S.on June 18, 2013

I purchased the kindle version of this book to tide me over whilst waiting for the hard copy to arrive in the mail. This important and informative book is, in this incarnation, riddled with typographical errors. It is not unreadable but it irritates as much as it informs (and the formulae ought not to be quoted).

0Comment*|*2 people found this helpful. Was this review helpful to you?YesNoReport abuse#### There was a problem loading comments right now. Please try again later.

Please write at least one word

You must purchase at least one item from Amazon to post a comment

A problem occurred while submitting your comment. Please try again later.

ByMichael Emmett Bradyon September 18, 2006

In this path breaking contribution to the logic of probability,Keynes showed how to adapt the work of George Boole for the purpose of estimating probabilities.Keynes is the first scholar in history to explicitly emphasize the importance of interval estimates in decision making.For Keynes there are only two types of probability estimates,point estimates and interval estimates.Unfortunately,Keynes decided to call interval estimates " non-numerical "probabilities.His reasoning is really quite obvious.A precise estimate of probability used a single numeral for the point estimate.Therefore,an imprecise estimate of probability used two numerals to denote an interval(set).Thus, an interval estimate is not based on a single numeral but two. These types of probabilities are thus " non-numerical "because you are not using a single numeral.In 1922 and 1926,Frank Ramsey reviewed Keynes's book based on his reading of chapters 1-4 plus 3 pages from Part II and 4 pages from Part V.Keynes's discussion of non-numerical probabilities takes place in chapters 5,10,15 and 17.Keynes then applies his new approach to induction and analogy in chapters 20 and 22,using his concept of " finite probability " ,which applies to both precise ,numerical probabilities and imprecise, non-numerical probabilities.All of Keynes's discoveries ,however,were ignored by the ignorant Ramsey.It is unfortunate that the editorial foreword to the 1973 Collected Writings of JMK edition of the TP, written by Richard Braithwaite ,simply repeats all of the errors made by Ramsey in his reviews.Consider Braithwaite's paraphrase of Ramsey's argument that " On Keynes's theory it is something of a mystery why the probability relations should be governed by the probability calculus."(p.xx,1973).The answer is quite simple. First,the " non numerical " interval estimates will not be governed by the probability calculus.Second,numerical probability calculations,such as the blue-green taxi cab problem of Tversky and Kahneman,will only satisfy the probability calculus if the weight of the evidence,w,is equal to 1,where w is defined as an element on the unit interval between 0 and 1 and measures the relative completeness of the available evidence upon which the probability estimates are to be calculated.(To this day(2006)one can regularly read about Keynes's " strange,mysterious,unfathomable,undefined " non-numerical probabilities in literally hundreds of economics and philosophy journal articles and books that have been written about Keynes's approach to probability since the Ramsey reviews were first published 80 years ago.These reviews are still cited as " overwhelming " evidence that Keynes agreed that Ramsey's critique had completely demolished the entire structure of his logical approach to probability.Nothing could be further from the truth.Ramsey's reviews were so poor that Keynes and Bertrand Russell attempted to downplay their relevance so as to save Ramsey from being embarrassed in the academic community.)Keynes then showed that interval estimates,because they frequently overlap,would very likely also,in many cases,be nonmeasurable,noncomparable and/or nonrankable if a decision maker used such order preserving operators like " greater than or equal to " or "less than or equal to ".While this is quite obvious to any reader of Part II of the TP,it went completely over Ramsey's head. Keynes's second major advance was to create his "conventional coefficient of weight and risk", c=p/(1+q)[2w/(1+w)] in sections 7 and 8 of chapter 26 . The goal of the decision maker is to Maximize cA,where A is some outcome.This decision rule solves most of the paradoxes and anomalies that plague subjective expected utility theory.A major accomplishment made by Keynes in chapter 26 of the TP was to specify that the weight of the evidence variable,w,was defined on the unit interval [0,1].It would be forty years before Daniel Ellsberg would define his practically identical variable,rho,on the unit interval between 0 and 1 also,where rho measured the degree of confidence in the decision maker's information base.Since these two measures are one to one onto and isomorphic,Keynesian weight(uncertainty in the General Theory) and Ellsbergian ambiguity measure the same thing and are interchangeable.This means that Ellsberg's analysis can be applied when studying the GT and used to buttress Keynes's theory of liquidity preference in the GT.In Part 5 of this book ,Keynes showed how one could use Chebyshev's Inequality as a lower bound to the normal probability distributions overly precise and inaccurate point estimate . Part 5 of the Treatise also includes Keynes's advocacy of the Lexis Q test for stability of a statistical frequency[law of large numbers].It is this part of the TP that forms the basis,along with chapter 17,of Keynes's exchange with Tinbergen over the logical foundations of econometrics in the Economic Journal in 1939-1940.Keynes pointed out that ,in order to justify his assumption of normality,Tinbergen needed to apply the Lexis Q test.Tinbergen never applied either that test or the Chi- Square test for goodness of fit.This will then bring the reader back to Keynes's chapter 8 of the Treatise ,where he presents his own logical frequency interpretation of probability as a special case of his general logical approach to probability after criticizing Venn's particular version of a frequency approach.

0Comment*|*15 people found this helpful. Was this review helpful to you?YesNoReport abuse#### There was a problem loading comments right now. Please try again later.

Please write at least one word

You must purchase at least one item from Amazon to post a comment

A problem occurred while submitting your comment. Please try again later.

byJohn Maynard Keynes

$19.99

byJohn Maynard Keynes

$9.13

Let us know here.

There's a problem loading this menu right now.

Get fast, free shipping with Amazon Prime

Prime members enjoy FREE Two-Day Shipping and exclusive access to music, movies, TV shows, and Kindle books.

Your Recently Viewed Items and Featured Recommendations

After viewing product detail pages, look here to find an easy way to navigate back to pages you are interested in.

Back to top

Get to Know Us | Make Money with Us | Amazon Payment Products | Let Us Help You |

- Conditions of Use
- Privacy Notice
- Interest-Based Ads
- © 1996-2016, Amazon.com, Inc. or its affiliates

|31 people found this helpful. Was this review helpful to you?YesNoReport abuse