This book is another collection of essays written by F P Ramsey between 1922 and 1929.These essays cover practically all of Ramsey's important contributions to philosophy,logic,universals,pragmatism,mathematics,probability(subjective probability) and decision theory.I recommend the purchase of this volume for the reader who does not yet own any of the earlier published collections of Ramsey's papers.Unfortunately,there are major errors present in essay four,titled"Truth and Probability".These errors have never been corrected and essentially are passed down from one generation of philosophers ,economists and decision theorists to the next.Ramsey's fundamental error is his misinterpretation of the words J M Keynes used to describe his interval estimate approach to probability in chapter 3 of the A Treatise on Probability in 1921.Keynes used the terms "nonnumerical " and "nonmeasurable" to describe the numerical approximation of probabilities( indeterminate probabilities)by means of two numbers,a lower bound and an upper bound.In Keynes's general theory of probability,only a partial ordering is possible.There is no sigma algebra or measure defined on the real numbers between( and including) 0 and 1 so that all conjunctions and disjunctions(unions and intersections) of probabilities, using addition and multiplication operations,results in a unique single number answer.If a complete order can be specified,then Keynes's logical approach to probability will simplify to the special case given by assuming a complete ordering of the probability space.Keynes gave his most general axiomatic presentation on pp.135-138 of the TP;it develops a set theoretic analysis that holds for both unique probabilities as well as intervals.Keynes gave additional axioms that would allow the special cases of statistical frequences and unique numerical probabilities to be calculated in chapters 8(29-31)and 15 of the TP.Unfortunately,Ramsey decided that Keynes was arguing that probabilities ,in general, could not be calculated using numbers at all ,except in the special case of the Principle of Indifference .Similarly,Ramsey came to another strange conclusion-that Keynes was opposed to the idea of basing estimates of probabilities on frequency data.These false and misleading claims by Ramsey simply mean that he had no idea of the generality of Keynes's approach.Ramsey also failed to realize that his approach to probability is in fact a very special case of Keynes's general theory of probability. The same conclusion holds with respect to Ramsey's decision theoretic approach -it is a special case of Keynes's general approach,which applies to all areas of human decision making and probability estimation,such as everyday practical decision making,social science,liberal arts,economics and business,education,and not just to "...Gibbs phase space...". Another reoccurring problem ,in this book as well as in all other books containing collections of Ramsey's papers,is the inaccurate and misleading introduction provided by the editor of this volume,D. H. Mellor.Mellor makes two unsubstantiated claims.First,Mellor claims that"...in his 1922 Review of the Treatise,and in his 1926 paper,"Truth and Probability",Ramsey criticised the idea of partial entailment...so effectively that Keynes himself abandoned it;...(Mellor,p.xiv)".With the exception of some areas of physics,engineering,chemistry,and biology,partial ordering is simply a fact.Nowhere in any of Keynes's published works does Keynes ever state that a complete ordering of probability space is the general case.Second,Mellor claims that"The fact that Keynes did not resent Ramsey's demolition of his Theory of Probability is shown by his getting Ramsey a Fellowship at King's College Cambridge in 1924 at the ripe age of 21..."(Mellor,p.xv).This claim makes no sense at all,since Ramsey fails to present a formal deductive argument with clearly specified premises and a conclusion that follows from them.Ramsey's major "arguments" are the informal fallacies of appeal to authority and argument from ignorance.No where in any of Mellor's publications has he ever shown that Keynes would substitute Ramsey's very special theory for his own general theory.Lastly,the claim made on the back jacket cover of the book that Ramsey was the greatest Cambridge philosopher of all time is highly questionable,since Bertrand Russell is usually considered to be the greatest.
