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Chapter 2: The quantitative rules
 p. 31, line after eqn. (2.44): It appears that the reference to (2.25)
should be (2.40).
 p. 31, eqn. (2.45): The constraint should be , to avoid division by 0.
 p. 32, eqn. (2.49): A right parenthesis is missing in the expression
``
''.
 p. 33, sentence starting at top of page: to account for the restriction
, this sentence should probably be rewritten as ``Using continuity, the
only solution of this satisfying
is...''
 p. 33, second paragraph: ``Again, Aczel (1966) derives the same
result without assuming differentiability.'' (This refers to equation
(2.58).) I checked out the Aczél reference in preparing a review paper on Cox's
Theorem, and nowhere did I find anything like the result of equation (2.58); I
can only assume that the result appears in some other work of Aczél. I did
find, however, that a similar result appears in Paris's book, The
Uncertain Reasoner's Companion.
 p. 34, eqn. (2.65), second term after first "=" sign:
should be
.
 p. 34, Exercise 2.2: In two places (lines 23 and equation (2.67)) a
right parenthesis is missing:
should be
 p. 40, second paragraph: ``The argument we have just given is the
first `baby' version of the group invariance principle for
assigning plausibilities; it will be extended greatly in Chapter 6, when we
consider the general problem of assigning `noninformative
priors.' '' I believe that ``Chapter 6'' should actually
be ``Chapter 12'' (``Ignorance priors and transformation
groups'').
 p. 42, second full paragraph, line six: ``kelvin'' should be
``Kelvin.''
Several people have written asking how to derive (2.50) from (2.48); here is
the derivation:
 Rewrite (2.48) as
.
 Note that, for all ,
.
 Rewrite step 1 as
 Apply to both sides:
 Now do a Taylor series expansion around :
since has no dependence on .
Commentary: Additional treatments of Cox's Theorem
The following references not appearing Jaynes' book provide
additional perspective on Cox's Theorem:
 J. B. Paris, The Uncertain Reasoner's Companion: A Mathematical
Perspective, Cambridge University Press, 1994. Chapter 3 proves a
version of Cox's Theorem, with great care taken to explicitly list all of the
assumptions required.
 K. S. Van Horn, ``Constructing a logic of plausible
inference: a guide to Cox's Theorem,'' International Journal of
Approximate Reasoning 34, no. 1 (Sept. 2003), pp. 324. Reviews
Cox's Theorem, explicitly listing the assumptions required and discussing (1)
the intuition and reasoning behind these requirements, and (2) the most
important objections to these requirements. (Preprint:
Postscript,
PDF.)
 G. Shafer, ``Comments on `Constructing a logic of plausible inference: a
guide to Cox's Theorem', by Kevin S. Van Horn,'' IJAR 35, no. 1
(Jan. 2004), pp. 97105. Comments by Glenn Shafer (of DempsterShafer
belief function theory). (Preprint:
PDF,
or try Glenn Shafer
c.v.
and look under ``Other
Contributions.'')
 K. S. Van Horn, ``Response to Shafer's comments,'' IJAR 35, no. 1 (Jan. 2004), pp. 107110. Van Horn's rejoinder. (Preprint:
Postscript,
PDF.)
 J. M. Garrett, ``Whence the laws of probability?'', in G. J. Erickson,
J. T. Rychert, and C. R. Smith (eds.), Maximum
Entropy and Bayesian Methods. Boise, Idaho, USA, 1997, Kluwer Academic
Publishers. Another derivation of the laws of probability theory, very
similar to the Cox derivation but starting from a single logical operation
(NAND) instead of two (AND, NOT).
(Online, slightly updated:
Postscript,
PDF)
Note that, like Cox, Jaynes does not explicitly list all of his precise
assumptions in one place (although he gives desiderata that motivate them) 
Paris and Van Horn both address this issue.
Section 2.6.2 discusses the question of whether the rules of
probability theory are consistent. Jaynes brings up Godel's result that no
mathematical system can provide a proof of its own consistency, and later
writes that ``These considerations seem to open up the possibility that,
by going into a wider field by invoking principles external to probability
theory, one might be able to prove the consistency of our rules. At the
moment, this appears to us to be an open question.''
Actually, it is not an open question: the rules of probability theory can
easily be proven consistent, and the proof can be found in any undergraduate
mathematical text discussing settheoretic probability theory. As I wrote in
the abovementioned review of Cox's Theorem,
But how do we know that our requirements [Cox's axioms] are not
contradictory? How do we know that there is any system of
plausible reasoning... that satisfies all of our requirements?
The settheoretical approach to probability theory may be taken
as an existence proof that our requirements are not contradictory,
by taking states of information to be [settheoretical] probability
distributions, and defining [state of information] to be the
probability distribution obtained from by conditioning on the set
of values for which is true. In the terminology of mathematical
logic, settheoretical probability theory then becomes the model
theory for our logic, a tool to enable us to construct consistent
sets of axioms (plausibility assignments from which we derive other
plausibility assignments).
Viewing probability theory as an extension of the propositional calculus,
Jaynes's ``wider field'' is just the predicate calculus with the
axioms of finite set theory and real numbers added.
