Corrections to the book:
Steps Towards a Unified Basis for Scientific Models and Methods
p. 11, l. 5-6: …data which can be imagined to be obtained in later steps.
p. 11, l. 13-14: In some cases we have the choice between…
p. 11, l. 17: But according to the unprevisional…
p. 18, l. -14: …, we choose and perform one maximal experiment a,…
p. 23, l. -5: for an accessible conceptually defined variable.
p. 26, l. -4: convention will also turn out to be…
p. 40, . l. -17: Nevertheless, can we…
p. 72, l. -8: Add in parenthesis: Already now it can be seen that it gives the right
succession in group composition: yg1g2=g2(g1(y)).
p. 92, l. 12-13: …, (3.8) implies…. Minimizing the risk leads to a unique…
p. 107, l. 3: Let the c-variable space be…
p. 107, l. 16: … space Sa. Consider potential experiments (models) with the same sample
space S. It is crucial then…
p. 107, l. -9: … the sample space S for…
p. 120, . l. 13: For each a in A one has chosen a maximal estimable parameter λa, which
exists by Zorn’s lemma.
p. 120, l. 15: Add: An upper bound in this ordering is given by φ.
p. 123, l. -11 and p. 145, l. 16: Add:
(v) The two experiments are maximal in the ordering where λ<<µ is defined as λ=f(µ).
p. 123, l. -8—7: satisfies all the axioms 1, 2, 3 and 4.
p.123, last sentence: Replace with: Since all permutations are generated by the
interchange of two elements, Axiom 2 also holds.
p. 131, l. 13: Add: In fact this is always true: One can take G to be the automorphism
group of Φ.
p. 131, l. -18: Add: This assumption is always true for the automorphism group.
p. 135, l. 15: Let Wa be a fixed unitary operator in L2(Φ, ν). Then we define H a=WaL a …
p. 138, l. 3: For some choice of Wa, the fixed space H a=WaL a …
p. 139, l. 7: Theorem 5.3.1, we can choose Wa such that Va(g)=WaU(g)(Wa)-1 is this
representation.
p. 139, l. 8-9: Theorem 5.3.2. Then from Hb=Va(gab)Ha we can take H=Ha as the
basic quantum-mechanical Hilbert space, and let Hb, similarly Hc etc. be unitary
transformations of this Hilbert space.
p. 139, after line 9: In fact, for this basic theorem we need only Axiom 1. We hope to
publish the details of this elsewhere along with its implications.
p. 147, l. -1: After ‘comments.’, add: After the rotation (see below) the two experiments
have the same parameter. Since the parameters are maximal, the experiments cannot be
distinguished in any way. Hence we can arrange it so that a person choosing randomly,
will not know which experiment is chosen. Then appeal to Example 2.13.3 on p. 63.
p. 169, l. 3: Add: The c-variable ε is inaccessible, but even so we assume that
E(ε.b|λa)=0.
p. 208, l. -6: In this case, however, the integral in corollary 3.5.5 does not converge, but
we can use an approximating proper prior.
p. 209, l. 15: … covariance matrix for the y-variable.
p. 212, l. -13: The main result of [118] is a further development of the following:
p.213, l. 7: The results from [118] indicate what one might expect: