Interpretations, or generalizations, of quantum theory that are applicable to cosmology are of interest because they must display and resolve the “paradoxes” directly. The Everett interpretation is reexamined and compared with two alternatives. Its “metaphysical” connotations can be removed, after which it is found to be more acceptable than a theory which incorporates collapse, while retaining some unsatisfactory features.

The “Ignorance Interpretation” of quantum mechanical mixtures holds, roughly, that whenever a system S belongs to an ensemble, which is represented by a mixed statistical operator U = Σpi P[ψi] (0 ≤ pi ≤ 1, Σipi = 1, P[ψi] is the projection operator for the state ψi), then S is in some pure state, although we are ignorant as to which one. It has been concluded, e.g. by van Fraassen, that “the ignorance interpretation is untenable,” and he presumably favors adopting “the position that mixtures of pure states are themselves new states ... to say that a system is in a proper mixture is to say that it is not in a pure state.” I wish to argue in this paper that there are no good grounds for rejecting the ignorance interpretation.

It is commonly thought that the dispositional view of purposiveness is itself incompatible with the programmatic claims of neurophysiologists. In this paper, various versions of four arguments for this incompatibility are examined, and rejected as unsound. Central to the argument is a rough sketch of a “mechanistic” position which seems clearly compatible with a dispositional view of purposiveness.

This paper states two sets of axioms sufficient for extensive measurement. The first set, like previously published axioms, requires that each of the objects measured must be classifiable as either greater than, or less than, or indifferent to each other object. The second set, however, requires only that any two objects be classifiable as either indifferent or different, and does not need any information about which object is greater. Each set of axioms produces an extensive scale with the usual properties of additivity and uniqueness except for unit. Moreover, the axioms imply Weber's Law: whether two objects are indifferent depends only upon the ratio of their scale values.

Axiomatizations of measurement systems usually require an axiom—called an Archimedean axiom—that allows quantities to be compared. This type of axiom has a different form from the other measurement axioms, and cannot—except in the most trivial cases—be empirically verified. In this paper, representation theorems for extensive measurement structures without Archimedean axioms are given. Such structures are represented in measurement spaces that are generalizations of the real number system. Furthermore, a precise description of “Archimedean axioms” is given and it is shown that in all interesting cases “Archimedean axioms” are independent of other measurement axioms.