Browsing by Author "Bozin, Dragana"

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    Alternative scales for extensive measurement: Combining operations and conventionalism
    (1993) Bozin, Dragana; Grandy, Richard E.
    This thesis concerns alternative concatenating operations in extensive measurements and the degree to which concatenating operations are matter of convention. My arguments are directed against Ellis' claim that what prevents us from choosing alternative ways of combining extensive quantities is only convenience and simplicity and that the choice is not based on empirical reasons. My first argument is that, given certain relational theories of measurement, there can be no more than one concatenating operation per quantity; because combining operations are the only conclusive distinguishing characteristic among distinct extensive measurements and thus the only thing that can serve as an indicator for the identity of a quantity. Rectangular and collinear concatenation, for example, cannot both be used as a way of combining lengths. However, rectangular concatenation could be used to measure some other extensive quantity since it fulfills the necessary conditions for adequate numerical assignment. For those that adopt theories of measurement which can support the claim that dinches measure length, I demonstrate, in the second argument, that rectangular concatenation would be a bad alternative and thus no alternative at all. Implementation of rectangular concatenation requires a new science; a science compatible with dinches violates present invariance principles and a new set must be provided, if possible. It is not clear that there is a set of invariance principles compatible with dinches which also gives basis for a science that explains the phenomena as well as the old one. Moreover, new invariance principles would be unintuitive and would require that certain fundamental concepts change their meaning. For these reasons the choice between them is guided by a number of empirical reasons and is not only a matter of convention.
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    An inquiry concerning fundamental measurement (Measurement)
    (1989) Bozin, Dragana; Grandy, Richard E.
    Non-standard scales for fundamental measurements obtained by a change of operation of concatenation satisfy the axioms in the same manner as standard scales. One possible change of operation for length measurement is from linear juxtaposition to rectangular juxtaposition. Some argued that the choice between standard and non-standard scales can be guided by no other reason but simplicity of science and convenience. Non-standard scales for length measurement however, would require either change of laws, or introduction of a universal force or a change of all other scales which would preserve the laws, and a complicated practice which consists of many partial measurements that affect the precision of measurement. The set of permissible scales for length measurement divides naturally into two subsets: symmetric and asymmetric scales. The set of permissible scales can be reduced to the symmetric scales by either adding an axiom or by stating a symmetry requirement as a law dictated by the nature of the magnitude under consideration (length).