Instead of looking for the interpretations of the nonlogical constants that will make a sentence true, we fix the interpretations of the nonlogical constants by choosing a particular structure A, and we look for assignments of elements of A to variables which will make a given formula true in A. If we assign the number −3 to v1 and the number −6 to v2, the formula works out as true in Z.
For \(\mathbf{H}\) does not fix the interpretation of \(Tr\) in all interpretations of \(L\).
Like any definition, (18) fixes the interpretation of the definiendum \ if\) the interpretations of the non-logical constants in the definiens are given.
Under Napoleon, Merlin became procurator-general (1804) and did more than any other lawyer to fix the interpretation of the Napoleonic Code.
To fix an interpretation of these passages, we can look to a number of different places.
In particular, Einstein had reservations about the uncontrollable physical effects invoked by Bohr in the context of measurement interactions, and about their role in fixing the interpretation of the wave function.
Briefly, he argued that as long as the only constraints available to fix the interpretation of 'set' are theoretical and operational ones (all the measurements humans will ever make) there will be an interpretation of set theory on which V=L turns out true, which since it passes all constraints is an intended one.
The model-theoretic interpretation is obtained by letting the significance of "∈" be fixed by the interpretation function of M, letting the quantifiers in Ω x) range over the domain of M, and letting the significance of "=" and the propositional connectives be fixed by the recursion clauses in the the definition of first-order satisfaction.
This can be justified, e.g., keeping fixed the usual interpretation of "0" and "N" but observing that "M" can be interpreted by means of the reflexive relation of being less than or equal to; under this interpretation, "∀x(Nx→¬Mxx)" is false, although "N0" is true.
In Carnap's case predicate constants are the only primitive constants to which the models assign values, since individual constants are given a fixed pre-model interpretation and value assignments to variables are done independently of the models (1963a).
