520 Paul Thompson
first-order predicate logic may turn out to be the most appropriate mathematical
framework but in the vast majority of cases it will not.
Some philosophers have taken the position that a first-order predicate logic
account of the dynamics of a system can always be provided for an account in
another mathematical framework. This is an abstract possibility. However, that
onecantranslate from one framework to another, and hence into the framework
of mathematical logic, does not entail that onemustdo so; nor does it entail that
there is anadded value to doing so — indeed, experience suggests most often
something is lost.
A second, and more decisive, reason for accepting the theory-model equiva-
lence centres on the purposes of theorising. Among the most important purposes
of developing theories are: integration of knowledge, determination/specification
of an appropriate ontology, make possible explanation and prediction of events,
make possible the generation of new knowledge about causal relations, entities,
etc. that could not, or has not been, obtained through empirical investigation.
Mathematical models satisfy all of these purposes.
However, if one still insists that theories are linguistic structures and first-order
predicate logic is the natural formal language of linguistic structures, at least the
forgoing provides a clear sense in which the wider context of formalisation in science
— the context employing a wide and diverse array of mathematical domains — is
rich, varied and powerful.
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