On 2011-02-10 18:48, Jurriaan Bendien wrote:
> Sure, you can construct an elegant metaphor and test out the quantitative
> implications of the metaphor, but there is no guarantee it captures anything
> about reality. A model is not a theory. A model is a likeness, an
> isopmorphism, a simplifying analogy for some of the features of the subject
> studied. A theory provides an in-depth, comprehensive causal explanation.
When I wrote 'model' before I didn't mean a formalized model. Instead it
was a carefully chosen analogy, in that theories *model* underlying
causal mechanisms. As such all theories are models of reality.
Some theories are indeed possible to formalize into mathematical or
logical models, and can then improve in-depth, comprehensive
explanations, i.e. reliably infer empirical outcomes. Take Boolean
algebra for instance. Once you have a theory that explains how basic
digital components can perform, or approximately perform, Boolean
operations under certain conditions, the formalism of Boolean algebra
allows for an in-depth, comprehensive explanation of the observed
behaviour of very complicated digital circuits.
Similarly, probability theory allows for the formalization of a few
basic laws in statistical mechanics with remarkably predictive power
based on quite simple assumptions. Again, the formalized model provides
in-depth, comprehensive explanations of the property of gases without
ever requiring knowledge of individual particle trajectories.
In short, any theory that can reliably infer empirical outcomes is a
good model of the underlying causal mechanisms. Whether its uses
mathematical language or not.
//Dave Z
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Received on Thu Feb 10 13:56:03 2011
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