In mathematics, so far, we have been dealing with
various static (abstract) structures.
For example, in group theory, which does study the
subgroup lattice of a given
group, there are, quite naturally, no expectations that one subgroup is obtained by modifying
another one.
Even in a more “continuous” setting of a
topological space, there are again
no expectations that a
topological structure itself is evolving.
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In contrast, in ETS formalism, some
of the central building blocks of the
formal structure, the set of transformations, are being modified on the basis of the inductive experience.