Witti-Buch2 2001.qxd - Austrian Ludwig Wittgenstein Society

Finitism and Symmetry
generally some variant of the logical fact that a finite series is compatible with an
indefinite number of possible extensions of that series. It is thus argued, for instance,
that past applications of a term leave its future applications undetermined; that a finite
disposition is compatible with an indefinite number of extensions of that disposition; that
a finite mental content is entailed by an indefinite numbers of representations of that
content (etc.). Thus, any fact that can possibly be argued to satisfy the subjective
condition fails to satisfy the objective condition (Bloor 1973, Barnes 1982, Barnes et al.
1996, and Bloor 1997).
Consequently, finitism implies that it is not possible to explain why someone applied
an empirical term correctly in a particular case by saying that s/he perceived the import
of a conceptual constraint and acted accordingly. But if conceptual constraints cannot
explain correct usage, then correct and incorrect usage will stand on par with each other;
both will require the same types of explanation. Instead of presuming that the individual
is conceptually compelled to apply the term in one way rather than in any other possible
way (in so far as s/he intends to apply the term correctly), the advocates of finitism
endorse causal compulsion. They invoke the full range of contingencies that operate
causally on the episode of application-i.e. past precedents, the indications of experience,
habits, dispositions, current goals and interests. Here we have a clear picture of the
significance of finitism for the requirement of symmetry with respect usage of empirical
terms: the symmetry is lost if meaning can be shown do determine usage, and that the
symmetry is gained if usage determines meaning.
Meaning and use
We need a clear example to assess finitism and its significance for the requirement of
symmetry. I shall use an example from geometry and ask whether the concept of
'parallel line' determines its use in geometry. Consider how the concept appears in the
following axioms:
1. Euclidean geometry: Through one point not on a given line, only one line can
be drawn parallel to the given line.
2. Non-Euclidic hyperbolic geometry: Through one point not on a given line,
more than one line can be drawn parallel to the given line.
3. Non-Euclidic elliptical geometry: Through one point not on a given line, there
are no parallel lines, i.e. lines that intersect the given line.
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