231 / 298
Vico’s Ring
231
442
In view of the fact that model theory has been particularly fruitful in
mathematics, the following example may be illustrative: The mathematician D.
Hilbert constructed an axiom system for Euclidean geometry (
Grundlagen der
Geometrie
, Leipzig, Teubner, 1899), leaving the notions of “point”, “line”, and
“plane” undefined; he then showed that it is possible to give concrete mean-
ing to these undefined fundamental concepts, and thus construct a
model
of
the axiomatic system by
interpreting
points, lines, and planes as pairs of real
numbers on the real number plane, subject to certain equations, thus making
the axiom system
true
in this interpretation (see A. B. Sossinsky,
Geometries
,
Providence, Rhode Island, American Mathematical Society, 2012, p. 6). The
model-theoretic perspective has not been limited to mathematics, however; it
has found application in cognitive psychology (see Ph. N. Johnson-Laird,
Mental models and human reasoning
, in «PNAS», 107, 2010, 43, pp. 18243-18250);
cultural anthropology (see M. Bang et al.,
Cultural mosaics and mental models of
nature
, in «PNAS», 104, 2007, 35, pp. 13868-13874).
While borrowing model-theoretic concepts and language for the present
discussion, the underlying concepts do not depend, however, on this particu-
lar terminology in whole or in part. For example, what we have called
model
,
has also been termed
universe of interpretation
, and the targeted state of affairs,
interpretable entities
(see D. Kayser,
Abstraction and natural language semantics
, in
«Philosophical Transactions of the Royal Society B», 2003, 358, pp. 1261-
1268, p. 1267). On a higher, philosophical level, the equivalent, not necessarily
isomorphic or coextensive, term for
model
might be
field of sense
(see M. Gabri-
el,
Is the world as such good? The question of theodicy
, in
Dimensions of Goodness
, ed. by
V. Hösle, Newcastle upon Tyne, Cambridge Scholars Publishing, 2013, pp.
45-65, p. 53; see also Id.,
Warum es die Welt nicht gibt
, Berlin, Ullstein, 2013, pp.
91-96, for the German equivalent
Sinnfeld;
published in English as
Why the
World Does Not Exist
, trans. by G. S. Moss, Cambridge-Malden, Polity Press,
2015, as well as the extensive treatment in Id.,
Fields of Sense: A New Realist On-
tology
, Edinburgh, Edinburgh Univeristy Press, 2015; for the Italian equivalent
regione d’essere,
see M. Ferraris,
Manifesto del nuovo realismo
, Rome-Bari, Laterza,
2012, p. 71).
443
Walther points out: «Meyers Beweisziel im
Interpres
ist es […] in
kon-
struktiver
Absicht the Philosophie als einziges Kriterium […] der authentischen
Bedeutung der biblischen Texte […] als auch […] der Wahrheit der so ermit-
telten Aussagen zu erweisen […] (Meyer’s objective in
Interpres
is […] to
demonstrate,
constructively
, how philosophy proves to be the only criterion […]
of the authentic meaning of biblical texts […] as well as […] the truth of the
propositions arrived at in this manner)» (Id.,
Biblische Hermeneutik und historische
Erklärung
, cit., p. 239; italics original).