Compositionality

On the connection between a proper view on compositionality and strict finitism: Weyl’s idea that universal formulae ranging over the natural numbers are not statements, but ‘Anweisungen auf Urteile’ (as cited in Marion, Wittgenstein, Finitism, and the Foundations of Mathematics, chapter 4) is congenial. The assumption that there exists an infinite number of sentences that satisfy a pattern in quite a similar manner can be seen as the result of mistaking rules with the set of all their instances. As actual sentences of a language these simply do not (yet) exist.

Martin Stokhof
from: Interpretation
date: fall 2001