Conclusion

The here proposed pragmatic insight into the relation between structures and systems leads to an alternative interpretation of Quine’s thesis of the incompleteness of mathematical objects and the ideas to which they belong: the incompleteness is neither an epistemic deficiency possessed finally by all objects according to Poincare, nor a purely verbal accommodation which in fact hides an ontological commitment with respect to a set theoretic progression (Quine 1986, 401), but a functional peculiarity of a new sort: it is the result of a stipulation of a system of relations connected with the relatively concrete by a practice of semiotic analysis linked to our capacity of harmonization.