There's no to 'I can write this.'

Same sitch in German, you have as in er will lernen 'he wants to learn' vs er hatt Lust, den Dom zu besichtigen 'he'd like to visit the cathedral'.

[Addendum: In Indo-European languages, the infinitival forms are thought to have developed after the break up into daughter dialects. (Cf. Latin -Vre, Greek -ειν (-ein), Sanskrit -tum, and Germanic -Vn.]

Ceci n'est pas un seing.