If logical thinking is, as you say, imperfect, is it possible that your own conclusion that no perfect things exist is itself an imperfect conclusion? If you use this word perfect, you at least have the Idea of Perfect, even if no perfect things exist. This kind of funny talk I'm using about Ideas of perfect things goes back 2400 years to Plato and his Theory of Forms[1]. According to the philosopher-logician A. N. Whitehead:

  The safest general characterization of the European philosophical tradition
  is that it consists of a series of footnotes to Plato.