The present paper is exploratory. The large number of approximate concepts we discuss are approximate in different ways, but we don't have a classification.
Many of the applications of approximate objects will result from theories connecting different levels and kinds of approximation.
I thank Eyal Amir, Johan van Benthem, Sasa Buvac, Tom Costello, Aarati Parmar for helpful comments.
This research has been partly supported by ARPA contract no. USC 621915, the ARPA/Rome Laboratory planning initiative under grant (ONR) N00014-94-1-0775 and ARPA/AFOSR under (AFOSR) grant # F49620-97-1-0207.