  This paper presents an in-depth analysis of the anatomy of both
thermodynamics and statistical mechanics, together with the relationships
between their constituent parts. Based on this analysis, using the
renormalization group and finite-size scaling, we give a definition of a large
but finite system and argue that phase transitions are represented correctly,
as incipient singularities in such systems. We describe the role of the
thermodynamic limit. And we explore the implications of this picture of
critical phenomena for the questions of reduction and emergence.
