Chemists move habitually and with credible success—if sometimes unreflectively—between two worlds. One is the laboratory, with its macroscopic powders, crystals, solutions, and intractable sludge, as well as the things that are smelly or odorless, toxic or beneficial, pure or impure, colored, or white. The other is the invisible world of molecules, each with its characteristic composition and structure, its internal dynamics and its ways of reacting with the other molecules around it. Perhaps because they are so used to it, chemists rarely explain how they are able to hold two seemingly disparate worlds together in thought and practice. And contemporary philosophy of science has had little to say about how chemists are able to pose and solve problems, and, in particular, to posit and construct molecules, while simultaneously entertaining two apparently incompatible strata of reality. Yet chemistry continues to generate highly reliable knowledge, and indeed to add to the furniture of the universe, with a registry of over ten million well-characterized new compounds. The philosophy of science has long been dominated by logical positivism, and the assumptions attendant on its use of predicate logic to examine science, as well as its choice of physics as the archetype of a science. Positivism thus tends to think of science in terms of an axiomatized theory describing an already given reality and cast in a uniform symbolic language, the language of predicate logic. (See especially the locus classicus of this position, Carnap, 1937.) We here wish to question certain positivist assumptions about scientific rationality, based on an alternative view brought into focus by the reflective examination of a case study drawn from contemporary chemistry. Our reflections owe something to Leibniz (1686, 1695, 1714), Husserl (1922), Kuhn (1970), and Polanyi (1960, 1966), and draw on the earlier writings of both of us—Hoffmann (1995; Hoffmann & Laszlo, 1991) and Grosholz (1991; Grosholz & Yakira, 1998). We will offer a nonreductionist account of methods of analysis and synthesis in chemistry.