We give some basic mathematical ideas of partially ordered sets (posets), which frame into the mathematical way of thinking illustrated in the Erlangen Programme by Felix Klein. The programme entails extracting relevant variables to study, symbolising them and relating them through a function. We show several examples where the mathematical way of thinking, restricted to partial orders, is found in chemistry. The examples are: Geoffroy’s affinity table, benzene’s structure, posetic predictive methods, multicriteria situations and derivation of concepts. Finally we question the ranking process by showing how it disregards its underlying, and not always recognised, posetic nature.
Keywords: Partial order, partially ordered sets, mathematical way of thinking, erlangen programme, posets, mathematical chemistry, ranking, affinity tables, benzene’s structure, posetic predictive methods, multicriteria approaches, formal concept analysis, mutagenicity, estimation of properties, philosophy of chemistry.