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.
