On the formal impossibility of analysing subfunctions as parts of functions in design methodology

In this paper, a proof is given that in design methods, the relation between technical functions and their subfunctions in functional descriptions of technical products cannot be analysed as a formal relation of parthood. This result holds for design methods in which transformations of flows of energy, material and signals are accepted as functions. First, two specific categories of such technical functions are modelled. Second, the composition relation by which ordered sets of these functions define other functions is characterised. Third, it is shown that this composition relation for technical functions does not meet the basic postulates of parthood relations as given by mereology, the theory of parthood. It still may be beneficial to designing to take subfunctions informally as the parts of the functions they compose. Yet, the proof shows that when functional descriptions are formalised for, for instance, the development of automated design reasoning tools or for incorporation in engineering ontologies, the composition relation for technical functions cannot unconditionally be taken as a parthood relation.