%A Meixner, Uwe
%D 2017
%T Axiomatic Method
%! Axiomatic Method
%X <p>Whether in mereology or any other area, applying the axiomatic method means to specify an axiomatic system S, consisting of <italic>the axioms of</italic> S and <italic>the logic</italic> of S. The axioms of S are certain basic statements, and the logic of S is a set of basic inferencerules which can be used to generate further statements from given statements (ultimately from the axioms). The specification of S must be <italic>effective</italic>, that is, it must be in every case decidable whether or not a given statement belongs to the axioms of S, and whether or not a given inference-rule belongs to the logic of S. Relative to the axiomatic system S – the axioms plus <italic>the logic</italic> – a notion of <italic>provability</italic> is recursively defined: (1) <italic>the axioms of</italic> S are provable in S; (2) if the premise(s) of an inference-rule of the logic of S are provable in S, then also the conclusion of that inference-rule is provable in S; (3) only statements that can be obtained by (1) and (2) are provable in S. Any statement that is provable in S but is not an axiom of S is called a <italic>theorem of</italic> S.</p>
%U
%0 Journal Article
%J PCM: Philosophia Contributions – Mereology
%V 1
%N 1