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Axiomatic Method

Uwe Meixner

Pages 89 - 91

Whether in mereology or any other area, applying the axiomatic method means to specify an axiomatic system S, consisting of the axioms of S and the logic 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 effective, 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 the logic – a notion of provability is recursively defined: (1) the axioms of 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 theorem of S.

1Institute of Philosophy, University of Augsburg

1 Meixner, U., (1997), Axiomatic Formal Ontology, Dordrecht: Kluwer.

2 Simons, P., (1987), Parts. A Study in Ontology, Oxford: Clarendon Press.

3 Ridder, L., (2002), Mereologie, Frankfurt a. M.: Klostermann.


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