Non Locality Proofs in Quantum Mechanics Analyzed by Ordinary Mathematical Logic

The so-called non-locality theorems aim to show that Quantum Mechanics is notconsistent with the Locality Principle. Their proofs require, besides the standard pos-tulates of Quantum Theory, further conditions, as for instance the Criterion of Reality,which cannot be formulated in the language of Standard Quantum Theory; this di±-culty makes the proofs not veri¯able according to usual logico-mathematical methods,and therefore it is a source of the controversial debate about the real implications ofthese theorems. The present work addresses this di±culty for Bell-type and Stapp'sarguments of non-locality. We supplement the formalism of Quantum Mechanics withformal statements inferred from the further conditions in the two di®erent cases. Thenan analysis of the two arguments is performed according to ordinary mathematicallogic.