# Two-Stage Interpretation in Formal Logic

## The most famous logical process you have never heard of

Two-Stage Interpretation (TSI) in formal logic is the most famous process you have never heard of.

Kurt Gödel used TSI in his Incompleteness Theorems of formal logic.

There are three steps and two interpretations:

- Create a set of theorems in the system of Principia Mathematica;
**Interpretation 1**: Interpret instances of those theorems as numbers (Gödel Numbers); and**Interpretation 2**: Interpret those numbers as theorems (proofs) under the system of Principia Mathematica.

Two-Stage Interpretation not only appears in formal logic, but also the logic of computer science.

Take, for instance, the four-layer architecture of the OMG’s (Object Management Group’s) Meta-Object Facility.

Models stored in the M3-layer (the meta-metamodel), as instances of the M2-layer (metamodel) have in turn instances that are models (the M1-layer). But M2-layer artifacts/instances (models) may be expressed as XML, of which is not intended for…