**In English: “This sentence is not true”.**

**Liar_Paradox ≡ ∃X ~Provable(X, Liar_Paradox) **

**Minimal Type Theory (MTT) Knowledge Tree of the Liar Paradox:**

Translated into a directed acyclic graph (DAG) by the MTT compiler

[01] Liar_Paradox (02)(04)

[02] THERE_EXISTS (03)

[03] X

[04] NOT (05)

[05] Provable (03)(01) // **cycle indicates infinite evaluation loop**

The above formalism shows that the Liar Paradox gets stuck in an infinite evaluation loop and is thus not a Truth Bearer. Any expression that is impossibly true and impossibly false is not a truth bearer and therefore not a member of any Formal System even though it may otherwise be a syntactically WFF.

Copyright 2016 and 2017 Pete Olcott