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

**English Translated to Minimal Type Theory:**

** LP @ ∀L ∈ Formal_Systems ~∃Γ ⊂ L (Γ ⊢ LP)**

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

[00] LP (01)(05)(09)

[01] FOR_ALL (02)

[02] ELEMENT_OF (03)(04)

[03] L

[04] Formal_Systems

[05] NOT (06)

[06] THERE_EXISTS (07)

[07] SUBSET_OF (08)(03)

[08] Γ

[09] PROVES (08)(00) // **cycle indicates error: evaluation infinite 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