Test historical explanations of the Trinity to reveal their logical paradoxes and associated heresies.
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Select an explanation to test whether it maintains identity while preserving distinction.
Trinitarian Formal Logic Solver
Classical Trinitarian doctrine attempts to assert four axioms simultaneously using identity logic:
Axiom 1: Father = God
Axiom 2: Son = God
Axiom 3: Spirit = God
Axiom 4: Father ≠ Son ≠ Spirit
Axiomatic Truth Table Assessment
Explanation Type
One Substance?
Three Persons?
Co-Eternal?
Logical Outcome
Orthodoxy (Standard)
True
True
True
Violates Law of Transitivity
Modalism
True
False
True
Heresy (No distinction)
Partialism
False
True
True
Heresy (Fractions of God)
Tritheism
False
True
True
Heresy (Polytheism)
Arianism
True
True
False
Heresy (Created Son)
The Transitivity Paradox
By the Transitive Property of Identity, if $A = B$ and $C = B$, then $A = C$.
If Father ($A$) = God ($B$), and Son ($C$) = God ($B$), then Father ($A$) must equal Son ($C$).
Denying $A = C$ while maintaining $A = B$ and $C = B$ breaks standard classical logic systems,
which is why every simplified analogy collapses into one of the heretical states above.