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Paraconsistent Physiology Checklist

Oh yeah, the main thing is that it's a feature of the Rational Universe, not the Irrational Universe which Cacophany represents. Before the Time Lords set down rationality and logic as the ruling principles of Reality it didn't apply to the Irrational Universe.
Okay, that statement, plus the one about logical states, should be good enough to give PP Type 2 to anyone within the Irrational Universe, or sharing in its nature.
 
Okay, that statement, plus the one about logical states, should be good enough to give PP Type 2 to anyone within the Irrational Universe, or sharing in its nature.
Shouldn't it be Type 3 as it has more than 5 logic values ("true", "false", "true and false" and "neither true nor false") since, as the description says, these entities would:

"instead operating on a many-valued logic system with at least five truth values. Such characters occupy a state where they are neither A, nor not A, nor both A and not A, nor neither A nor not A, instead existing in a state one can't describe using simple combinations of A and not A."

Existing outside of potentially millions or even billions of logic states (depends on how many colours of there are, even at the most literal, absolute lowest is 7)

These beings would have to use many-valued logic
 
Shouldn't it be Type 3 as it has more than 5 logic values ("true", "false", "true and false" and "neither true nor false") since, as the description says, these entities would:

"instead operating on a many-valued logic system with at least five truth values. Such characters occupy a state where they are neither A, nor not A, nor both A and not A, nor neither A nor not A, instead existing in a state one can't describe using simple combinations of A and not A."

Existing outside of potentially millions or even billions of logic states (depends on how many colours of there are, even at the most literal, absolute lowest is 7)
Not exactly, the scan about the rainbow was referring to logic states, logic states are: (Life & Nonlife, Being and Nonbeing, Existent or Nonexistent, etc)

There can be infinite logical states, each of which only has 4 Truth States, which are as you mentioned: ("true", "false", "true and false" and "neither true nor false")

So, existing outside of logical states would mean you are neither A nor Not A, which is the 4th Truth State, which is still PP Type 2.
 
Might need more context, since in Doctor Who, it does give Logic states to the Rational Universe, with there being an analogue between each colour in the Rainbow and the amount of logic states:
Adding even more context:

The universe originally lacked dualities, as dual concepts were created by the Grey Man's people — Falls The Shadow


And the Grey Man, in an attempt to counteract this, created a computer capable of generating the opposite effect: "ambiguity", which shattered certainties. To achieve this, they needed to access the mathematical core of the universe: the little numbers at the edge of the quantum event horizon, where the macro and micro worlds become interchangeable — Falls The Shadow



The laws of rationality and mathematics had been woven by the Time Lords — Cwej: Down the Middle¹, The Book of the Snowstorm²



The laws of logic and mathematics are more fundamental than the laws of physics — Liberating Earth

Reality is founded upon existence and non-existence, 0 and 1 — Cwej: Fragments of Totality

However, the rational universe created by the Time Lords is merely one flavour of reality in comparison to the pre-universe, which operated through infinite possibilities — Christmas on a Rational Planet

The pre-universe existed within a vast flux of stories and realities that conflicted with the laws of rationality that Rassilon sought to establish. Thus, "infinite possibilities" essentially refers to infinite stories, each with its own rules that contradict the rational laws of the Time Lords — Cwej: Lungbarrow by Loomlight

The Time Lords banished all irrational concepts that did not align with their rational worldview — Cwej: Lungbarrow by Loomlight

The pre-universe allowed for things that were literally impossible, things that violated every known and unknown law — Christmas on a Rational Planet

And the Queen is simply all possible (rational) forms and all impossible (irrational) forms simultaneously — Christmas on a Rational Planet
 
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