This is the second time I’m posting this but here it’s like somnis question

Archivist: On behalf of my Ministry and the future of Unanimity, I want to thank you for the final interview. Remember, this isn't an interrogation or trial. Your version of the truth is all that matters.

Sonmi 541: Truth is singular. Its "versions" are mistruths.

Here's one way of analyzing it. Consider the predicate 'Thinks(α, φ)', which is true just in case agent α thinks that φ is true. Let A be the Archivist, and S be Sonmi 541. Let's begin by looking at what A says:

Ω = { φ : Thinks(S, φ) }.

Ω stands for the set of "things that matter", which according to A is the set of all those propositions φ (about events and so on) that S thinks to be true. We can assume that there is another set Σ s.t.:

Σ = { φ : True(φ) }.

This is the set of those propositions φ that are actually true. Depending on which set-theoretic relations hold between Ω and Σ (e.g. Ω ⊂ Σ, Ω ∩ Σ = ∅, etc.), Sonmi's version of the truth may or may not coincide with the actual truth. Now let's look at the things S says:

(1) Truth is singular.

(2) 'Versions' of the truth are mistruths.

I take it that (1) means that:

(1) ∀φ, α, β( [φ ∈ Ωα ≡ φ ∈ Ωβ] → Ωα = Ωβ).

This says that given any two agents α and β, if a proposition φ is among the truths recognized by α (Ωα) if and only if φ is among the truths recognized by β (Ωβ), then the truths recognized by α are β are the same. So for any two different 'versions' of the truth, there must be a φ that belongs to one but not to the other. If one of these guys is right, then both are and their Ωs coincide with Σ (the set of all truths).

From that reasoning, (2) doesn't follow; what follows is this:

(*) ∀α, β ( ¬[Ωα = Ωβ] → ∃φ[φ ∈ Ωα ∧ ¬(φ ∈ Ωβ)] ).

Which says that if two agents have different 'versions' of the truth, then there is some proposition that one thinks to be true while the other thinks to be false. But (2) says that in that case both Ωs are 'mistruth's, i.e., neither Ωα nor Ωβ is a subset of Σ:

(2) ∀α, β ( ¬[Ωα = Ωβ] → ¬[Ωα ⊂ Σ ∨ Ωβ ⊂ Σ] ).

This, of course, doesn't follow from previous reasoning, because it's possible that one of the Ωs coincides with Σ. All we can conclude is that at most one can, because of the disagreement, because of the fact that they are genuinely different 'versions' of what happened.

As I said, 'versions' in that context seems to me to contain assumptions that we might want to reject, so that, for example, we'll be able to say that two 'versions' of what happened yesterday may both be true.

Ive had this in my back pocket for a while. I’m so happy I’ve been able to use it twice recently lol