Istaro wrote:Since nested footnotes are right-associative for the same reason that exponentiation is right-associative, note that footnote 6 says "actually a 1^4", i.e. "actually a 1^3". Also note that since 3 relates to truth, not numerical value, it must be applying to the entire preceding string, not just the 1: "(actually a 1)^3", not "actually a (1^3)".

Now, take a look at footnote 5: "true^(2^(6^3))".

We know that the 6^3 applied to the 2 must change said 2 somehow, because if the 2 were left as is, we'd end up having to apply it to the "true" at the bottom, and true^2 is a syntax error.

Looking at all the footnotes, there are only two conceivable ways in which 6^3 could change 2 (because there are only two footnote effects that can change numbers): increment it, or make it actually a 1.

But 6^3 can't increment 2, because 6^3 doesn't ever take us to the incrementing footnote (footnote 2). See my first line if you're unsure about that. (Specifically, 6^3 only involves the statement "actually a 1" and the stuff pertaining to truth or the lack thereof.)

So that leaves us with one option: 6^3 must equal "actually a 1"—that's the only way in which 6^3 can safely dispose of the 2 under it, preventing that 2 from illegally applying to "true".

I agree with everything so far.

Istaro wrote:If 6 is "actually a 1", that means that "(actually a 1)^(2^2)" = "(actually a 1)^4" = "(actually a 1)^3" is equal to "actually a 1"; i.e., 3 is "true".

If 3 is "true", the original text says "no^true", i.e. "no". No evidence was found in the data.

I disagree with this. I don't see how you inferred "6 = (actually a 1)", given that up until that point, you had only shown that "6^3 = (actually a 1)". In fact, the assignments "3 = true" and "6 = (actually a 1)" are inconsistent, because we also have:

3

= (Not true)^5 <definition of footnote 3>

= (Not true)^(True^(2^(6^3))) <definition of footnote 5>

= (Not true)^(True^(2^((actually a 1)^true))) <substituting assignments>

= (Not true)^(True^(2^(actually a 1))) <evaluating>

= (Not true)^(True^1) <evaluating>

= (Not true)^(True^(ignore this)) <definition of footnote 1>

= Not true <evaluating>

Which is a contradiction with our one of our assignments "3 = true".

However, if we begin with the assumption that "3 = Not true", we get the following complete assignment, which is consistent as far as I can tell. Note that footnote 5 actually has no effect.

1 = Ignore this

2 = Increment by 2 before following

3 = Not true

4 = Not true

5 = ""

6 = Not actually a 1

Verifying consistency of 3, 5, and 6:

3 = (Not true)^5 = (Not true)^("") = Not_true

5 = True^(2^(6^3)) = True^(2^((Not actually a 1)^(Not true))) = True^(2^(Actually a 1)) = True^(1) = True^(Ignore this) = ""

6 = (Actually a 1)^3 = (Actually a 1)^(Not true) = Not actually a 1

Under these interpretations (ibid meaning that 4 = 3, subfootnotes applying to the whole footnote rather than a single number or word), I don't see any other consistent assignments. So if this is the only consistent assignment, then the claim in the text is false, evidence was found.