This is either a very elaborate joke or the future of computing.
There is one ground truth, origin, fixed point like the North Star: zero. There are an infinite number of possible falsehoods: all nonzero numbers. But Urbit chooses 1 as the canonical false.
So it's not very original at all.
Conversely, here it's just because "it's different". I feel that this is a bit if a shame - some of the other parts of the project appear quite interesting, but making fundamental decisions in downright wrong ways just to mess with expectations comes across as silly to say the least. Why deliberately increase the learning barrier and drive people away?
"As you may remember, to decrement 'a' we need to count up to it."
However, years later I was introduced to boolean algebra, where 1 should be true and 0 — false, if we want multiplication to be "and" and addition "or". And it feels right, because intersection of two sets is (intuitively) multiplication, and joining — addition.
So, yeah, it doesn't seem like a good idea to me as well after all these years.
My expectation is that a set multiplication would give me a new set consisting of all pairs consisting of a single element from each set.
"Pairs" (and, respectively, cartesian product) is a bit more complex, and not so much related to boolean algebra deduction concept.
edit: I should add that I'm not claiming "you can't build measure theoretic probability from this formulation of booleans" is a strike against the project. Just addressing the math question.
g(y) = ∑ᵢ cᵢ × (y ∈ Aᵢ)
which is useful when you define integrals and expectations:
E g(Y) = ∫ g(y) f(y) dy = ∑ᵢ g(cᵢ) P(y ∈ Aᵢ)
where Y is a random variable with density function f. Any integrable function can be approximated as the limit of step functions, so this is a well-behaved way to get a general theory of integration.
Of course, one could replace (y ∈ Aᵢ) with 1 - (y ∈ Aᵢ) if one wanted to use "0" to represent the event (y ∈ Aᵢ) and "1" to represent its complement and not affect the truth of the math, but then there will be lots of termf floating around just to convert the notation into the terms that you need for the math.