In another respect, boolean logic is popular because it's easy to reason about. The truth tables are relatively small in size and quantity. Not the case with ternary.
Ternary is probably way better at modeling the real world, but the complexity could make code hard to understand. Maybe that can be solved.
That said, boolean logic is more expressive than I think the blog post gives it credit for because it's usually only a part of the code. Like, it gets used a lot in SQL, where you're reasoning about with several columns. So, yeah, it's binary thinking on each dimension, but there are N dimensions.
The alternative presented is intuitionist logic, which is practically what in the computing world? Where is it used? Or where could or should it be used? I guess it can be represented in lamba calculus...
Ternary truth values combines two dependent binary questions - do we know the truth value of X and what is the truth value of X. The second one is meaningless if the first one is false. You can merge the two binary values into one ternary unknown, yes, and no but this does not really change much. Depending on the context one or the other might be easier to work with. Option types generalize this, there is always a binary choice between the value is known or unknown, and if it is known, then there will also be the actual value. A ternary logic value is just Maybe<Boolean>.
Is it not true that the brain process in ternary?
From the point of view of perception, I believe that we process the world in terms of pairwise comparisons. For example, the atomic indivisible of visual processing is figure/ground separation.
It can arduously crank through simple logic problems with its ludicrously tiny memory (around 8 bytes). Everything else is intuition and guesswork.
You can try to model those heuristics with various logics. Some logics work better in certain situations. Classical first order logic is actually really bad at modeling brain work, but it's simple to automate, so we use it even where it's wildly inappropriate.
Back in ancient CS classes my prof said that was a Russian attempt of building ternary processors with +1, 0, -1 represented as voltages.
Another strike in for-ternary column is that it's the most efficient in the number of digits for representing numbers. Pi is optimally efficient but non-integer bases would break anyone's brain, I think.
Why? Boolean logic is older than its namesake, George Boole (1815-1864). Syllogisms are ancient. And we've had ternary systems, as well as others.
And what does the third value represent? True and false are pretty universal when it comes to predicates, but anything in between is rather subjective.
Except it explicitly is not strictly Boolean in SQL because of nulls.
X = Y can take the value true, false or null if either or both X and Y are null.
It has 2 operators: + and x (or more commonly: dot (.) - but this is more confusing on HN)
Also both + and x operations distribute, so A+(BxC) = (A+B)x(A+C)
We could bring quantum physics as a simple example of binary logic collapsing, but in programming there are countless ones.
A simple one is a table of users in SQL, where age can be `null` and not just a positive number.
For filters like "age < 18" and "age > 18" a binary answer cannot model business logic decisions on this set of data properly.
Thus SQL implements a third logic value, UNKNOWN.
Another simple example "is the room hot?".
This is by intuition a bad fit for binary logic. Even if you define "hot" as 30C it's quite clear that the problem is way too nuanced and context dependent to model with binary logic, you need more than two possible answers than yes/no.
Probability theory presupposes that there's a 0 to 1 or 0 to 100 scale of "truthiness" (depending on which scale one might prefer), while the true non-boolean logic has the guts to fully embrace Parmenides's view on One and the Multiple.
We could also try and approach "knowledge" the way that the 5th-6th century Christian mystics were trying to do during their quest to approach the nature of the Divine (or of the Truth, taken in a more restricted manner) via negatives, more exactly via "turning away their faces from said Truth". Interesting that those Christian mystics were an intellectual continuation of the 3rd-4th century Neoplatonists.
https://en.wikipedia.org/wiki/Brouwer%E2%80%93Hilbert_contro...
You can prove more stuff with classical logic while intuitionistic logic restricts you.
For example given a real number x constructed in intuitionistic logic. You can't determine if x > 0 or x = 0 or x < 0. While you can in classical logic.
Also, more generally you can't prove existence statements in general without construction in intuitionistic logic.
So, there exists an x such that P(x) can be proven without actually finding x classically, but in intuitionistic logic I must provide a procedure for constructing x.
All this said, even though you can prove less statements in intuitionistic logic I find it's restrictions satisfying because it forces us to prove things by showing they exist via construction. Which to me is more satisfying than just showing that a construction exists.
"On the odd day, a mathematician might wonder what constructive mathematics is all about. They may have heard arguments in favor of constructivism but are not at all convinced by them, and in any case they may care little about philosophy. A typical introductory text about constructivism spends a great deal of time explaining the principles and contains only trivial mathematics, while advanced constructive texts are impenetrable, like all unfamiliar mathematics. How then can a mathematician find out what constructive mathematics feels like? What new and relevant ideas does constructive mathematics have to offer, if any? I shall attempt to answer these questions"
https://ww2.ams.org/journals/bull/2017-54-03/S0273-0979-2016...
https://math.andrej.com/2016/10/10/five-stages-of-accepting-...
You can reduce any statement to a series of true/false statements. Now, it may take a lot of statements, but that’s not the point. The point is to have the base be as simple as possible