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A case against Boolean logic

abuseofnotation.github.io

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Re: A case against Boolean logic

#61

Post by ufocia »

Daub wrote: post #18
mcdonje wrote: post #13

In one respect, boolean logic is popular because of bits. If we had ternary processors, ternary logic would be more popular. 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…

> Ternary is probably way better at modeling the real world, but the complexity could make code hard to understand. Maybe that can be solved. 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.

Let's just skip to quantum which models the "real" world in "real" terms.

Re: A case against Boolean logic

#62

Post by matt_kantor »

ufocia wrote: post #60
matt_kantor wrote: post #47

Earlier quoted context omitted.

> 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? The Curry-Howard correspondence[1] tells us that every function is a proof (in the intuitionistic sense) of the proposition represented by its return type, given the axioms ("context" in the article) represented by its arguments. This fact is leveraged heavily by…

Fuzzy logic may be one approximation. Analog processors may be another.

Did you reply to the wrong comment? I don't see how this relates to what I wrote.

Re: A case against Boolean logic

#64

Post by meroes »

piekvorst wrote: post #51

Logic is identification of that which exists . Thus, a proposition either does correspond to reality or doesn’t at all. There is no partial semi-truths: the moment a concept or proposition ceases to describe reality, it becomes false. Contexts don’t change much. They are merely implicit knowledge, subject to the same binary standard. They don’t change the truth, only applicability. Mentioning Gödel here is not just c…

“The law of non contradiction exists”. Even Aristotle couldn’t “prove it” exists yet logic uses it all the time. I hardly think logic is about what exists but rather a tool, born out of interlocution.

https://plato.stanford.edu/entries/aristotle-noncontradictio...

Re: A case against Boolean logic

#65

Post by hcs »

tgv wrote: post #17
mcdonje wrote: post #13

In one respect, boolean logic is popular because of bits. If we had ternary processors, ternary logic would be more popular. 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…

> If we had ternary processors, ternary logic would be more popular. 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.

    enum Bool
    { 
        True, 
        False, 
        FileNotFound 
    };
https://thedailywtf.com/articles/What_Is_Truth_0x3f_

Re: A case against Boolean logic

#66

Post by bashmelek »

This is the second time I’ve heard of “Platonism” referring to false dichotomies, and as someone who has casually read a bit of Plato I am very confused. Am I misunderstanding or is this a common technical term?

Re: A case against Boolean logic

#67

Post by zombot »

> We might not be able to construct neither

So we might be able to construct either, but they meant to say the opposite. Am I to take criticism of Boolean logic from someone who doesn't understand negation?

Re: A case against Boolean logic

#68

Post by nyrikki »

matt_kantor wrote: post #47
mcdonje wrote: post #13

In one respect, boolean logic is popular because of bits. If we had ternary processors, ternary logic would be more popular. 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…

> 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? The Curry-Howard correspondence[1] tells us that every function is a proof (in the intuitionistic sense) of the proposition represented by its return type, given the axioms ("context" in the article) represented by its arguments. This fact is leveraged heavily by…

The Curry-Howard correspondence formal relationship between intuitionistic logic and typed lambda calculus.

Intuitionistic logic doesn’t hold PEM as a priori.

Due to many issues like [0] you actually lose the univalent in HoTT.

That is what allows you to say two programs are equivalent by behavior.

No comment on the OP, but be careful as it is a rabbit hole.

[0] https://ncatlab.org/nlab/show/Diaconescu-Goodman-Myhill+theo...

Re: A case against Boolean logic

#70

Post by [deleted] »

gobdovan wrote: post #46

This blog is one of the most confused and inaccurate collection of writing that I recurrently find on HN. The account spams a deeply flawed blog post about 'Category theory illustrated' (also referenced from this article) where it misstates central theorems in CT and this 'Case against boolean logic' article, which promises an alternative to Boolean logic, but never formulates one. The article instead gestures toward…

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