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A case against Boolean logic

abuseofnotation.github.io

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Re: A case against Boolean logic

#51

Post by piekvorst »

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 cliche, it’s irrelevant. Gödel is about artificial formal deductive systems. They are not a claim to exclusive philosophy.

Re: A case against Boolean logic

#52

Post by mcphage »

In addition to the points other commenters here have made, there's a large number of different logics building up from boolean logic—predicate calculus, various modal logics, and more. So rather than argue it's wrong or useless, it seems better to see it as the lowest rung on a ladder, and if boolean logic ain't cutting it, then take a step up the ladder.

Re: A case against Boolean logic

#53

Post by andychiare »

Boolean logic/black-and-white thinking is convenient for simple processing. But the world isn't simple.

If you just consider time, there are statements whose truth you can't determine: "It will rain tomorrow" (BTW, tomorrow "tomorrow" will be the day after tomorrow)

Re: A case against Boolean logic

#54

Post by kikimora »

0xfedcafe wrote: post #4

fp folks trying to reinvent probability theory is hilarious

I don’t think this is anyhow about fp. Constructive logic appears naturally in proofs and type systems where it is very useful. Also it is quite fascinating to me to learn that law of excluded middle can be omitted and still such logic yields useful results.

I also admit that the blogpost is lacking in many respects.

Re: A case against Boolean logic

#55

Post by ecoherb »

In biological Boolean Networks, this is a long standing form of debate, particularly the last line: "And without the correct context, the statement might not make sense at all."

Should we build Boolean networks that represent biological systems that have specific configurational requirements or should the model itself encode the limited context?

Often we choose something in-between, where the Boolean model of our biological system has some configurational choices (the context), but we can modify the context to see how the system operates in non-standard conditions.

All of this is with the hope that the ways that the model produces contradictions and unexpected behaviors can inform how our reality produces contradictions and unexpected behaviors (most commonly cancers). The states of the representative system, the Boolean network, may make no sense, and we can diagnose why with a Boolean network, when it would be neigh impossible to understand that odd state in the real system.

Re: A case against Boolean logic

#56

Post by danbruc »

kqp wrote: post #50
danbruc wrote: post #30

Earlier quoted context omitted.

In one respect, boolean logic is popular because of bits. If we had ternary processors, ternary logic would be more popular. 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, true, and false but this does not really change…

The known/unknown question is not separate in the real world, computing avoids it by asking binary questions only when they’re answerable. Considered generally, though, if I ask a true/false question then read your answer from a single bit, it may be the case that there is no possible way for you to not lie to me.

Which is exactly what I wrote. [...] two dependent binary questions [...] The second one is meaningless if the first one is false.

Considered generally, though, if I ask a true/false question then read your answer from a single bit, it may be the case that there is no possible way for you to not lie to me.

Then you are not asking a binary question. If there is, for example, the possibility that I might not know the answer, then you are actually asking two dependent questions - do you know the answer and if so, what is the answer.

Re: A case against Boolean logic

#57

Post by epolanski »

naveen99 wrote: post #15
epolanski wrote: post #5

Earlier quoted context omitted.

Non-boolean logic is more than a century old. 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" a binary answer cannot model business logic decisions on this set of data properly. Thus SQL implements a third logic value, UN…

For 3 values, don’t you just need a pair of booleans ? Known or unknown… If known: 0 or 1 …

unknown | yes | no has the same cardinality (3) of unknown | boolean as you can replace boolean with yes | no.

If you write code that has to handle it, you still need to consider 3 cases, you can never reduce it to two cases only.

Re: A case against Boolean logic

#59

Post by ufocia »

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…

When "shifting from Newtonian to relativistic contexts [while] reality" does not stay the same. While the op has many shortcomings, this post itself falls into the binary trap. You conclude without proof and contrary to currently accepted models, e.g. Schrodinger's uncertainty principle, that objective/Platonic reality exists.

I agree with you that you can approximate continuous/analog systems with discrete/binary ones, but those approximations (almost) always have some loss of accuracy, assuming, arguendo, that accuracy even exists. For most purposes these "tolerances", if you will, are acceptable and even desirable. Thus the op also falls into the binary trap suggesting that the only right way to do things is the op's way.

The quasi-political rant at the end does feel misplaced. While I see the op's general point, e.g. political polarization, the introduction/switch into the topic feels at least jarring.

Re: A case against Boolean logic

#60

Post by ufocia »

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…

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