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A case against Boolean logic

abuseofnotation.github.io

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Re: A case against Boolean logic

#71

Post by ultrablack »

ufocia wrote: post #59
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 on…

I you don’t believe on objective reality, who are you posting to??

Re: A case against Boolean logic

#72

Post by adrian_b »

Nitpick: TFA discusses binary logic, i.e. logic with only 2 truth values, not Boolean logic, which is a particular form of binary logic, and which does not match the description from TFA.

The innovation brought by George Boole to logic was that he replaced the traditional logical values "true" and "false" with the numbers "1" and "0" and he identified the traditional logical operations with special cases of arithmetic operations.

This allowed him to view certain forms of logical reasoning as solvable by a kind of mechanical computation. Because of this, his work had an important influence on the development of automatic computers.

The modern fashion in computing science of calling a data type with the values "true" and "false" as "Boolean" is a misnomer that has nothing to do with George Boole, and which has its origin in the ALGOL 60 report and in its preliminary variants, which misused the term "Boolean". The IBM FORTRAN IV language did better than ALGOL 60, by calling the data type with "true" and "false" values as "logical", not "Boolean", but unfortunately most later languages used the ALGOL 60 term, not the FORTRAN IV term.

An example of a programming language with true Boolean logic is APL, where the logical truth values are the numbers "1" and "0" (which is very handy in expressing conditional operations on arrays), while all the programming languages that use "true" and "false" do not use Boolean logic, despite claiming to do so.

I agree with TFA that for dealing with most practical situations binary logic is insufficient and ternary logic is the minimal tool, if not using even more complex kinds of logic, like modal logic or probabilistic logic.

Re: A case against Boolean logic

#74

Post by NooneAtAll3 »

Tangurena2 wrote: post #39
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…

From an information theory perspective, the most efficient base for computations would be e (2.718). And trinary is closer than binary.

I still don't get what is being optimized for to get e as the answer

Re: A case against Boolean logic

#75

Post by kpentad »

This is so dumb.

Dichotomous thinking is, often, a cognitive disorder or maybe a disorder of mood or affect. It has nothing whatever to do with formal boolean logic, without which very little (i.e., none) of science or modern engineering (or, hell, pre-modern rationality!) would even exist.

Its remedies have even less (if that were possible!) to do with intuitionist logic.

Re: A case against Boolean logic

#76

Post by rhdunn »

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…

A better formulation would be something like Fuzzy Logic [1]. That represents floating point values from 0 (false) to 1 (true), so 0.5 could be "unsure", 0.9 could be "very likely", etc. However, that doesn't make boolean logic invalid.

Boolean logic is also the foundation of computing: logic gates, circuits like BCD, etc.

[1] https://en.wikipedia.org/wiki/Fuzzy_logic

Re: A case against Boolean logic

#77

Post by kittikitti »

Thank you for writing this post, I found it insightful and agreed with the fundamentals described. I also appreciated taking a look at the authors book, Category Theory: Illustrated, referenced in the article.

I must note that there is a trivial typo with a missing close-parenthesis, ")", where the article has "(see “When Universality Breaks”."

Re: A case against Boolean logic

#78

Post by carodgers »

"We’ve established that the truth or falsity of a statement depends on its context — that is, on the assumptions we take as true or false in order to justify it."

I am inexplicably and disproportionately irritated by people like this. They've an a priori commitment to epistemic relativism. Unnaturally allergic to any claim that certainty is possible, and dedicated to undoing the careful work of those who are building up what may be known.

No, not every statement requires assumptions in order to hold. "The assumptions A implies B and B implies C, taken together, yield A implies C." This statement contains assumptions and makes observations about them, but it is true regardless of whether the assumptions it describes are true. The statement as a whole is "true" in the exact sense that the no counterexample to it can ever be given in any universe, under any set of assumptions.

I cannot wait for the day that Lean and other proof systems become accessible enough, conversant enough, and interdisciplinary enough to put these eternal confusion peddlers out of business.

Re: A case against Boolean logic

#79

Post by gobdovan »

rhdunn wrote: post #76
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…

A better formulation would be something like Fuzzy Logic [1]. That represents floating point values from 0 (false) to 1 (true), so 0.5 could be "unsure", 0.9 could be "very likely", etc. However, that doesn't make boolean logic invalid. Boolean logic is also the foundation of computing: logic gates, circuits like BCD, etc. [1] https://en.wikipedia.org/wiki/Fuzzy_logic

Fuzzy logic is indeed a better formulation. One nit tho: the intermediary values don't mean 'very likely' or 'unsure' in general. They usually represent degrees of truth or degrees of membership. So it's more like '0.9 tall' means 'quite tall', while '0.5 tall' would be interpreted as 'this guy is tall to a degree of 0.5 out of 1'.

They could technically refer to 'very likely' or 'unsure' only if the predicate you're modeling is itself about certainty or belief. For example, you could say "I'm certain about X to degree 0.8 out of 1" meaning you're quite certain about X. But notice that the 0.8 is about your belief, not about X itself.

Re: A case against Boolean logic

#80

Post by athrowaway3z »

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…

I'm glad somebody called it out. This post reads like "the case against measuring hours" and then trying to vibe-splain how time works in general relativity.

abuseofnotation seems a bit of an understatement. More like abuse of formalisms to dance around old & well understood insights with miss-used jargon.

This goes beyond "not helpful" straight to "actively harmful" for anybody interested but not yet familiar with these concepts.

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