[gobdovan]

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 heavily conflated 4 epistemic 'categories' (True, False, Unknown / unknowable, Meaningless / senseless) that conflate semantic truth values, epistemic states, and linguistic well-formedness.

You can represent all of these distinctions inside ordinary first-order logic. You can have:

Meaningless(fact)= True/False

Unknown(fact) = True/False ...and so on and so forth.

Where's the escape from boolean logic now? If anything, it points you to the fact that boolean logic is much more flexible than the given categories, which box you, from infinite possibilities into a few. Ironically, this could be abused even better by authority. An institution could simply say 'Human rights is a meaningless question, in the context of progress and prosperity. Asking us if we're for or against it is binary thinking.'

The biggest blind spot however is the idea that a proof is a universal tool for getting to truth. This completely dismisses the central thesis in philosophy and science of analytic-synthetic distinction. Intuitionistic proof theory works for analytic claims (like math) because their truth is self-contained. But synthetic claims (clamis about how the real world actually is) cannot be proven with mathematical certainty, but only supported, challenged or revised via empirical observation.

By trying to map formal proof theory directly onto politics and psychology, the author ignores how empirical truth actually works, e.g. gravity isn't proven like a theorem. as Popper noted, scientific theories are falsifiable and subject to revision, shifting from Newtonian to relativistic contexts while reality stays the same.

[athrowaway3z]

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.

[rhdunn]

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

[gobdovan]

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.

[smaudet]

Yeah, this (the OPs) reads like a confused teenagers post, who has just started to explore the intracacies of logic. The whole post disproves itself...

Fuzzy logic is fine, I suspect they saw something like this and got confused. I would recommend they think harder about how very pertinent boolean logic is to everything they are doing before dismissing it...

[ufocia]

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.

[ultrablack]

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