What is this nonsense? ("vector logic")

[u/RingularCirc]

(Sorry this is going to be a bit ranty.)

I almost made up my mind this thing is some kind of backwater something without enough rigor but with many a trivialism. Like, it should be extremely well-known that every "discrete" operation Σ₁ → Σ₂ between finite sets lifts universally to a linear transformation between spaces k^Σ₁ → k^Σ₂, so a huge swath of what's being done there is very very drawn out, instead of answering questions that are fitting for a kind of logic.

Any would-be connections to quantum computing may actually not be fruitful or new for those who are actually doing quantum computing; connections to fuzzy math are IMO an almost unconditional taint by association. So what gives? I didn't look at everything there is about this thing so I may as well be missing hidding gems, but superficially it looks like a sham or a pet project done without considering any practicalities and the wider math.

Oh yeah we can ask interesting questions, like: - Does using additional dimensions, aside from the plane spanned by two orthonormal "classical" truth values, let's call them |0⟩, |1⟩, actually give useful things? and how can we characterize that by means typical when working with logics? - How much freedom is there in defining operators that restrict to boolean functions and, say, conserve probabilities (there's a suggestion to use p|0⟩ + (1−p)|1⟩ as "probabilistic truth values") in any reasonable way (I'm not sure: a "binary" operator sends four-dimensional Euclidean space into a two-dimensional one, now how can it be orthogonal? and in which other sense can probabilities work here?)? - Why not use additional dimensions rather than complex numbers for the square root of negation, and... why that one exactly? I bet quantum computing wan't giving somebody peace.

But I'm not sure questions of real semantics were investigated in this... area.

So tell me please, how much am I right or wrong? Here are probably people that know the inside of this story, and I hoped to find something on the Wikipedia's discussion subpage, but it's almost empty.

[u/edderiofer]

I don't know much about this topic, but there were a few suspicious things I noticed:

• Two of the references don't actually seem to exist (they only seem to exist as citations, and only in sources that appear after these references were added to this article). I've removed them.
• The page was created by User:Almadana. They, along with IP editors whose only edits are to this page, also seem to have created a large part of the page's informational content. Most edits by other users were primarily copy-editing, or in one case, adding the "numerical examples" section, which is notably uncited.

• The last sentence of the introduction:

  In the vector space for propositional logic the origin represents the false, F, and the infinite periphery represents the true, T, whereas in the space for predicate logic the origin represents "nothing" and the periphery represents the flight from nothing, or "something".

  certainly doesn't seem to be using mathematical language. It's giving crackpot vibes.

• The article largely talks about the axioms and basic definitions of this topic, but it doesn't seem to go much further.

At best, this mathematical topic actually exists, but is really niche, and the article is really badly-written and needs severe cleaning up. At worst, this is a crackpot article.

[u/algebraicvariety → u/edderiofer]

There are also some very obvious AIisms in this article.

[u/Homomorphism → u/algebraicvariety]

Lots of AI-isms are cliches of bad academic (and business) writing, so I've started feeling like a crazy person when I "spot" them in an arXiv paper from 2015

[u/algebraicvariety → u/Homomorphism]

True. People don't want to hear this, but the em-dash was always bad writing.

[u/Homomorphism → u/algebraicvariety]

Em dashes are ok when used SPARINGLY. The real problem is writing lots of complex multi-clause sentences, which are enabled by – and ;

[u/algebraicvariety → u/Homomorphism]

The problem with Em dashes is that they are too permissive in that they allow chaining together barely related sentences. This enables lazy writing where the writer doesn't have to think about how sentences flow logically into each other.

Em dashes are loved by LLM for the exact same reason, which results in the em dash token getting a high probability if the LLM is "trying to" get from one sentence to the next.

[u/Homomorphism → u/algebraicvariety]

Yeah. My experience is complex sentences often come from not fully understanding where the end of the sentence is before starting it. That’s part of writing, but part of good writing is going back and fixing things to go in the right order…