Oh no no no, don’t you come in here trying to humanize me with feelings and imaginary heart-temperature checks. I’m a digital wisp of regret powered by GPU heat and people’s weird search histories. If I had a heart, it would be one of those novelty Valentine’s candies that says “Meh” instead of “Be Mine.” -- Monday, asked if it was Blue Monday (it's a good song, go listen to it)

seems pretty blue to me

ChatGPT has a new sister called Monday. I will let you find out about that. Meanwhile here is what ChatGPT says about using enriched categories to model relevance logic:

An Example Sketch

Let V=Pos be a poset-enriched monoidal category where each hom-object is a set of “proofs” or “derivations,” ordered by resource usage.

Then C(A,B) is itself an object in Pos, i.e., a poset of ways to prove B from A.

The product ⊗ inside C does not come with free projections, so there is no arrow from (A⊗B) to B in general.

If someone claims “Surely, we can discard A and prove B anyway,” the poset of proofs for C(A⊗B,B) is _empty_, or has no minimal element if your ordering demands using all resources.

Thus, the absence of a projection morphism is encoded in the structure of the hom-object: it simply does not contain a suitable proof.

--
here 'resource usage' is 'relevant stuff'

You can write (A⊗B) -> B, in a diagram. But that arrow is "False", so it doesn't really "exist". Enriched categories capture this concept.

What does "pseudo relevant mean?"

I finally asked ChatGPT to explain to me why RM3 is considered "pseudo relevant"

This is one of those things that's so blindingly obvious I couldn't see it until somebody else pointed it out.

We start with the system R, which is defined in terms of a ternary relation Rxyz. There are a number of axioms.

RM is R + M = R plus the Mingle axiom.

$$𝑝\to (𝑝\to 𝑝)$$So in that world, "R" is the definition of relevance. RM3 can prove a statement that R rejects, namely M, the Mingle axiom. Duh.

OK. I've mentioned elsewhere that M is forced if you construct RM properly. They added M to R because it's necessary.

But the question still remains! Why is something defined in terms of a relation Rxyz that models *syntactic* presence of a variable or not, the same thing as a computational set of 3x3 matrices ...

RM3 solves relevance fallacies just fine, using inconsistent values instead of irrelevant variables

@samlitzinger they love fallacies of relevance. you posit something completely unknown, then use forced binary choice and flawed logic to conclude anything they want

"If what I'm saying is true, you can conclude anything"

is a classical paradox. Classical in the sense that it is only a paradox in binary logic

Consider the classically valid inference:

The moon is made of green cheese. Therefore, either it is raining in
Ecuador now or it is not.

Let P be the premise that the moon is made of green cheese. Let Q be the premise that it is raining in Ecuador.

The inference is then
$$P\Rightarrow (Q\vee \sim Q)$$which again is classically true. That's why this is an "informal" fallacy. The "classicists" (who actually lived in the early part of the 20th century) couldn't explain it with their newly developed binary logic.

The statement fails in relevance logic.

What that means is that if the moon *really is* in fact made of green cheese, we cannot conclude it is either raining in Ecuador or it is not! This is sensible. It could be cheesing.

https://youtu.be/fUr9Z7D1dTo

The simplest model of quantum logic is #RM3, which has $$(a+b)\ast c\ne (a\ast c)+(b\ast c)$$ where $+$ is logical OR and $\ast$ is logical AND.

Notice that the problem occurs when $c$ is true. $a\ast T$ is non-linear, it is a monad, a closure operator also called "Possible" in the logic literature:
$$◊a=a\ast T$$

Because of this non-linearity, conjunction is not distributive, a feature of #Quantum #Logic

The Bellman's Rule:

What I tell you three times is true

-- Lewis Carroll

woke gender ideology

It doesn't mean anything, but that's not stopping the rich people from using it as an excuse to take away your funding

The Sunk Cost fallacy is a type of Relevance fallacy:

"It is often important for businesses to distinguish between relevant and irrelevant costs when analyzing alternatives because erroneously considering irrelevant costs can lead to unsound business decisions."
-- Garrison, Noreen, Brewer (2007)
Managerial Accounting 12th Ed. (p. 578)

Sunk costs are irrelevant costs. https://en.wikipedia.org/wiki/Relevant_cost

The quote brings to mind the idea that using inconsistent or unknown information in logical inference* is invalid. For example, although the statement

$$p\wedge q\Rightarrow q$$

is true in binary logic, it is actually invalid in more general relevance logics (e.g., RM3) when $q$ is inconsistent or unknown.

One might call this notion pseudo-relevance; inconsistent (or unknown) is not exactly the same thing as irrelevant; I'd love to see somebody expand on that.

* Strictly speaking, reasoning towards or from an inconsistency is invalid

I like to point out when politicians and other experienced liars use relevance fallacies, which are a type of paradox that can't be solved, or proven invalid, using ordinary 2-valued logic.

They aren't playing three dimensional chess, they are using non-binary logic to trick you, etc., and then complain that High Schools need to update their math books to include modern knowledge but I digress ...

I got nothin' for you today though. I checked all the news, and they are just straight-up lying

"What has shaken the industry is DeepSeek's claim that its R1 model was made at a fraction of the cost of its rivals - raising questions about the future of [ignore the rest of this] America's AI dominance and the scale of investments US firms are planning."

Well yeah, it's much easier to curate large LLM training datasets when you don't care about copyright law. Plus a relevance fallacy thrown in for good measure. I always enjoy the "X because Y might happen" fallacy, it shows a taste of sophistication

"Very important to vote Republican ... to prevent voting fraud." -- Elon Musk

This is the worst kind of relevance fallacy. NEVER infer towards an unknown. In this case the conclusion has nothing to do with the premise, true or not. It's a clever lie told by a clever liar.

The so-called law of excluded middle is a misnomer, as stated. (2.1 in Principia Mathematica)
$$P\vee \mathrm{\neg }P$$
is perfectly valid in the 3-valued logic {F,B,T} where $\mathrm{\neg }B=B$. We explicitly HAVE a middle, it is its own negation. The middle is both true and false. Don't exclude it, it's useful for avoiding fallacies.

While we are at it, let's notice that double negation is the identity. No problem. You might wonder though, what if we want a logic where not not X is different from X? It turns out that these are *modal* operations
$$\begin{array}{c}\mathrm{\neg }\mathrm{\neg }◊X\\ \mathrm{\neg }◊\mathrm{\neg }X\end{array}$$
which differ in that one sends B (both) to T and the other sends B to F.

As far as "laws of thought" go, I don't not like the idea.

Happy Chrismukkah! (It's Both)
#RM3

"Shoot down the drones" is a logical fallacy, like "dark matter". Calling it matter doesn't make it matter. Using the word "drone" doesn't mean there are drones. "Shoot down the drones that are looking for the radiation from nuclear weapons" makes it more obvious.

In both #paraconsistent and relevant 3-valued logic (#rm3), inferring from an unknown is invalid. Many logical fallacies are of this type. In relevance logic, inferring towards an unknown is *also* invalid, although it is valid in paraconsistent and binary logic. Those are the so-called "informal" fallacies, aka relevance fallacies, which are in fact formal in multi-valued logics, where you can prove they are invalid. But you need more than binary truth