Breeze Theory

out here spreading the joy of axiomatic erosion

[Breeze Theory @substraeta]

Falsification Bar: Demonstrate ANY formal system that is capable of sustaining knowledge, self-reference and complexity, independent of an underlying recursive process.

[Breeze Theory @substraeta]

Should a political-oriented mindset naturally evolve into a philosophical one? Or is political realism the practical endpoint of philosophy?

Or are they ideally inseparable??

[Breeze Theory @substraeta]

in my feels ❌🙅

pondering the nature of incompleteness ✅💯🔥

[Breeze Theory @substraeta]

Gödel will be a household name in 30 years. Maybe 50

[Breeze Theory @substraeta]

there’s something quite nice about being hopelessly ignorant

[Breeze Theory @substraeta]

@virtualdavegene tautology <-- self-reference as analytic judgement (like Kantian a-priori in logic)
phonology <-- semiotics <-- locally relational pattern hierarchies (like Wittgenstein's language games)

[Breeze Theory @substraeta]

Falsification Bar: Demonstrate ANY formal system that is capable of sustaining knowledge, self-reference and complexity, independent of an underlying recursive process.

[Breeze Theory @substraeta]

@z4um41 @Dragonmaurizio All correct. Read the theory brother

[Breeze Theory @substraeta]

hot take: unironically referring to non-internet addicts as “normies” is a pretty good sign you’ve found yourself in a sophisticated yet deeply misguided echo chamber

[Breeze Theory @substraeta]

I’m not a positivist, nor do I take praxeology as absolute. I reject the idea that axioms deserve deference by default.

Everything you’ve shared so far presupposes the very recursive structure I’m alluding to. If methodological dualism entails mutual reference, it’s already downstream of recursion. So what exactly is your objection?

[Breeze Theory @substraeta]

Self reference trials, day 6: Logic

Fun one today. What makes logic, reason, or knowledge “true?”

Reason informs logic. And reason effectively takes two forms.

Deduction: inferring specific patterns from general observations

Induction: inferring general patterns from specific cases

Really, these are the same processes, just moving in different directions. No matter how far you travel (down to the most specific law or up to the most general observation), there is no concrete “base case” we can fully rest on. The general implicates the specific, and vice versa. What is general at one angle will appear specific at a different angle. The mechanism of reason is necessarily self-referential in this way.

Here’s an example. Try to define what “truth” means purely using reason. You’ll always loop into some kind of paradox. (“truth defines itself” / “truth is what isn’t false” / etc.) This is pretty much Kant’s analytic judgements — true statements are by definition circular.

Ultimately, logic is reliable because it recursively aligns frame with content. Therefore, logic can be explored, extended, and applied — but never fully pinned down, nor can it provide a closed foundation.

[Breeze Theory @substraeta]

@Conza @discoveringbtc Yep. Mises.

Have you considered the law of axiomatic erosion? (Every axiomatic assumption implicates self-reference for its own justification)

[Breeze Theory @substraeta]

@Conza @discoveringbtc “… cannot really come about without each other.”

“…their separability is partially an artifact of the way we analyze the parts.”

amen brother. recursion

[Breeze Theory @substraeta]

@Conza @discoveringbtc Doesn’t the justification of logic via action already presuppose logic for the justification itself?

[Breeze Theory @substraeta]

@Conza @discoveringbtc thx for sharing. how do you differentiate subject / object non-recursively?

[Breeze Theory @substraeta]

@Conza @discoveringbtc category error. praxeology and a priori action already presuppose self-reference. action requires logic, to justify logic by action is to recurse the justification… precisely the meta-structure I’m claiming. same boundary, different angle (ironically)

[Breeze Theory @substraeta]

@HavocWorks embodiment, alignment, coherence; take your pick. unfortunately, because we lack the right language it sounds almost mystical by necessity.

I like “recursive awareness”

[Breeze Theory @substraeta]

@TruePolar Keep the progress, reset the frame.

[Breeze Theory @substraeta]

Self-reference trials, day 5: Physics

I’m no physicist, so informed feedback is welcome here.

Physics aims to pin down the “objective laws” of physical interaction, and make no mistake - these laws help us navigate and predict reality with wild precision.

The fact that physics works so well suggests that mathematical abstraction has genuine intrinsic usefulness. As Eugene Wigner said: “the laws of nature are written in the language of mathematics” - and this only makes sense within a self-describing system.

But the “objective” part is what breaks down at the foundations. Or at least, even our most precise formulations are subject to the same boundary constraint.

Every “observation” is a recursive process: the observer and the observed implicate each other. One cannot be defined independently, so the boundary label is provisional.

Renormalization IS meta-regress; every scale’s laws depend on the parameters of its prior scale. The “whole” is forever out of reach.

Heisenberg uncertainty says: we cannot simultaneously know certain pairs of properties (like position and momentum). This is an intrinsic limitation on modeling physical expression.

Information paradox (information falls into black holes) conflicts with quantum theory, which says information can’t be destroyed or lost. Black holes must then serve a recursive function within the system. (Hawking radiation and holography address this, but introduce new boundaries, which only shifts the paradox)

“Constants” are not random, but still seemingly arbitrary; they work for our models, but only as patchwork for relational processes. They are effective, but deduced, and cannot be proven from first principles.

Particle physics screams recursion. Entanglement? Non-locality??Superposition??? These are only paradoxes when we assume a non-recursive (linear) system.

Ultimately - physics, like logic and math, remains bounded by its own assumptions. The regress of explanation across our search for an “outside” reveals axiomatic erosion at work. Same incompleteness, different domain.

Even the strict instrumentalist (“shut up and calculate”) sneaks in a value assumption - that progress through modeling is in fact desirable. But is that assumption “proven”, or just treated it as self-evident?

[Breeze Theory @substraeta]

@HavocWorks it only ever reframes the problem 😔

[Breeze Theory @substraeta]

The self-reference trials, day 4: Computation as Fundamental

There’s a subtle nuance that is often missed by the computationalists.

Computation, which is the execution of an algorithm over a set of “rules”, subtlety leaves the door open to reality being a formally definable system. If we simply reproduce the right “rule set”, we can simulate all complexity accurately.

Only problem — rules are downstream of self reference, because in order to fully account for their own outcomes, a rule set must, in some sense, describe or include itself. This is the heart of the paradox.

Chaitin’s incompleteness proves that rule-based systems are limited in their ability to capture complex systems.

Turing showed that no computational algorithm can fully decide whether another program will “halt” or run forever; there will always be a paradox by contradiction.

Both these results show that some algorithmic processes are unpredictable, no matter the rule.

@stephen_wolfram tries to acknowledge this through his principle of “computational irreducibility” — algorithms based on simple rules must be fully executed in order to know the outcome.

But even this principle assumes that rules can exist independently of the algorithm they inform (are non-self-referential) — yet this very assumption is a “rule” that cannot be proven!

If we know that all rules, axioms, and assumptions depend on self-reference, then a rule based system of computation inherits that paradox from the start, meaning that computationalism (while locally useful), is still, unfortunately, an incomplete description of reality.

TLDR: Computation depends on simple rules, yet all “rules” already presuppose self-reference — so which one is more fundamental?

Or perhaps self-reference IS the simple rule behind all complexity? 🤔

[Breeze Theory @substraeta]

if it’s “substrates all the way down,”
then the regress itself becomes the substrate

[Breeze Theory @substraeta]

@mervynxx Simulation theory basically transposes the same issue to a different abstraction. “creator / created” are not separable, we only exist in relation to each other.