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I hereby decree that the Republican Party is illegal and banned. All Republicans must cease being identified as such or will be identified and dealt with as enemy terrorists of the USA ♥️🤍💙

The only place a Republican belongs is Hell 🇺🇸

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#Artists are a better class of people than most #Christians I've met. For example, eternal damnation for eating all the cherries (gluttony), or I am better at something than my neighbor (pride), or we had sex after a coffee date (lust). It's mean.
#creativity #art #sculpture
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Burn that motherfucker at the stake.

Trump is scared to death.

#epsteintrumpfiles

He MUST be destroyed, or he will continue. I don't know about you, but I am FUCKING SICK of being held hostage by a fucking Orange CRIMINAL.

It’s happening right now in Washington DC. Protesters are flocking in the streets to demand the release of the Epstein Files and against the deployment of the national guard.

Washington, DC is responding to the military occupation of this city bright and early today.

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Every day in LA they are #Resisting 💪🏽💙
This is yesterday, 8/9/2025
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YouTube video by MeidasTouch Trump makes FATAL DECISION as MASS PROTESTS Erupt

GO LA CA❤️‍🔥❤️‍🔥❤️‍🔥❤️‍🔥
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* get lifted

* is a deeper symbolic level

Mathematics is buried deep in the symmetry of how we use symbols logically, which is not tautological knowledge in logic. We have to add axioms about how we use symbols.

One such axiom is the core axiom of Path Semantics:

(a : b) & (c : d) -> (a ~~ c : b ~~ d)

Which is just the beginning.

Before you can study mathematics in depth, you have to learn how to use symbols. There's no need to have a model of something "real" behind how we use symbols.

However, it turns out that when we model how we use symbols directly without any underlying model, we can prove lots of mathematical stuff.

Intuitively, when we use the symbol `x`, we know that the string "x" refers to how the symbol `x` is used, but we only know this at the pure symbolic level of mathematics. We don't have any underlying model that justifies *how* we know this.

We just know it.

We are used to say that mathematics is the language of reality, but in fact mathematics is a language that makes fewer assumptions than reality. It is both for reality and the imaginary.

You don't need an underlying model e.g. Set Theory in mathematics. There is a deeper level symbolic level.

Path Semantics is not a theory about Ontology, because Ontology is concerned about what is real. The only thing we care about in Path Semantics, is how people use symbols. That's all.

So, you can't use Path Semantics to argue what's real or not.

When you have a normal path `f[g]`, we don't care whether this actually has a solution or not at the symbolic level. We can still use it as a building block for theorem proving.

This means, Path Semantics is a theory about how people use symbols.

When formalizing Path Semantics in Set Theory or Dependent Type Theory, you need a solution of the imaginary inverse before composition of normal paths, so these theories are weaker than Path Semantics.

Path Semantics handles normal paths as first class citizens. They are fundamental.

Now, normal paths in Path Semantics can be written:

f[g -> h] <=> h . f . inv(g)

We use the imaginary inverse to compose normal paths:

f[g1 -> h1][g2 -> h2] <=> f[g2 . g1 -> h2 . h1]

This is how the foundation of Path Semantics solves the problem of normal path composition.

So, in Path Semantics you can design axioms for the imaginary inverse that only hold if there exists a solution to the imaginary inverse, at the same time using other axioms where you don't need to know whether the solution is real or imaginary.

This is how you can have an "imaginary inverse" in Path Semantics. The imaginary inverse of `a` is `inv(a)`.

If `~inv(a)`, which is a shorthand for `inv(a) ~~ inv(a)`, which is provable from `inv(a) ~~ b` e.g. by `inv(a) == b` and `sd(inv(a), b)`, then you tell the imaginary inverse has a solution.

Intuitively, when you define something, you don't define it to itself, but to something else. So, definitions behave like propositions of equality that gets lifted to quality by symbolic distinction.

Path Semantics "defines" how definitions behave, logically.

Now, in Path Semantics, if you have `a == b` and `sd(a, b)`, then you can lift this into `a ~~ b` ("quality" `a, b`).

This means, equality can produce quality, but only if you have some way to show that they are symbolic distinct.

If you don't allow Hilbert's hotel in your language, then you can use the axiom `sd(a & b, a)` safely.

Logic doesn't actually know whether Hilbert's hotel makes sense or not. You choose it by design, if it makes sense to you.

For example, if you have `a & b` and `a`, then you know intuitively by construction that they are symbolic distinct, except for the case where `a := b & b & b & b & b & ...`. This is a version of Hilbert's hotel. You choose in your language whether you allow Hilbert's hotel or not, by design.

So, our knowledge about symbolic distinction is only partial, but by working with partial knowledge, we can "approach" propositional infinity (symbolic indistinction) step-wise in logic, by using an infinitely number of mostly unknown axioms, out of only which a few axioms are used in practice.

While symbolic indistinction is not safe, it is safe to work with symbolic distinction. For example, `a` and `b` are symbolic distinct `sd(a, b)`. If you have `sd(a, a)` or `sd(b, b)`, then this does not tell us about symbolic indistinction, but that some symbolic distinction exists "somewhere".

The string "x" when we use the symbol `x` can be thought of as the "code" of `x` that determines how it is generated. This code should be hidden from logic by design, so you are allowed to reason hypothetically, as if programs and code exist in some unobserved potential of possible worlds.

If the taboo knowledge of symbolic indistinction is revealed to logic internally, then it is no longer sound to assume that two propositions are equal (even they are not) for some specific theory.

E.g. you use the symbol `x`, logic is not allowed to know this uses the string "x".