Simplest possible notion of a formal system

[HexHammer]

Overly fancy wording, the meaning gets lost.......

[Skepdick]

The formal system that I propose can even formalize natural language semantics within its stipulated relations between finite strings.

Relational databases do that already. https://en.wikipedia.org/wiki/Relational_algebra
You can define all kinds of relationships between objects: 1-to-1 (1:1), 1-to-many (1:M), many-to-one (M:1), many-to-many (M:N).

When we change the word labels between dogs and cats the underlying semantics remains unchanged.
A rose by any other name would never become a pile of dog shit.

Have you heard of synonyms and homonyms?

A synonym is an example of M:1 relationship.
Many words - 1 meaning.

A homonym is an example of a 1:M relationship.
1 word - many meanings.

Truth is not merely linguistic.

Formal truth is merely linguistic. Because symbol manipulation is merely computation.

It seems to me that in your pursuit for disambiguation, you are really after a formal system with normalisation.

A lambda calculus system with the normalisation property can be viewed as a programming language with the property that every program terminates. Although this is a very useful property, it has a drawback: a programming language with the normalisation property cannot be Turing complete.

So back to the question of giving up expressive power. If you are asking me to give up Turing completeness, what are you offering in return?

You can't even write a self-interpreter in a normalising language.

[Eodnhoj7]

The formal system that I propose can even formalize natural language semantics within its stipulated relations between finite strings.

Relational databases do that already. https://en.wikipedia.org/wiki/Relational_algebra
You can define all kinds of relationships between objects: 1-to-1 (1:1), 1-to-many (1:M), many-to-one (M:1), many-to-many (M:N).

When we change the word labels between dogs and cats the underlying semantics remains unchanged.
A rose by any other name would never become a pile of dog shit.

Have you heard of synonyms and homonyms?

A synonym is an example of M:1 relationship.
Many words - 1 meaning.

A homonym is an example of a 1:M relationship.
1 word - many meanings.

Truth is not merely linguistic.

Formal truth is merely linguistic. Because symbol manipulation is merely computation.

It seems to me that in your pursuit for disambiguation, you are really after a formal system with normalisation.

A lambda calculus system with the normalisation property can be viewed as a programming language with the property that every program terminates. Although this is a very useful property, it has a drawback: a programming language with the normalisation property cannot be Turing complete.

So back to the question of giving up expressive power. If you are asking me to give up Turing completeness, what are you offering in return?

You can't even write a self-interpreter in a normalising language.

These databases are replications of the alchemical nature inherent within philosophy.

It is grounded in the convergence of divergences of points.

[Skepdick]

It is grounded in the convergence of divergences of points.

Is this what you mean ?

https://en.wikipedia.org/wiki/Bijection ... surjection

[Eodnhoj7]

It is grounded in the convergence of divergences of points.

Is this what you mean ?

https://en.wikipedia.org/wiki/Bijection ... surjection

• -> •• -> •

With "•" equivalent to all abstract and physical axioms.

I can continue if you wish, that is a very, very primitive example .

Actually I will continue.

• -> •• -> •

(• -> •• -> •) • -> •• -> •

((• -> •• -> • ) • -> •• -> •) • -> •• -> •

....

⊙ as one point manifesting itself through infinite points.

[Skepdick]

• -> •• -> •

With "•" equivalent to all abstract and physical axioms.

I can continue if you wish, that is a very, very primitive example .

What you have said is the same as:

f: x -> y
g: y -> x

Which is the same as f(g(x)) = x

Which is exactly the same notion as reversible computing or Morphism (in mathematics).

Fact is you have arrived at the notion of a function. Input -> magic -> output

[Eodnhoj7]

• -> •• -> •

With "•" equivalent to all abstract and physical axioms.

I can continue if you wish, that is a very, very primitive example .

What you have said is the same as:

f: x -> y
g: y -> x

Which is the same as f(g(x)) = x

Which is exactly the same notion as reversible computing
or Morphism (in mathematics).

Read again.

[Skepdick]

• -> •• -> •

With "•" equivalent to all abstract and physical axioms.

I can continue if you wish, that is a very, very primitive example .

What you have said is the same as:

f: x -> y
g: y -> x

Which is the same as f(g(x)) = x

Which is exactly the same notion as reversible computing
or Morphism (in mathematics).

Read again.

No, you read again. You specified "•" as "all abstract and physical axioms.". It's too particular and specific.

The abstract notion of a function is even more generic and more abstract than that.

input-MAGIC -output

What's an input? ANYTHING! Sensory perception.
What's an output? ANYTHING! A fart.

The notation is irrelevant. It's saying the same thing.

f: • -> ••
g: •• -> •

f(•) = ••
g(••) = •

• MAGIC ••

You have arrived at the Black box.

Something exists.
If I prod it (input) - it reacts (output)

[Eodnhoj7]

What you have said is the same as:

f: x -> y
g: y -> x

Which is the same as f(g(x)) = x

Which is exactly the same notion as reversible computing
or Morphism (in mathematics).

Read again.

No, you read again. You specified "•" as "all abstract and physical axioms.". It's too particular and specific.

ROFL !!!!! Tell me how "all" is too particular and specific. That is a first...ROFL!!!!!

The abstract notion of a function is even more generic and more abstract than that.

False, the symbols you use are relegate to certain cultures...the dot and line is not. If man is measurer, than the mathematical symbols you use are not universal and apply to specific groups of men...not all men.

input-MAGIC -output

What's an input? ANYTHING! Sensory perception.
What's an output? ANYTHING! A fart.

The notation is irrelevant. It's saying the same thing.

No reread again, this notation sets the foundations for even the symbols you use to program with.

f: • -> ••
g: •• -> •

f(•) = ••
g(••) = •

• MAGIC ••

You have arrived at the Black box.

Something exists.
If I prod it (input) - it reacts (output)

False, as the output is still an extension of the input and a such the input exists through recursion.

[Skepdick]

ROFL !!!!! Tell me how "all" is too particular and specific. That is a first...ROFL!!!!!

Because you added a qualifier to "ALL" thus making it a sub-set to the set of all sets.

The set of ALL(axioms), is smaller than the set of ALL(axioms, functions), is smaller than the set of ALL(axioms, functions, universes) is smaller than the set of ALL(ALL())

False, the symbols you use are relegate to certain cultures...the dot and line is not.

The dot and the line come from Euclid. So you are relegating to the Greeks.

AΓΕΩΜΕΤΡΗΤΟΣ ΜΗΔΕIΣ ΕIΣΙΤΩ

If man is measurer, than the mathematical symbols you use are not universal and apply to specific groups of men...not all men.
No reread again, this notation sets the foundations for even the symbols you use to program with.

If that's what upsets you - go ahead and invent your own symbols/alphabet.

False, as the output is still an extension of the input and a such the input exists through recursion.

It's only recursive when the input of the function is the function itself.

f(f(f(f(f(f(.....))))))).

And if you don't like my notation - use Turtles.

[Eodnhoj7]

ROFL !!!!! Tell me how "all" is too particular and specific. That is a first...ROFL!!!!!

Because you added a qualifier to "ALL" thus making it a sub-set to the set of all sets.

Not really considering empricality and abstractness are subsets as well...they are part of "all".

The set of ALL(axioms), is smaller than the set of ALL(axioms, functions), is smaller than the set of ALL(axioms, functions, universes) is smaller than the set of ALL(ALL())

False, the symbols you use are relegate to certain cultures...the dot and line is not.

The dot and the line come from Euclid. So you are relegating to the Greeks.

Not really, I am not limiting it to euclidian axioms. Look upm the history of the dot and line.

If man is measurer, than the mathematical symbols you use are not universal and apply to specific groups of men...not all men.
No reread again, this notation sets the foundations for even the symbols you use to program with.

If that's what upsets you - go ahead and invent your own symbols/alphabet.

I don't have to, all symbols are grounded in the above mentioned. Try programming a 1 or 0 without using a dot.

False, as the output is still an extension of the input and a such the input exists through recursion.

It's only recursive when the input of the function is the function itself.

f(f(f(f(f(f(.....))))))).

And if you don't like my notation - use Turtles.

Yes, and a dot existing through a dot, as a dot is recursive...and isomorphic...say what !?!?!?

[Skepdick]

Not really considering empricality and abstractness are subsets as well...they are part of "all"

Precisely. Which is why ALL is the most general and complex concept in existence - https://en.wikipedia.org/wiki/ALL_(complexity)
Not ALL(axioms), not ALL(universes), not ALL(multiverses).

ALL is all there is!

Not really, I am not limiting it to euclidian axioms. Look upm the history of the dot and line

But you are limiting ALL(axioms). Which is a subset of ALL.

Try programming a 1 or 0 without using a dot.

We don't use dots. We use voltages in classical computers, or eigenstates in quantum computers.

Yes, and a dot existing through a dot, as a dot is recursive...and isomorphic...say what !?!?!?

What you call a dot - I call a Bit

There is either a dot, or there is no dot. 0 or 1. Something or nothing.

[Eodnhoj7]

Not really considering empricality and abstractness are subsets as well...they are part of "all"

Precisely. Which is why ALL is the most general and complex concept in existence - https://en.wikipedia.org/wiki/ALL_(complexity)
Not ALL(axioms), not ALL(universes), not ALL(multiverses).

ALL is all there is!

All is recursive then, all in all, hence it is both a generality and a particulate.
As such we are left with a formal system requiring its symbols to have this very same nature as extensions of the reality they are observing.

Not really, I am not limiting it to euclidian axioms. Look upm the history of the dot and line

But you are limiting ALL(axioms). Which is a subset of ALL.

False, the dot, line and circle exist through infinite variations. All can be observed as ⊙ without contradicting anything. All is both limit and no limit and as such it exists through this triad.

Try programming a 1 or 0 without using a dot.

We don't use dots. We use voltages in classical computers, or eigenstates in quantum computers.

And these are grounded on wave functions, empirically, which require point space.

Second the mimicry of symbols in computers is an extension of the basic movement of a point form one position to another until a form is given. The "1" of the computer is a recursion of the "1" symbol written by hand.

Third each piece of information, but, etc, is quantifiable and as such is a localization of a phenomenon equivalent to a point.

Yes, and a dot existing through a dot, as a dot is recursive...and isomorphic...say what !?!?!?

What you call a dot - I call a Bit

There is either a dot, or there is no dot. 0 or 1. Something or nothing.

convergence and divergence of axioms is what you are observing, " what you call...I call..." all are grounded in points of awareness and follow the same notation I am arguing.

lor]

The simplest notion of a formal system would require a geometric configuration.

[Skepdick]

The simplest notion of a formal system would require a geometric configuration.

What does the simples notion of a geometry require?

[Eodnhoj7]

The simplest notion of a formal system would require a geometric configuration.

What does the simples notion of a geometry require?

Point line and circle.

These are also required for quantification as the basic elements of counting.

These are required for language as well, in not just its form and function, but how the symbols are historically written out.