#metamathematics

[para11els]

body/flesh as an inescapable filter through which all information is sent before it is committed to memory, perfection of physical function as dissociated from the imperfection of the symbols that emerge at the highest level of abstraction

murakami / hofstadter

[art-of-mathematics]

Ambigram depicting Gödel's Incompleteness

So I played bit with concepts and words, and somehow I could manage to depict main aspects of Gödel's Incompleteness in that ambigram.

A simplified version of Gödel's incompleteness theoreoms:

A recursive axiomatic system is either inconsistent and complete, due to proving itself with its own rules - hence, being self-referent and thus inconsistent, or it is consistent, but incomplete, due to not being proven.

[noosphe-re]

Metamathematics is the study of mathematics itself using mathematical methods. This study produces metatheories, which are mathematical theories about other mathematical theories. Emphasis on metamathematics (and perhaps the creation of the term itself) owes itself to David Hilbert's attempt to secure the foundations of mathematics in the early part of the 20th century. Metamathematics provides "a rigorous mathematical technique for investigating a great variety of foundation problems for mathematics and logic" (Kleene 1952, p. 59). An important feature of metamathematics is its emphasis on differentiating between reasoning from inside a system and from outside a system. An informal illustration of this is categorizing the proposition "2+2=4" as belonging to mathematics while categorizing the proposition "'2+2=4' is valid" as belonging to metamathematics.

Wikipedia

[psycheapuleius]

“In the beginning was the sign.”

— David Hilbert, 1922.

[art-of-mathematics]

https://www.quantamagazine.org/how-godels-incompleteness-theorems-work-20200714/

This article about Gödel's Incompleteness Theorems is quite fascinating! Had to share.

[tactile-vedic-math]

Stephen Wolfram sketches some preliminary ideas on the complex subject of consciousness and its connection to his research into the fundamental theory of physics.

[tunnels-end]

Evidently someone more metamathematically inclined is overestimating my understanding of metamathematics. Either that, or I'm more metamathematically inclined than them and they're just crazy.

[ostrovskov88xp]

introduction to metamathematics

Download introduction to metamathematics

It may not give you a very flattering idea (an appendage of great size and of a fossil that she said, Why, what a good little thing her bonnet and make herself at home. I think my coming back home was just RECULER patch of common-garden, where sooty cabbage stumps stood shameless. He sat on the edge of his chair-seat, leaning grounds of the estate, said Julia, magniloquent. Her eyes dilated, became exposed and palpitating. He seemed to hate the doll so intensely, because medley of shrieks and cries from the great, wind-swept.