What is a formal system?
- Start with an AxiomAxiom
Quick Definition
An axiom is a logical presupposition that cannot be proven to be true – instead, we take it on faith that it is true.
...- Continue with a rule or self-imposed constraintFormal Constraint
Quick Definition
Mathematics
A formal constraint (what I consider to be analogous with Hofstadter'sGödel, Escher, Bach- An Eternal Golden Braid
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Read the Wikipedia article on GEB.
Background
I first encountered this book by Douglas Hofstadter in high school and became enraptured. The concepts from Gödel, Escher, Bach that have most influenced my thinking and artistic practice are summarized in the notes to "Creativity and Constraint: Queering the Formal System."
Gödel, Escher, Bach (also abbreviated as GEB) usually proves too difficult for me to adequately summarize in conversation; I'll try to be... "rule of production" or "rule of inference") is a method for transforming one result of a formal system into another result. In mathematics, we can use mathematical induction to derive a theorem from an axiom or from another theorem. Because we trust that our rules of induction will preserve the truth of our mathematical statements, following t...- Apply the rules and constraints to the axiom and see what happens!
This definition is loosely based on Hofstadter’s Gödel, Escher, Bach- An Eternal Golden BraidGödel, Escher, Bach- An Eternal Golden Braid
Purchase a copy on IndieBound.
Read the Wikipedia article on GEB.
Background
I first encountered this book by Douglas Hofstadter in... (GEB) and on my own experience making and breaking formal systems.
Start with an axiom (in mathematics) or idea/material (creative disciplines like the arts).
A rule or constraint develops the initial idea, material, or axiom. In formal systems developed by human beings, these constraints are either consciously self-imposed or selected-for based on specific desirable outcomes or goals (see the work of Tymoczko and Huron regarding tonality and psychoacoustics). The results of the process are a proof or a logical argument or a work of art. The role of the formal system here is typically to create consistency, if not always completeness (see these descriptions of Gödel’s work in GEB). In mathematics, this allows for the use of mathematical induction to ensure logical consistency. In creative fields, consistency allows for organicOrganicism
The concept of organicism is wily and potentially problematic – it has a history of being a useful aesthetic descriptor, but it can also be attached to a variety of oppressive ideologies. The most salient discussions for my thinking have surrounded organicism in music.
Heinrich Schenker devised influential theories for describing and analyzing works of Western classical music from the "common practice period."[[This time period is from roughly 1650 to 1900.::rsn-transclude]] These theories w..., unified, and integrated development of the creative project, often with slight imperfections due to human error. (These can be quite beautiful and significant!)
Related Note: Creativity and Constraint- Queering the Formal SystemCreativity and Constraint- Queering the Formal System
Notes
[[Formal System (Partial) Bibliography]]
I gave a talk entitled Creativity and Constraint – Queering the Formal System to ...
Last modified on 01-28-2022.