Trivalent
a 21st century musical project
a 21st century musical project
Trivalent is a musical solo project that happens to be based out of PDX. Trivalent is a personal musical outlet and a way to explore sounds and musical composition.
Trivalent has no academic, national, state, nor industrial affiliations or origins. Trivalent is not a part of and is not affiliated with any artistic/musical movements, musical scenes, nor musical genres, though it may be influenced by some of them.
Trivalent is not signed to any label(s) and is not affiliated with any music corporations; all of the output of Trivalent is free content/culture, legally available to anyone under the terms of the Creative Commons Attribution-ShareAlike license, version 4.0 (or any later version of the same license, at your option).
The origin of the name “Trivalent” is in three-valued logic, otherwise known as trivalent logic, to distinguish it from bivalent logics like classical logic and intuitionistic logic.
The name does not refer to any particular axiomatization of a trivalent logic, although the usual suspects are Kleene’s strong logic of indeterminacy and Łukasiewicz logic.
Trivalent logics are not necessarily interesting from a logical point of view (modern treatments of logic are largely algebraic/categorical, and/or arise from the geometry of proof nets and things like that), but they are somewhat algebraically interesting, and more importantly for this purpose, are philosophically interesting. It’s worth noting that there are really only three interesting valencies (in terms of just the cardinality of the set of truth values) that a logic can have: 2, 3, and ℵ₀ (or something larger, usually for the set [0, 1]; technically not the same cardinality as ℵ₀, but not meaningfully different in this case). Fewer than 2 is trivial, and finite valencies greater than 3 either look like overcomplicated trivalent logics, or like finite-valence fuzzy logics (although quadrivalent logics notably have application in electrical engineering as well as a philosophical interpretation in terms of the powerset of {T, F}).
Intuitionistic logic (a bivalent logic, to be sure) is — at least when equipped with its usual BHK interpretation — a kind of crypto-trivalent logic, because it says nothing about propositions of which we have no proof nor any proof of their negation. Similarly, ordinary reasoning is often trivalent: we know things, we know not-things, and we don’t know things. Partial information, indeterminacy, and the unknown are all things that we have to deal with frequently.
The official Trivalent color palette consists of the following set of three colors:
#623eeb
#1eaff0
#f2f2f2
Along with the following color, to be used for backgrounds, as needed:
#171717