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<!DOCTYPE html>
<!--
This file is part of trivalent_website.
trivalent_website is free software: you can redistribute it and/or modify it
under the terms of the GNU Affero General Public License as published by the
Free Software Foundation, either version 3 of the License, or (at your option)
any later version.
trivalent_website is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE. See the GNU Affero General Public License
for more details.
You should have received a copy of the GNU Affero General Public License along
with trivalent_website. If not, see <https://www.gnu.org/licenses/>.
-->
<html dir="ltr" lang="en">
<head>
<meta charset="UTF-8" />
<title>Trivalent | about</title>
<meta name="viewport" content="width=device-width,initial-scale=1" />
<meta
name="description"
content="home of the Trivalent musical project | about"
/>
<meta name="theme-color" content="#171717" />
<link href="./style.css" rel="stylesheet" />
<link rel="icon" type="image/png" href="./img/favicon.png" />
</head>
<body>
<div class="section">
<div class="inner-section">
<header id="main-header">
<div id="header-div">
<h1>Trivalent</h1>
<p class="subheader">a 21<sup>st</sup> century musical project</p>
</div>
<div id="main-logo-container">
<img
src="./img/Trivalent_logo.svg"
id="main-logo"
alt="Trivalent logo"
title="Trivalent logo; CC BY-SA 4.0+ licensed"
/>
</div>
</header>
<nav>
<ol class="navlist">
<li><a href="./index.html">main</a></li>
<li><a href="./audio.html">audio</a></li>
<li><a href="./scores.html">scores</a></li>
<li><span class="non-link">about</span></li>
<li><a href="./contact.html">contact</a></li>
<li>
<a href="https://github.com/AugmentedFifth/trivalent_website"
>source</a
>
</li>
</ol>
</nav>
</div>
</div>
<main>
<div class="section">
<div class="inner-section">
<h2>about</h2>
<p>
Trivalent is a musical solo project that happens to be based out of
<a href="https://en.wikipedia.org/wiki/Portland,_Oregon">PDX</a>.
Trivalent is a personal musical outlet and a way to explore sounds
and musical composition.
</p>
<p>
Trivalent has no academic, national,
<a href="https://en.wikipedia.org/wiki/State_(polity)">state</a>,
nor industrial affiliations or origins. Trivalent is not a part of
and is not affiliated with any
<a href="https://en.wikipedia.org/wiki/Art_movement"
>artistic/musical movements</a
>, musical scenes, nor musical genres, though it may be influenced
by some of them.
</p>
<p>
Trivalent is not signed to any
<a href="https://en.wikipedia.org/wiki/Record_label">label(s)</a>
and is not affiliated with any music corporations; all of the output
of Trivalent is
<a href="https://en.wikipedia.org/wiki/Free_content"
>free content/culture</a
>, legally available to anyone under the terms of the
<a href="https://creativecommons.org/licenses/by-sa/4.0/"
>Creative Commons Attribution-ShareAlike license, version 4.0</a
>
(or any later version of the same license, at your option).
</p>
</div>
</div>
<div class="section">
<div class="inner-section">
<h2>etymology</h2>
<p>
The origin of the name “Trivalent” is in
<a href="https://en.wikipedia.org/wiki/Three-valued_logic"
>three-valued logic</a
>, otherwise known as <strong>trivalent</strong> logic, to
distinguish it from bivalent logics like
<a href="https://en.wikipedia.org/wiki/Classical_logic"
>classical logic</a
>
and
<a href="https://en.wikipedia.org/wiki/Intuitionistic_logic"
>intuitionistic logic</a
>.
</p>
<aside>
<p>
See Kleene’s “On Notation for Ordinal Numbers”
[1938] (<a href="https://doi.org/10.2307/2267778"
>doi:10.2307/2267778</a
>) for the origin of the strong logic of indeterminacy.
</p>
</aside>
<p>
The name does not refer to any particular axiomatization of a
trivalent logic, although the usual suspects are
<a href="https://en.wikipedia.org/wiki/Stephen_Cole_Kleene"
>Kleene’s</a
>
strong logic of indeterminacy and
<a href="https://en.wikipedia.org/wiki/%C5%81ukasiewicz_logic"
>Łukasiewicz logic</a
>.
</p>
<p>
Trivalent logics are not necessarily interesting from a logical
point of view (modern treatments of logic are largely
<a href="https://en.wikipedia.org/wiki/Algebraic_structure"
>algebraic</a
>/<a href="https://en.wikipedia.org/wiki/Category_theory"
>categorical</a
>, and/or arise from
<a href="https://doi.org/10.1017/S096012950100336X"
>the geometry of proof nets and things like that</a
>), but they are
<a
href="https://en.wikipedia.org/wiki/De_Morgan_algebra#Kleene_algebra"
><em>somewhat</em> algebraically interesting</a
>, 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
<a href="https://en.wikipedia.org/wiki/Cardinality">cardinality</a>
of the set of
<a href="https://en.wikipedia.org/wiki/Truth_value">truth values</a
>) that a logic can have: 2, 3, and ℵ₀ (or
<a href="https://en.wikipedia.org/wiki/Cardinality_of_the_continuum"
>something larger</a
>, usually for
<a href="https://en.wikipedia.org/wiki/Interval_(mathematics)"
>the set [0, 1]</a
>; technically
<a href="https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument"
>not the same cardinality as ℵ₀</a
>, but not meaningfully different in this case). Fewer than 2 is
<a href="https://en.wikipedia.org/wiki/Trivialism">trivial</a>, and
finite valencies greater than 3 either look like overcomplicated
trivalent logics, or like finite-valence
<a href="https://en.wikipedia.org/wiki/Fuzzy_logic">fuzzy logics</a>
(although
<a href="https://en.wikipedia.org/wiki/Four-valued_logic"
>quadrivalent logics</a
>
notably have application in electrical engineering as well as a
philosophical interpretation in terms of the
<a href="https://en.wikipedia.org/wiki/Power_set">powerset</a> of
{<b>T</b>, <b>F</b>}).
</p>
<p>
Intuitionistic logic (a bivalent logic, to be sure) is — at
least when equipped with its usual
<a
href="https://en.wikipedia.org/wiki/Brouwer%E2%80%93Heyting%E2%80%93Kolmogorov_interpretation"
>BHK interpretation</a
>
— a kind of crypto-trivalent logic, because it says nothing
about
<a href="https://en.wikipedia.org/wiki/Law_of_excluded_middle"
>propositions of which we have no proof nor any proof of their
negation</a
>. Similarly, ordinary reasoning is often trivalent: we know things,
we know not-things, and we don’t know things.
<a href="https://en.wikipedia.org/wiki/Complete_information"
>Partial information</a
>, indeterminacy, and the unknown are all things that we have to
deal with frequently.
</p>
</div>
</div>
<div class="section">
<div class="inner-section">
<h2>colors</h2>
<p>
The official Trivalent color palette consists of the following set
of three colors:
</p>
<ul class="swatch-list">
<li>
<div id="swatch-1" class="swatch">
<code>#623eeb</code>
</div>
</li>
<li>
<div id="swatch-2" class="swatch">
<code>#1eaff0</code>
</div>
</li>
<li>
<div id="swatch-3" class="swatch">
<code>#f2f2f2</code>
</div>
</li>
</ul>
<p>
Along with the following color, to be used for backgrounds, as
needed:
</p>
<ul class="swatch-list">
<li>
<div id="swatch-4" class="swatch">
<code>#171717</code>
</div>
</li>
</ul>
</div>
</div>
</main>
<footer>
<a href="https://github.com/AugmentedFifth/trivalent_website"
>All HTML & CSS content</a
>
on this site is licensed to anyone under the terms of the
<a href="https://www.gnu.org/licenses/agpl-3.0.en.html"
>GNU Affero General Public License, version 3</a
>
(or any higher version, at your option). All other content on this site
(including, but not limited to, images, audio, and musical scores) is
licensed to anyone under the terms of the
<a href="https://creativecommons.org/licenses/by-sa/4.0/"
>Creative Commons Attribution-ShareAlike license, version 4.0</a
>
(or any higher version, at your option).
</footer>
</body>
</html>