Generator

connectives

A generator in the logic library, called 6 times across 2 essays. Below: what it draws at its defaults and at each mode an essay asks for, what it checks while drawing, and everywhere it is used.

connectives is one function. Everything below came out of it during this build, at parameters taken from the essays rather than invented for this page — so a figure here is the same figure a reader meets in an essay, and if the generator changes, this page changes with it.

At its defaults

`show: "closure"`

`show: "post"`

What it checks while it draws

Collected by running the family and recording what it asserted, not written here. The count is how many separate times the claim was put to the test while these drawings were made.

between one and five bases are compared ×1
between two and eight connectives are tabulated ×1
no two of the sixteen have the same table ×1
Post's criterion and the closure agree about whether a connective is complete on its own ×1
the closure and Post's criterion agree about this basis ×1
the connective is one of the sixteen ×1
the number of columns is a whole number between 4 and 8 ×1
there are sixteen binary connectives and no more ×1

Where it is called

Changing this generator changes every figure on this list. That is what makes the list worth publishing rather than keeping in a check script.

Logic

A formula is a corner of a cube

A formula about three letters is a set of eight rows. Written as a table that is a list; drawn on a cube it is a shape — and the shape is what almost every later question in this field turns out to be about.

Logic

One connective is enough

Of the sixteen ways to combine two truth values, exactly two can build all the others by themselves. Which two is not obvious, and the reason turns out to be five properties that a connective either has or escapes.

The whole library · What the figures prove