The sixteen binary connectives
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.
With nothing chosen
The closure of 4 bases, against the 256 functions of three variables
Post's five classes, and which connectives escape them
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
Every figure on this list is drawn by the same rule, so a change to the rule changes all of them at once. That is why the list is published.
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.
LogicOne 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.