Generator

The four categorical forms

A generator in the logic library, called 7 times across 1 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.

syllogism 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

The four categorical forms. Two overlapping circles four times, shaded or dotted to show what each of the four sentence forms says.

`show: "count"`

The 256 syllogistic forms, and the 24 that work. A grid with one cell per syllogistic form, marked according to whether it is valid and what it needs to be valid.

`show: "argument"`

EIO-2: No P is M; Some S is M. Three circles for the three terms, with the regions the premises empty shaded and the regions they populate dotted.

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.

a form valid without existential import is valid with it ×1
every letter in the set expression names a drawn curve ×1
fifteen forms are valid with no assumption that anything exists ×1
nine more become valid once every term is assumed non-empty ×1
the form is three mood letters and a figure number, like AAA-1 ×1
there are 256 syllogistic forms — four figures and sixty-four moods ×1
twenty-four forms are valid in the traditional list ×1
two circles realise all four patterns ×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

Twenty-four out of two hundred and fifty-six

Aristotle's syllogisms are four sentence forms in four arrangements, which makes 256 patterns of argument. Fifteen of them are valid. Nine more become valid if you assume the things being talked about exist, and the gap between those numbers is a two-thousand-year-old disagreement.

The whole library · What the figures prove