Diairesis

What it is

Diairesis defines by successive division. You begin with a kind broad enough to include the target, split it into two exhaustive parts, keep the part containing the target, and split again. The definition is the path taken.

Plato's image is of carving an animal at its joints rather than hacking through the bones — the cuts are supposed to follow divisions that are really there, not divisions imposed for convenience.

How it works

Choose a starting kind that certainly contains the target. Divide it into two parts that between them exhaust it. Discard the part that does not contain the target. Repeat on what remains. Stop when the remaining class has only the target in it, and read the definition off the sequence of cuts.

The hard part is choosing cuts that matter. Any class can be divided in endless ways, and only some of those divisions track anything real.

The moves, in order

1. Take a kind K that contains the target
2. Divide K exhaustively into two subkinds
3. Keep the subkind containing the target and discard the other
4. Repeat on the kept subkind
5. Stop when only the target remains; the sequence of cuts is the definition

What it is good for

Classification, diagnosis and definition in any domain where the divisions are real and binary. Biological keys, fault-finding trees and taxonomies are all diairesis in working clothes.

Where it fails

Aristotle's objection, made within a generation, still stands: division cannot prove that the cuts are the right ones. Nothing in the method tells you to divide animals into footed and footless rather than into aquatic and terrestrial, and different cuts yield different definitions of the same thing.

It also handles only what divides in two. A kind with three genuinely equal subkinds must be forced into a false binary, and Plato's own examples strain visibly when he tries.

And it defines by exclusion, so the definition tells you where a thing sits without telling you what it is. Plato's definition of the angler in the Sophist is a famous demonstration of the method that produces a nearly useless result.

Common misconceptions

That it is the same as genus and differentia. They are close relatives, but that method gives one containing kind and one distinguishing feature, where this one gives a whole chain of cuts and no single differentia.

Where it came from

The Sophist and the Statesman are extended demonstrations of it, with the definition of the angler in the Sophist as the standard example.

What became of it

Criticised by Aristotle almost immediately, absorbed into his own theory of definition, and revived in the taxonomies of the seventeenth and eighteenth centuries.

Lasting influence

Linnaean taxonomy, biological identification keys and every decision tree in computing descend from it, mostly without the debt being noticed.

Why it still matters

In constant practical use, under other names.

Put another way

Twenty questions, if the questions have to carve nature at its joints.

Texts

Where to start

Use a field guide's identification key on an actual plant. That is the method, in your hands, in ten minutes.

The surprising bit

The method Aristotle rejected as unable to prove anything became, two thousand years later, the organising principle of biological classification and then of machine learning.

In their own words

Who held it

Linnaeus

Connections

Relies on

Disjunctive syllogism

Influenced

Genus and differentia, Distinction-drawing

Parallel to

Distinction-drawing

The verdict

A fine instrument for finding things and a poor one for saying what they are.

Sources

• Stanford Encyclopedia of Philosophy: Plato's Sophist