Necessary and sufficient
from 350 BCE Implicit in Aristotle; the modern vocabulary is nineteenth-century
Two different questions that sound like one: what must be present for this to hold, and what is enough on its own to make it hold.
- Active
- from 350 BCE
- Where
- Athens, later Cambridge
- Status
- In use
- Tradition
- Analytic tools
What it is
A necessary condition is one without which the thing cannot hold. A sufficient condition is one whose presence settles that it does. They are different, they can come apart entirely, and confusing them is among the most common failures in careful writing.
As a device rather than a procedure, it is applied to somebody else's account rather than used to build one. You take a proposed definition or rule and ask, of each condition, which of the two it is claiming to be.
How it works
Take each condition in the account. Ask whether the thing could hold without it — if not, it is necessary. Ask whether its presence alone settles the matter — if so, it is sufficient. Then ask whether the account claims the conditions are jointly sufficient, and test that claim as a whole.
Most defective definitions turn out to have listed necessary conditions and quietly assumed they add up to a sufficient one.
How it is applied
- Take each stated condition in turn
- Ask whether the thing can hold in its absence: if not, it is necessary
- Ask whether its presence alone settles the matter: if so, it is sufficient
- Ask whether the conditions together are enough, which is a separate question
The device applied
Proposition The grant conditions do not do what the guidelines say they do.
- The guidelines state that an applicant qualifies if the organisation is incorporated, based in the shire, and has been operating for two years.
- Incorporation is necessary: an unincorporated group cannot hold the funds, and the finance rules make no provision for it.
- Being based in the shire is necessary: the funding source is restricted to the shire by the trust deed.
- Two years of operation is neither. A group can plainly be eligible in principle without it — the guidelines elsewhere provide for new groups auspiced by an established one — and meeting it settles nothing on its own.
- So the three conditions are not three necessary conditions, and the guidelines present them as though they were.
Therefore As drafted the conditions are not jointly sufficient and one of them is not necessary, which is why the panel keeps having to make exceptions it has no stated power to make.
Nothing was analysed or defined here. The device was applied to somebody else's document, and it located the fault without anybody needing a theory of what a grant is.
What it is good for
Auditing definitions, rules, eligibility criteria and contracts written by other people. It is the fastest way to find out whether a rule can actually be applied as written.
Where it fails
It presumes the account is trying to be exact, and many are not. Applied to a concept that works by family resemblance, or to a rule deliberately drafted with room for judgement, it will report a fault that is really a design decision.
It also has nothing to say about degree. Conditions that are usually necessary, or that matter more when others are absent, cannot be classified by a device with only two boxes, and forcing them into one produces a misleading verdict.
Common misconceptions
That necessary and sufficient are opposites or extremes of one scale. They are independent: a condition can be one, the other, both or neither, and all four combinations are common.
Also that if A is sufficient for B then B is necessary for A sounds like a trick, and is simply true, and forgetting it is the source of a great deal of confused drafting.
Where it came from
The distinction is at work in Aristotle without the vocabulary. The modern terms and their formal treatment come from nineteenth-century logic.
What became of it
Standard equipment everywhere in analytic philosophy, law and mathematics, and the backbone of the analysis of knowledge and everything that followed from it.
Lasting influence
Every attempt to define anything in the analytic tradition is stated in these terms, and the whole Gettier literature is a fight about whether a set of conditions is jointly sufficient.
Why it still matters
Constant, and the source of the single most useful question to ask of any rule: is this necessary, or is it enough?
Put another way
A key and a doorway. You need the key, and having it is not the same as being through.
Texts
Bertrand Russell, The Problems of Philosophy
Not a treatment of the device itself, but the clearest short demonstration of a philosopher using it throughout.
Where to start
Take a rule you have to apply at work and classify each of its conditions. Most people find at least one that is neither.
The surprising bit
The distinction is elementary and the failure to keep it is responsible for a large share of unworkable legislation and unenforceable contracts.
In their own words
Whenever we can say that a thing must be so, we are saying that its opposite is impossible
Who held it
the legal drafters
Connections
- Influenced
- Conceptual analysis
- Parallel to
- Genus and differentia
The verdict
The sharpest small instrument on this list, and the one most likely to be useful tomorrow.