Slide 1
Required or enough
A necessary condition must be present for something to qualify. A sufficient condition, by itself, guarantees qualification within the stated rule.
More to Read
Imagine a club requiring both registration and a valid pass. Registration is necessary, but someone registered without a pass still cannot enter. The example separates a requirement from a complete package of requirements.
Slide 2
One route can be enough
A condition can be sufficient without being necessary. One accepted route may work even when other routes also work.
More to Read
Suppose either a staff badge or a visitor pass grants entry. Holding a staff badge suffices, but visitors show why it is not required of everyone. The word either changes the logical structure.
Slide 3
Read only if carefully
In a rule saying entry is allowed only if registration is complete, registration is necessary. The rule does not promise entry to everyone registered.
More to Read
Compare “entry is allowed if registration is complete.” If the rule has no unstated requirements, registration is sufficient. Ordinary notices can be ambiguous, so any other conditions still need to be stated explicitly.
Slide 4
Definitions can need both
A complete definition aims to include every qualifying case and exclude every nonqualifying case. Necessary and sufficient conditions help test it.
More to Read
Defining a square merely as a four-sided figure includes rectangles that are not squares. Requiring four equal sides and four right angles narrows the class correctly. Such a counterexample shows why the proposed definition is incomplete.
Slide 5
Specify the setting
Conditions depend on the question and its background assumptions. A practical requirement is not automatically a universal law.
More to Read
A key may be necessary for ordinary entry through a locked door under stipulated rules, while a broken lock changes the situation. Logical analysis becomes clearer when hidden assumptions are brought into view.
Sources
- Necessary and Sufficient Conditions
Stanford Encyclopedia of Philosophy
- Propositional Logic
Internet Encyclopedia of Philosophy