This document introduces key philosophical terminology used to precisely specify conditions: necessity, sufficiency, contingency, and biconditionality. It explains that necessity means a condition is needed but not sufficient, while sufficiency means a condition or set of conditions are the only things required. Contingency means a condition is not necessary. The biconditional "if and only if" (iff) precisely connects two statements. The document aims to teach this terminology and start thinking about definitions of belief, truth, justification and knowledge by considering necessary, sufficient and contingent conditions.

1. Biconditionality, Contingency,
Necessity, Sufficiency
Or: Being very precise about
conditions for things

2. Today’s aim (s)
• To teach you some key terminology:
necessity, sufficiency, contingency, iff.
• To begin to think about definitions of
belief, truth, justification and
knowledge.

3. The Biconditional If(f)
• Sometimes the word ‘if’ only conveys a loose connection
between statements: “I will come with you to the pictures
if you go on Friday”. But I could go with you to the
pictures on another day.
• However, if I say, “I will come with you to the pictures if,
and only if, you go on Friday”, I am excluding other
possibilities (such as going on Tuesday).
• Philosophers call this if the ‘Biconditional If’ and spell it
‘iff’. Using ‘iff’ allows philosophers to specify conditions
for things more precisely.

4. If or Iff?
1. I will die if I stop breathing
2. I can make a hot cup of tea if I have hot
water
3. I will pass my exams if there is a miracle
4. If I eat any more I will be sick

5. Sufficiency,Contingency,Necessity
Take the example of the
statement, “I will grow up to
be very fit if I exercise and
eat sensibly”.
• Might it be possible to be
very fit without eating
sensibly and exercising?
• Are diet and exercise the
only things that have a
bearing on fitness?

6. Contingency, Sufficiency, Necessity
• If you can be very fit without a good diet and
plenty of exercise, then these conditions simply
aren’t necessary. They are contingent.
• But if, amongst other conditions, I must follow a
good diet and take exercise to be healthy, then
these conditions would be necessary.
• And if diet and exercise were the only conditions
that had to be met, then these conditions would
be sufficient.

7. Why bother?
• Because for philosophers interested in analysing a
concept, only an exhaustive list of conditions for that
concept to exist is good enough.
• Philosophers like lists of conditions that are ‘individually
necessary and jointly sufficient’. Because then these
lists are really precise.
• Necessity (needed, but not enough for) isn’t the same as
sufficiency (the only thing(s) you need).
• It is usually easy to think of necessary conditions. But
very hard to think of sufficient ones.
Try: defining what conditions must obtain for your
smartphone to play music to your ears.

8. To sum up
• A condition is necessary when it must be the case for
something to be true. But other conditions could be
needed too.
• A condition or set of conditions is sufficient when only
those things and nothing else must occur for something
to be true.
• Precisely specifying conditions allows for precise
definitions.
• It can be very hard to specify sufficient sets of
conditions.