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Necessary and Sufficient Conditions
Sandra LaFave
A is necessary
for B iff (“if and only if”) B can’t occur without A. Whenever you have B, you
have A. Anything B is A. A is sufficient
for B iff A guarantees B. Whenever you have A, you have B. Anything A is B. Examples: A B Condition Being female Being
pregnant A is necessary for B. Getting an A Passing the class A
is sufficient for B. Gas in car Car runs A is necessary for B. Decapitation Death A is sufficient for B. To build a “formal” or
“essential” definition of X (the kind Socrates and Plato are looking for), you
need to specify what properties all and
only X’s have. Then you’ll know the
Form of X, or X-ness itself. To do this, you simply need each property to be
necessary, and the properties together to be sufficient. For example, here is how we get a formal
definition of “square”: A B Condition Being equilateral Being a square A
is necessary for B. Being a rectangle Being a square A
is necessary for B. Being an equilateral
rectangle Being a square A
is both necessary and sufficient for B. All squares are
equilateral, all squares are rectangular, and only squares are equilateral and
rectangular. Plato’s basic idea is
that everything in the world fits into some class, and the classes can be
precisely defined. In other words, Plato presupposes that all concepts are what
Wittgenstein calls closed: i.e., Plato believes it is possible to
specify the necessary and sufficient conditions for membership in the class of
things denoted by any concept. This basic idea of Plato’s had a profound effect
on Western thought; it led people to think we could, just by thinking, say
exactly what goodness or beauty or philosophy or persons are. Until quite
recently, the idea defined philosophy’s task: figure out those conditions.
Ludwig Wittgenstein revolutionized Western philosophy by arguing that this
underlying idea is wrong. He points out that most concepts are open: i.e., that
we define concepts in terms of paradigms, and argue that a particular thing
either is or is not a member of the class in question on the basis of
resemblance or lack of resemblance of the thing in question to the paradigm. Sample essay
questions 1.
Explain the
difference between a necessary and a sufficient condition. 2.
Explain the difference
between an open and a closed concept. 3. Why do philosophers not worry very much about
formulating a strict definition of “philosophy”? |