PAW ASSIGNMENT 2:
1. Necessary and Sufficient Conditions
Is each of the following statements true or false? If the statement is false, explain why.

Being human is a sufficient condition for being a mammal.

Being human is a necessary and sufficient condition for being a mammal.

Having been married is a sufficient condition for being a widow.

Having been married is a necessary condition for being a widow.

Being a living woman whose spouse has died is a necessary and sufficient condition for
being a widow.

Breathing is necessary for being alive.

Breathing is sufficient for being alive.

Getting full marks in all your exams is necessary and sufficient for passing your degree.

Having four sides is sufficient for being a square.
2. Conceptual Analysis
For each of the three conceptual analyses below, briefly state whether the analysis is
too strong, too weak, or both, and why.
(If the analysis is too strong, give an example of a case which the analysis excludes which it
should include. If the analysis is too weak, give an example of a case which the analysis
includes which it should exclude. If both, give both kinds of example)

“X is dead if and only if X has been beheaded”.

“X is a bird if and only if X can fly”.

“X is a university graduate if and only if X has been to university”.
3. Distinctions
Are the following proper distinctions? State whether the distinction is exhaustive and
mutually exclusive.
Animals in the categories: Mammals, Fish, Sheep, Others
Exhaustive?
Mutually exclusive?
Philosophers in the categories: Ancient Greeks, British Empiricists, German Idealists
Exhaustive?
Mutually exclusive?
Planets of the Solar System in the categories: Rocky planets, Gas giants
Exhaustive?
Mutually exclusive?
Living things in the categories: Animals, Plants, Fish
Exhaustive?
Mutually exclusive?
4. Formulating Arguments
Think about an argument which you have seen or heard recently—it could be from a
philosophical paper or lecture, from a teacher or another student in class, from a
newspaper or on TV, or from a friend in a bar.
Analyse this argument, writing it out in the form of a series of premises and a conclusion.
Remember the two rules of formulating arguments:


If possible, it should be logically valid.
Every premise must matter to establish the conclusion.