Minds and Computers : An Introduction to the Philosophy of Artificial Intelligence

on one side, there is an even number on the other side. Which of the
four cards must you turn over to determine whether or not this
rule does hold?
4. Adrian has wealthy parents and went to an elite grammar school.
He works as an investment banker, is married to a corporate exec-
utive and drives a Porsche. Which of the following is more likely?
(a) Adrian is concerned about public health and welfare.
(b) Adrian is concerned about public health and welfare but votes
conservative.
154

---

5. All the people in Queensland wear hats in the sun. No one who
wears a hat in the sun gets facial melanomas. Does it follow that
no one in Queensland gets facial melanomas?
6. A flipped coin has landed on heads nine times in a row. What are
the odds it will land on tails on the next flip?
(a) Even
(b) Better than even
(c) Less than even
7. Jon and Nicole have two children. One of them is a boy. What is
the chance that the other one is a boy?
(a) 50%
(b) 33.33%
(c) 25%
8. All the vegetarians on campus are members of the Organic Food
Cooperative. None of the vegetarians on campus purchase food
known to be treated with pesticides or preservatives. Does it follow
that none of the members of the Organic Food Cooperative pur-
chase food known to be treated with pesticides or preservatives?
9. You draw a card from a standard deck. Which of the following is
more likely?
(a) You draw an ace.
(b) You draw a red ace.
10. You are given eight cards from a standard deck and are told that
only one of the following two statements is true:
[1] There is either an ace or a king in your hand (or both).
[2] There is either an ace or a queen in your hand (or both).
Which of the following is more likely?
(a) There is a king in your hand.
(b) There is an ace in your hand.
11. If you drink co
ffee at lunchtime then you will be more alert in the
afternoon. Dave is not more alert this afternoon. Does it follow
that Dave didn’t drink co
ffee at lunchtime?
12. The rule for collecting unemployment benefits states – If you
collect benefits then you must not be employed. Which of the
 
155

---

following four people must you gather further information about
to make sure they are not breaking the rule?
(a) The person you know to be employed.
(b) The person you know to be unemployed.
(c) The person you know to be receiving benefits.
(d) The person you know to be not receiving benefits.
15.1 FOLLOWING LOGICALLY
It is a recognised empirical fact that people generally perform quite
poorly on this set of reasoning problems. The reader of this volume
is clearly more intelligent than average – simply by virtue of having
purchased this book if nothing else – but I would still be surprised if
you made no mistakes on the problem set (unless you’ve previously
been exposed to these problems).
The question of whether a conclusion follows logically from some
premises is spelled out in terms of the validity of the inference. An
inference is valid i
ff the truth of its premises is sufficient to guarantee
the truth of its conclusion. The validity of a particular inference
depends on the validity of the logical form which it instances.
Technically speaking, it is logical forms of inference which are valid
or not. A logical form is valid i
ff there is no instance of the form which
has true premises and a false conclusion. In other words, a logical
form is valid if there is no instance of the form which is a counter-