Formal Reasoning

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Chapter 7 Thought, Language, and Intelligence
Thinking Strategies
䉴 Do people always think logically?
PITFALLS IN LOGICAL REASONING
“Elderly people cannot be astronauts; this
is an elderly man; therefore, he cannot be
an astronaut.” The logic is correct, but because the first statement is wrong, so is
the conclusion. In 1962, John Glenn became the first American astronaut to orbit the earth. Here he is in 1998, at the
age of seventy-seven, just before he returned to space as a full-fledged member
of the crew of the space shuttle Discovery.
reasoning The process by which people generate and evaluate arguments
and reach conclusions about them.
formal reasoning A set of rigorous
procedures for reaching valid
conclusions.
algorithms Systematic procedures that
cannot fail to produce a correct solution to a problem.
rules of logic A set of statements that
provide a formula for drawing valid
conclusions.
We have seen that our thinking capacity is based largely on our ability to manipulate
mental representations—the ingredients of thought—much as a baker manipulates the
ingredients of cookies. The baker’s food-processing system combines and transforms
these ingredients into a delicious treat. Our information-processing system combines,
transforms, and elaborates mental representations in ways that allow us to engage in
reasoning, problem solving, and decision making. Let’s begin our discussion of these
thinking strategies by considering reasoning: the process through which we generate
and evaluate arguments, as well as reach conclusions about them.
Formal Reasoning
Astronomers tell us that the temperature at the core of the sun is about 27 million
degrees Fahrenheit. How do they know this? They can’t put a temperature probe inside
the sun, so their estimate is based on inferences from other things that they know about
the sun and about physical objects in general. For example, telescopic observations
allowed astronomers to calculate the energy coming from one small part of the sun.
They then used what geometry told them about the surface area of spheres to estimate
the sun’s total energy output. Further calculations told them how hot a body would
have to be to generate that much energy.
In other words, astronomers’ estimates of the sun’s core temperature are based on
formal reasoning (also called logical reasoning)—the process of following a set of rigorous steps for reaching valid, or correct, conclusions. Some of these steps included the
application of specific mathematical formulas to existing data in order to generate new
data. Such formulas are examples of algorithms—systematic methods that always
reach a correct solution to a problem, if a correct solution exists.
The astronomers also followed the rules of logic, a set of statements that provide
a formula for drawing valid conclusions about the world. For example, each step in
the astronomers’ thinking took the form of “if-then” propositions: If we know how
much energy comes from one part of the sun’s surface, and if we know how big the
whole surface is, then we can calculate the total energy output. You use the same logical reasoning processes when you conclude, for example, that if your friend José is
two years older than you are, then his twin brother, Juan, will be two years older, too.
This kind of reasoning is called deductive reasoning, because it takes a general rule
(e.g., twins are the same age) and applies it to deduce conclusions about specific cases
(e.g., José and Juan).
Most of us try to use logical or deductive reasoning to reach valid conclusions and
avoid invalid ones (Rips, 1994). However, even when our logic is perfect, we can make
mistakes if we base our reasoning on false assumptions. Likewise, correct assumptions
combined with faulty logic can lead to errors. Do you think the following example leads
to a valid conclusion?
Assumption 1: All women want to be mothers.
Assumption 2: Jill is a woman.
Conclusion: Jill wants to be a mother.
If you said that the first assumption is not necessarily correct, you’re right. Now consider this example:
Assumption 1: All gun owners are people.
Assumption 2: All criminals are people.
Conclusion: All gun owners are criminals.
Here, the assumptions are correct, but the logic is faulty. If “all A’s are B” and “all
C’s are B,” it does not follow that “all A’s are C.”