A Field Guide to Lies: Critical Thinking in the Information Age (23 page)

The type of deductive argument about Márquez is called a syllogism. In syllogisms, it is the
form
of the argument that guarantees that the conclusion follows. You can construct a syllogism with a premise that you know (or think to be) false, but that doesn’t invalidate the syllogism—in other words, the logic of the whole thing still holds.

The moon is made of green cheese.

Green cheese costs $22.99 per pound.

Therefore, the moon costs $22.99 per pound.

Now, clearly the moon is
not
made of green cheese, but IF it were, the deduction is logically valid. If it makes you feel better, you can rewrite the syllogism so that this is made explicit:

IF the moon is made of green cheese

AND IF green cheese costs $22.99 per pound

THEN the moon costs $22.99 per pound.

There are several distinct types of deductive arguments, and they’re typically taught in philosophy or math classes on formal logic. Another common form involves conditionals. This one is called
modus ponens
. It’s easy to remember what it’s called with this example (using Poe as in
ponens
):

If Edgar Allan Poe went to the party, he wore a black cape.

Edgar Allan Poe went to the party.

Therefore, he wore a black cape.

Formal logic can take some time to master, because, as with many forms of reasoning, our intuitions fail us. In logic, as in running a race, order matters. Does the following sound like a valid or invalid conclusion?

If Edgar Allan Poe went to the party, he wore a black cape.

Edgar Allan Poe wore a black cape.

Therefore, he went to the party.

While it
might
be true that Poe went to the party, it is not
necessarily
true. He could have worn the cape for another reason (perhaps it was cold, perhaps it was Halloween, perhaps he was acting in a play that required a cape and wanted to get in character). Drawing the conclusion above represents an error of reasoning called the
fallacy of affirming the consequent,
or the
converse error
.

If you have a difficult time remembering what it’s called, consider this example:

If Chuck Taylor is wearing Converse shoes, then his feet are covered.

Chuck Taylor’s feet are covered.

Therefore, he is wearing Converse shoes.

This reasoning obviously doesn’t hold, because wearing Converse shoes is not the only way to have your feet covered—you could be wearing any number of different shoe brands, or have garbage bags on your feet, tied around the ankles.

However, you
can
say with certainty that if Chuck Taylor’s feet are not covered, he is not wearing Converse shoes. This is called the
contrapositive
of the first statement.

Logical statements don’t work like the minus signs in equations—you can’t just negate one side and have it automatically negate the other. You have to memorize these rules. It’s somewhat easier to do using quasi-mathematical notation. The statements above can be represented this way, where A stands for any premise, such as “If Chuck Taylor is wearing Converse shoes,” or “If the moon is made of green cheese” or “If the Mets win the pennant this year.” B is the consequence, such as “then Chuck’s feet are covered,” or “then the moon should appear green in the night sky” or “I will eat my hat.”

Using this generalized notation, we say
If A
as a shorthand for “If A is true.” We say
B
or
Not B
as a shorthand for “B is true” or “B is not true.” So . . .

If A, then B

A

Therefore, B

In logic books, you may see the word
then
replaced with an arrow (→) and you may see the word
not
replaced with this symbol: ~. You may see the word
therefore
replaced with
∴
as in:

If A → B

A

∴
B

Don’t let that disturb you. It’s just some people trying to be fancy.

Now there are four possibilities for statements like this: A can be true or not true, and B can be true or not true. Each of the possibilities has a special name.

1. Modus ponens. This is also called affirming the antecedent. “Ante” means before, like when you “ante up” in poker, putting money in the pot before any cards are played.

If A → B

A
∴
B

Example: If that woman is my sister, then she is younger than I am.

That woman is my sister.

Therefore, she is younger than I am.

2. The contrapositive.

If A → B

~ B
∴
~ A

Example: If that woman is my sister, then she is younger than I am.

That woman is not younger than I am.

Therefore, she is not my sister.

3. The converse.

If A → B

B
∴
A

This is a
not
a valid deduction.

Example: If that woman is my sister, then she is younger than I am.

That woman is younger than I am.

Therefore, she is my sister.

This is invalid because there are many women younger than I am who are not my sister.

4. The inverse.

If A → B

~A
∴
~B

This is a
not
a valid deduction.

Example: If that woman is my sister, then she is younger than I am.

That woman is not my sister.

Therefore, she is not younger than I am.

This is invalid because many women who are not my sister are still younger than I am.

Inductive reasoning is based on there being evidence that suggests the conclusion is true, but does not guarantee it. Unlike deduction, it leads to uncertain but (if properly done) probable conclusions.

An example of induction is:

All mammals we have seen so far have kidneys.

Therefore (this is the inductive step), if we discover a new mammal, it will probably have kidneys.

Science progresses by a combination of deduction and induction. Without induction, we’d have no hypotheses about the world. We use it all the time in daily life.

Every time I’ve hired Patrick to do a repair around the house, he’s botched the job.

Therefore, if I hire Patrick to do this next repair, he’ll botch this one too.

Every airline pilot I’ve met is organized, conscientious, and meticulous.

Lee is an airline pilot. He has these qualities, and he’s also good at math.

Therefore, all airline pilots are good at math.

Of course, this second example doesn’t necessarily follow. We’re making an inference. With what we know about the world, and the job requirements for being a pilot—plotting courses, estimating the influence of wind velocity on arrival time, etc.—this seems reasonable. But consider:

Every airline pilot I’ve met is organized, conscientious, and meticulous.

Lee is an airline pilot. He has these qualities, and he also likes photography.

Therefore, all airline pilots like photography.

Here our inference is less certain. Our real-world knowledge suggests that photography is a personal preference, and it doesn’t necessarily follow that a pilot would enjoy it more or less than a non-pilot.

The great fictional detective Sherlock Holmes draws conclusions through clever reasoning, and although he claims to be using deduction, in fact he’s using a different form of reasoning called
abduction
. Nearly all of Holmes’s conclusions are clever guesses, based on facts, but not in a way that the conclusion is airtight or inevitable. In abductive reasoning, we start with a set of observations and then generate a theory that accounts for them. Of the
infinity of different theories that could account for something, we seek the most likely.

For example, Holmes concludes that a supposed suicide was really a murder:

HOLMES:
The wound was on the right side of his head. Van Coon was left-handed. Requires quite a bit of contortion.

DETECTIVE INSPECTOR DIMMOCK:
Left-handed?

HOLMES:
Oh, I’m amazed you didn’t notice. All you have to do is look around this flat. Coffee table on the left-hand side; coffee mug handle pointing to the left. Power sockets: habitually used the ones on the left . . . Pen and paper on the left-hand side of the phone because he picked it up with his right and took down messages with his left . . . There’s a knife on the breadboard with butter on the right side of the blade because he used it with his left. It’s highly unlikely that a left-handed man would shoot himself in the
right
side of his head. Conclusion: Someone broke in here and murdered him . . .