### Valid deductive argument - Greer Middle College || Building the Future

```TOD (individually—your own paper—name, date, TOD, block)
For each passage decide (a) if there is an argument being made;
(b) if so, list the premise(s) and conclusion (e.g. P1, P2…)
1. Given that all reptiles are cold-blooded and all snakes are reptiles, it
must be that all snakes are cold-blooded.
2. I think a student like you, with your reputation for hard work and good
grades, should invest some extracurricular time in community service.
3. Mrs. Casey clearly cares about her students. She always greets us with
enthusiasm and asks how things are going. She even finds time to look
over papers that aren’t being written for her class.
4. Since Mr. Simms was born, there have been no new states added to the
Union.
Argument types: Deductive
 Deductive argument:
an argument in which
the arguer claims that
the premise(s) cannot be
true and the conclusion
false; the conclusion
follows necessarily from
the premise(s)
Examples:
 Mathematics (except statistics!)
 Argument from definition
 Categorical syllogism

All poodles are canines.
Smitty is a poodle.
Thus, Smitty is a canine.
 Hypothetical syllogism
 If Smitty is mad, he’ll bite.
Thus, Smitty will bite.
 Disjunctive syllogism

Either Smitty’s asleep or he’s awake.
Smitty’s not asleep.
Therefore, Smitty’s awake.
Argument types: Inductive
 Inductive argument: an
argument in which the
arguer claims it is
improbable that the
premise(s) be true and the
conclusion false; the
conclusion follows probably
from the premise(s)
Examples:
 Prediction
 Grey clouds are moving in, so
it’s probably about to rain.
 Causal inference
 Mom’s car is smashed, so I
guess she got in a wreck.
 Argument from analogy
 Mrs. Casey’s Ferrari handles
nicely, so Mr. Simms’s Ferrari
must handle nicely, too.
 Generalization
 2 of the first 4 TODs I looked at
had logical errors in them, so
half the class is making errors.
 Argument from authority
 We know that Smitty has
cancer, because the vet
diagnosed him.
In groups, decide whether the argument is deductive or inductive. To help you decide,
(1) read indicator words carefully, (2) think about inferential link between premises
and conclusion, and (3) consider the form of the argument.
1. Because triangle A is congruent with triangle B, and triangle A is isosceles, it follows
that triangle B is isosceles.
2. Paying off terrorists in exchange for hostages is not a wise policy, since such action
will only lead them to take more hostages in the future.
3. The Encyclopaedia Britannica has an article on symbiosis. The Encyclopedia
Americana, like the Britannica, is an excellent reference work. Therefore, the
Americana probably also has an article on symbiosis.
4. Dr. Roach is the principal, so he is in charge of administration over the whole
school.
5. Either Mrs. Casey is in the café or she’s in her portable, and I don’t see her in the
café, so clearly she’s in her portable.
6. Amoco, Exxon, and Texaco are all listed on the New York Stock Exchange. It must
be the case that all major American oil companies are listed on the New York Stock
Exchange.
Evaluating inferential claims
 Valid deductive
argument: one in which
it is impossible for the
premise(s) to be true and
the conclusion false
 Invalid deductive
argument: one in which
it is possible for the
premise(s) to be true and
the conclusion false (a
 All dogs are mammals.
Lassie is a dog.
Therefore, Lassie is a
mammal.
 All SUVs have 4 wheels.
Mrs. Casey’s car has 4
wheels.
Therefore, Mrs. Casey’s
car is an SUV.
Evaluating factual claims
 Sound argument: a
valid deductive argument
with all true premises
 All cats are mammals.
Garfield is a cat.
Thus, Garfield is a
mammal.
 Unsound argument: a
deductive argument in
which one or more
premise is false (or when
the argument is invalid)
 All cats are mammals.
Godzilla is a cat.
Thus, Godzilla is a
mammal.
(Valid, but unsound.)
Zoom out: Detecting fallacies
 Fallacy: defect in an argument consisting of
something other than just false premises
 Formal fallacy: a fallacy which may be identified
just by examining the form or structure of an
argument
 Informal fallacy: a fallacy that can only be detected
by examining the content of the argument (Later—
these are fun . . . and may involve clubbing people)
By yourself, classify the arguments as either valid or invalid; note whether
premises and conclusion are true or false; then classify the arguments as sound
or unsound.
1. Since Moby Dick was written by Shakespeare, and Moby Dick is a science fiction
novel, it follows that Shakespeare wrote a science fiction novel.
2. The longest river in South America is the Amazon, and the Amazon flows through
Brazil. Therefore, the longest river in South America flows through Brazil.
Use counterexample method with the terms “cats,” “dogs,” “mammals,” “fish,”
and “animals” to prove that the forms of the arguments below are invalid.
1. All detentions are punishments and all suspensions are punishments, so all
detentions are suspensions.
2. All cars are vehicles. No trucks are cars. Therefore, no trucks are vehicles.
3. Some trees are pines. All pines are conifers. Thus, all trees are conifers.
4. All SUVs have 4 wheels. Mrs. Casey’s car has 4 wheels. Therefore, Mrs. Casey’s
car is an SUV.
```