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Cengage Advantage Books: Understanding Arguments: An Introduction to Informal Logic

Walter Sinnott-Armstrong, Robert J. Fogelin

Chapter 7

Categorical Logic - all with Video Answers

Educators

Chapter Questions

01:22

Problem 1

Using just the four basic categorical forms, indicate what information is given in each of the following diagrams:
DIAGRAM CAN'T COPY.

Eva R
Eva R
Numerade Educator
04:43

Problem 2

Translate each of the following sentences into an A, E, I, or O proposition. Be sure that the subjects and predicates in your translations use nouns that refer to classes of things (rather than adjectives or verbs). If the sentence can be translated into different forms in different contexts, give each translation and specify a context in which it seems natural.

Rosina Dapaah
Rosina Dapaah
Numerade Educator
02:10

Problem 3

1. Is an A proposition a contradictory of its corresponding E proposition? Why or why not?
2. Is an I proposition a contradictory of its corresponding O proposition? Why or why not?
3. If one proposition is the contradictory of another, is the latter always the contradictory of the former? Why or why not?

Abhijith V
Abhijith V
Numerade Educator

Problem 4

Give two new examples of contexts in which:
1. Stating an A proposition does not seem to commit the speaker to the existence of the things to which the subject term refers.
2. Stating an A proposition does not seem to commit the speaker to the existence of the things to which the predicate term refers.
3. Stating an E proposition does not seem to commit the speaker to the existence of the things to which the subject term refers.
4. Stating an E proposition does not seem to commit the speaker to the existence of the things to which the predicate term refers.

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02:18

Problem 5

Use Venn diagrams to determine whether the following immediate inferences are valid:
1. All dinosaurs are animals. Therefore, all animals are dinosaurs.
2. Some pterodactyls can fly. Therefore, some flying things are pterodactyls.
3. Some eryopses are not meat eaters. Therefore, some things that eat meat are not eryopses.
4. No tyrannosaurus is a king. Therefore, no king is a tyrannosaurus.
5. Some dinosaurs are reptiles. Therefore, all dinosaurs are reptiles.
6. Some dinosaurs are not alive today. Therefore, no dinosaurs are alive foday.
7. All dimetrodons eat meat. Therefore, some dimetrodons eat meat.
8. No dinosaurs are warm-blooded. Therefore, some dinosaurs are not warm-blooded.

Adithya Ramanujam
Adithya Ramanujam
Numerade Educator

Problem 6

In each of the last two syllogisms, what is the subject term? The predicate term? The middle term? The major premise? The minor premise? The form of the syllogism (using $S, P$, and $M$ )? Is the syllogism valid? Why or why not?

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Problem 7

Using Venn diagrams, test the following syllogistic forms for validity:
1. All $M$ is $P$. All $M$ is $S$.
$\therefore$ All $S$ is $P$.
2. All $P$ is $M$. All $M$ is $S$.
$\therefore$ All $S$ is $P$.
3. All $M$ is $P$.

Some $M$ is $S$.
$\therefore$ Some $S$ is $P$.
4. All $P$ is $M$.

Some $M$ is $S$.
$\therefore$ Some $S$ is $P$.
5. All $P$ is $M$.
$\therefore$ Some $S$ is $M$.
6. All $P$ is $M$

Some $S$ is not $M$.
$\therefore$ Some $S$ is not $P$.
7. All $M$ is $P$. Some $S$ is not $M$.
$\therefore$ Some $S$ is not $P$.
8. All $M$ is $P$. Some $M$ is not $S$.
$\therefore$ Some $S$ is not $P$.
9. No $M$ is $P$. Some $S$ is $M$.
$\therefore$ Some $S$ is not $P$.
10. No $P$ is $M$. Some $S$ is $M$.
$\therefore$ Some $S$ is not $P$.
11. No $P$ is $M$. Some $S$ is not $M$.
$\therefore$ Some $S$ is not $P$.
12. No $M$ is $P$. Some $S$ is not $M$.
$\therefore$ Some $S$ is not $P$
13. No $P$ is $M$. Some $M$ is not $S$.
$\therefore$ Some $S$ is not $P$.
14. No $P$ is $M$. No $M$ is $S$.
$\therefore$ No $S$ is $P$.
15. No $P$ is $M$ All $M$ is $S$.
$\therefore$ No $S$ is $P$.
16. No $P$ is $M$. All $S$ is $M$.
$\therefore$ No $S$ is $P$.
17. All $P$ is $M$.
No $S$ is $M$.
$\therefore$ No $S$ is $P$.
18. All $M$ is $P$.
No $S$ is $M$.
$\therefore$ No $S$ is $P$.
19. Some $M$ is $P$. Some $M$ is not $S$.
$\therefore$ Some $S$ is not $P$.
20. Some $P$ is $M$.
Some $S$ is not $M$.
$\therefore$ Some $S$ is $P$.

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Problem 8

Explain why it is a good strategy to diagram a universal premise before diagramming a particular premise in a syllogism with both.

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