Deduction (Classical)

Question 1

Define: deductive argument.

Answer 1

An argument whose premises are claimed to provide conclusive grounds for the truth of its conclusion.

Question 2

Define: validity.

Answer 2

a characteristic of any deductive argument whose premises, if they were all true, would provide conclusive grounds for the truth of its conclusion. Such an argument is said to be valid.

Question 3

Define: classical or Aristotelian logic.

Answer 3

The traditional account of syllogistic reasoning, in which certain interpretations of categorical propositions are presupposed.

Question 4

Define: modern of modern symbolic logic.

Answer 4

The account of syllogistic reasoning accepted today. It differs in important ways from the traditional account.

Question 5

Define: class.

Answer 5

The collection of all objects that have some specified characteristic in common.

Question 6

Define: categorical proposition.

Answer 6

A proposition that can be analyzed as being about classes, or categories, affirming or denying that one class, s, is included in some other class, p, in whole or in part.

Question 7

What are the four kinds of categorical proposition?

Answer 7

1. universal affirmative propositions (all s is p), or A propositions
2. universal negative propositions (no s is p), or E propositions
3. particular affirmative propositions (some s is p), or I propositions
4. particular negative propositions (some s is not p), or O propositions

Question 8

Define: quality.

Answer 8

An attribute of every categorical proposition, determined by whether the proposition affirms or denies class inclusion. Thus every categorical proposition is either affirmative in quality or negative in quality.

Question 9

Define: quantity.

Answer 9

An attribute of every categorical proposition, determined by whether the proposition refers to all members or only some members of the class designated by its subject term. Thus every categorical proposition is either universal in quantity or particular in quantity.

Question 10

Define: copula.

Answer 10

Any forms of the verb “to be” that serve to connect the subject term and the predicate term of a categorical proposition.

Question 11

Define: distribution.

Answer 11

An attribute that describes the relationship between a categorical proposition and each one of its terms, indicating whether or not the proposition makes a statement about every member of the class represented by a given term.

Question 12

Predicate term Predicate term
undistributed distributed
Subject term distributed w x
Subject term undistributed y z

Answer 12

w=A
x=E
y=I
z=O

Question 13

Define: opposition.

Answer 13

The logical relation that exists between two contradictories, two contraries, or in general between any two categorical propositions that differ in quantity, quality, or other respects. These relations are displayed on the square of opposition.

Question 14

Define: contradictories.

Answer 14

Two propositions so related that one is the denial or negation of the other. On the traditional square of opposition, the two pairs of contradictories are indicated by the diagonals of the square: A and E propositions are the contradictories of O and I propositions, respectively.

Question 15

Define: contraries.

Answer 15

Two propositions so related that they cannot both be true, although both may be false.

Question 16

Define: contingent.

Answer 16

Being neither tautologous nor self-contradictory. A contingent statement may be true or false.

Question 17

Define: subcontraries.

Answer 17

Two propositions so related that they cannot both be false, although they may both be true.

Question 18

Define: subalternation.

Answer 18

The relation on the square of opposition between a universal proposition (an A or an E proposition) and its corresponding particular proposition (an I or an O proposition, respectively). In the relation, the particular proposition (I or O) is called the “subaltern,” and the universal proposition (A or E) is called the “superaltern.”

Question 19

Define: square of opposition.

Answer 19

A diagram in the form of a square in which the four types of categorical propositions (A, E, I, O) are situated at the corners, exhibiting the logical relations (called “oppositions”) among these propositions.

Question 20

The ___altern implies the truth of the ___altern.

Answer 20

a) super

b) sub

Question 21

Define: immediate inference.

Answer 21

an inference that is drawn directly from one premise without the mediation of any other premise. Various kinds of immediate inferences may be distinguished, traditionally including conversion, obversion, and contraposition.

Question 22

Define: mediate inference.

Answer 22

Any inference drawn from more than one premise.

Question 23

Define: conversion.

Answer 23

A valid form of immediate inference for some but not all types of propositions. To form the converse of a proposition the subject and predicate terms are simply interchanged. Thus, applied to the proposition “No circles are squares,” conversion yields “No squares are circles,” which is called the “converse” of the original proposition. The original proposition is called the
“convertend.”

Question 24

Conversion is valid for all __ and __ propositions.

Answer 24

E and I (A by limitation)

Question 25

Define: complementary class.

Answer 25

The collection of all things that do not belong to a given class.

Question 26

Define: obversion.

Answer 26

A valid form of immediate inference for every standard-form categorical proposition. To obvert a proposition we change its quality (from affirmative to negative, or from negative to affirmative) and replace the predicate term with its complement. Thus, applied to the proposition “All dog are mammals,” obversion yields “No dogs are nonmammals,” which is called the “obverse” of the original proposition. The original proposition is called the “obvertend.”

Question 27

Define: contraposition.

Answer 27

A valid form of immediate inference for some, but not for all types of propositions. To form the contrapositive of a given proposition, its subject term is replaced by the complement of its predicate term. Thus the contrapositive of the proposition “All humans are mammals” is “All nonmammals are nonhumans.”

Question 28

Contraposition is valid for all __ and __ propositions.

Answer 28

A and O (E by limitation)

Question 29

Define: Boolean interpretation.

Answer 29

The modern interpretation of categorical propositions, adopted in this book and named after the English logician George Boole. In the Boolean interpretation, often contrasted with the Aristotelian interpretation, universal propositions (A and E propositions) do not have existential import.

Question 30

Define: existential import.

Answer 30

An attribute of those propositions that normally assert the existence of objects of some specified kind. Particular propositions (I and O propositions) always have existential import; thus the proposition “Some dogs are obedient” asserts that there are dogs. Whether universal propositions (A and E propositions) have existential import is an issue on which the Aristotelian and Boolean interpretations of propositions differ.

Question 31

What is the crux of the problem with existential import?

Answer 31

If I and O propositions have existential import, then A and E propositions must have it, too, because you cannot validly derive a proposition with existential import (here, I or O) out of one without it (here, A or E). But A and O propositions are contradictories, so both cannot be true. But if they have existential import, they both could be true!

Question 32

With what key new element is the problem of existential import first attempted to be resolved? Why is it not sufficient?

Answer 32

a) presupposition

b) denials; hypotheticals; scientific reasoning

Question 33

What does the Boolean interpretation change to address this problem?

Answer 33

Universal propositions are interpreted as having no existential import.

Question 34

Define: existential fallacy.

Answer 34

Any mistake in reasoning that arises from assuming illegitimately that some class has members.

Question 35

In a Venn diagram, how do you indicate that there a) are, or b) are not members in a class?

Answer 35

a) put an x

b) shade it out with lines