Introductory Logic: The Fundamentals of Thinking Well Flashcards Preview

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1
Q

Logic

A

the science and art of reasoning well

2
Q

Law of Identity

A

If a statement is true, then it is true.

3
Q

Law of Excluded Middle

A

Any statement is either true or false.

4
Q

Law of Non-contradiction

A

A statement cannot be both true and false.

5
Q

Formal Logic

A

branch of logic which deals with

the proper modes of reasoning

6
Q

Informal Logic

A

branch of logic which deals with
operations of thinking that are
indirectly related to reasoning

7
Q

Induction

A

reasoning with probability from

examples or experience to general rules

8
Q

Deduction

A

reasoning with certainty from

premises to conclusions

9
Q

Categorical Logic

A

connects one category (or term) with another

uses syllogisms

10
Q

Propositional Logic

A

connects entire propositions together in arguments

11
Q

term

A

a concept that can be expressed precisely.

12
Q

definition

A

a statement that gives the meaning of a term.

13
Q

6 purposes of definitions

A
  1. show relationships
  2. remove ambiguity
  3. reduce vagueness
  4. increase vocabulary
  5. explain concepts theoretically
  6. influence attitudes
14
Q

ambiguous word

A

word with more than one meaning.

15
Q

lexical definition

A

definition which shows relationships or
reduces ambiguity by providing
a single, established meaning of a term
(dictionary definition)

16
Q

vague word

A

word whose extent is unclear.

17
Q

precising definition

A

definition which makes more precise
what was vague or fuzzy
(applies only to the situation in which it is used)

18
Q

stipulative definition

A

definition needed when a new word is invented

or an existing word is applied in a new way

19
Q

theoretical definition

A

definition given for a term, not when the word is unfamiliar, but when the term is not understood
(often scientific or philosophical in nature)

20
Q

persuasive definition

A

definition that aims at persuading the listener one way or another toward the term being defined

21
Q

genus

A

a term that is more general, broad, or abstract

than the original term and includes it

22
Q

species

A

term that is more specific, narrow, or concrete
than the original term and is included by it
(a type, kind or example of the term)

23
Q

mutually exclusive

A

not overlapping

24
Q

exhaustive

A

complete, no other types exist

25
Q

3 basic errors to avoid

in genus-species charts

A
  1. overlapping species (by changing the dividing principle or by placing a term at the wrong level)
  2. changing definitions for an ambiguous term
  3. using parts of the term (should be kinds)
26
Q

extension

A

the sum of all the individual obects
described by a term
(how broad is the term?)

27
Q

intension

A

the sum of all the common attributes
denoted by the term
(how specific is the term?)

28
Q

3 methods of defining terms

A
  1. synonym
  2. example
  3. genus-difference
29
Q

defining by synonym

A

giving another word with the same meaning

(problem if the meaning of the synonym is not known
or if no synonym exists)

30
Q

defining by example

A

demonstrating the term; giving several and various examples; listing species of the term

(problem because of ambiguity of this method)

31
Q

defining by genus and difference

A

naming the genus and then adding descriptive words which distinguish that term from all other species under that genus (OR what group is it in? what makes it different from everything else in the group?)

32
Q

6 rules for defining by

genus and difference

A
  1. state essential attributes
  2. should not be circular
  3. should not be too broad or narrow
  4. should not be unclear or figurative
  5. state positively if possible
  6. be the same part of speech as the term
33
Q

statement

A

a sentence which is either true or false.

34
Q

3 types of sentences

that are not statements

A
  1. question
  2. command
  3. nonsense
35
Q

self-supporting statements

A

a statement whose truth value can be determined

from the statement itself

36
Q

3 types of self-supporting statements

A
  1. self-reports
  2. true or false by logical structure
  3. true of false by definition
37
Q

self-report

A

a statement by a person concerning his own

desires, beliefs or feelings.

38
Q

true or false by

logical structure

A

a statement which can be seen to be true or false

by how the sentence is put together

39
Q

tautology

A

a statement which is always true
because of its logical structure
(e.g., Jesus is God OR Jesus is not God.)
A or ~A

40
Q

self-contradiction

A

a statement which is always false
because of its logical structure
(e.g., Jesus is God AND Jesus is not God)
A and ~A

41
Q

true or false by

definition

A

a statement which is necessarily true or false

becaue of the definitions of the words in the sentence

42
Q

supported statement

A

a statement whose truth value depends on

evidence or information from outside itself

43
Q

3 ways to determine the truth value

of supported statements

A
  1. authority
  2. experience
  3. deduction
44
Q

authority

A

a trustworth, authoritative source

e.g., scripture, encyclopedia

45
Q

experience

A

trusting our own senses to determine truth value

46
Q

deduction

A

reasoning to some conclusion based on

other statements, whose truth value we know

47
Q

4 relationships between statements

A
  1. consistency/inconsistency
  2. implication
  3. logical equivalence
  4. independence
48
Q

consistency

consistent

A

when 2 statements can both be true

at the same time

49
Q

inconsistency

inconsistent

A

when there is a conflict between 2 statements

so they cannot both be true at the same time

50
Q

implication

A

when the truth of 1 statement requires

the truth of the other.

51
Q

logical equivalence

A

when 2 statements imply each other

the statements must both be true or both be false

52
Q

independence

A

when the truth or falsity of 1 statement

has no effect on the truth or falsity of the other

53
Q

3 kinds of disagreements

A
  1. real
  2. apparent
  3. verbal
54
Q

real disagreement

A

an actual inconsistency between 2 statements;
they cannot both be true at the same time
(e.g.: Jesus is God. Jesus is not God.)

55
Q

apparent disagreement

A

a difference of opinion or perception
(e.g., Ann: I think logic is easy;
Bob: I think logic is hard)

56
Q

verbal disagreement

A

a missunderstanding due to differing definitions

for one or more words

57
Q

the ONE basic verb
in Categorical Logic
(list all forms)

A

the BEING (to be) verb
am was be
is were being
are been

58
Q

3 steps
to change statements into
standard categorical form

A

1) identify and write entire SUBJECT (noun)
2) choose the proper “TO BE” VERB
(right number and tense)
3) rewrite the entire predicate as a
PREDICATE NOMINATIVE (noun)

59
Q

categorical statements

A

statements which affirm or deny something

about a given subject

60
Q

subject

in a categorical statement

A

the term being described,

or about which something is asserted

61
Q

predicate

in a categorical statement

A

the term that describes

or asserts something about the subject

62
Q

quantity

of a statement

A

the scope of a statement’s claim
about the extension of the subject
~ either UNIVERSAL (All or No)
or PARTICULAR (Some or Some…not)

63
Q

quality

of a statement

A

the positive or negative nature
of a statement’s claim about the subject
~ either AFFIRMATIVE (asserts something)
or NEGATIVE (denies something)

64
Q

square of opposition

A

a diagram of the basic relationships
between statements WITH THE SAME
subject and predicate

65
Q

A

statements

A

universal affirmative statements

All S are P

66
Q

E

statements

A

universal negative statements

No S are P

67
Q

I

statements

A

particular affirmative statements

Some S are P

68
Q

O

statements

A

particular negative statements

Some S are not P

69
Q

contradiction

A

the relationship between statements
when they ALWAYS have OPPOSITE truth values
(cannot be both true or both false)
A ↔ O contradict I ↔ E contradict

70
Q

contrariety

A

the relationship between statements
when they CAN both be FALSE,
but CANNOT both be TRUE
only A ↔ E can be contrary

71
Q

subcontrariety

A

the relationship between statements
when they CAN both be TRUE,
but CANNOT both be FALSE
only I ↔ O can have subcontrariety

72
Q

subimplication

A
the relationship between statements
OF THE SAME QUALITY
in which the TRUTH of the UNIVERSAL
necessitates the TRUTH of the PARTICULAR
A → I              E → O
73
Q

superimplication

A
the relationship between statements
OF THE SAME QUALITY
in which the FALSITY of the PARTICULAR
necessitates the FALSITY of the UNIVERSAL
I → A              O → E
74
Q

argument

A

a set of statements, one of which appears to be implied or supported by the others

75
Q

premise

A
the statement(s) in an argument 
which support or imply the conclusion
76
Q

conclusion

A

the statement in an argument
which is supported or implied by the premise(s);
the endpoint or terminus of the argument

77
Q

syllogism

A

a particular form for organizing categorical statements into an argument; OR a deductive argument with 2 premises and 1 conclusion.

78
Q

categorical syllogism

A

a deductive argument consisting of 3 statements
in categorical form that use only 3 terms
~ major, minor and middle
(3-2-1: 3 terms, 2 premises, 1 conclusion)

79
Q

major term

A

the predicate term of the conclusion,

used in one premise

80
Q

minor term

A

the subject term of the conclusion,

used in one premise

81
Q

middle term

A

the term found once in each premise,

and is not in the conclusion at all

82
Q

major premise

A

the premise which contains the major term

83
Q

minor premise

A

the premise which contains the minor term

84
Q

5 steps to put a categorical syllogism into standard form

A
  1. find the conclusion
  2. find the major term
  3. find the major premise
  4. find the minor premise
  5. write the syllogism in standard order
85
Q

schema

A

a representation of a syllogism with statements in standard order and standard abbreviations of the terms
e.g. All M are P
All S are M
\ All S are P

86
Q

mood

A

a 3-letter description of the types of
categorical statements a syllogism contains
when arranged in standard order
e.g. AEO

87
Q

figure

A

a number from 1 to 4 identifying the placement

of the syllogism’s middle term (forms a smiley face :)

88
Q

form

A

the mood + the figure
of a syllogism, listed together

e.g. AEO-3

89
Q

valid syllogism

A
a syllogism in which the conclusion is 
necessarily true given that the 
premises are true
**depends ONLY on the form, 
NOT the truth of the statements**
90
Q

sound syllogism

A

a syllogism which is valid AND has true premises

91
Q

2 ways to test

the validity of syllogisms

A
  1. counter-example

2. rules

92
Q

counter-example

A
another syllogism with DIFFERENT TERMS
but the SAME FORM as the original,
with obviously TRUE PREMISES and
 a FALSE CONCLUSION, which proves 
the original syllogism to be invalid
93
Q

distributed term

A

a term that, within a statement, refers to ALL MEMBERS of its class/category

94
Q

When are terms distributed in A, E, I, & O statements

A

the subjects of universal statements and the predicates of negative statements are distributed

95
Q

5 rules for valid syllogisms

A
  1. Middle term must be distr. in at least 1 premise
  2. Any term distr.in concl.must be distr.in its premise
  3. Cannot have 2 negative premises
  4. Cannot have neg. prem. with affirmative concl.
  5. Cannot have 2 aff. prem. with neg. concl.
96
Q

5 corresponding fallacies for syllogism rules

A
  1. Fallacy of Undistributed Middle
  2. Fallacy of an Illicit Major/Minor
  3. Fallacy of 2 negative premises
  4. Fallacy of neg. premise & aff. conclusion
  5. Fallacy of 2 aff. premises and neg. conclusion
97
Q

immediate inference

A

a statement which can be inferred directly

from another statement

98
Q

3 types of immediate inferences

A
  1. converse
  2. obverse
  3. contrapositive
99
Q

converse

A

a statement that reverses
the subject and predicate of the original

(only E & I)

100
Q

obverse

A

a statement that has the opposite quality and a negated predicate of the original

(A, E, I, & O)

101
Q

contrapositive

A

a statement that reverses and negates
both the subject and predicate of the original

(only A & O)

102
Q

complement

A

the set of all terms NOT included in the given term

P → non-P

103
Q

translating singular statements

A

statements that refer to a single person or thing are best translated as universal

affirming: Tom is a cat. → All Tom is a cat.
denying: Tom is not a cat. → No Tom is a cat

104
Q

translating indefinite statements

A

indefinite statements may be translated as universals or particulars, depending on the statement’s meaning

e.g., Cats are mammals. → All cats…
Cats are my pets. → Some cats…

105
Q

translating hypothetical statements

A

hypotheticals should be translated as universals:
affirming: If you love chocolate, then you will love this cake.. → All choc. lovers will be lovers of this cake.
denying: If this is a hard test, then I will not pass.
→ No hard test is a test I will pass.

106
Q

inclusives

A

words that refer to a broad range of
things/times/people/places/ways
(“ever” words: whoever, whatever, whenever,
wherever, however, always, never, that (=whatever))

107
Q

translating inclusives

A
whoever → All people … are people …
whatever → All things … are things …
wherever → All places … are places …
whenever / always → All times … are times …
however → All ways … are ways …
never → No times … are times …
108
Q

exclusives

A
words that set boundaries referring to 
a limited class of things

(only/nobody but/nothing but, unless, except)

109
Q

translating exclusives

A
  1. Only the good die young
    → All people who die young are good people.
  2. The plants will die unless you water them
    → All plants you don’t water are plants that will die. (or contrpos)
  3. Everyone was invited to the party except sisters.
    → All non-sisters… OR No sisters…(depends on use)
110
Q

enthymeme

A

an argument in which a statement is
unstated and assumed
(i.e., a syllogism with one assumed statement)

111
Q

hypothetical statement

A

a statement that affirms an outcome
based on a condition

If P, then Q.

112
Q

pure hypothetical syllogism

A

a syllogism what uses only

hypothetical statements

113
Q

antecedent

A

the condition in a hypothetical statement

follows “If …”

114
Q

consequent

A

the result in a hypothetical statement

follows “then … “

115
Q

mixed hypothetical syllogism

A

a syllogism that uses both

hypothetical and categorical statements

116
Q

modus ponens

A

If P then Q P É Q
P OR P
\ Q \ Q
Valid

117
Q

modus tolens

A

If P then Q P É Q
Not Q OR ~ Q
\ Not P \ ~ P
Valid

118
Q

affirming the consequent

A

If P then Q P É Q
Q OR Q
\ P \ P
INVALID

119
Q

denying the antecedent

A

If P then Q P É Q
Not P OR ~ P
\ Not Q \ ~ Q
INVALID

120
Q

establishing a conclusion

A

finding a valid syll. form to establish a given concl. as true:
1. write the concl. in standard form.
2. find a valid form that has that type of stmt (A,E,I,O)
as its conclusion
3. fill in the known terms in the premises for the form
4. find a middle term that makes premises true

121
Q

informal fallacies

A

popular but invalid (or unhelpful)

forms of argument

122
Q

3 types of

informal fallacies

A
  1. Fallacies of Distraction
  2. Fallacies of Ambiguity
  3. Fallacies of Form
123
Q

Fallacy of Distraction

A

an argument that confuses the issue
by pointing to information that is actually irrelevant
to the conclusion

124
Q

Ipse Dixit

A

an illegitimate appeal to authority

Latin for “He said it himself”

125
Q

Ad Populum

A

an illegitimate appeal to majority

Latin for “to the masses”

126
Q

Ad Baculum

A

an illegitimate appeal to force;
a thinly veiled threat

Latin for “to the stick”

127
Q

Ad Hominem

A

a verbal attack on a person rather than his argument
~depends on whether the attack is true
AND whether it is relevant
Latin for “to the man”

128
Q

Bulverism

A

attacking a position/belief by pointing out how the person came to hold it
~depends whether the “how” is relevant to the argument
Form: “You only believe that because ______”

129
Q

Tu Quoque

A

points to an inconsistency between a person’s argument and his behavior
~ no fallacy if the behavior is not wrong
Form: “Don’t tell me not to ___; you do/did it, too!”

130
Q

Ad Ignorantium

A

an argument from lack of evidence

Latin for: “to ignorance”

131
Q

Chronological Snobbery

A

an argument based merely on the passage of time

Form: “I accept/reject ________
because it is too old/new.”

132
Q

Fallacy of Ambiguity

A

an argument that confuses the real issue

with multiple, vague, or otherwise unclear meanings

133
Q

Equivocation

A

changing the definition of a term

in the middle of an argument

134
Q

Accent

A

altering the meaning of a statement through
changed emphasis
~ must make the meaning different
than the speaker intended

135
Q

Amphiboly

A

a vagueness of grammar that

disguises or alters meaning

136
Q

Composition

A

transfers attributes from parts to whole

~assumes that what is true for the parts
is true for the whole

137
Q

Division

A

transfers attributes from whole to parts

~assumes that what is true for the whole
is true for the parts

138
Q

Fallacy of Form

A

an argument that fails to establish its conclusion because of a weakness in logical structure

139
Q

Circular Reasoning

A

secretly assuming what you are trying to prove
(i.e., one of the premises contains the conclusion
in disguise)

140
Q

Post Hoc Ergo Propter Hoc

A

improperly assuming that a sequence in time
implies cause and effect

Latin for “after this, therefore because of this”

141
Q

Either / Or

A

making an argument based on a false dilemma
(i.e., oversimplifying the choices)

also called Bifurcation

142
Q

Complex Question

A

a question crafted in a way that excludes

any possible legitimate response

143
Q

Apriorism

A

a hasty generalization

(i.e., applying what is true of one member
to the whole group)

144
Q

2 questions to ask about the person
making an argument, in order
to detect informal fallacies

A
  1. What is he trying to prove?
  2. How is he trying to prove it?

(or: What is the conclusion and how is it reached?)