Introductory Logic: The Fundamentals of Thinking Well Flashcards
Learn Introductory Logic Terms for Challenge B in Classical Conversations.
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
- show relationships
- remove ambiguity
- reduce vagueness
- increase vocabulary
- explain concepts theoretically
- 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
3 basic errors to avoid
| in genus-species charts
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
extension
the sum of all the individual obects
described by a term
(how broad is the term?)
27
intension
the sum of all the common attributes
denoted by the term
(how specific is the term?)
28
3 methods of defining terms
1. synonym
2. example
3. genus-difference
29
defining by synonym
giving another word with the same meaning
(problem if the meaning of the synonym is not known
or if no synonym exists)
30
defining by example
demonstrating the term; giving several and various examples; listing species of the term
(problem because of ambiguity of this method)
31
defining by genus and difference
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
6 rules for defining by
| genus and difference
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
statement
a sentence which is either true or false.
34
3 types of sentences
| that are not statements
1. question
2. command
3. nonsense
35
self-supporting statements
a statement whose truth value can be determined
| from the statement itself
36
3 types of self-supporting statements
1. self-reports
2. true or false by logical structure
3. true of false by definition
37
self-report
a statement by a person concerning his own
| desires, beliefs or feelings.
38
true or false by
| logical structure
a statement which can be seen to be true or false
| by how the sentence is put together
39
tautology
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
self-contradiction
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
true or false by
| definition
a statement which is necessarily true or false
| becaue of the definitions of the words in the sentence
42
supported statement
a statement whose truth value depends on
| evidence or information from outside itself
43
3 ways to determine the truth value
| of supported statements
1. authority
2. experience
3. deduction
44
authority
a trustworth, authoritative source
| e.g., scripture, encyclopedia
45
experience
trusting our own senses to determine truth value
46
deduction
reasoning to some conclusion based on
| other statements, whose truth value we know
47
4 relationships between statements
1. consistency/inconsistency
2. implication
3. logical equivalence
4. independence
48
consistency
| consistent
when 2 statements can both be true
| at the same time
49
inconsistency
| inconsistent
when there is a conflict between 2 statements
| so they cannot both be true at the same time
50
implication
when the truth of 1 statement requires
| the truth of the other.
51
logical equivalence
when 2 statements imply each other
| the statements must both be true or both be false
52
independence
when the truth or falsity of 1 statement
| has no effect on the truth or falsity of the other
53
3 kinds of disagreements
1. real
2. apparent
3. verbal
54
real disagreement
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
apparent disagreement
a difference of opinion or perception
(e.g., Ann: I think logic is easy;
Bob: I think logic is hard)
56
verbal disagreement
a missunderstanding due to differing definitions
| for one or more words
57
the ONE basic verb
in Categorical Logic
(list all forms)
the BEING (to be) verb
am was be
is were being
are been
58
3 steps
to change statements into
standard categorical form
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
categorical statements
statements which affirm or deny something
| about a given subject
60
subject
| in a categorical statement
the term being described,
| or about which something is asserted
61
predicate
| in a categorical statement
the term that describes
| or asserts something about the subject
62
quantity
| of a statement
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
quality
| of a statement
the positive or negative nature
of a statement's claim about the subject
~ either AFFIRMATIVE (asserts something)
or NEGATIVE (denies something)
64
square of opposition
a diagram of the basic relationships
between statements WITH THE SAME
subject and predicate
65
A
| statements
universal affirmative statements
All S are P
66
E
| statements
universal negative statements
No S are P
67
I
| statements
particular affirmative statements
Some S are P
68
O
| statements
particular negative statements
Some S are not P
69
contradiction
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
contrariety
the relationship between statements
when they CAN both be FALSE,
but CANNOT both be TRUE
only A ↔ E can be contrary
71
subcontrariety
the relationship between statements
when they CAN both be TRUE,
but CANNOT both be FALSE
only I ↔ O can have subcontrariety
72
subimplication
```
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
superimplication
```
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
argument
a set of statements, one of which appears to be implied or supported by the others
75
premise
```
the statement(s) in an argument
which support or imply the conclusion
```
76
conclusion
the statement in an argument
which is supported or implied by the premise(s);
the endpoint or terminus of the argument
77
syllogism
a particular form for organizing categorical statements into an argument; OR a deductive argument with 2 premises and 1 conclusion.
78
categorical syllogism
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
major term
the predicate term of the conclusion,
| used in one premise
80
minor term
the subject term of the conclusion,
| used in one premise
81
middle term
the term found once in each premise,
| and is not in the conclusion at all
82
major premise
the premise which contains the major term
83
minor premise
the premise which contains the minor term
84
5 steps to put a categorical syllogism into standard form
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
schema
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
mood
a 3-letter description of the types of
categorical statements a syllogism contains
when arranged in standard order
e.g. AEO
87
figure
a number from 1 to 4 identifying the placement
| of the syllogism's middle term (forms a smiley face :)
88
form
the mood + the figure
of a syllogism, listed together
e.g. AEO-3
89
valid syllogism
```
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
sound syllogism
a syllogism which is valid AND has true premises
91
2 ways to test
| the validity of syllogisms
1. counter-example
| 2. rules
92
counter-example
```
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
distributed term
a term that, within a statement, refers to ALL MEMBERS of its class/category
94
When are terms distributed in A, E, I, & O statements
the subjects of universal statements and the predicates of negative statements are distributed
95
5 rules for valid syllogisms
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
5 corresponding fallacies for syllogism rules
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
immediate inference
a statement which can be inferred directly
| from another statement
98
3 types of immediate inferences
1. converse
2. obverse
3. contrapositive
99
converse
a statement that reverses
the subject and predicate of the original
(only E & I)
100
obverse
a statement that has the opposite quality and a negated predicate of the original
(A, E, I, & O)
101
contrapositive
a statement that reverses and negates
both the subject and predicate of the original
(only A & O)
102
complement
the set of all terms NOT included in the given term
| P → non-P
103
translating singular statements
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
translating indefinite statements
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
translating hypothetical statements
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
inclusives
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
translating inclusives
```
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
exclusives
```
words that set boundaries referring to
a limited class of things
```
(only/nobody but/nothing but, unless, except)
109
translating exclusives
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
enthymeme
an argument in which a statement is
unstated and assumed
(i.e., a syllogism with one assumed statement)
111
hypothetical statement
a statement that affirms an outcome
based on a condition
If P, then Q.
112
pure hypothetical syllogism
a syllogism what uses only
| hypothetical statements
113
antecedent
the condition in a hypothetical statement
| follows "If …"
114
consequent
the result in a hypothetical statement
| follows "then … "
115
mixed hypothetical syllogism
a syllogism that uses both
| hypothetical and categorical statements
116
modus ponens
If P then Q P É Q
P OR P
\ Q \ Q
Valid
117
modus tolens
If P then Q P É Q
Not Q OR ~ Q
\ Not P \ ~ P
Valid
118
affirming the consequent
If P then Q P É Q
Q OR Q
\ P \ P
INVALID
119
denying the antecedent
If P then Q P É Q
Not P OR ~ P
\ Not Q \ ~ Q
INVALID
120
establishing a conclusion
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
informal fallacies
popular but invalid (or unhelpful)
| forms of argument
122
3 types of
| informal fallacies
1. Fallacies of Distraction
2. Fallacies of Ambiguity
3. Fallacies of Form
123
Fallacy of Distraction
an argument that confuses the issue
by pointing to information that is actually irrelevant
to the conclusion
124
Ipse Dixit
an illegitimate appeal to authority
Latin for "He said it himself"
125
Ad Populum
an illegitimate appeal to majority
Latin for "to the masses"
126
Ad Baculum
an illegitimate appeal to force;
a thinly veiled threat
Latin for "to the stick"
127
Ad Hominem
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
Bulverism
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
Tu Quoque
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
Ad Ignorantium
an argument from lack of evidence
Latin for: "to ignorance"
131
Chronological Snobbery
an argument based merely on the passage of time
Form: "I accept/reject ________
because it is too old/new."
132
Fallacy of Ambiguity
an argument that confuses the real issue
| with multiple, vague, or otherwise unclear meanings
133
Equivocation
changing the definition of a term
| in the middle of an argument
134
Accent
altering the meaning of a statement through
changed emphasis
~ must make the meaning different
than the speaker intended
135
Amphiboly
a vagueness of grammar that
| disguises or alters meaning
136
Composition
transfers attributes from parts to whole
~assumes that what is true for the parts
is true for the whole
137
Division
transfers attributes from whole to parts
~assumes that what is true for the whole
is true for the parts
138
Fallacy of Form
an argument that fails to establish its conclusion because of a weakness in logical structure
139
Circular Reasoning
secretly assuming what you are trying to prove
(i.e., one of the premises contains the conclusion
in disguise)
140
Post Hoc Ergo Propter Hoc
improperly assuming that a sequence in time
implies cause and effect
Latin for "after this, therefore because of this"
141
Either / Or
making an argument based on a false dilemma
(i.e., oversimplifying the choices)
also called Bifurcation
142
Complex Question
a question crafted in a way that excludes
| any possible legitimate response
143
Apriorism
a hasty generalization
(i.e., applying what is true of one member
to the whole group)
144
2 questions to ask about the person
making an argument, in order
to detect informal fallacies
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?)
