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Introduction to Logic (UNO) > 3: Statements and Truth > Flashcards

3: Statements and Truth Flashcards

1
Q

What is a class?

A

a collection of individuals having a certain attribute, feature, trait, or property

  • “persons”
  • “living things”
  • “eaters”
  • etc.
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2
Q

What is communication?

A

what occurs when the expression of a thought is mutually understood

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3
Q

What is a conceptual analysis?

A

the method of identifying the necessary and sufficient conditions that must be met for something to be a thing of a certain sort, or for a certain belief to be true.

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4
Q

What is analysandum?

A

the concept, idea, or statement being analyzed

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5
Q

What is analysans?

A

the necessary and sufficient conditions

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6
Q

What is a connective?

A
  • a word, phrase, or symbol whose linguistic or logical function is to conjoin statements into a compound statement.
    • and
    • but
    • or
    • then
    • that
    • if and only if
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7
Q

What is a counterexample?

A

an argument that has exactly the same structure (“form”) as the argument you wish to evaluate, but where it is obvious that the conclusion is false even when the premises are true

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8
Q

What is a definite description?

A

a descriptive phrase beginning with ‘the’

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9
Q

What is emotionally neutral language?

A

terms, rhetoric, or writing that are not

  • derogatory,
  • inflammatory, or
  • laudatory
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10
Q

What is an exclusive disjunction?

A
  • a statement of the form ‘(p or q) but it is false that (p and q)’
  • the assertion that exactly one alternative is true
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11
Q

What is a function?

A

a rule or algorithm for taking an INPUT and producing an OUTPUT

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12
Q

What are the four functions of language?

A
  1. interrogative: to ask questions
  2. directive: to cause (or to prevent) actions
  3. emotive: to express or to evoke emotions
  4. informative: to make assertions
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13
Q

What is inclusive disjunction?

A

the assertion that at least one alternative is true.

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14
Q

What is an individual?

A

Any person, creature, place or object about whom something can be said.

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15
Q

What is a main connective?

A

the connective that determines what type of compound statement is being asserted

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16
Q

What are the types of names?

A

Everything that we can name is an individual.

  1. proper (or possessive),
  2. pronoun phrase (a descriptive phrase beginning with ‘my’, ‘your’, ‘his’, ‘her’, ‘our’, or ‘their)
  3. definite description (a descriptive phrase beginning with ‘the’)
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17
Q

What is a necessary condition?

A

something such that it MUST be the case for a certain event to occur or for a certain belief to be true: ‘p only if q’

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18
Q

What is necessary and sufficient condition?

A

all of the things that MUST be the case for a certain event to occur or for a certain belief to be true: ‘p if and only if q’

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19
Q

What is a nontruth-functional compound statement?

A

a compound statement whose truth-value is NOT determined just by the truth-values of its component(s)

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20
Q

What is predicate?

A

a property, trait or attribute

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21
Q

What are propositional attitudes?

A

the content of any thought expressible as a proposition (statement) together with the mental attitude toward that thought (e.g., believes, fears, desires, hopes, perceives, loves, hates, hopes, etc.)

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22
Q

What are quantifiers?

A

the quantity indicator of a general statement

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23
Q

What are universal quantifiers?

A

include such affirmative words as ‘all’, ‘every’, ‘everything’, ‘everyone’, and ‘anything’, along with such negative words as ‘no’ and ‘nothing.

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24
Q

What are existential quantifiers?

A

include such words or phrases as ‘some’, ‘someone’, ‘something’, ‘there exists’, and ‘there is’

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25
Q

What is a sentence?

A

the linguistic expression of a complete thought

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26
Q

What is a subject?

A

the individual (or class of individuals) asserted to have a certain property, trait, or attribute

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27
Q

What is a substitution instance?

A

the statement that results when a statement is substituted for a variable in a statement form

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28
Q

What is sufficient condition?

A
  • something such that if it is the case, it follows that a certain event will occur or a certain belief is true: ‘p if q’
  • “good enough”
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29
Q

What is truth-condition?

A

that which determines whether a statement is true

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30
Q

What is truth-function?

A

a rule for computing the truth-value of a truth-functional compound statement

31
Q

What is truth-value?

A

the property of being true or being false; every statement is one or the other — never both.

  • declarative sentences
  • statements
  • beliefs
    • These all have truth-value
32
Q

What is a statement (or proposition)?

A
  • what a declarative sentence asserts (or “means”), though it is not itself a declarative sentence
  • has truth-value
33
Q

Mention the whole outline of statements

A
34
Q

What are the two types of statements?

A
  1. Atomic statements
  2. Compound statement
35
Q

What is an atomic statement?

A

a statement that does not contain another statement as a component

36
Q

What are the different types of atomic statements?

A
  1. Singular atomic statement
  2. Identity statement
  3. General statement
37
Q

What is a singular atomic statement?

A
  • an atomic statement asserting that a specific (“named”) individual has a particular attribute, trait, or property.
    • God exists
    • Sophie is a cat
38
Q

What is the truth condition of singular atomic statement?

A
  • is true just in case the named individual has the property, trait, or attribute ascribed to that individual
39
Q

What is an identity statement?

A
  • a statement asserting that a specific (“named”) individual is the same thing as another specific (“named”) individual.
    • Superman is Clark Kent
40
Q

What is the truth condition of an identity statement?

A
  • is true just in case the two “names” refer to the same individual
41
Q

What is a general statement?

A
  • a statement asserting something about all or some members of a class of individuals
42
Q

What are the three categories of general statements?

A
  1. simple general statement
  2. standard general statement
  3. complex general statement
43
Q

What are the four types of simple general statements?

A
  1. Universal affirmative
  2. Universal negative
  3. Existential affirmative
  4. Existential negative
44
Q

What is a universal affirmative?

A
  • a statement asserting something about everything.
    • Everything is P
  • Truth-condition: a statement of the form ‘Everything is P’ is true just in case everything is P.
45
Q

What is a universal negative?

A
  • a statement asserting something about nothing.
    • Nothing is P
  • Truth-condition: a statement of the form ‘Nothing is P’ is true just in case nothing is P.
46
Q

What is an existential affirmative?

A
  • a statement asserting that there exists a member of a class.
    • Something is P
  • Truth-condition: a statement of the form ‘Something is P’ is true just in case there exists at least one thing that is P.
47
Q

What is an existential negative?

A
  • a statement asserting that there exists something that is not a member of a class.
    • Something is not P
  • Truth-condition: a statement of the form ‘Something is not P’ is true just in case there exists at least one thing that is not P.
48
Q

What are the four types of standard general statements?

A
  1. (A) Universal affirmative
  2. (E) Universal negative
  3. (I) Existential affirmative
  4. (O) Existential negative
49
Q

What is an (A) universal affirmative?

A
  • a statement asserting that all of the members of one class are members of another class.
    • All S is P
  • Truth- condition: a statement of the form ‘All S is P’ is true just in case every member of the subject class is a member of the predicate class
50
Q

What is an (E) universal negative?

A
  • a statement asserting that all of the members of one class are not members of another class.
    • No S is P
  • Truth- condition: a statement of the form ‘No S is P’ is true just in case no member of the subject class is a member of the predicate class
51
Q

What is an (I) Existential affirmative?

A
  • a statement asserting that there exists a member of one class that is a member of another class.
    • Some S is P
  • Truth-condition: a statement of the form ‘Some S is P’ is true just in case there exists at least one member of the subject class that is a member of the predicate class
52
Q

What is an (O) existential negative?

A
  • a statement asserting that there exists a member of one class that is not a member of another class.
    • Some S is not P
  • Truth-condition: a statement of the form ‘Some S is not P’ is true just in case there exists at least one member of the subject class who is not a member of the predicate class
53
Q

What is a complex general statement?

A
  • a general statement that is neither simple nor standard
54
Q

What is a compound statement?

A
  • a statement that contains at least one statement as a component
  • they will always have at least one connective
55
Q

What are the two types of compound statements?

A
  1. nontruth-functional compound statement
  2. truth-functional compound statement
56
Q

What is a nontruth-functional compound statement?

A
  • a compound statement whose truth-value is NOT wholly determined by the truth- value(s) of its component(s):
  • Truth-condition: is true just in case what it asserts corresponds to the way the world was, is, or will be
57
Q

What is a truth-functional compound statement?

A
  • a compound statement whose truth-value is wholly determined by the truth-value(s) of its component(s)
58
Q

What are the five truth-functions?

A
  1. Negation
  2. Conjunction
  3. Disjunction
  4. Conditional
  5. Biconditional
59
Q

What is a negation?

A
  • a statement of the form ‘it is false that p’; a negation is true just in case p is false
  • any statement in the universe can be denied
  • variety of ways to express negation:
    • dis-
    • im-
    • in-
    • un-
    • “it is false that…”
    • “it is not true that…”
60
Q

What are different ways to express negation?

A
61
Q

What is a conjunction?

A
  • a statement of the form ‘p and q’ (where ‘p’ and ‘q’ are conjuncts);
  • a conjunction is true just in case each conjunct is true
62
Q

What are the different ways to express conjunctions?

A
63
Q

How do you calculate the truthfulness of a conjunct statement?

A

p•q

t+t = T

t+f = F

f+t = F

f+f = F

64
Q

What is a disjunction?

A
  • a statement of the form ‘p or q’ (where ‘p’ and ‘q’ are disjuncts);
  • a disjunction is true just in case at least one disjunct is true
65
Q

What are the different ways of expressing disjunctions?

A
66
Q

How do you calculate the truthfulness of a disjunct statement?

A

p v q

t+t = T

t+f = T

f+t = T

f+f = F

67
Q

What is a conditional?

A
  • a statement of the form ‘if p then q’ (where ‘p’ is the antecedent and ‘q’ is the consequent);
  • a conditional is false if and only if the antecedent is true when the consequent is false
68
Q

What are the different ways of expression of conditionals?

A
69
Q

How do you express the different conditions in conditional statements?

A
  • Sufficient Condition
    • “p if q”
      • q is antecedent
  • Necessary Condition
    • “p only if q”
      • p is the antecedent
  • Necessary and Sufficient Condition - the strongest of the conditions
    • “p if and only if q”
      • biconditional
70
Q

How do you calculate the truthfulness of a conditional statement?

A

p⊃q

t+t = T

t+f = F

f+t = T

f+f = T

71
Q

What is a biconditional?

A
  • a statement of the form ‘p if and only if q’ (where ‘p’ and ‘q’ are bijuncts);
  • a biconditional is true if and only if the bijuncts have the same truth-value
72
Q

What are different ways of expressing the biconditional connective?

A
  • p if and only if q
  • p just in case q
  • p when and only when q
73
Q

How do you calculate the truthfulness of a biconditional statement?

A

p≡q

t+t = T

t+f = F

f+t = F

f+f = T

Introduction to Logic (UNO) (4 decks)

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