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Philosophy Ch. 1, 2, & 3 > Midterm 2 Definitions > Flashcards

Midterm 2 Definitions Flashcards

1
Q

When is a (particular) argument Deductively Valid?

A

If and only if it is an instance of a valid form.

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2
Q

When is an argument FORM Deductively Valid?

A

If and only if there are no instances of that form in which all the premises are true and the conclusion false, aka it has no counterexample.

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3
Q

When is a sentence a Compound Sentence?

A

If and only if it logically contains another complete sentence (simple sentence) as a component.

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4
Q

When is a sentence a Simple Sentence?

A

If and only if it is not a compound sentence.

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5
Q

What is a Sentential Operator?

A

An expression containing blanks such that, when the blanks are filled with complete sentences, the result is a complete sentence.

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6
Q

When is a sentential operator Truth-Functional?

A

If and only if the truth or falsity of a compound sentence containing that operator is completely determined by the truth or falsity of its component sentences.

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7
Q

What is a Counterexample to an argument form?

A

An instance of that form where all the premises are true and the conclusion false.

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8
Q

When is a statement form a Tautology?

A

If and only if every instance of that form is true; that is, it is true in every row in its truth table.

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9
Q

When is a statement form a Contradiction (or inconsistent)?

A

If and only if every instance of that form is false; that is, it is false in every row in its truth table.

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10
Q

When is a statement form a Contigency?

A

If and only if some instance of that form is true and some is false; that is, it is true in at least one row in its truth table and false in at least one row in its truth table.

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11
Q

Fill in the blank: Deductive Validity of an argument depends on its ____.

A

Form.

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12
Q

What is the study of argument forms called?

A

Formal Logic.

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13
Q

What is an Instance of a form?

A

When a form’s variables (ex: “p” and “q” in “p->q”) are replaced with sentences (ex: “cold” and “windy” in “if cold then windy”).

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14
Q

Is the following sentence compound or simple: Jason Bay hit 3 homers and struck out.

A

Compound. Can be deconstructed as “JB hit 3 homers and JB struck out.” – still logically means the same thing though.

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15
Q

Fill in the blanks: Compound sentences are built from _____ sentences by means of ______.

A

Component, sentential operators.

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16
Q

True or False: Component sentences are simple sentences.

A

True.

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17
Q

Name four common sentential operators.

A

“Either – or –.”
“– and –.”
“If –, then –.”
“— if and only if —“

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18
Q

True or False: There are an infinite number of sentential operators in the English language.

A

True.

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19
Q

Fill in the blank: If you want to know whether a (compound) sentence is true or not, determine the truth or falsity of the ___ sentences.

A

Component.

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20
Q

Name the five Truth-Functional Sentential Operators.

A

Conjunction, disjunction, negation, conditional, and biconditional.

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21
Q

What are a conjunction’s component sentences are called?

A

Conjuncts.

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22
Q

What is an ampersand and what is it used for?

A

“And” or “&”
Used for conjunctions.

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23
Q

What are a disjunction’s component sentences are called?

A

Disjuncts.

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24
Q

What is the TFSO in this sentence: (B&F).

A

“&” or “and”
This is a conjunction.

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25
Q

What is a wedge and what is it used for?

A

“Either, or” or “v”
This is a disjunction.

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26
Q

What is the TFSO in this sentence:
(LvF).

A

“v” or “either, or”
This is a disjunction.

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27
Q

What are a negation’s component sentences called?

A

Negated formulas.

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28
Q

What is a tilde and what is it used for?

A

“Not” or “it is not the case that” or “~”
It is used for negations.

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29
Q

What is the TFSO in this sentence: ~W.

A

”~” or “not” or “it is not the case that”
This is a negation.

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30
Q

What are a conditional’s component sentences called?

A

First component sentence is called the Antecedent. Second component sentence is called the Consequent.

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31
Q

What is the only TFSO where order matters?

A

Conditional.

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32
Q

What is an arrow and what is it used for?

A

“If, then” or “->”
Used for conditionals.

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33
Q

What is the TFSO in this sentence: (T->S).

A

”->” or “if, then”
This is a conditional.

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34
Q

Which goes first, “if” or “then”?

A

If, always.

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35
Q

True or False: Consequent arrow Antecedent.

A

False, it is Antecedent arrow Consequent.

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36
Q

What is a double arrow and what is it used for?

A

”<->” or “if and only if”
Used for biconditionals.

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37
Q

What is the TFSO in this sentence: (R<->A).

A

”<->” or “if and only if”
This is a biconditional.

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38
Q

Translate this sentence: The would be WET if i had STIRRED it.

A

(S -> W). “If” goes first always.

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39
Q

True or False: Only if = If.

A

False, “Only if” = “then.”

40
Q

True or False: Only if = Then.

A

True!

41
Q

True or False: Only if = If and only if.

A

False.

42
Q

Translate this sentence: The dog will BITE only if PROVOKED.

A

(B -> P). Only if = then.

43
Q

Fill in the blank: “Unless” can also be “___” plus a _____.

A

“if”, negation.

44
Q

Translate this sentence using a negation: W unless C.

A

(~C -> W).

45
Q

True or False: “I believe that” is a TFSO.

A

False.

46
Q

True or False: “___ because ___” is a TFSO.

A

False

47
Q

How do TFSOs differentiate from SOs?

A

With regular SOs, it is not enough to just know components to determine if the sentence is true or not. With TFSOs, it is.

48
Q

True or False: All compound sentences have TFSOs.

A

False, all compound sentences have SOs but not all of them are TFSOs.

49
Q

What is a WFF?

A

A well-formed formula (or grammatically correct sentence)

50
Q

Fill in the blank: S, L, and R are all examples of ___?

A

Sentence letters.

51
Q

Fill in the blanks: WFFs are built from ______ in _____ using the 5 _____.

A

Sentence letters, stages, sentential operators.

52
Q

What is a Major Operator?

A

The last operator added when a wff is built up in stages.

53
Q

True or False: Any sentence that uses sentence letters that are WFFs are NOT also WFFs.

A

False, they ARE also WFFs.

54
Q

How do you say a particular argument is valid/invalid?

A

“This particular argument is invalid/valid because its form is invalid/valid. Its form is invalid/valid because it has counterexamples/no counterexamples.”

55
Q

How do you say a statement form is a contradiction/tautology/contingency?

A

“Since the statement form is — in every row, it is a contradiction/tautology/contingency.”

56
Q

When are two statement forms are Logically Equivalent?

A

When the columns below their major operators are identical (i.e. all T or all F), aka they agree in every row.

57
Q

How do you say a statement form is logically equivalent?

A

“The 2 statement forms are logically equivalent because their major operators agree in every row.”

58
Q

Fill in the blank: If an argument p,q :. r is invalid, then (p&q) & ~r is a ____.

A

Contingency or tautology.

59
Q

Fill in the blank: If an argument p,q :. r is valid, then (p&q) & ~r is a ____.

A

Contradiction.

60
Q

Fill in the blank: If p is a contradiction, then p,q :. r is ____.

A

Valid.

61
Q

Fill in the blank: If r is a tautology, then p,q :. r is ____.

A

Valid.

62
Q

Fill in the blank: If an argument p,q :. r is valid, then (p&q) -> r is a _____.

A

Tautology.

63
Q

Fill in the blank: If an argument p,q :. r is invalid, then (p&q) -> r is a _____.

A

Contingency or contradiction.

64
Q

What part of a statement form determines if it is a contradiction/tautology/contingency?

A

The major operator.

65
Q

Fill in the blank: When testing deductive validity using truth tables, you can start with the _____ to rule out “T” rows (as they cannot be counterexamples) as a shortcut.

A

Conlusion.

66
Q

Fill in the blanks: (I v W) is a ____ and (p v q) is a ______.

A

Instance, form.

67
Q

True or False: Each row in a truth table is a possible world.

A

True.

68
Q

Recite the Conditional Truth Table.

A

T, T = T
T, F = F
F, T = T
F, F = T

69
Q

Recite the Biconditional Truth Table.

A

T, T = T
T, F = F
F, T = F
F, F = T

70
Q

Recite the Conjunction Truth Table.

A

T, T = T
T, F = F
F, T = F
F, F = F

71
Q

True or False: (B & O) is an instance of (p & q).

A

True. Note that for a sentence to be an instance of a form it must have the same MO.

72
Q

Recite the Negation Truth Table.

A

T = F
F = T

73
Q

Recite the Disjunction Truth Table.

A

T, T = T
T, F = T
F, T = T
F, F = F

74
Q

What is the hint for Conjunction Truth Tables?

A

True if both conjuncts are true, false otherwise.

75
Q

What is the hint for Negation Truth Tables?

A

Flip-flop, opposites. If p=true, ~p=false and vice versa.

76
Q

What is the hint for Disjunction Truth Tables?

A

If its both or one or the other, then its true. If its neither, its false.

77
Q

What is the hint for Conditional Truth Tables?

A

No counterexamples, aka TF is only false.

78
Q

What is the hint for Biconditionals Truth Tables?

A

Same truth value on both sides of <-> means its true.

79
Q

Why do logicians only care about the part of the sentences that represent the conditions under which they are true/false?

A

Because they give meaning to the sentential operators.

80
Q

Translate “q if p.”

A

p -> q.

81
Q

Can “q if p” be translated as q -> p?

A

No, it must be p -> q because “if” always goes first.

82
Q

True or False: “Unless” can be translated to “either, or.”

A

True.

83
Q

Rewrite “p unless q.”

A

(Either) p or q.

84
Q

Rewrite “unless p, q.”

A

(Either) p or q.

85
Q

Which one is “only if”?
1) (p <-> q)
2) (p -> q)

A

2. #1 is “if and only if.”

86
Q

True or False: “Only if” = “then.”

A

True.

87
Q

Rewrite and translate “p only if q.”

A

“if p then q”
(p -> q)

88
Q

Rewrite and translate “only if p, q.”

A

“p, if q” or “if q then p”
(q -> p)

89
Q

True or false: “Neither, nor” = “not either, or.”

A

True.

90
Q

What are the two ways to translate “neither p nor q” ?

A

~(p v q) and (~p & ~q)

91
Q

True or False: “Neither p nor q” can be translated as (~p v ~q) or ~(p & q).

A

False, these are translations for “not both” which is different from “neither, nor.”

92
Q

Fill in the blanks: When translating “not both,” use ____ or ____.

A

Negation, disjunction.

93
Q

What are the two translations of “not both p and q” ?

A

~(p & q) and (~p v ~q)

94
Q

True or False: “Not both” can be translated as ~(p v q) and (~p & ~q).

A

False, those are translations for “neither, nor” which is different.

95
Q

Fill in the blank: Use the sentence’s _____ to point you towards the major operator.

A

Commas.

Philosophy Ch. 1, 2, & 3 (4 decks)

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