Course Content Flashcards
1
Q
______ is expressed by a declarative sentence
A
Proposition
2
Q
“it’s going to rain tomorrow”
Is this a proposition?
A
Yes
3
Q
“I like bacon”
Is this a proposition?
A
Yes
4
Q
“close the window because I’m cold”
Is this a proposition?
A
No
5
Q
“Will this be on the exam?”
Is this a proposition?
A
No
6
Q
“the Italian flag has 3 colours”
Is this a proposition?
A
Yes
7
Q
Logic is in part the study of _______
A
Arguments
8
Q
All arguments have a _________
A
Conclusion
9
Q
“Don’t touch the wire, because it’s hot.”
Is this an argument?
A
No
10
Q
An ______ has to be able to be true or false
A
Argument
11
Q
In a formal argument, what format is followed
A
-First sentences are the premises.
-last sentence is the conclusion
12
Q
Each sentence in an argument must be a _________
A
Proposition
13
Q
What are some common argument conclusion indicators?
A
So, therefore, etc.
14
Q
Validity is a ______ of an argument
A
Property
15
Q
An argument is valid if and only if _________________.
A
it is impossible for the premises to be true while at the same time the conclusion is false.
16
Q
“If all insects are tasty, then scorpions are tasty.”
Is this a valid argument?
A
Yes
17
Q
“Only a secret Muslim would bow to the Saudi king. Obama bowed to the Saudi king. Therefore, Obama is a secret Muslim.”
Is this a valid argument?
A
Yes
18
Q
Jonathan has a cat and Jonathan does not have a cat. Therefore, tomato-based dishes are best paired with wines from colder regions.
Is this a valid argument?
A
Yes
19
Q
Arguments with impossible premises are always ______
A
Valid
20
Q
Why are arguments with impossible premises always valid?
A
Because the premises CAN’T be true, there is no possible way to make the premises true while the conclusion false.
21
Q
Does the premise have to be intuitively relevant to the conclusion for an argument to be technically valid?
A
No
22
Q
An argument is sound if and only if (2)
A
1) it is valid
2) all of the premises are true
23
Q
Sound arguments always have ____ conclusions
A
True
24
Q
“Only a secret Muslim would bow to the Saudi king. Obama bowed to the Saudi king. Therefore, Obama is a secret Muslim.”
Is this argument sound?
A
No
25
"Opera singers are sexy. Therefore, opera singers are sexy."
Is this argument sound?
Yes
26
Soundness assumes all propositions are _______
True or false
27
Valid argument form example (Modus Ponens)
If P, then Q.
P.
So, Q.
28
A form is valid iff
any argument with that form must be valid.
29
If P, then Q.
Q.
So, R.
Is this a valid argument form
No
30
An argument form is invalid when
It fails to guarantee that the argument will be valid.
31
Can arguments be valid with an invalid argument form?
Yes, but the form does not explain why it is valid.
32
If P, then Q. So R
P: I have a pet dog.
Q: I have a pet cat.
R: I have at least one pet.
Is this a valid argument?
Is the form of the argument valid?
The argument is valid because the conclusion can't be false while the premises are true.
The form is invalid.
33
Propositional connectives (6)
Conjunction
Disjunction
Recursion
Conditional
Biconditional
Negation
34
for any two sentences you can make a new sentence that is their _____
Conjunction
35
P & Q is a
Conjunction
36
In P & Q, P and Q are each
Conjuncts
37
If a conjunction sentence is true, ______ are true
Both conjuncts
38
Do conjunctions always have to be represented using "and"
No
39
"France is over-rated, but susan wants to go there anyway."
Is this a conjunction?
Yes
40
"Dmitri loves to sing and his hair is white."
Is this a conjunction?
Yes
41
"Simon and Alex are going to hook up tonight."
Is this a conjunction?
No, because the normal way to read it is that they are going to hook up together, which is one proposition.
42
“One false move and I’ll shoot.”
Is this a conjunction?
No, it's a conditional
43
Is this a conjunction?
“John is afraid that Eliza and Delia will come to the party.”
No
Could very well mean that he doesn’t want them to come together, but is okay if they come alone, meaning this expresses one proposition.
44
A disjunction means that
One of the two disjuncts is true, or both
45
Disjunctions are true any time ____________
at least one disjunct is true.
46
P V Q represents
A disjunction
47
Making complex sentences by conjoining or disjoining non-atomic sentences is called
Recursion
48
Is there a limit to the length and complexity of a recursive sentence?
No
49
If P, then Q is a _______
Conditional
50
P ⊃ Q means
If P, then Q
51
"If I don't eat soon, then I will be sad."
Is this a conditional?
Yes
52
"If he is going to the beach, then it is sunny"
Is this a conditional?
Yes
53
Ways to write conditionals (4)
P ⊃ Q
P, Q
Q if P
P only if Q
54
Conditional that works in both directions is called
Biconditional
55
If and only if / iff is a
biconditional
56
P ≡ Q is a
Biconditional
57
Ways to represent a biconditional (3)
P ≡ Q
P iff Q
P if and only if Q
58
Every sentence has another sentence that is its ______
Negation
59
the negation of P is
¬P
60
P is the _____ of ¬P
Negand
61
"I'm not wearing a red tie"
Is this a negation?
Yes
62
(P v Q) & ¬ (P &Q)
this means
"one or the other, but not both"
63
T or F:
All arguments with true premises and true conclusions are sound.
False
64
T or F:
Only valid arguments are sound.
True
65
T or F:
If an argument to the conclusion A is sound, then an argument to the conclusion not A is not sound.
True
66
T or F
All arguments with at least one impossible premise are valid.
True
67
T or F:
All invalid arguments are instances of invalid argument forms.
True
68
No invalid arguments have impossible premises.
True
69
Is the following valid and/or sound?
PHIL 220 is a history class. Therefore, PHIL 220 is a history class or a linguistics class.
Valid, but not sound
70
Is the following valid and/or sound?
If it rained yesterday, it means that Beyonce is the prime minister. It rained yesterday. Therefore, Beyonce is the prime minister.
Valid, but not sound
71
A valid argument with an impossible conclusion is not _______
Sound
72
Is it possible to have a sound argument with an impossible premise?
No
73
Impossible premises make ____ arguments but not ______ arguments.
Impossible premises make VALID arguments but not SOUND arguments.
74
For an argument of this form to be sound, how must it be formatted?
if P then Q
R
therefore, Q
R entails P or R entails Q will make it valid, and then the premises must be true to make it sound
75
Form of this argument:
If I have more than $10, then I can afford this sandwich.
I have more than $100 dollars.
Therefore, I can afford this sandwich.
if P then Q
R
.˙. Q
76
The following proposition can be categorized as which 2 connectives:
I did not tell Mother or Father.
Negation OR conjunction
77
What does "P only if Q" mean?
Q is a necessary condition for P
78
What does "If P, Q" mean?
P is a sufficient condition for Q
79
What does "P if and only if Q" mean?
is necessary and sufficient for Q
80
How can "P only if Q" be represented in SL? (2)
¬Q ⊃ ¬P or P ⊃ Q
81
A grammatical sentence in SL is called a
well-formed formula (wff)
82
What is an atom in SL
A capital letter (with optional numerical subscript)
83
the connective that
governs the whole formula
Main connective
84
Remember, our disjunction is ________, not ______.
inclusive, not exclusive
85
Disjunctions are true any time _________
either disjunct is true.
86
When constructing a truth table, _____ with the main connective.
End
87
1 atom has ____ possibilities
2
88
2 atoms have ____ possibilities
4
89
3 atoms have ____ possibilities
8
90
When is a conditional false
False only if antecedent is true and consequent is false
(1, 0 = 0)
True in all other cases
91
Note that (P ⊃ Q) has the same truth conditions as.
(¬Q ⊃ ¬P)
92
The biconditional (P ≡ Q) is true if P and Q have ________
the same truth value
93
What should you do at the end of constructing a truth table?
Indicate the main connective column.
94
Interpretations correspond to ______ in the truth table.
rows
95
An interpretation satisfies a formula if __________
if the main connective of that formula receives a 1 in that row.
96
If the main connective column has 0 in every row, the proposition is a
_______.
contradiction
97
Contradictions are logically ________
Impossible
98
If the main connective column has 1 in every row, the proposition is a _______
tautology
99
A tautology proposition is logically _______
Necessary
100
If the main connective column has 1 in at least 1 row and 0 in at least one row, the proposition is ________ .
contingent
101
Two formulas are logically equivalent if and only if they have the same ___________
truth value on every interpretation
102
An SL argument form is valid iff no interpretation satisfies all the
premises while _______ the conclusion
falsifying
103
The argument form is valid iff there are no rows in which the premises are true and the conclusion is ____.
false
104
Φ, Ψ |= Ω indicates an argument is _____
valid
105
Φ, Ψ |/= Ω means that the argument is
invalid
106
Entailment means
Any interpretation
that satisfies the left-hand side will also satisfy the right-hand side.
107
|= means
Entailment
108
Is the entailment symbol a part of SL
No, it just says something about SL
109
How is P ⊃ Q different from
P |= Q
1st is a sentence of SL, 2nd is a claim about all interpretations
110
The entailment claim is equivalent to saying the conditional is __________
true in all interpretations
111
Any entailment claim is false if and only if there is a _____________.
counterexample —
an interpretation that satisfies the left and falsifies the right
112
Conditionals with false _________
are always true.
antecedents
113
So any entailment claim with a tautology on the right-hand side will be _______
True
114
Entailment claims with an empty set on the left are always
right
115
Any entailment claim with a contradiction on the left is ______
true
116
⊥means
unsatisfiability
117
What does unsatisfiability mean
every interpretation that satisfies the left will satisfy the
impossible
You can't satisfy the impossible, so no interpretation on the left will be satisfied
118
What is a partial truth table equivalent to
trying to force an invalid interpretation
119
How do you draw a partial truth table
-Put a 0 under the main operator of the conclusion and a 1 under the main operator of each premise.
-Write down the truth value of anything you’re forced at this point.
-If nothing is forced, write a row for each possibility.
-If you can complete the process, then you have a counterexample to the validity of the argument.
120
What is a partial truth table good for
Answering questions about
entailment more efficiently than drawing a complete truth table.
If you find they key pattern — satisfying the premises and falsifying the conclusion — the entailment claim is false.
