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36 Cards in this Set
- Front
- Back
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logically true
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all instances come out true
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logically false
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all instances come out false
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valid (in truth tables)
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every time the premise is true, the conclusion is true -
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valid argument form
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all substitution instances are deductively valid
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formally valid argument
truth functionally valid argument |
argument whose specific form is valid
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disjunctive syllogism
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valid argument
p v q -p therefore, q |
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disjunctive transitivity
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valid
p v q -q v r therefore, p v r |
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truth tables
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truth tables do not prove validity if the conclusion of the argument is logically true or false
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Addition rule
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p
therefore, p v q |
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Simplification rule
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p & q
therefore p |
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Double negation
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--p = p
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Commutation rule
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p & q == q & p
p v q == q v p |
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De Morgan's rule
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-(p v q) == -p & -q
-(p & q) == -p v -q |
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Modus Ponens (MP)
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p-->q
p therefore q |
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logically incompatible
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truth of one logically implies the falsity of the other
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logically equivalent
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their forms are logically equivalent
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countercases
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counter cases (using p and q) to disprove an argument
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counterinstances
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use word cases to disprove argument
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indicative conditionals
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"if Oswald did not kill Kennedy, then someone else did"
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subjunctive conditionals
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"If Oswald had not killed Kennedy, then someone else would have"
implies that oswald did in fact kill kennedy |
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strong vs weak conditionals
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If you open the refrigerator door, it won't explode (weaker)
If you open the refrigerator door, then it won't explode (stronger) provided you you open it, the refrigerator will not explode (even stronger) |
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p-->q is only true if it is not the case that
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that p is true and q is false
- (p & -q) -p v q |
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Modus Tollens
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p-->q
-q therefore -p |
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constructive dilemma
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p-->q
r-->s p v r therefore q v s |
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hypothetical syllogism
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p --> q
q --> r therefore p-->r |
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contraposition
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p-->q
therefore -q-->-p |
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p if q
p if only q p only if q p if and only if q |
q-->p
q-->p -q-->-p (q-->p) & (-q-->-p) |
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p provided q
p unless q |
q-->p
-q-->p |
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Conjunction
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p
q p & q |
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Simplification
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p & q
therefore p |
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double disjunction
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p v p = p
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double conjunction
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q & q = q
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law of excluded middle (EM)
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p v -p
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law of non contradiction (NC)
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- (p & -p)
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law of identity
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p-->p
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laws of thought
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law of identity
law of noncontradiction law of excluded middle |
