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27 Cards in this Set
- Front
- Back
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Modus Ponens
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P > Q
P _______ Q |
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Modus Tolens
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P > Q
-Q _______ -P |
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Constructive Dilema
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P v Q
P > R Q > S _________ R v S |
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Tautology
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P v P = P
P ^ P = P |
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DeMorgans
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~ (P v Q) = ~ P ^ ~ Q
~ (P ^ Q) = ~ P v ~ Q |
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Double Negation
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P = ~ ~ P
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Disjunctive Syllogism
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P v Q
~ Q ____________ P P v Q ~ P ____________ Q |
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Conjunction
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P
Q ___________ 3. P ^ Q |
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Hypothetical Syllogism
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P -> Q
Q -> R ______________ P -> R |
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Simplification
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P ^ Q
------- P P ^ Q ------- Q |
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Substitution
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"X"
X |
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T-Scheme
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“ P ” is true if and only if P
Ex. “snow is white” if and only if the snow is white |
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Learner's Paradox
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Let P be a proposition
Either you know P or you don’t If you know P, you cannot learn it If you don’t know P, then you cannot learn it _____________ Therefore you cannot learn anything |
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Liar's Paradox
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This proposition is not true
Is that true or not? Something cannot be and not be |
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Problem of Evil
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Either that is gratuitous suffering or human cause evil
If there is gratuitous suffering God is blameworthy for not eliminating it If humans are cause of evil, God is blameworthy for permitting it _____________________ Therefore God is blameworthy But if God exist, it is false that he is blameworthy _____________________ Therefore there is no God |
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Ontological Argument
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If that then which nothing greater can be conceived exists in the mind but not in reality then I can conceive of something greater than TTWNGCBC
I cannot conceive of something greater that TTWNGCBC ____________________ Thus it doesn’t exist in the mind or it doesn't not exist in reality Does reside in the mind ____________________ Thus it exists in reality |
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Science and Religion
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Sometimes a religious text affirms P but Science affirms NOT P
So either our religious text is wrong or our very best science is wrong The religious text is not wrong ________________ So our very best science is wrong -- but, or vice versa |
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Descartes
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If I can be certain of anything, I can be certain of it through sense perception or influence
Sense perception cant be certain Inference cannot be certain __________________ So I cannot be certain of anything |
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Psychological Egoism and Altruism
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If I act I expect benefit or to avoid harm
Is I expect benefit or avoid harm, I am protecting my interest ________________ I act to protect my interest |
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Free Will and Determinism
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Humans are wholly a part of nature
Nature is governed by regular, necessary and immutable laws If humans are wholly part of nature and nature is governed by regular, necessary and immutable laws then my actions are determined If they are determined then they are not free ________________ Thus I have so free will |
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Perception
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Perceptions are not beliefs
The only thing that can justify a belief is another belief _______________ So perceptions cannot justify beliefs |
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Personal Identity
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If I am anything then I am my brain, conscious, or a unity of the two
I am not my brain I am not my conscious I am not the unity of them ________________ So nothing is me |
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Curry's Paradox
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If this sentence if true then cats bang on my eardrums
The second sentence on this list is true, the moon is made of cheese ________ Thus the moon is made of cheese |
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Liar's Paradox
Law of non-contradiction |
No proposition is both the case and not the case
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Liar's Paradox
Law of the excluded middle |
There is no middle ground
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Liar's Paradox
Principle of Contravalence |
It is false that P is both true and P is false
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Liar's Paradox
Principle of bivalence |
Every proposition is either true or false
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