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Formal Deductions
Phil 101
18
Philosophy
Undergraduate 3
05/19/2014
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Cards

Term
Simplification

+
 Definition
a + b :: a

a + b :: b
Term
modus ponens

⊃
 Definition
a ⊃ b
a
:: b
Term
modus tollens

⊃
 Definition
a ⊃ b
-b
:: -a
Term
disjunctive syllogism

v
 Definition
a or b
-a
:: b

a or b
-b
:: a
Term
hypothetical syllogism

⊃
 Definition
a ⊃ b
b ⊃ c
:: a ⊃ c
Term
addition

v
 Definition
a
:: a v b
Term
double negation
 Definition
--a
:: a
Term
commutation

+/v
 Definition
a + b
:: b + a

a v b
:: b v a
Term
association

v
 Definition
a v (b v c)
:: (a v b) v c
Term
tautology

+
 Definition
a ==
:: a +a
Term
transposition

⊃
 Definition
a ⊃ b
:: - b ⊃ -a
Term
material equivalence

+
 Definition
a == b
:: ( a ⊃b ) + (b ⊃ a)
Term
de morgans

+/v
 Definition
1. change front sign
2. change variable signs
3. change +/v
Term
material implication

⊃/v
 Definition
1. change sign on antecedent
2. change ⊃/v
Term
exportation

⊃
 Definition
(a+b) ⊃ c
::: a ⊃ (b+c)
Term
distribution

+/v
 Definition
a + (b v c) == (a +b) v (a +c)
a v (b +c) == (a v b) + (a v c)
Term
conjunction

+
 Definition
a
+ b
:: a +b
Term
constructive dilemma

v
 Definition
( a ⊃b) + (c ⊃ d)
a v c
::
b v d
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