Philosophy Rules

Front 1

p C q
p
____
q

Back 1

modus Poenens (MP)

Front 2

p C q
~q
_______
~p

Back 2

Modus Tollens (MT)

Front 3

p C q
q C r
_______
p C r

Back 3

Hypothetical Syllogism

Front 4

p v q
~p
_____
q

Back 4

Disjunctive Syllogism

Front 5

(p C q).(r C s)
p V r
_____
q v s

Back 5

Constructive Dilemma

Front 6

p . q
________
p

Back 6

Simplification

Front 7

p
q
__
p.q

Back 7

Conjunction

Front 8

p
___
p v q

Back 8

Addition

Front 9

~(p . q )= (~p v ~q)
~ ( p v q)= (~p.~q)

Back 9

DeMorgan's Theorem

Front 10

(pvq)= (qvp)
p.q = q.p

Back 10

Commutation

Front 11

[(pvq)vr]=[p v (q v r )]
[p .(q .r)]= [(p.q).r]

Back 11

Association

Front 12

[p.(qvr)]= [(p.q)v (p.r)]
[p v(q.r)]= [(pvq).(pvr)]

Back 12

Distribution

Front 13

p=~~p

Back 13

Double Negation

Front 14

(pCq)=(~pvq)

Back 14

Material Implication

Front 15

(pcq)=(~qc~p)

Back 15

Transposition

Front 16

(p=q)=[(pcq).(qcp)]
(p=q)= [(p.q)v (~p . ~q)]

Back 16

Material Equivalence

Front 17

[(p.q)c r]= [(pc (q c r)]

Back 17

Exportation

Front 18

p=(pvp)
p=(p.p)

Back 18

Tautology

Front 19

What does Modus Ponens allow us to do?

Back 19

assert the consequent of a conditional statement on a line by itself

Front 20

What does Modus Tollens allow us to do?

Back 20

allows us to assert the negation of the antecendent

Front 21

What does Hypothetical syllogism allow us to do?

Back 21

used to derive a conditional statement from two other conditionals

Front 22

what does Disjunctive Syllogism allow us to do?

Back 22

allows us to assert the righ-hand disjunct of a disjunctive statement on a line by itself

Front 23

What does Constructive Dilemma allow us to do?

Back 23

it's two modus ponens steps from (p c q) and (r c s) and p v r to infer q v s

Front 24

What does Simplification allow us to do?

Back 24

from p.q infer p . Reverse of conjunction statement is true, then each of its atomic statements is true. 2 propositions are given as ture on a single line, then each of them is true separately

Front 25

What does a conjunction allow us to do?

Back 25

two propositions asserted separately on different lines may be conjoined on a single line

Front 26

What does addition allow us to do?

Back 26

whenever a proposition is asserted on a line by itself it may be joined disjunctively w/any other proposition we choose. From p to infer pvq fir a disjunction to be true, only one of them needs to be true

Front 27

What does DeMorgan's Theorem allow us to do?

Back 27

only for conjunctive and disjunctive statements. When moving a tilde inside or outside a set of parentheses, a dot switches with a wedge and vice versa

Front 28

What does Commutation allow us to do?

Back 28

asserts the truth value of a conjunction or disjunction is unaffected by the order in which the components are listed. The statement may be commuted or switched fro one another w/0 affecting the truth value

Front 29

What does Association allow?

Back 29

states that the truth value of a conjunction or disjunctive statement is unaffected by the placement of ()when the same operator is used throughout

Front 30

What does distribution allow?

Back 30

applies only to conjunctive and disjunctive statements. When a proposition is conjoined to a disjunctive statement in () or disjoined to a conjunctive statement in () the rule allows us to put the proposition together w/each of the components inside the () and go in the reverse direction

Front 31

What does double negation allow?

Back 31

pairs of tildes immediately adjacent to one another may be either deleted or introduced w/o affecting the truth value

Front 32

What does Material Implication allow?

Back 32

substitute actual statements in place of letters; states that a horseshoe may be replaced by a wedge if the left-hand component is negated, and the reverse replacement is allowed if a tilde is deleted from the left-hand component

Front 33

What does Transposition allow?

Back 33

the antecendent and consequent may swith places if and only if both are negated

Front 34

What does Material Equivalence allow?

Back 34

either p and q are both true or p and q are both false

Front 35

what does exportation allow?

Back 35

if we have p then if we have r is logically equivalent to if we have both p and q we have r

Front 36

What does tautology allow?

Back 36

to eliminate the redundancy in disjunctions and conjunctions

Front 37

What does double negation allow?

Back 37

pairs of tildes immediately adjacent to one another may be either deleted or introduced w/o affecting the truth value

Front 38

What does Material Implication allow?

Back 38

substitute actual statements in place of letters; states that a horseshoe may be replaced by a wedge if the left-hand component is negated, and the reverse replacement is allowed if a tilde is deleted from the left-hand component

Front 39

What does Transposition allow?

Back 39

the antecendent and consequent may swith places if and only if both are negated

Front 40

What does Material Equivalence allow?

Back 40

either p and q are both true or p and q are both false

Front 41

what does exportation allow?

Back 41

if we have p then if we have r is logically equivalent to if we have both p and q we have r

Front 42

What does tautology allow?

Back 42

to eliminate the redundancy in disjunctions and conjunctions