Handout, Phil 102
Craig Fox
Class #12, 7/7/05
1 The Tree Method
p∨qp·qp⊃qp≡q
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pqp∼pqp∼p
qq∼q
∼(p∨q)∼(p·q)∼(p⊃q)∼(p≡q)∼∼ p
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∼p∼p∼qp p qp
∼q∼q∼q∼p
If both pand ∼poccur in the same path, then an ‘X’ is placed under that path, and it is closed.
•Each open path in the tree represents a possible way of making everything above it true.
•When testing an argument for validity, we start the tree with the premises and the negation of
the conclusion. (We’re seeing if this set is consistent: think of the tree method as a “consistency
machine”.)
•If all paths close, then the argument is valid. (I.e., there is no way to make the premises true
while making the negation of the conclusion true.)
•If there is at least one path open, then the argument is invalid. The path identifies a coun-
terexample.
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