Examples 7.6
Indirect Proof
Again, like conditional proof, an indirect proof is a method for deriving conclusions.
This method works in the following way: we’ll assume the opposite of the conclusion
we’re trying to derive, and then see whether we can find a contradiction.
If we can derive
a contradiction from our assumption, we know the opposite of that assumption must be
true.
This form of argument is commonly known as a ‘reductio ad absurdum’ (or just a
‘reductio’ for short).
In other words, you’re reducing the assumption to absurdity—then
concluding the opposite.
So, as always, let’s just consider some examples and maybe things will make more sense.
1.
(A v B)
⊃
(C
⋅
D)
2.
C
⊃
~D
/ ~A
3.
| A
AIP
4.
| A v B
3 Add
5.
| C
⋅
D
1,4 MP
6.
| C
5 Simp
7.
| ~D
2,6 MP
8.
| D
5 Simp
9.
| D
⋅
~D
7,8 Conj
10. ~A
3-9 IP
The same principles as with conditional proof are at work here.
You make the
assumption and put it out on a different scope line.
Remember, you can’t pull anything
out of the assumption line because you don’t know whether that stuff is true or not.
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- Spring '08
- Barrett
- Indirect Proof, Reductio ad absurdum, conditional proof
-
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