Talk:Conditional proof

Short description

I added the short description: "formal proof." If anyone can improve on this, that would be much appreciated (if seen fit). As it stands, it appears fine for now.

SpiralSource (talk) 12:55, 31 December 2021 (UTC)[reply]

Untitled

I feel the example given is too similar to syllogism and thus slightly confusing. A better example is as follows, from http://marauder.millersville.edu/~bikenaga/mathproof/condproof/condproof.pdf:

As an example of a conditional proof in symbolic logic, suppose we want to prove (A → B)→ ~C (If [If A, then B], then not C)from the first two premises below:

1. A∧ ~ D    ("A and not D")
2. B → (C → D)    ("If B, then [If C, then D]")
3. A → B   (conditional proof assumption, "Suppose "If A, then B" is true")
4. A   (Law of Simplification, based on line 1)
5. B   (Modus Ponens, based on lines 1 and 3)
6. C → D   (Modus Ponens, based on lines 2 and 5)
7. ~D    (Law of Simplification, based on line 1)
8. ~C    (Modus Tollens, based on lines 6 and 7)
9. (A → B)→ ~C   (Conditional Proof, based on lines 3 and 8)

The conclusion ∼ C was deduced on line 8. Together with the assumption A → B in line 3, this proves the conditional (A → B) → C. —Preceding unsigned comment added by 70.18.214.96 (talk) 01:04, 25 July 2009 (UTC)[reply]

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