Talk:Conditional proof

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Philosophy: Logic High‑importance

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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]