Thread: Confusion about Conditional Premises in Sentential Calc?

I know how to use the Conditional Premises rule, but I'm not sure how it works when to apply it. For example:

Using sentential calculus (with a four column format), prove s ⇒ r follows from the premises p ⇒ (q ⇒ r), p ∨ ~s, and q.

The proof looks like this:

Code:

{Pr1}			1. p ⇒ (q ⇒ r)		P
{Pr2}			2. p ∨ ~s		P
{Pr3}			3. q			P
{Pr4}			4. s			P (for CP)
{Pr2, Pr4}		5. p			DS (2, 4)
{Pr1, Pr2, Pr4}		6. q ⇒ r		MP (1, 5)
{Pr1, Pr2, Pr3, Pr4}	7. r			MP (3, 6)
{Pr1, Pr2, Pr3}		8. s ⇒ r		C (4, 7)

How do I know *when* to use Conditional Premises? Is it only after I've exhausted all other methods? Also, could you explain to me briefly why one is allowed to say that a statement true, if its truth is based on something that you simply defined earlier? It just doesn't make sense to me at this point.

Originally Posted by mxrider530

How do I know *when* to use Conditional Premises? Is it only after I've exhausted all other methods? Also, could you explain to me briefly why one is allowed to say that a statement true, if its truth is based on something that you simply defined earlier? It just doesn't make sense to me at this point.

The statement “If S then R” means if S is true then R must be true.
Another way to put that is: “R follows from the truth of S”
So if the conclusion of an argument is a hypothetical then by assuming the premise the hypothetical is true and demonstrating that the conclusion of the hypothetical must follow then we have shown that hypothetical is true.

Does that help at all?