The Importance of Conditional Proof

Here is a super quick illustration of the importance and value of conditional proof:

Suppose I am trying to show that God’s existence makes a difference to our lives, and in particular, God’s existence makes a difference to ethics (to how we should live). Now one way to go about doing that would be to first attempt to show that God does, in fact, exist. But doing that requires a decent amount of work, and it’s not really relevant to what I am interested in at the time. What I am interested in showing is something different, namely, that IF God exists, then how we should live is significantly different from how we should live if God does not exist. Here’s a helpful way of showing what I am interested in:

1.     If God exists, then ethics has the features x, y, and z.
2.     If God does not exist, then ethics does not have features x, y, and z.


To attempt to “prove” those conditionals, I do not need to waste time attempting to prove their antecedents. All I need to do is assume the antecedent of 1 and attempt to derive x, y, and z, and then assume the antecedent of 2 and attempt to show that neither x, y, nor z follows. In other words, I need to do a couple conditional proofs.

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