If someone is going to use a falsity to support a conclusion, they''ll probably use one which supports it well — Metaphysician Undercover
Hmmm.
Here's another way to look at the issue. The word "reason" is ambiguous in an interesting way: we reason from our knowledge of effects to their causes and call those beliefs about effects our "reasons" for our belief about their causes; on the other hand, the cause is the "reason" for the effects. That I can see an iceberg is my reason for believing it's right in front of me; that an iceberg is right in front of me is the reason I can see it. We strive to perfect our conditionals, to believe that we can see iceberg right in front of us if,
and only if, it's right in front of us. Thus our reasoning would be not a groping about in the dark, but our way of discovering the true structure of the universe, the real connections between things. We want to believe the universe is itself rational, has a rational structure, a structure we can come to understand through reasoning, a process of matching the movements of our minds to the movements of the universe without.
The interesting case is when we hold reasonable beliefs but derive from them a conclusion that turns out to be false. What has gone wrong? We have a choice: we could give up the vision sketched above, draw in our horns a bit, and take reason to be something
we do, setting aside faith in the rational structure of the universe; or we could say that we must've failed, that reasoning that reaches a false conclusion cannot be "true reasoning" -- that the premises must only
appear to support the conclusion but could not
really support it.
Responses to Gettier along the lines of, "Well, he had a false belief -- garbage in, garbage out," rather miss the point, I think. Do we allow falsehoods to have
real connections? Traditional logic says yes, valid but unsound, But how can this be? If our reasoning mirrors the rationality of the universe, those connections must also be only seemings, conditionals that cannot ever be perfected, for there is no truth underlying them.