Given a philosophical analysis or definition of the form
X = a and b and c
then there are two ways to test it.
1) Look for instances of X which do not fit the analysis (a and b and c)
2) Look for instances that fit the analysis (a and b and c) which are not X.
Gettier aims to construct an instance of Justified True Belief which is not knowledge (ie the second).
In the first case, Smith has a justified false belief that Jones will get the job and has 10 coins in his pocket from which he deduces a claim, which is weaker, that the person who gets the job – whoever he is - will have 10 coins in his pocket. Since the first claim is justified, then so is the second. But by luck, the second claim turns out to be true (whilst the first is false).
So it is a Justified True Belief.
But, intuitively, it is not knowledge. Smith thinks that the person whose pocket will make the claim true is Jones. In fact it is Smith.
One response to this is to say that Smith is not really justified. We need to beware, though, because in everyday life we often take justifications to be factors which in other situations could hold when the claim they justify in this case would be false. That is, in everyday life we do not insist that we are infallible. There would be little knowledge if we did.
Still, one might say that the justification fails in this case for a specific reason: it is based on an intermediate claim (Jones will get the job and has 10 coins in his pocket) which is false. So we could rule that out with a 4th condition on knowledge: no false lemmas.
Knowledge = i) Justified ii) True iii) Belief and iv) the belief is not based on any false belief.
But we can construct something that is akin to Gettier’s examples but which does not rely on a false belief. Barn facade county. Like the Gettier cases Henry is unlucky that his normal justification for recognising barns (what they look like from a distance) is undermined by BAD LUCK but then that is compensated for by GOOD LUCK in that he stops the car by the one real barn in Barn Facade County.
(Likewise: Smith was unlucky that the normal way of justifying a belief that Jones would get the job – being told this by the boss – failed but was lucky that the person who did get the job had 10 coins.)
So the no false lemmas idea will not solve the Barn Facade County example.
What will? Well one idea is that Reliabilism can solve it.