Gettier Problem. Gettier Problem
JTB theory of knowledge
S = somebody
P = a proposition
S knows P IFF
1. S believes P
2. P is justified
3. P is true
Justification
1. Deduction: An argument that is sound (true premises + valid form). If a deductive argument is sound, it's impossible for the conclusion to be false or, phrased differently, the conclusion of a sound deductive argument is necessarily true.
In other words, P (deductively) justified implies and is implied by P is true i.e. (deductive) justification (for P) is both necessary and sufficient for truth (P is true).
In this case, criterion 3 (P is true) is unnecessary as 2 (P is justified) implies 3 (P is true). The JTB theory can be shrunk down to JB (justified belief).
2. Induction: A cogent inductive argument is one in which the premises are true and the argument strong which translates as the conclusion is likely to be true. There's no necessity that the conclusion be true i.e. the conclusion's truth is partially independent of an inductive argument, cogent or otherwise. Criterion 3 (P is true) is necessary (it must be mentioned separately).
Are Gettier problems about induction rather than deduction? Gettier problems occur when chance (re induction which is probabilistic) is invovled (re Gettier cases).
Also, if I include criterion 3 (P is true) in my definition of knowledge, I'm also claiming truth is (partially/wholly) independent of justification - this is a hallmark of induction.
Type specimen, Gettier case
Smith & Brown go for a job interview. Smith overhears the interviewer saying "White will be hired". Smith known Brown has 10 coins in his pocket. Smith then, so Gettier claim, justified to form the belief that the man with 10 coins in his pocket will be given the job1.
Later ... Smith is the one who actually bags the prize (is hired). Smith checks his pockets - he has exactly 10 coins. Smiths belief is true.
To sum up, Smiths's belief (the man with 10 coins will be hired) is true and justifed, but then his having 10 coins in his pocket was a chance occurrence i.e. a justified, true, belief that is not knowledge (the no luck principle)
1. Is Smith justified in inferring from what he heard about Brown and what he knows about Brown (10 coins in Brown's pocket) that the man with 10 coins in his pocket will get hire?
I don't think so because there are many people with 10 coins in their pocket who haven't even attended the interview, forget about being rejected/accepted. Smith fails to realize that he himself could have 10 coins in his pocket. In other words Smith's premise is false because e.g. Jones has 10 pockets in his pocket and he hasn't even applied for the job i.e. he is definitely not going to get hired (10 coins in pocket & Not hired).