In his seminal paper “Is justified true belief knowledge?” Edmund Gettier shows how the classical definition of knowledge which all philosophy students now know by heart, JTB, is not a sufficient definition. In case you haven’t heard the definition I’ll give it here:
S knows p if and only if
(i) p is true
(ii) S believes that p
(iii) S is justified in believing that p
Gettier gave two counter-examples where the three conditions listed are met but for some reason or other most would deny S knowledge. In this text I’ll willfully forget and ignore most of the discussion that Gettier spawned and only investigate Gettier’s second counter-example or case II.1
Now, both of Gettier’s cases have the following general form: S is justified in believing some proposition p and believes that p, from p S infer, in line with the rules of elementary logic, some proposition q and therefore comes to believe q; as it turns out p is false but q is true. Gettier’s argument against knowledge as JTB hinge on one major tacit assumption:
(JP): logical inference preserves and transmits justification.
What Gettier means to show us is that the inferred proposition q is a true proposition which S has justified belief about but fails to know. If it turns out that S’s belief in q is not justified then in conformity with the JTB-analysis there is no wonder S lacks knowledge. In other words, Gettier have failed in providing a counter-example. I think there are good reasons to doubt the assumption of justification preservation in logic, (JP), that Gettier seems to accept. I will not argue that logic never preserves justification2 but I will argue that Gettier’s second case gives us good reason to doubt that justification always carries over logical inference.
I will now give a homemade example instantiating the general pattern of case II: Peter has two sons, Rob and Carl. Rob is a wayward son. Peter hasn’t seen him in ten years and has no new information about him. Carl, on the other hand, is a brilliant young man studying philosophy. Peter has strong enough reasons to believe this3 and therefore has the justified belief
(p): Carl is studying philosophy.
From (p) Peter infers three further propositions:
(q): Carl is studying philosophy or Rob has a full beard.
(r): Carl is studying philosophy or Rob is clean-shaven.
(s): Carl is studying philosophy or Rob has some stubble.
For the sake of argument let us assume that Peter’s belief in (p) makes him believe (q), (r) and (s). As it turns Carl just quit his studies in philosophy but Rob has a full beard, thus rendering (p), (r) and (s) false. (q) remains true and Peter believes that (q). My question: Is Peter’s belief in (q) justified in virtue of being inferred from a distinct justified belief or not? If yes, then he has JTB but not knowledge.4 If no, then he lacks JTB and, in line with the classical definition, knowledge.
Let’s take a quick look at the general form of the logical rule of disjunction introduction (DI). A disjunction is a statement of the form ‘p V q’ which reads ‘p or q’ where the letters ‘p’ and ‘q’ are sentence variables standing for any sentence with a propositional form (sentences capable of being true or false); in the case of disjunction each sentence variable flanking a disjunction sign is called a disjunct. If either both or one of the disjuncts are true, then the disjunction is true. If both disjuncts are false, then the disjunction is false. The rule of (DI) can be stated: If p is true, then you can infer p or q (i.e. p or q must be true). The added disjunct q can stand for any proposition you like. This is what Peter is doing in the aforementioned case. Taking the proposition (p) as true Peter infers, in line with (DI), three more or less random disjunctions where the second disjunct is about Rob. (DI), like any inference rule in logic, preserves truth. This means that if (p) were to be true then all the inferred disjunctions would have been true. But (p) is not true; therefore all the inferences are invalid. Yet (q) is, accidentally, true because the second disjunct ‘Rob has a full beard’ is true and Peter has come to believe in (q) due to his invalid use of (DI). Still a question remains: Does Peter’s use of disjunction introduction preserve justification?
I think there are good reasons for answering no. Disjunction introduction does not seem to preserve justification. We must remember that (DI) allows us to infer any disjunction we want as long as we take one of the disjuncts to be true. Is this a way of gaining knowledge? My view is that it is not. One way of looking at justification is that the reason we want to be justified in our beliefs is because it is conducive to knowledge. Now, I think it is unproblematic to say that (DI) preserves truth but I just don’t see how it preserves justification. Whatever (DI) is, it is not a part of the scientific methods extending our knowledge. What Gettier needs to accept for his second case is that if you are justified in believing some proposition p, then you are justified in believing both disjuncts in any disjunction you infer from p in line with (DI). Thus later if the starting disjunct turns out to be false but the added disjunct true, then you’re still justified in believing the disjunction. This seems wrong. If justification plays any role in logic I think the justification stays with and originates from the disjunct you were initially justified in believing and does not transmit to the other disjunct. The two views can be visualized using the underline to track justification:
Gettier: If p, then you can infer p or q. If p turns out false but q is true, then still p or q.
My view: If p, then you can infer p or q. If p turns out false but q is true, then p or q.
If I am correct in this view two things follow: First, Gettier’s second case is not a counter-example showing that JTB is not knowledge because the inferred statement isn’t justified and therefore expectedly not knowledge. Second, logical inference does not always preserve justification.
Of course I haven’t done much in this text, I still think Gettier is essentially right about JTB. Still the role of logic in all of this is at least interesting to discuss. And I have come to think of Case II as rather weak because of the problems discussed in this text. Maybe I’m wrong about all of this (if you know why please tell me in a comment!) but I still think there is something fishy about (DI) in an epistemological sense, i.e. related to knowledge and justification.
 Also, I must apologize if the points I make here have already been elaborated elsewhere. I can easily have missed out on it.
 I will not discuss Gettier’s first case, in part because it seems to preserve justification over the inference and saying otherwise demands more than for the second case.
 I will not discuss justification in itself and even though there might be ways of construing justification in a way that makes Peter’s belief in (p) unjustified. I will assume that Peter is justified in believing (p).
 Gettier and most philosophers seems to take it as obvious that Gettier’s counter-examples show that there is more to knowledge than JTB. One should of course question why this is so.