Gettier states:

I shall begin by noting two points. First, in that sense of "justified" in which S's being justified in believing P is a necessary condition of S's knowing that P, it is possible for a person to be justified in believing a proposition that is in fact false.

I would concur.

Secondly, for any proposition P, if S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction, then S is justified in believing Q.

This is not always true. To be as precise as ordinary language allows:S must first arrive at a belief before we can say that S is justified in forming/holding that belief. In Gettier Case II, the above formulation is utterly inadequate for S's arriving at belief that:((p v q) is true).

Keeping these two points in mind I shall now present two cases in which the conditions stated in (a) are true for some proposition, though it is at the same time false that the person in question knows that proposition.

This I outright deny.

Gettier's aims at a case that Smith forms/holds a Justified True Belief that:((p v q) is true) by virtue of going through the thought/belief process set out in the above formulation beginning with "Secondly..." Belief that:((p v q) is true) is the only value appropriate for Q in that formulation, for Q is (p v q) and believing Q is nothing less than belief that (p v q) is true. Hence, believing Q is belief that:((p v q) is true).

I will show that Gettier's formulation is inadequate regarding it's ability to take proper account of the thought/belief process required for S's belief that:((p v q) is true). S cannot arrive at that without another step that Gettier leaves out. To be clear, if the astute reader looks carefully at that formulation, s/he will note that only one deduction is purportedly necessary in order to satisfy the formulation. Namely, S's deducing Q from P.

I'm strongly asserting that it takes more than one deduction for S to arrive at belief that:((p v q) is true), and since that is the case, it only follows that Gettier's criterion is inadequate. That will be clearly shown.

To be clear, for any proposition P, if S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction then S is not necessarily justified in believing Q, for - in this case in particular - believing Q is nothing less than belief that:((p v q) is true) and S cannot arrive at that following Gettier's formulation. Belief that:((p v q) is true) requires yet another deduction that is left sorely unaccounted for. It's been said heretofore, but it now bears repeating...

S must first arrive at a belief before we can say that S is justified in forming/holding that belief. In Gettier Case II, the above formulation is utterly inadequate for S's arriving at belief that:((p v q) is true). The following argument represents the process of thought/belief that is necessary prior to even being able to arrive at believing Q and is an exhaustive account thereof.

p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q) is true because (p))(from p1,p3)

Gettier wrote:

Let us suppose that Smith has strong evidence for the following proposition:

(f) Jones owns a Ford.

Smith's evidence might be that Jones has at all times in the past within Smith's memory owned a car, and always a Ford, and that Jones has just offered Smith a ride while driving a Ford. Let us imagine, now, that Smith has another friend, Brown, of whose whereabouts he is totally ignorant. Smith selects three placenames quite at random and constructs the following three propositions:

(g) Either Jones owns a Ford, or Brown is in Boston.
(h) Either Jones owns a Ford, or Brown is in Barcelona.
(i) Either Jones owns a Ford, or Brown is in Brest-Litovsk.

Each of these propositions is entailed by (f). Imagine that Smith realizes the entailment of each of these propositions he has constructed by (0, and proceeds to accept (g), (h), and (i) on the basis of (f). Smith has correctly inferred (g), (h), and (i) from a proposition for which he has strong evidence...

Note the above stopping point. The quote ends at the precise point where Gettier's next line concludes(by necessary implication) that Smith believes Q. Believing Q is precisely what's at issue here. Q is (p v q). Believing (p v q) is believing that (p v q) is true. Hence, Smith's believing Q is nothing less than Smith's belief that:((p v q) is true). So, using Case II, Gettier has filled out his earlier formulation. Here it is again...

Gettier wrote:

S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction...

Note here that this quote's stopping point coincides with Case II's, as shown directly above. As Gettier says, Smith believes Jones owns a Ford. Smith constructs (g), (h), and (i); all of which are (p v q). Smith believes p, and deduces (p v q) from p and accepts (p v q) as a result of this deduction. There is nothing about Smith's thought/belief process that the first two premisses below cannot effectively exhaust...

p1. ((p) is true)
p2. ((p v q) follows from (p))

Now, it is well worth mentioning here that nowhere in any of this(the above direct quotes from Gettier) is anything at all about Smith's believing Q. That is of irrevocable significance. It is a crucial point to consider here. Smith has yet to have gotten to the point where he has formed and/or holds belief that:((p v q) is true). Gettier thinks otherwise, as is shown by his saying...

Gettier:

...Smith is therefore completely justified in believing each of these three propositions...

...and...

...S is justified in believing Q.

He lost sight of exactly what believing Q requires. It requires precisely what follows...

p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q) is true because (p))(from p1,p3)


Thus, we can clearly see that Gettier's formulation is inadequate to account for the belief that he needs for Smith to hold in order to make his case. Getting to belief that:((p v q) is true) requires both p3. and C1. Further we can also see that Smith's belief is not true, for he does not ever get to belief that:((p v q) is true). Gettier wants us to believe that Smith holds the belief that:((p v q) is true). This post has shown all sorts of problems with Gettier's formulation, and the aforementioned want of Gettier is just yet another.

Belief that:((p v q) is true) is not equivalent to belief that:((p v q) is true because (p)). The former is existentially contingent upon the latter and has a different set of truth conditions. The latter consists in part of the deduction missing in Gettier's account. The missing necessary deduction clearly shows that Smith's belief is false, Gettier's formulation is inadequate, and the 'problem' regarding Case II is non-existent.

Salva veritate

Smith believes Jones owns a Ford. Smith believes that 'Jones owns a Ford' is true. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' follows from 'Jones owns a Ford'. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' is true if either 'Jones owns a Ford' or 'Brown is in Barcelona' is true. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' is true because Jones owns a Ford.

QED