I believe that A is true. I believe that B is true if A is true. Therefore, I believe that B is true. B is true. Therefore, I have a true belief, even if A is false. This is the form that all of these arguments follow.
I think now that going down this road eviscerates entailment in a way we don't want. If we have a web of beliefs, connected by various degrees of the relation "is a reason for", we still need to individuate those beliefs, even if they confront reality in groups or as a totality, not singly, because we have to be able to revise them individually.
I think the usual approach to Gettier is probably right: we feel that the justification Smith has for believing (f) turns out to be irrelevant to the truth of (h). It's that irrelevance we want to capture. We need rules about how justification passes from one belief to another, something more precise than Gettier's principle that entailment preserves justification just as it preserves truth.
(1) Smith does not believe that (h).
(2) Smith's inference of (h) from (f) is faulty.
What is your claim?
Smith realizes the entailment of each of these propositions he has constructed and proceeds to accept (g), (h), and (i) on the basis of (f).
Michael Dummett makes a distinction (when talking about assertion, as usual -- here it is Smith's acceptance that is at issue) that may be helpful here: there are the grounds upon which you make an assertion (which he calls its "justification"), and then there is what you are committed to by making the assertion. It is clear that Smith's belief that P is the grounds upon which he accepts that P ∨ Q, but by accepting that P ∨ Q he is committed to accepting all four possible models.
The idea I sketched a couple months ago, that justification cannot cross the boundary between one interpretation and another, is essentially the mainstream response to Gettier, that something is needed to guarantee the relevance of the belief's justification to its truth for that belief to count as knowledge. You must get the right answer for the right (sort of) reasons.
You wrote:
You are correct that is what Smith believes. But why does that mean the Gettier case is wrong? Smith does not need to believe q or use q as a point of inference to arrive at (p v q). The propostion q can be anything that is not ~p. It can even be something Smith does not really have any opinion on. All Smith needs to be justified in believing (p v q). And if Smith is justified in believing p is true, then, by extension, he is justified believing (p v q) is true, as only one of the propositions in a disjunction is required for it to be true.
In this case, Smith is justified in p and believes p. By extension, he is justified in believing (p v q) is true, though Smith is indifferent to q's truth value or thinks q is false (he might even be justified in believing q). Therefore, Smith is justified in believing (p v q).
Smith has justified belief in (p v q). He is two thirds the way there.
It turns out (p v q) is true, but not because p; p is false and q is true. Smith has a justified false belief that p, so he is still justified in (p v q). It's just that his grounds for justification are false. However, q is true. Therefore, Smith believes a true proposition (p v q) and is justified in believing (p v q). Therefore, Smith has knowledge under the traditional account of knowledge: he has justified, true belief. But this seems wrong. Smith does not have knowledge of (p v q). Therefore, the traditional account fails.
a half-century worth of misunderstanding — creativesoul
You wrote:
No.
1. Your reading of Gettier's original paper is wrong on its face and you're never going to convince anyone.
2. Even if you were right, and there was something faulty in Gettier's original cases, no one would care. Once you've seen the trick, it is child's play to construct new Gettier-type cases.
Gettier wrote:
Various attempts have been made in recent years to state necessary and sufficient conditions for someone's knowing a given proposition. The attempts have often been such that they can be stated in a form similar to the following:1
(a) S knows that P IFF (i.e., if and only if)
(i) P is true,
(ii) S believes that P, and
(iii) S is justified in believing that P.
For example, Chisholm has held that the following gives the necessary and sufficient conditions for knowledge:2
(b) S knows that P IFF (i.e., if and only if)
(i) S accepts P,
(ii) S has adequate evidence for P, and
(iii) P is true.
Ayer has stated the necessary and sufficient conditions for knowledge as
follows:3
(c) S knows that P IFF
(i) P is true,
(ii) S is sure that P is true, and
(iii) S has the right to be sure that P is true.
I shall argue that (a) is false in that the conditions stated therein do not constitute a sufficient condition for the truth of the proposition that S knows that P. The same argument will show that (b) and (c) fail if "has adequate evidence for" or "has the right to be sure that" is substituted for "is justified in believing that" throughout.
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. 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. 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.
<snip>
CASE II
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. Smith is therefore completely justified in believing each of these three propositions. Smith, of course, has no idea where Brown is.
But imagine now that two further conditions hold. First, Jones does not own a Ford, but is at present driving a rented car. And secondly, by the sheerest coincidence, and entirely unknown to Smith, the place mentioned in proposition (h) happens really to be the place where Brown is. If these two conditions hold, then Smith does not KNOW that (h) is true, even though (i) (h) is true, (ii) Smith does believe that (h) is true, and (iii) Smith is justified in believing that (h) is true.
These two examples show that definition (a) does not state a sufficient condition for someone's knowing a given proposition. The same cases, with appropriate changes, will suffice to show that neither definition (b) nor definition (c) do so either
I believe that A is true. I believe that B is true if A is true. Therefore, I believe that B is true. B is true. Therefore, I have a true belief, even if A is false. — Michael
That's not what Gettier sets out. — creativesoul
(p v q) is true because (p) is true — creativesoul
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.
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.
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.
1. S believes P
2. S deduces Q from P
3. S believes Q
4, S is justified in believing P
5. S is justified in believing Q
I'm not misreading. I'm strongly asserting that 1 and 2 are not always adequate for believing Q. — creativesoul
Now, now. — Srap Tasmaner
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)
...
Works fine.
Not a Gettier case though. — creativesoul
Belief that:((p v q) is true) is not equivalent to ((p v q) is true because (p)). — creativesoul
Let's change P: I am not adopted.
I think I am fairly justified in this belief. No one said anything, I look like a bit like my father, and such.
Let's change Q: Michael lives in New York City.
I have no idea whether this is true or not. I suspend judgement. I can't be justified in believing Q.
Now, we look at (P v Q).
I am justified in believing (P v Q) is true on account of my justification in P.
Is this correct?
(p v q) is true because (p) — creativesoul
The former cannot be substituted for the latter, for it leaves out the necessary deduction within Smith's thought/belief process. The latter is Smith's thought/belief — creativesoul
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