Cabbage Farmer describes Smith somewhere as having a defeasible warrant to assert that p, and that's all he needs. — Srap Tasmaner
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if...(insert belief statement(s) regarding what makes this particular disjunction true))
C1. ((p v q) is true because... (insert belief statement(s) corresponding to the prior 'if'))
That is what believing a disjunction takes. That is what it consists in/of. I've invited anyone to imagine a disjunction arrived at by a rational agent on the basis of believing P that is not completely exhausted by the above solution. There are no problems. Fill it out.
— creativesoul
The first problem that comes to mind is that (p2) can fill in the blank at (p3), which makes (p3) redundant. — Cabbage Farmer
From "defeasibly p", (p v q) does not follow. In logic a thing follows or it doesn't; there is no 'defeasibly follows'. — unenlightened
1. I am claiming that believing a disjunction is necessary for knowing one
— creativesoul
Agreed, at least for the sake of argument. — Cabbage Farmer
2. Believing a disjunction is not being taken proper account of
— creativesoul
Agreed, in that Smith's belief is not an isolated "belief in a disjunction", but has an epistemic structure. I've sketched my take on that structure, and I'm not sure I understand your take. — Cabbage Farmer
3. Belief that:((p v q) is true) is an utterly inadequate account of what believing a disjunction consists in/of
— creativesoul
Agreed, same as (2). — Cabbage Farmer
4. An adequate account of believing a disjunction clearly shows that Smith's belief is false
— creativesoul
Every account on the table clearly shows that the premise p is false and that the premise ~q is false. That's the problem. The justification is flawed because it's based on false premises, but it still reaches a true conclusion by way of valid inferences. — Cabbage Farmer
Is there something else you show to be false, some other proposition relevant to the problem? — Cabbage Farmer
Justification is useful in discerning mistakes of reasoning — javra
So one big flaw in Gettier is that he takes the justification to be one or two supporting propositions, and not holistic. — Banno
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.
Gettier's paper is a critique of the concept of knowledge, not a critique of belief and justification, and not a critique of the validity of disjunction. It seems to me he takes ordinary epistemological concepts of belief, justification, and truth for granted in his paper.
So do you have some thoughts on justification? — Srap Tasmaner
Belief and knowledge are compatible with doubt. — Cabbage Farmer
Yes, this seems like another example. On the basis of his strong evidence that Jones owns a Ford, Smith might feel the bet's practically a sure thing. If he learns how he came to get the payout, he'll recognize it was pure luck.What about my example of Mary giving Smith £10?
1. Mary tells Smith that she will give him £10 if Jones owns a Ford or if Brown is in Barcelona
2. Smith justifiably believes that Jones owns a Ford
3. So, Smith justifiably believes that Mary will give him £10
4. Jones doesn't own a Ford but Brown is in Barcelona
Is this "unfit" justification? Is this a case of "that's not what I meant"? — Michael
That's a fair analysis on the surface of the problem, but arguably leaves too much out of the picture.He's correct in his belief that Mary will give him £10, but incorrect in his belief that she will do so because Jones owns a Ford. — Michael
No.Are you saying that a belief is only justified if it's true? — Michael
If S knows p, then by force of logic, he knows (p v q). This works, because if he knows p, then p is true, by the definition of knowledge. But he doesn't know p and cannot possibly know p, because p is not true, and it is because beliefs are not always true that the truth preserving logic does not work for beliefs. — unenlightened
I still don't see how adding skeptical couching helps to address this specific problem. — Cabbage Farmer
What I'm suggesting is thatRedundancy applies if there is no meaningful difference in the change being made. You're suggesting that Smith holds the belief that:((p v q) is true if (p v q) follows from (p)). So the solution would look like this after filling in the blanks...
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if (p v q) follows from (p))
C1. ((p v q) is true because (p v q) follows from (p)) — creativesoul
This is to say that believing a disjunction has some sort of epistemic structure. You offered the following...
1. p [for reasons assumed in the scenario]
2. ~q [for reasons assumed in the scenario]
3. if (p and ~q) then (either p or q) [empty formalism]
4. either p or q [by inference from 1, 2, 3]
I can understand why it would seem to be helpful to formally set out an exclusive 'or'. I mean, Smith's thought/belief process results in his believing a disjunction, and he is admittedly ignorant about Brown's location, so he would not believe anything at all about Brown's location. — creativesoul
That sounds right. I suppose we're all talking about best practices for formalization of the case at hand.It seems very clear to me that there is a stark contrast between formalization of thought/belief(taking an account of thought/belief) and how thought/belief actually works. — creativesoul
What contradiction is inherent in (3), and how does it carry over to (4)?That is partially understood by virtue of our recognizing the performative contradiction inherently within 3 that would surely carry over to 4 if we were to take your offering as an adequate account of Smith's believing a disjunction. — creativesoul
The exclusive disjunction is true if and only if one but not both of the terms in the disjunction are true. That's the logical form of exclusive disjunction.Belief that either p or q is true, in the sense of truth that is presupposed within all thought/belief and statements thereof, is to believe that either could be the case. — creativesoul
I wouldn't say "could". We have no indication that Smith thinks it's impossible that ~p and impossible that q. And we have no indication he counts himself absolutely certain that p and ~q.Smith believes neither that p could be false nor that q could be true. — creativesoul
I reject this claim. I take the following to be consistent statements:For him to think/believe and/or state that either p or q could be true would be for him to arrive at self-contradiction. — creativesoul
Of course he can. His belief in that implication should not be influenced by his beliefs about the truth values of p and q.Smith can believe that (p v q) follows from (p) despite his not believing (q). — creativesoul
The truth of an inclusive disjunction follows from the truth of any of its terms.Believing that a disjunction follows from a belief is not equivalent to believing a disjunction. — creativesoul
The truth conditions of (p V q) are met as soon as the truth conditions of p are met. Or as soon as the truth conditions of q are met. Or as soon as the truth conditions of (p AND q) are met.The former is belief about the rules of correct inference, and the latter is believing that the truth conditions of a particular disjunction have been met. — creativesoul
I don't think I've neglected anything. We only need to focus on q if we want to follow Gettier and analyze the case as an exclusive disjunction. Smith's beliefs about q are quite relevant in that case. Because in that case, Smith must believe he has strong evidence for both p and ~q.You've set out the former while leaving the latter sorely neglected. I've found focusing upon q to be entirely irrelevant, for Smith does not believe any of the q's, and we are taking an account of Smith's thought/belief process on his way to arriving at believing a disjunction. — creativesoul
That's my point. We don't need the rest of it.Given that, what is there in your above epistemic structural offering that is both germane and not effectively exhausted by p1 and p2 below? — creativesoul
I have agreed that (p V q) is not in itself an adequate representation of Smith's belief. I have offered what I take to be an adequate representation, which consists of more than the mere claim (p V q).This doesn't make much sense to me. I'm saying that belief that:((p v q) is true) is not an adequate account of believing a disjunction. You've agreed to this and subsequently offered an account of believing a disjunction that results in belief that:(p or q) which is exactly what I've shown to be inadequate. — creativesoul
I might argue this discussion is prima facie evidence that you don't understand what you've argued. Instead let's proceed by assuming that neither of us adequately understands the other's point of view, and that neither of us completely understands his own point of view, at least until such time as we may attain some sort of mutually satisfactory resolution.This is prima facie evidence that you've not understood what I've argued. — creativesoul
I don't know what all the others have said.I understand that historically people have understood the problem to be that Smith arrives at JTB by virtue of working from false premisses and valid inference/form. I understand that folk want to take an account of Smith's thought/belief process by virtue of displaying some logical argument or another. I'm saying that they're all found to be sorely lacking in much the same way... explanatory power. — creativesoul
Why can't they? The truth of p is a truth condition for (p V q). Smith believes that p, and has strong reasons for believing that p. What is left unexplained?None of them can account for Smith's considering the truth conditions of his particular disjunctions and subsequently concluding that the disjunction is true because those conditions have been met. — creativesoul
So far as I can see, it's already accounted for by Gettier. It's already clear that Smith's view of the facts is incorrect because he holds a false belief; and clear that accordingly his beliefs about the broader context are flawed; and clear accordingly that his justification for the disjunction is, though reasonable in context, sorely off the mark.That's precisely what believing a disjunction requires. When that is properly accounted for, it becomes crystal clear that Smith forms and holds false belief. — creativesoul
I don't see anything daunting about the Gettier problems, and I'm not sure you have worked out a coherent response to them. I do think they're interesting puzzles that force epistemologists to clear up their conception of knowledge as JTB. And I think your approach -- clearing up the representation of Smith's beliefs -- is promising in its broad features.The scope of those consequences are daunting. The Gettier 'problem' is irrefutably shown to be nothing more than an utterly inadequate account of what believing a disjunction requires and/or consists in/of. — creativesoul
Believing that (g), (h), and (i) are entailed by (f) is not equivalent to believing the disjunctions.
— creativesoul
It is if you believe that f is true. For example, if I believe that it is Sunday and if I believe that it being Sunday entails that the Post Office isn't open then I must believe that the Post Office isn't open.
This gives a weighted disjunction, (p(99%) v ~p(1%)). And that does not lead to (p v q). It's so simple it seems to be invisible to everyone, but as soon as it is possible that ~p, the damaging disjunction (p v q) cannot be made at all. — unenlightened
So in your view we are only entitled to infer p v q from p if p is a necessary truth. — Srap Tasmaner
I wrote:
Redundancy applies if there is no meaningful difference in the change being made. You're suggesting that Smith holds the belief that:((p v q) is true if (p v q) follows from (p)). So the solution would look like this after filling in the blanks...
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if (p v q) follows from (p))
C1. ((p v q) is true because (p v q) follows from (p))
You replied:
What I'm suggesting is that
(p AND (IF p THEN (p V q))
is already enough to give a truth condition for (p V q). Or in other words:
(p V q) is true if p.
I'm not sure what else you think is required, or how your view is coordinated with ordinary propositional logic. So far as I can see, all that's missing is sufficient warrant for the claim that p, which is provided by Gettier.
Which is not to say that (p V q), taken in isolation, is an adequate representation of Smith's belief in Gettier II.
No, only if it is an actual truth. Only if it is known, because then it is true. If it is only believed then it may not be true — unenlightened
But in practice, beliefs are normally not known to be knowledge unless they are necessary. — unenlightened
Aren't you just conflating validity with soundness? — Srap Tasmaner
What's a person to do then? — Srap Tasmaner
I wrote:
None of them(logical arguments meant to account for believing a disjunction) can account for Smith's considering the truth conditions of his particular disjunctions and subsequently concluding that the disjunction is true because those conditions have been met.
You replied:
Why can't they? The truth of p is a truth condition for (p V q). Smith believes that p, and has strong reasons for believing that p. What is left unexplained?
Jones owns a Ford.
IF Jones owns a Ford, THEN (Jones owns a Ford OR Brown is in Barcelona)
THEREFORE (Jones owns a Ford OR Brown is in Barcelona)
Your attempt to "solve" Gettier II by focusing on the formal features of "believing a disjunction" -- even if it were successful -- might leave dissatisfied those of us who'd prefer a single unified solution to all Gettier-type problems. Not all Gettier problems involve disjunction.
IF p, then (p v q). That's valid, sound, true and contentless — unenlightened
A person is to acknowledge the fallibility of his beliefs and refrain from making arbitrary unconnected pointless disjunctions of them as if they were necessarily true, because they ain't. — unenlightened
This gives a weighted disjunction, (p(99%) v ~p(1%)). — unenlightened
1. Substitution into belief statements can fail salva veritate
2. Substitution into Justification statements can fail salva veritate
3. S has in inadequate justification for (p v q). — Banno
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