Cabbage Farmer describes Smith somewhere as having a defeasible warrant to assert that p, and that's all he needs. — Srap Tasmaner

No, that's not all he needs, and that is my whole point. From "defeasibly p", (p v q) does not follow. In logic a thing follows or it doesn't; there is no 'defeasibly follows'.

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

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))

It doesn't seem redundant from here. In such a scenario, Smith hods false belief about what makes a disjunction true. It does not follow from the fact that (p v q) follows from (p) that (p v q) is true. Being the result of a valid inference is insufficient for being true. That scenario also posits a Smith that does not take into consideration the actual truth conditions of (p v q). Rational people do not assent to believing a disjunction if they do not know what it means. Knowing what makes a disjunction true is knowing what it means. Rational people would know what makes a disjunction true and assent to believing a disjunction based upon believing that those conditions have been met. That is what my solution puts on display...

Is John Harris Back? Sure seems like it.

From "defeasibly p", (p v q) does not follow. In logic a thing follows or it doesn't; there is no 'defeasibly follows'. — unenlightened

We agree that whether B follows from A is purely a matter of logic, nothing to do with belief. I don't know why you think I'm arguing for extra logical constants. I've never ever said anything remotely like that.

If you infer B from your belief that A, and if your belief that A is defeasible, then so too should your belief that B be. That's normal inference, not some special kind just for defeasible beliefs.

Suppose you think A might be the case, but it's difficult to test for directly, but you know that A→B, and it's comparatively easy to test for B. If B comes back false, you apply modus tollens and conclude ¬A.

One way to look at this is like so:
1. A→B
2. ¬B
∴ 3. ¬A
That is, in the Great Book of Established Truth, A was never entered at all.

But in practice what happens is more like this:
1. A→B
--- 1.1. Assume A
--- 1.2. B
--- Test B
--- 2. ¬B
--- 2.1. A→⊥
3. ¬A
To get to the point of having something to test, you take A hypothetically, and infer B from it.

I think most scientists would be inclined to say there is no Great Book of Established Truth. Instead there is the Great Book of Not Disconfirmed Hypotheses. If B comes back true (as best we can tell), that's another tally mark for A, and that's the best we can do. That's why we have the book, to keep track of the A's that are doing pretty well in the confirmation department. As Hume said, all arguments about matters of fact are probable, not demonstrative. You can have a Great Book of Established Truth if you want, but you might as well leave it in the Math Dept. because they're the only ones who'll ever put anything in it.

If later there's even better evidence against B, they may both have to be moved to whatever the current volume is of the Great Book of Discredited Hypotheses.


** ADDED: We could of course have a "defeasibly follows from" in the sense that we could hold A→B to be only probable. It's a premise too, no real difference from holding A to be only probable. That's not our situation here, because though we can write P→P ∨ Q if we want, that's not really a premise. We're not entertaining the option that it could be false. It's an inference rule rather than a premise, and should really be written P⊢P ∨ Q, or $\small \frac{P}{P \lor Q}$.

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

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.

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. 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. 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. Smith believes neither that p could be false nor that q could be true. 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.

However...

Smith can believe that (p v q) follows from (p) despite his not believing (q). Believing that a disjunction follows from a belief is not equivalent to believing a disjunction. 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. 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.

Given that, what is there in your above epistemic structural offering that is both germane and not effectively exhausted by p1 and p2 below?

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'))

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

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.

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

This is prima facie evidence that you've not understood what I've argued.

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.

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.

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. 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.

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'))

Is there something else you show to be false, some other proposition relevant to the problem? — Cabbage Farmer

The 'argument' I'm putting forth is the thought/belief process that is required for a rational agent to arrive at believing Q when Q is a disjunction deduced from believing P. Believing a disjunction is not belief that:((p v q) is true). Believing a disjunction requires considering what makes that particular disjunction true and believing that those conditions have been met. Thus, Smith's believing all three of his particular disjunctions consists exactly in/of the thought/belief process I've set out.

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))


Jones owns a Ford. "Jones owns a Ford" is true. "Either Jones owns a Ford or Brown is in Barcelona" follows from "Jones owns a Ford". "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. "Either Jones owns a Ford or Brown is in Barcelona" is true because Jones owns a Ford.

Smith does not have true belief.

Justification is useful in discerning mistakes of reasoning — javra

Justification does not appear in the Theaetetus; it's a modern variant. In the Theaetetus the third component is the Logos; analysed in various ways. The idea is perhaps a sort of coherentism - a piece of knowledge has to fit in with the other stuff you know.

So one big flaw in Gettier is that he takes the justification to be one or two supporting propositions, and not holistic.

So one big flaw in Gettier is that he takes the justification to be one or two supporting propositions, and not holistic. — Banno

I don't think he does. The way Gettier sketches in the "strong evidence" Smith has is clearly just a gesture toward whatever we would generally count as strong evidence:

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.

So do you have some thoughts on justification? What is this holism of which you speak?

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.

A nice small bit of context may serve us well.

I strongly suggest that if one is offering a critique on the JTB concept of knowledge that s/he had better get belief right. Gettier aims at satisfying three popular formulations of knowledge as JTB. Those three formulations claim to set out the necessary and sufficient conditions for knowing a given proposition.

Something that has not been given due attention...

The necessary and sufficient conditions for knowing a proposition must exhaust the necessary and sufficient conditions for believing one. The necessary and sufficient conditions for believing a proposition vary according to the complexity of the proposition. The necessary and sufficient conditions for knowing a proposition vary in accordance to the complexity of the belief.

This is not reflected in any of the three formulations for JTB. It is also not reflected in Gettier's formulation. His cases follow the outline of his formulation, so this is also not reflected in either of those cases.

That gets to the root of the problem(s).

"Belief that P" is an outline meant to be able to adequately represent any and all belief. "P" is a meaningless placeholder, and as such - if the formula holds good for all P's - it ought be able to adequately take an account of any and all belief simply by substituting "P" with a belief statement. Belief statements presuppose their own truth(as correspondence to fact/reality). Propositions do not necessarily.

That is another root of the problem(s) and leads to the performative contradiction mentioned earlier when we confuse Smith's believing that:((p v q) follows from (p)) with Smith's believing that:((p or q) is true).

So do you have some thoughts on justification? — Srap Tasmaner

In the dream of Socrates, the account that accompanies true belief is an analysis of the complex in terms of the simple. The rejection of that account in the Theaetetus curiously parallels the move from logical atomism to meaning as use in analytic philosophy.

Belief and knowledge are compatible with doubt. — Cabbage Farmer

An intersting notion. So Moore might believe he has a hand, and yet doubt it. Or Moore might know he has a hand, and yet doubt it. But not Moore might be certain he has a hand, and yet doubt it.

That might be right.

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

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.

Of course he still gets the payout, just like he still gets a hold of true claims in Gettier's original examples. But he gets them by a stroke of luck, not by virtue of understanding the relevant facts.

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

That's a fair analysis on the surface of the problem, but arguably leaves too much out of the picture.

How is the isolated claim "Mary will give me £10" supported in the context of Smith's beliefs? creativesoul has been arguing that we need a more thorough representation of Smith's beliefs in order to make sense of the problem. I'm inclined to agree.

We can't adequately understand what Smith believes -- we can't adequately interpret his propositional attitude with respect to the proposition we purport to represent by way of the English sentence "Mary will give me £10" -- without getting some of Smith's reasons into the picture. We need to show a relation among Smith's beliefs that supports the belief in question.

I suppose a JTB account of knowledge always requires us to dig deeper than a single knowledge claim, to show how the claim is justified for a given believer. In Gettier's cases, that digging turns up such a mess, it seems unreasonable to count them as cases of "knowing" -- as Smith himself would be prepared to admit, were he apprised of the relevant facts.

Are you saying that a belief is only justified if it's true? — Michael

No.

What counts as a sound justification from Smith's ill-informed point of view does not count as a sound justification from any well-informed point of view. Smith's "argument" is valid but not sound, as it depends on false premises.

Once Smith is apprised of the relevant facts, he realizes that he only got hold of a true conclusion by chance, not by sound reasoning. What had previously seemed a sound justification now turns out to be an unsound justification, because the premises on which it was based now appear to be false. (Not all variations on Gettier's theme turn on false premises in such an obvious way, so I'm not suggesting that "soundness" is the road to a general solution.)

It's interesting that philosophers like Gettier seem prepared to count such valid inference from false premises as "complete justification", while presumably they would not count invalid inference from true (or false) premises as justification. Why treat the norms of inference as if they were more objective than the facts? On the other hand, why not treat justifications involving invalid inferences as nonetheless justifications for the one who doesn't notice his fallacy?

My suggestion is that we make a theoretical distinction between a claim i) "justified" from an ill-informed epistemic context or finite point of view, and ii) "justified" from a well-informed epistemic context or omniscient point of view. Then we might say, the J in JTB is justification in sense (ii).

This seems in line with Plato's original suggestion. I suppose it also makes justification a mercurial little trickster like truth and knowledge.

We count claims as true, as known, as justified, each of us from his own point of view. But we take for granted that there is a fact of the matter that determines whether we are correct in those judgments.

Except when there is no fact of the matter.

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

This bit I can agree with: In Gettier's cases, Smith believes that p but does not know that p, because p is in fact and unbeknownst to Smith, false.

That's why his justification for the disjunction is problematic. It's a valid argument from false premises that accidentally lands on a true conclusion. It seems to me Smith's ignorance is the whole problem, and this is what is preserved on what I take to be a common response to the puzzle: Smith does not know that p, and he does not know that (p V q), although (p V q) is true in fact and Smith believes with justification that (p V q).

I still don't see how adding skeptical couching helps to address this specific problem.

I still don't see how adding skeptical couching helps to address this specific problem. — Cabbage Farmer

However one couches it, the sceptical element amounts to, by malign accident, improbable circumstance, alternative interpretation of the evidence, or whatever, '~p'.

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.

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)) — creativesoul

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.

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

I only offer to revert to the exclusive disjunction because it seems to be the form of the thought Gettier intends to put in Smith's head.

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

That sounds right. I suppose we're all talking about best practices for formalization of the case at hand.

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

What contradiction is inherent in (3), and how does it carry over to (4)?

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

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.

I suppose believing that an exclusive disjunction is true, or having beliefs with the form of an exclusive disjunction, requires believing that one but not both of the terms in the disjunction are true. For instance, by believing that p and believing that ~q.

Smith believes neither that p could be false nor that q could be true. — 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.

None of that is required for us to count Smith as believing with justification that p and ~q.

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

I reject this claim. I take the following to be consistent statements:

I believe that p and that possibly ~p. I believe that p, and I believe it's possible that my belief-that-p is wrong. I have beliefs and I believe it's possible that any of my beliefs are wrong.

I know that p but it's possible that I am wrong and that ~p. I have knowledge but it's possible that any knowledge claim of mine is wrong.

Moreover, I take it this way of speaking is consistent with Gettier's arguments.

Smith can believe that (p v q) follows from (p) despite his not believing (q). — 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.

Believing that a disjunction follows from a belief is not equivalent to believing a disjunction. — creativesoul

The truth of an inclusive disjunction follows from the truth of any of its terms.

To believe that one or more of those terms is true is to have beliefs in accord with the truth of the disjunction, and is to be disposed to assent to the claim expressed in the disjunction.

Moreover, if Smith is rational and understands the conventions of formal logic, and believes that p, and entertains the proposition (p V q) in light of his belief that p, we should be surprised indeed if he does not acknowledge that he believes that (p V q) is true.

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

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.

It seems this is the point you're neglecting, which has sent you off on a search for red herring.

Smith believes that p.

Smith does not merely believe that there are abstract inferential relations between any pair of propositions and their disjunction. He believes the truth condition for a particular disjunctive claim has been satisfied. He believes that Jones owns a Ford.

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

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.

I'm happy to go with the flow here and focus on the case as if Smith had constructed an arbitrary inclusive disjunction instead of an arbitrary exclusive disjunction. I don't think it makes much difference for the underlying issue.

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

That's my point. We don't need the rest of it.

The relevant epistemic structure is exhausted by:

warrant for p
belief that p
understanding that (IF p THEN (p V q))

That's enough to make Smith disposed to assent to (p v q), and enough to make Smith's beliefs accord with (p V q).

Add that, given that epistemic context, Smith entertains the proposition (p V q) and makes a rational judgment. In my book that's enough to attribute to Smith the belief that (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 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).

You have claimed repeatedly, but not shown to my satisfaction, that my sketch is inadequate. You have insisted that something extra is required, but you have not made clear why or what the extra item is supposed to be.

By now it seems we're going in circles. This is beginning to get tiresome.

This is prima facie evidence that you've not understood what I've argued. — 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.

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

I don't know what all the others have said.

In my view Smith's "belief" is justified in one sense, and not justified in a stricter sense. And his "belief" is not adequately represented by the isolated disjunctive claim, but only by that claim in the context of his supporting beliefs about the facts of the case, which supporting beliefs function as his justification for the isolated claim in question.

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

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?

Perhaps the abstract symbols are causing the confusion? I'll reiterate, Smith's beliefs here aren't merely about abstract inferential relations. He believes:

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)

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

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.

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

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.

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.

Believing that (g), (h), and (i) are entailed by (f) is not equivalent to believing the disjunctions.
— creativesoul

The above marks a common point of conflation. The below marks a typical red herring response to the above...

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.

A careful reader will note that the objection does not offer an example of believing the disjunction. Rather, it poses a single statement as the belief candidate, namely "the Post Office isn't open". The problem of course, is that "the Post Office isn't open" is not a disjunction.

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.

So in your view we are only entitled to infer p v q from p if p is a necessary truth. — Srap Tasmaner

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. But in practice, beliefs are normally not known to be knowledge unless they are necessary. But this is not merely 'my view', it is the way logic works, as developed over the millennia.

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.

What's missing is an adequate account of believing a disjunction. Belief that:((p v q) is true if (p) is true) is necessary but insufficient for believing this particular disjunction. Believing it requires another deduction.

What you've offered covers one aspect of what believing a disjunction requires. That is, belief that:((p v q) is true if (p) is true) is a perfect representation of an agent's considering the truth conditions regarding what it would take for a disjunction to be true if and when it is deduced from belief that:((p) is true). In Gettier's second case, what you've presented would cover an exclusive 'or', and would be in complete agreement/congruence with p3 of my solution.

p3.((p v q) is true if... (insert belief statement(s) regarding what makes this particular disjunction true))

Filling it out...

p3.((p v q) is true if (p) is true)

We're after the agent's believing the disjunction. That requires one more deduction.

C1.((p v q) is true because (p))

The notation I'm using packs as much as possible into the belief statement, as it should on my view given that belief is the target. That said, I'm not well-versed in any formal notation.

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I want to note that you shouldn't take anything I say personally. My apologies for the poorly worded bits about misunderstandings, and not openly accepting some responsibility for them. My position carries quite the burden, and I gladly accept it...

That said, this post left much out. I think, however, that it gets to the heart of what you've asked for.

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

Aren't you just conflating validity with soundness? I just don't understand the idea that inference is only possible from actual truths.

But in practice, beliefs are normally not known to be knowledge unless they are necessary. — unenlightened

What's a person to do then? Suppose I think I know that A. Should I infer B from it? Or only if I know that I know? Maybe I only think I know that I know ...

Aren't you just conflating validity with soundness? — Srap Tasmaner

No.

IF p, then (p v q). That's valid, sound, true and contentless.

But if not, then q can really just fuck off.

What's a person to do then? — Srap Tasmaner

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.

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?

Smith's considering the truth conditions of his particular disjunctions and subsequently concluding that the disjunction is true because those conditions have been met.

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)

p1.If P then Q
p2.P
C.Therefore Q(from 1 and 2)

If modus ponens is used as a means for accounting for Smith's thought/belief process leading up to his believing a disjunction, then that thought/belief process would certainly include Smith's concluding that the disjunction is true because the truth conditions have been met(from 1 and 2). That cannot be left out, for doing so renders an incomplete account of Smith's belief. The incomplete account has a very different meaning.

If "Jones owns a Ford" is true then "either Jones owns a Ford or Brown is in Barcelona" is true. "Jones owns a Ford" is true. Therefore, "either Jones owns a Ford or Brown is in Barcelona" is true because "Jones owns a Ford" is true and if "Jones owns a Ford" is true then "either Jones owns a Ford or Brown is in Barcelona" is true.

Smith has false belief.

Salva veritate

Belief that:((p v q) is true because ((p) is true) and (if (p) is true then ((p v q) is true)) is not equivalent to belief that:((p v q) is true).

p1. (if (p) is true then ((p v q) is true))
p2. ((p) is true)
C. ((p v q) is true because ((p) is true) and (if (p) is true then ((p or q) is true)).

That is taking proper account of Smith's thinking about the truth conditions(from 1 and 2), and subsequently believing the disjunction as a result of believing that those conditions have been met. That is what has been left completely unexplained by every account on the table except my own...

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.

I would readily agree that not all Gettier problems involve disjunction. They do all involve his formula though, and it has been proven to be inadequate for providing the necessary and sufficient conditions for believing all Q's.

IF p, then (p v q). That's valid, sound, true and contentless — unenlightened

It's only sound if p is true.

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

The conclusion of an inference merits no more or less credence than what you grant your premises. If you're uncertain about your premises, then you should be just that uncertain about your conclusions.

Why in your view is that not a sufficient acknowledgement of fallibility?

I agree, of course, that there is something odd about Smith's inference. Maybe there should be another rule brought to bear here. I just don't know what that rule would be.

I'm just thinking this through for my own sake. It's supposed to be a reductio, disproving the definition:

If r, and S believes r, and r is justified, then by definition S knows r

by presenting a case in which S would, by this definition, be said to know r; and yet our intuition says otherwise.

And it might go like this:

S believes p
If p, then (p v q)
therefore S believes (p v q)
At this point one might object that adding the disjunction is infelicitous, since one cannot substitute into belief statements salva veritate. Is that one of Un's points?

Leaving that aside, how must the argument proceed? Is (p v q) justified?

Well, ex hypothesi, q is true but not p. So for the argument to work, the following substitution must work;

p is justified, therefore (p v q) is justified.

again, it is debatable that this can be done salva veritate.



As it turns out, and unbeknownst to S,

q and ~p, therefore (p v q)

bring down: If r, and S believes r, and r is justified, then by definition S knows r

Substitute (p v q) for r, and take (p v q) as true since q is true. Discarding the two salva veritate objections,

S believes (p v q)

and

q is justified, therefore (p v q) is justified

So therefore, by definition, S knows (p v q)

But S holds that (p v q) is justified because p is justified, not because q is justified. That is, S was wrong in thinking he had an adequate justification for (p v q).

SO I see three objections:
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).

And then there is the further point, made previously, that no one actually thinks the definition worthwhile, anyway.

This gives a weighted disjunction, (p(99%) v ~p(1%)). — unenlightened

Not that it matters, but I think you want that to be a conjunction.

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

I don't think we're talking about substitution here exactly. No one thinks p v q is equivalent to p; it's inferred from p. And explicitly we're not inferring what Smith believes. Smith makes these inferences and we're just told that he does.