Smith believes that f is true. Smith knows that g, h, and i follow from f as per the rules of correct inference. Therefore, Smith knows that g, h, and i are valid inferences. — creativesoul

And if (f) were true, so would (g), (h), and (i) be.

It's rather the point that Smith thinks he is applying modus ponens but he isn't, because (f) is actually false. That's valid, in the sense that it will preserve truth, but there's no truth to preserve.

Gettier's claim is that if an inference is valid, it preserves justification as well as truth, and thus even though there was no truth to preserve, what justification Smith had for his belief that (f), is passed to (g), (h), and (i) by modus ponens.

Since (h) is true entirely by coincidence, Smith now has one justified true belief, (h), but he has increased his store of justified false beliefs:
(f) Jones owns a Ford;
(g) Either Jones owns a Ford, or Brown is in Boston;
(i) Either Jones owns a Ford, or Brown is in Brest-Litovsk.

What will happen if he ever comes to correct his false belief (f)? Will he now have this inconsistent set of beliefs?
(g') Brown is in Boston;
(h') Brown is in Barcelona;
(i') Brown is in Brest-Litovsk.
No, as a matter of fact he won't: he believed he was applying modus ponens; once he knows that (f) is false, he will no longer infer (g), (h), and (i). Modus ponens is no use if (f) is false.

To believe that you have made a valid inference from a true premise is to believe that the conclusion is true. It is the whole point of making valid inferences. We only do this to get truths we do not yet know from truths that we do.

If you presented an argument here on this forum, what would you think of the following response?

I accept that your premises are true, and I accept that your conclusion may be validly inferred from those premises, but that is all; I do not accept that your conclusion is in fact true.

And here you'd gone to all that trouble of establishing your premises and making careful inferences, all for nought ...

ADDED: Where I say "no truth" above, that's technically wrong, of course, because all of the conditionals are fine:
(f)→(g)
(f)→(h)
(f)→(i).

Does it make sense to say that "London is the capital city of England or I am a woman" is an invalid conclusion? — creativesoul

No. And neither does it make sense to say that a conclusion is valid. Arguments are valid or invalid; propositions (whether premise or conclusion) are true or false.

"London is the capital city of England or I am a woman" is a conclusion that follows from the premise "London is the capital city of England". The argument is valid. Given that the premise is true, so too is the conclusion, and so the argument is sound.

It is nothing less than knowledge that (p v q) follows from p. The truth conditions of p and q are irrelevant to knowing that (p v q) follows from p. — creativesoul

Here are three arguments:

1. London is the capital city of England
2. London is the capital city of England or I am a woman

2 follows from 1. 1 is true and 2 is true.

3. London is the capital city of France
4. London is the capital city of France or I am a woman

4 follows from 3. 3 is false and 4 is false.

5. London is the capital city of Germany
6. London is the capital city of Germany or I am a man

6 follows from 5. 5 is false and 6 is true.

There is more to Smith's belief than just believing that p ∨ q follows from p. He also believes that p is true and that p ∨ q is true. His argument is akin to the first of the three above.

Either an inference is not inferred, or being inferred doesn't count as being an inference. — creativesoul

So then, g, h, and i are only valid inferences when you say so? What sense does this make? — creativesoul

Clearly there's some ambiguity here with the term "inference". On the one hand it can mean "a conclusion reached on the basis of evidence and reasoning", but I meant it in the sense of "the process of inferring something". I should have perhaps used the term "argument". Arguments are valid or invalid; propositions are true or false. g, h and i are propositions, not arguments, and so are either true or false, not either valid or invalid. Inferring g, h, and i from f is either valid or invalid.

Smith believes that f is true. Smith knows that g, h, and i follow from f as per the rules of correct inference. Therefore, Smith knows that g, h, and i are valid inferences. Because Smith knows that g, h, and i are valid, his belief is not that g, h, and i are all true unless he conflates being valid with being true. Smith is rational and knows the rules, so doesn't do this. Rather Smith knows that g, h, and i are all true if and only if his belief that f is. — creativesoul

There's more to it than this.

Smith believes that f is true. Smith knows that g, h, and i follow from f as per the rules of correct inference. And Smith believes that g, h, and i are true.

Again with my previous example:

I believe that "it is wrong to steal" is true. I know that "it is wrong for me to steal" follows from "it is wrong to steal" as per the rules of correct inference. And I believe that "it is wrong for me to steal" is true.

Compare with:

I believe that "it is right to steal" is false. I know that "it is right for me to steal" follows from "it is right to steal" as per the rules of correct inference. And I believe that "it is right for me to steal" is false.

And compare with:

I believe that "all Presidents are men" is false. I know that "President Trump is a man" follows from "all Presidents are men" as per the rules of correct inference. And I believe that "President Trump is a man" is true.

There are three things to consider here: 1. is the premise true? 2. does the conclusion follow from the premise? 3. is the conclusion true? For some reason you are ignoring 3. Why?

So then, let's say that Smith is just a regular joe, and says with unshakable certainty "Well, either Jones owns a Ford or Brown is in Barcelona" even though he knows that he's ignorant regarding Brown's whereabouts.

He would believe that f, but would not know that h followed. Thus, his assertion would be unjustified, and the case ends there. — creativesoul

But it does follow. If "Jones owns a Ford" is true then "Jones owns a Ford or Brown is in Barcelona" is true. If he's justified in believing that Jones owns a Ford then he is justified in believing that Jones owns a Ford or Brown is in Barcelona.

Gettier's claim is that if an inference is valid, it preserves justification as well as truth, and thus even though there was no truth to preserve, what justification Smith had for his belief that (f), is passed to (g), (h), and (i) by modus ponens.

Smith's justification for (f) is all relevant to (f). Smith's inferring (g), (h), and (i) from (f) has nothing to do with the justification for (f). This is obvious because Smith could have correctly inferred (g), (h), and (i) even if it were the case that (f) was unfounded. Rather, (g), (h), and (i) are justified by virtue of Smith knowing the rules and applying them accordingly to his belief that (f).

I would disagree with Gettier's claim.

...And Smith believes that g, h, and i are true.

The position you're arguing for hinges upon the above. I appreciate the time and effort that you put into the posts here Michael. However, it is much more appropriate to make your case by virtue of using Gettier's example...

Could you?

Smith's justification for (f) is all relevant to (f). Smith's inferring (g), (h), and (i) from (f) has nothing to do with the justification for (f). This is obvious because Smith could have correctly inferred (g), (h), and (i) even if it were the case that (f) was unfounded. — creativesoul

Well, yes and no. He doesn't make the inference because his belief that (f) is justified, but Gettier claims that inference preserves what justification he has for that belief, just as it preserves truth.

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. — Gettier

Rather, (g), (h), and (i) are justified by virtue of Smith knowing the rules and applying them accordingly to his belief that (f). — creativesoul

The trouble with this view is that valid inference from unjustified belief would confer justification upon the conclusion of the inference.* Inference isn't supposed to do that. Valid inference doesn't confer truth upon your conclusion, but guarantees that if the premises are true then the conclusion is too. Inference itself is not the source of the conclusion's truth -- that's still the premises.

I would disagree with Gettier's claim. — creativesoul

Yeah, like I've been saying for a while, you disagree with Gettier's premises. So you should be arguing that the quote above, beginning "Secondly, ...", is false.


* Here's an example of that:

I wake up on a Tuesday morning, groggy, remembering that I didn't have to get up yesterday, and thinking it's Monday and I have to be at work at 9. As it happens, Monday was a holiday and I have forgotten. I have a true belief that I need to be at work at 9, but it is not justified, as it is a valid inference from my unjustified belief that it is Monday, not Tuesday.

1. London is the capital city of England
2. London is the capital city of England or I am a woman

2 follows from 1. 1 is true and 2 is true.

3. London is the capital city of France
4. London is the capital city of France or I am a woman

4 follows from 3. 3 is false and 4 is false.

5. London is the capital city of Germany
6. London is the capital city of Germany or I am a man

6 follows from 5. 5 is false and 6 is true.

What makes the following claims true?

"1 is true and 2 is true"
"3 is false and 4 is false"
"5 is false and 6 is true"

"2 follows from 1"
"4 follows from 3"
"6 follows from 5"

What makes the following claims true? — creativesoul

What kind of answer are you expecting here?

Because it looks like you are asking, in so many words, for a theory of truth.

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.

I would say that that would be the case if, and only if, P and Q have the same truth conditions.

Michael wrote:

1. London is the capital city of England
2. London is the capital city of England or I am a woman

2 follows from 1. 1 is true and 2 is true.

3. London is the capital city of France
4. London is the capital city of France or I am a woman

4 follows from 3. 3 is false and 4 is false.

5. London is the capital city of Germany
6. London is the capital city of Germany or I am a man

6 follows from 5. 5 is false and 6 is true.

I replied:

What makes the following claims true?

"1 is true and 2 is true"
"3 is false and 4 is false"
"5 is false and 6 is true"

"2 follows from 1"
"4 follows from 3"
"6 follows from 5"

Srap asked:

What kind of answer are you expecting here?

Because it looks like you are asking, in so many words, for a theory of truth.

Well, the theory of truth one works with is at hand, regardless of whether or not that is currently the focus of discussion. However, I am teasing out the differences between statements that are called 'true' by virtue of being a valid inference, and those that are true.

I strongly suspect that there is conflation between the two at work.

I would say that that would be the case if, and only if, P and Q have the same truth conditions. — creativesoul

That would make them the same proposition.

However, I am teasing out the differences between statements that are called 'true' by virtue of being a valid inference, and those that are true. — creativesoul

"Called 'true'"? So you still don't accept that the conclusion is true?

I strongly suspect that there is conflation between the two at work. — creativesoul

There might be if you persist in thinking that being the conclusion of a valid inference makes a proposition true. It doesn't. If you don't think that, then you don't need two different kinds of truth. Or three. Or twelve. Truth is truth.

I wrote:

Rather, (g), (h), and (i) are justified by virtue of Smith knowing the rules and applying them accordingly to his belief that (f).

You replied:

The trouble with this view is that valid inference from unjustified belief would confer justification upon the conclusion of the inference. Inference isn't supposed to do that...

I wake up on a Tuesday morning, groggy, remembering that I didn't have to get up yesterday, and thinking it's Monday and I have to be at work at 9. As it happens, Monday was a holiday and I have forgotten. I have a true belief that I need to be at work at 9, but it is in not justified, as it is a valid inference from my unjustified belief that it is Monday, not Tuesday.

I would not claim that all valid inference is justified by virtue of being valid. Disjunctions are unique.

(g), (h), and (i) all consist of (f) and different statements about Brown's location. None of those statements (Q's) are believed by Smith. Smith derives them all by virtue of knowing the rules.

Regarding the difference between being called 'true' as a result of being the conclusion of a valid inference and being true, I expressed suspicion of conflation...

You replied:...There might be if you persist in thinking that being the conclusion of a valid inference makes a proposition true...

Assuming a hypothetical "you"...

We agree here.

Disjunctions are unique. — creativesoul

That's not going to work out. I can define all the logical constants in terms of disjunction and negation.

It feels like we're wandering around here. I'm having trouble keeping track of what you accept and what you don't.

Gettier asserted:

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.

I commented:

I would say that that would be the case if, and only if, P and Q have the same truth conditions.

You replied:

That would make them the same proposition.

You think/believe that every proposition has it's own unique set of truth conditions?

I do not accept Gettier's notion of belief. I've said that from the beginning. Our discussion allows those differences to show themselves. The formulation of JTB works from the same notion.

Disjunctions are unique.

(g), (h), and (i) all consist of (f) and different statements about Brown's location. None of those statements (Q's) are believed by Smith. Smith derives them all by virtue of knowing the rules.

What's wrong with the above Srap?

You see what's happening here regarding the clear distinction being drawn between believing that a proposition is validly inferred, and believing that a proposition is true?

You think/believe that every proposition has it's own unique set of truth conditions? — creativesoul

I think that's a pretty reasonable way to define propositions, yeah. You can express the same proposition in multiple ways, in multiple languages, and there will be all sorts of differences that logic just doesn't care about. Insofar as they have the same truth conditions they are different ways of expressing the same proposition.

I do not accept Gettier's notion of belief. — creativesoul

Why not?

Disjunctions are unique. — creativesoul

No they're not, not if we're talking about the logical constants. Are we talking about that, or are we talking about linguistics?

(g), (h), and (i) all consist of (f) and different statements about Brown's location. None of those statements (Q's) are believed by Smith. Smith derives them all by virtue of knowing the rules. — creativesoul

And you've not shown why this matters. At no point does Gettier attribute to Smith a belief in any of the "Q's".

You see what's happening here regarding the clear distinction being drawn between believing that a proposition is validly inferred, and believing that a proposition is true? — creativesoul

Nope.

So are propositions equivalent to belief?

I wrote:

(g), (h), and (i) all consist of (f) and different statements about Brown's location. None of those statements (Q's) are believed by Smith. Smith derives them all by virtue of knowing the rules.

You replied:

And you've not shown why this matters. At no point does Gettier attribute to Smith a belief in any of the "Q's".

But I have shown why it matters. Assuming sincerity in speech, statements are statements of belief. Smith's lack of belief in Q shows that his belief that (p v q) has nothing at all to do with his belief except his belief that (p v q) follows from p.

That is JTB.

In this context: beliefs have propositional content. If that's what you mean, yes.

"I believe that ...", "I know that ...", "I suspect that ...", "I hope that ...", "I doubt that ..." -- these are all propositional attitudes. All of these words have other uses, none of which are relevant here.

nothing at all to do with his belief except his belief that (p v q) follows from p. — creativesoul

... and is therefore true. That Smith believes (g), (h), and (i) -- i.e., believes all of them to be true -- is a premise of the argument.

What exactly are your grounds for rejecting this premise? That it is impossible for Smith to believe the conclusion of a valid argument from premises he believes? That it is not rational to do so? That as a matter of fact people do not do this?

Believing (f) and properly inferring (g), (h), and (i) from (f), why on earth should he not believe any of his own conclusions?

I wrote:

But I have shown why it matters. Assuming sincerity in speech, statements are statements of belief. Smith's lack of belief in Q shows that his belief that (p v q) has nothing at all to do with his belief except his belief that (p v q) follows from p.

You replied:

... and is therefore true.

No!

This is an opportune reminder...

I wrote:

Regarding the difference between being called 'true' as a result of being the conclusion of a valid inference and being true, I expressed suspicion of conflation...

You replied:

...There might be if you persist in thinking that being the conclusion of a valid inference makes a proposition true...

Allow me to hold a mirror up for you Srap.

That Smith believes (g), (h), and (i) -- i.e., believes all of them to be true -- is a premise of the argument.

His premiss works from an utterly inadequate notion of belief that (p v q).

QED.

Believing (f) and properly inferring (g), (h), and (i) from (f), why on earth should he not believe any of his own conclusions?

He believes that they're all valid inferences.

Belief that (p v q) follows from p is knowing that if either p or q is true then so too is (p v q). That's it. There's nothing more to it.

The truth conditions of q are utterly irrelevant.

Disjunctions are unique — creativesoul

So let's say that I know that my girlfriend is in the bathroom washing. I believe that the disjunction "she's having a shower or she's having a bath" is true. Let's also assume that this isn't a dichotomy, and that she could in fact just be using the sink.

According to you, to believe that this sentence is true is just to believe that it follows from "she's having a shower" (and/or from "she's having a bath")? That's quite clearly wrong. Believing that a disjunction is true is no different in kind to believing that a conjunction is true, or to believing that a simple proposition such as "she's having a shower" is true.

Given the argument:

1. p
2. p → r
3. r

One can believe in the truth (or falsity) of 1, 2, and 3. Contrary to your repeated claims, it isn't just a case of believing in the truth of 1 and 2.

I can believe that p is true, I can believe that if p is true then r is true, and I can believe that r is true. In our case, r is p ∨ q.

You wrote:

So let's say that I know that my girlfriend is in the bathroom washing. I believe that the disjunction "she's having a shower or she's having a bath" is true. Let's also assume that this isn't a dichotomy, and that she could in fact just be using the sink.

According to you, to believe that this sentence is true is just to believe that it follows from "she's having a shower" (and/or from "she's having a bath")? That's quite clearly wrong.

That would be clearly wrong. I agree that believing a disjunction is true is not equivalent to believing that it follows from p.

That is precisely my point. Smith's belief that (p v q) is of the latter, not the former.

There's a few remarkable differences between your example and the Gettier case. In your case, both statements(p & q) are about the same situation(your girlfriend's washing). You did not accept the disjunction as a result of recognizing the entailment. You believe that one or the other is true, and that it could be either. You asserted it as further clarification of your own belief. They're both kinds of washing, and you know that she's washing.

Smith doesn't believe that (p v q) is true. Smith didn't assert it as further clarification of his belief. He constructed g, h , and i by virtue of adding three different q's - none of which were belief. None of which were about p. All of which were propositions. His acceptance of g, h, and i is the result of realizing the entailment. He believed that each followed from p.

Believing that a disjunction is true is no different in kind to believing that a conjunction is true, or to believing that a simple proposition such as "she's having a shower" is true.

It's the notion of belief that that is at issue. More specifically, it seems to be an issue with how classical logic attempts to account for it. The shortcomings of logic is a topic in it's own right, so I'm trying to not focus too much upon that, although some of those shortcomings bear upon this particular Gettier case. I'm also trying to avoid talking about the content of thought/belief, but that is beginning to seem inevitable, it is most certainly germane.

To directly address the above quote:It is false. If there were no difference in kind, then there would be no difference between the content, but there is.

Belief that a simple proposition such as "she's having a shower" is true is to believe that "she's having a shower" corresponds to what she's doing in the bathroom.

Belief that a disjunction such as "she's having a shower or she's having a bath" is true, is to believe that one statement or the other corresponds to what she's doing in the bathroom.

Belief that the conjunction "she's having a shower, and she's having a bath" is to believe that both statements correspond to what she's doing in the bathroom.

Note that all three are about what she's doing in the bathroom. Further note the difference between the above disjunction and Smith's.

I can believe that p is true, I can believe that if p is true then r is true, and I can believe that r is true. In our case, r is p ∨ q.

Seeing how none of the variables above have a meaningful value other than being a place-marker for any given proposition, all you're doing here is asserting conviction in the representational ability of this particular formulation.

How you arrive at r matters.

Belief that a disjunction such as "she's having a shower or she's having a bath" is true, is to believe that one statement or the other corresponds to what she's doing in the bathroom. — creativesoul

And to believe that a disjunction such as "Jones owns a Ford or Brown is in Barcelona" is true is to believe that one statement or the other corresponds to some fact about the world.

Gettier asserted:

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.

I commented:

I would say that that would be the case if, and only if, P and Q have the same truth conditions.

You replied:

That would make them the same proposition.

I then asked:

You think/believe that every proposition has it's own unique set of truth conditions?

You answered:

I think that's a pretty reasonable way to define propositions, yeah. You can express the same proposition in multiple ways, in multiple languages, and there will be all sorts of differences that logic just doesn't care about. Insofar as they have the same truth conditions they are different ways of expressing the same proposition.

Can I surmise that each of these same propositions is about the same states of affairs?

Belief that a disjunction such as "she's having a shower or she's having a bath" is true, is to believe that one statement or the other corresponds to what she's doing in the bathroom.

And belief that a disjunction such as "Jones owns a Ford or Brown is in Barcelona" is true is to believe that one statement or the other corresponds to some fact about the world.

The former is about the same fact, and it consists entirely in/of statements of belief about that fact. The latter is about different facts and does not consist entirely of belief about those facts.

The former clarifies belief about the same fact. The latter clarifies belief about the rules.

How you arrive at (p v q) matters.

If one believes that either this(p) or that(q) is true, then one believes that both cannot be. The only way for that to be the case is when and if the agent believes that a single state of affairs determines the truth/falsity of both, this(p) and that(q).

The above is what (p v q) ought represent, but it doesn't. It represents more than that. It also represents Gettier's case where q isn't believed, there are two separate truth conditions for p and q, therefore Smith doesn't believe that a single state of affairs determines the truth/falsity of both.

That difference sheds light upon the problem.

How one arrives at (p v q) matters.