If you accept everything up to the end, then you accept that as well, or you don't understand it. I'm certain that you understand it.

Start from the top...

I know how strong that argument is and I perfectly understand it's scope of application.

Fill it out...

Follow Gettier's formula, and you'll find yourself at p2

One can have a true belief arrived at from a false reason.

False premisses and an invalid form/inference can get you there. So what? It's irrelevant to the argument being made and you know it.

Do you not grasp the differences in complexity?

Look at the notation.

False premisses and an invalid form/inference can get you there. So what? It's irrelevant to the argument being made and you know it. — creativesoul

It isn't. If the conclusion is true and if I believe that the conclusion is true then I have a true belief. It doesn't matter if I believe it to be true because I believe a false premise to be true.

I believe that John is a man because he is a bachelor. My premise "John is a bachelor" is false but my conclusion "John is a man" is true. I have a true belief (and a false one).

Follow Gettier's formula and stop just prior to the conclusion.

You'll be at p2

Fill it out.

Gettier:

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...

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

The above exhausts Gettier's thought/belief process as described above. You don't get here...

Gettier:

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

One must first arrive at belief that:((p v q) is true) before one can be justified in believing that:((p v q) is true). One cannot arrive there without going through another deduction...

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

That's specific to Case II. All cases require these two steps. Fill it out.

I believe that John is a man because he is a bachelor.

Are you claiming that there is/are no other truth condition(s) and/or justificatory ground for your belief that John is a man?

Can I get paid yet?

Start from the top...

Are you claiming that there is/are no other truth condition(s) and/or justificatory ground for your belief that John is a man? — creativesoul

Yes. I have simply been told by a person I trust that John is a bachelor. If it would make it a better example, let's use a gender-neutral name like "Max" instead of "John", or even an online alias like "creativesoul".

I only believe that this person is a man because I believe that this person is a bachelor. This person isn't a bachelor but is a man. I have a true belief (as well as a false one).

Fill it out.

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 in Gettier's formulation. 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

As a result of...

This covers them all

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'))(from p1,p3)

An astute reader will take note of the fact that that solution further discriminates between knowing what truth conditions are for a disjunction and believing that the disjunction is true as compared/contrasted to just believing that it follows from p.

It's worth noting here that there are no disjunctions immune. None. When we fill in the blanks accordingly, there are no problems with any of the conclusions. None.

It is also worth mentioning that this isn't an outright and total rejection of Gettier's formula. In the main, it shows us that that particular formula is inadequate in it's ability to take proper account of how one arrives at believing a disjunction. That is not to say that the formulation is inadequate for taking account of all believing any and all Q's. To quite the contrary...

It is to say that it is inadequate for taking account of Q's that are disjunctions. Not all Q's require another deduction to arrive at believing them...

So earlier Michael presented a sample of an actual case of deducing (p v q) from p.

1. London is the capital city of England or pigs can fly
2. London is the capital city of England or pigs can't fly
3. London is the capital city of England or there are no pigs

S/he claimed that s/he believed London is the capital city of England.

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'))

There's the formula. Let's fill it it out in numerical order.

Michael believes London is the capital city of England. Michael believes that: 'London is the capital city of England' is a true proposition(p1); the disjunction 'London is the capital city of England or 'Pigs can fly' follows from 'London is the capital city of England'(p2); the disjunction 'London is the capital city of England or 'Pigs can fly' is true if either 'London is the capital city of England' or 'Pigs can fly' is true. Michael believes that the disjunction 'London is the capital city of England' or 'Pigs can fly' is true because London is the capital city of England.

No problem there.


Michael believes London is the capital city of England. Michael believes that: 'London is the capital city of England' is a true proposition(p1); the disjunction 'London is the capital city of England or 'Pigs can't fly' follows from 'London is the capital city of England'(p2); the disjunction 'London is the capital city of England or 'Pigs can't fly' is true if either 'London is the capital city of England' or 'Pigs can't fly' is true. Michael believes that the disjunction 'London is the capital city of England' or 'Pigs can't fly' is true because London is the capital city of England.

No problem there.

3 is no different...

No problems, but not like Case II to begin with.

I believe that John is a bachelor. I believe that "John is a bachelor" is true. I believe that "John is a man" follows from "John is a bachelor". I believe that "John is a man" is true if "John is a bachelor" is true. I believe that "John is a man" is true because John is a bachelor.

John is a man but isn't a bachelor. So my belief that 1) ["John is a man" is true because John is a bachelor] is false, but my belief that 2) ["John is a man" is true] is true.

Smith's belief that 1) ["Jones owns a Ford or Brown is in Barcelona" is true because Jones owns a Ford] is false, but his belief that 2) ["Jones owns a Ford or Brown is in Barcelona" is true] is true.

Ignoring 2 doesn't make it go away.

This is also not like Case II.

With regard to my argument. I'm not ignoring it. I've rendered it inadequate. Belief that ((p v q) is true because (p)) cannot be gotten around. One never gets to belief that:((p v q) is true). It stops at the former for reasons already argued for ad nauseum without subsequent refutation...

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'))(from p1,p3)




S believes P, P entails Q, S deduces Q from P and accepts Q as a result of that deduction only gets us to belief that:((p v q) follows from (p)).

Therefore S does not yet believe that:((Q) is true)

When we're talking about thought/belief that is as complex as belief that:((p v q) follows from (p)), our account and/or report thereof had better well include everything necessary. S's believing Q is existentially contingent upon S's thinking about thought/belief in terms of P's and Q's. That only gets through p2.

Half a century of bewitchment.

The Merrillian Lie-Trap

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'))(from p1,p3)

An insincere purveyor of disjunction cannot pass through. I'm gonna be famous...

X-)

S believes P, P entails Q, S deduces Q from P and accepts Q as a result of that deduction only gets us to belief that:((p v q) follows from (p)).

Therefore S does not yet believe that:((Q) is true) — creativesoul

You're misreading. Let's replace the terms with a real example:

Smith believes that Max is a bachelor, Max being a bachelor entails that Max is a man, Smith deduces that Max is a man from Max being a bachelor and accepts that Max is a man as a result of that deduction.

The accepts Q is Gettier saying that Smith believes that Q is true. He accepts that Q is true because he accepts that P is true and accepts that P entails Q.

We can set it out more clearly here:

1. S believes P
2. P entails Q
3. S deduces Q from P
4. S accepts Q

For some reason you're conflating 3 and 4. This is wrong. Gettier isn't repeating himself. Compare with:

1. S doesn't believe P
2. P entails Q
3. S deduces Q from P
4. S doesn't accept Q

Notice that in both cases Smith accepts that Q follows from P, but in the first case he accepts Q and in the second case he doesn't. So contrary to your repeated claims, Gettier's example (the first case) doesn't just get us to the belief that p ∨ q follows from p. It also gets us to the belief that p ∨ q (a belief that we don't get to in the second case).

I've explained this to you several times. In both of these cases I believe that p ∨ q follows from p:

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

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

But in the first case I also believe that p ∨ q. And the same with Smith: he doesn't just believe that p ∨ q follows from p; he also believes that p ∨ q.

Smith's belief isn't just on the validity of the inference. It's also on the truth of the conclusion (and the premise).

One never gets to belief that:((p v q) is true). It stops at the former for reasons already argued for ad nauseum without subsequent refutation... — creativesoul

No it doesn't. If you believe that p ∨ q ∵ p then you believe that p ∨ q.

It doesn't make sense to say "I believe that Donald Trump is the President because he won the popular vote but I don't believe that Donald Trump is the President".

And it doesn't make sense to say "I believe that Jones owns a Ford or Brown is in Barcelona because Jones owns a Ford but I don't believe that Jones owns a Ford or Brown is in Barcelona".

Use a disjunction. In Case II, Q is a disjunction.

Gettier claims that Smith believes that:((p v q) is true). Belief that:((p v q) is true) is the aim.

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'))

You cannot get to Gettier's aim without going through all of the above. Salva veritate

When we're talking about thought/belief that is as complex as belief that:((p v q) follows from (p)), our account and/or report thereof had better well include everything necessary. S's believing Q is existentially contingent upon S's thinking about thought/belief in terms of P's and Q's. That only gets through p2.

Half a century of bewitchment.

It doesn't make sense to say "I believe that Jones owns a Ford or Brown is in Barcelona because Jones owns a Ford but I don't believe that Jones owns a Ford or Brown is in Barcelona".

If Smith believes that Jones owns a Ford or Brown is in Barcelona because Jones owns a Ford then ipso facto Smith believes that Jones owns a Ford or Brown is in Barcelona. Smith has a true belief. This is basic logic.

Furthermore, Gettier states that Smith does in fact believe that Jones owns a Ford or Brown is in Barcelona.

Fill it out with any and all disjunction deduced from belief that ((p) is true)...

It's a proof, and you know it.

Fill it out, or show what step is not necessary. Gettier sets out one deduction. One deduction is insufficient.

I've done so numerous times. I'll repeat it again:

1. p
2. p ⊨ p ∨ q
3. p ∨ q

This is a valid argument. Therefore the rational person who believes 1 and 2 will also believe 3. And Gettier states that Smith is a rational person and believes 3.

Bewitched...

Start at the top...

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 in Gettier's formulation. 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. The term "because" in C1 is the necessary but missing deduction in Gettier's formula.

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.

That is Smith's believing Q as the result of another deduction.

QED

1. p
2. p ⊨ p ∨ q
3. p ∨ q

This is a valid argument. Therefore the rational person who believes 1 and 2 will also believe 3. And Gettier states that Smith is a rational person and believes 3.

Your attempts to refute this are nonsense.

I need not refute that. It's irrelevant


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)

S cannot arrive at belief that:((p v q) is true) without going through all of the above. Salva veritate