If p is true then p ∨ q is true. If there is strong evidence that p is true then there is strong evidence that p ∨ q is true. If one has strong evidence that p is true then one has strong evidence for believing that p ∨ q is true because p.

Smith believes p is true and so is justified in believing that p ∨ q is true because p.

How could it be any other way?

If g, h, and i follow from f and if I believe that f is true then I must believe that g, h, and i are true because f.

g is false.
i is false.
h is true because q.

I have false belief on all three counts.

Smith believes f, Smith recognises that g, h, and i follow from f, and so Smith believes g, h, and i. If his belief in f is justified then his belief in g, h, and i are also justified. If g is true then Smith has a justified true belief in g, and so according to the traditional definition, knowledge of g.

This works from the mistaken presupposition that the content of g, h, and i are equivalent to the content of Smith's believing g, h, and i.

It's not.

The part above that says ", and so Smith believes g, h, and i" doesn't follow from what precedes it. It ought read ", and so Smith believes that g, h, and i are true because f". If any of the three are true for any reason other than f being true, then Smith has false belief.

I only need to believe that London is the capital city of England. Which is exactly why I believe the following to be true (and why they are both true):

5. Either London is the capital city of England or pigs can fly
6. Either London is the capital city of England or pigs can't fly

So, then an adequate account of your belief would be...

You believe that either London is the capital city of England or pigs can fly is true because London is the capital city of England.
You believe that either London is the capital city of England or pigs can't fly is true because London is the capital city of England.

Michael wrote:

He believes that p ∨ q is true because he believes that p is true.

That was from page 5.

Smith believes p v q is true because p.

When we're actively establishing what counts as thought/belief, we're seeking to isolate and set aside common denominators that remain extant after identifying and setting aside the individual particulars(that which is subject to familial, cultural, and historical particulars). What's left is common to all. That which is common to all warrants nothing less than one's full attention.

It is ok to say that we're "defining thought/belief", as long as we keep certain facts in mind. We can get it wrong. Thought/belief formation happens long prior to language creation and/or acquisition begins in earnest. It requires an agent capable of drawing mental correlations/connections/associations between 'objects' of physiological sensory perception and/or itself.

There are no examples to the contrary.

That said, all usage of "thought" and "belief" consists entirely of mental correlations drawn between 'objects' of physiological sensory perception and/or oneself. There are no exceptions. All predication is correlation. Not all correlation is predication.

By virtue of drawing the aforementioned correlations, all initial thought/belief formation simultaneously and autonomously presupposes correspondence to fact/reality/events/happenings, attributes meaning, and presupposes the existence of it's own content, regardless of subsequent further qualification(real, imagined, or otherwise).

At conception, the agent is completely void of thought/belief. It doesn't have what all known examples take. This is the only reasonable presupposition to work from if we take care to choose our premisses carefully. Thought/belief is accrued, begins simply, and changes according to the complexity of the specific correlations involved.

Logic and all it's man-made rules consist of quite the complex set of mental correlations. As such it is existentially contingent upon more simple thought/belief formation. Logic is existentially contingent upon thought/belief. Thought/belief presupposes truth and meaning. Logic does as well by virtue of presupposing the truth of it's premisses.

Logic is existentially contingent upon thought/belief formation, not the other way around. Because that is the case, it only makes sense to conclude that the content of thought/belief cannot be adequately accounted for solely in terms of logical form.

Judging Smith's belief by virtue of measuring something that he does not believe is a categorical mistake in judgment.

The self-induced bewitchment of inadequate language use. It's not just Gettier.

I'm gonna be famous.

8-)

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.

The above works from an utterly inadequate, and all too common, (mis)conception of belief. Belief statements are always believed by the speaker. Statements that are always believed by the speaker do not include statements that are not(believed by the speaker). Disjunctions can.

Disjunctions are not belief statements.

During sincere speech acts, when someone is taking about the world and/or themselves, s/he is talking in ways that represent their own belief. One cannot believe a statement that s/he does not think is true. Sincere speech acts do not include statements that are not believed. Disjunctions can.

Disjunctions are neither always sincere speech acts, nor belief statements.

When sensibly talking in terms of belief that 'X', X is always a belief statement. The history of philosophy has held that the value of 'X' can be satisfied by virtue of using a proposition. Propositions include disjunctions. Disjunctions are not belief statements. Propositions are not always belief statements. When sensibly talking in terms of belief that 'X', X cannot be a disjunction.

In order to know that 'X is true', one must believe 'X'. When sensibly talking in terms of knowing that 'X', X cannot be a disjunction.

((p) is true)
((p v q) follows from (p))
((p v q) is true if...(insert belief statement(s) regarding what makes this particular disjunction true))
((p v q) is true because...(insert belief statements corresponding to the above "if"))

The above clearly puts the necessary thought/belief process for believing a disjunction on display for all to see. It reports upon the necessary content within believing a disjunction. Since Gettier's case hinges upon what counts as believing a disjunction, it lands squarely within the applicable bounds/scope of the above solution.

This account is also quite amenable to the common sense groundwork at the top of this post. Gettier's report of Smith's belief is not.

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.

The above works from an utterly inadequate, and all too common, (mis)conception of belief.

Belief statements are always believed by the speaker. Statements that are always believed by the speaker do not include statements that are not(believed by the speaker). Disjunctions can.

Disjunctions are not belief statements.

During sincere speech acts, when someone is talking about the world and/or themselves, s/he is talking in ways that represent their own belief. One cannot believe a statement that s/he does not think is true. Sincere speech acts do not include statements that are not believed. Disjunctions can.

Disjunctions are neither always sincere speech acts, nor belief statements.

When sensibly talking in terms of belief that 'X', X is always a belief statement. The history of philosophy has held that the value of 'X' can be satisfied by virtue of using a proposition. Propositions include disjunctions. Disjunctions are not belief statements. Propositions are not always belief statements. When sensibly talking in terms of belief that 'X', X cannot be a disjunction.

In order to know that 'X is true', one must believe 'X'. When sensibly talking in terms of knowing that 'X', X cannot be a disjunction.

((p) is true)
((p v q) follows from (p))
((p v q) is true if...(insert belief statement(s) regarding what makes this particular disjunction true))
((p v q) is true because...(insert belief statements corresponding to the above "if"))

The above clearly puts the necessary thought/belief process for believing a disjunction on display for all to see. It reports upon the necessary content within believing a disjunction. Since Gettier's case hinges upon what counts as believing a disjunction, it lands squarely within the applicable bounds/scope of the above solution.

This account is also quite amenable to the common sense groundwork at the top of this post. Gettier's report of Smith's belief is not.