The disjunction AvB is either an "is" statement or an "ought" statement. — Nicholas Ferreira

Why do you want to say this? It seems obviously false, as you have just declared it to be both. There is little point in this logical trick, even if it 'works'. It says nothing about the status of ethics, and Hume's point stands, that what is and what ought to be are separate domains.

I declared it to be both? I just said that AvB can be an "is" statement or an "ought" statement, then I showed an argument to be considered in each case. I assume here that i don't know what is the nature of "AvB" (if it's an "is" or "ought" statement), but I give an argument to each possibility. Actually, this isn't mine, but it's Russell's argument.
I don't know why this doesn't hit Hume's point, as it clearly shows that it's possible to derive an "ought" from an "is" statement.
Furthermore, if we can't make this derivation because they are from separate domains, different "kingdoms" of statements, then we couldn't derive "is" statements from "ought" statements too. But this argument shows that we actually can:

• 1. John ought to go to school
• 2. Kids and only kids ought to go to school
• 3. Therefore, John is a kid.

Is this wrong?
Thanks for answering!

The domains are connected by statements that declare what ought to be. The connection once made, logic can do its thing; it is in making the connection that neither logic nor being can get a foothold.

The is-ought problem seems to be a claim that the normative can't be deduced from the descriptive. The mistake is elucidated by claims such as:

Killing is a natural behavior. Therefore, we ought to kill.

However, the is-ought problem is not all encompassing error in my opinion. For example the following reasoning from an is to an ought isn't fallacious:

We like to be happy and not suffer. Therefore, we ought to make people happy and not let them suffer

Hume believed in hypothetical norms.

I don't know if I got it. Why isn't your example fallacious? I mean, why from "We like to be happy and not suffer" you can deduce "We ought to make people happy [...]"?

A := some "is" statement;
B := some "ought" statement;
The disjunction AvB is either an "is" statement or an "ought" statement. — Nicholas Ferreira

Asserting the disjunction itself would be to assert an "is" statement. It says that it is true that either A is true or B is true. And unless both A and B are false, then the statement is true.

If (AvB) is an "is" statement, then consider this:
1. (AvB) ["is" statement]
2. ¬A ["is" statement]
2. ∴ B (1,2, disjunctive syllogism) ["ought" statement] — Nicholas Ferreira

The form is valid. But can "ought" statements rightly be used in this way to begin with? Some people do not think that they're sufficiently like "is" statements. Some people think that they're not truth-apt.

Furthermore, if we can't make this derivation because they are from separate domains, different "kingdoms" of statements, then we couldn't derive "is" statements from "ought" statements too. But this argument shows that we actually can:
1. John ought to go to school
2. Kids and only kids ought to go to school
3. Therefore, John is a kid.
Is this wrong? — Nicholas Ferreira

It doesn't seem wrong, but it could be deceptive. I'm not sure. But for that reason alone, I'd say that it's a good argument. It's challenging.

I consider the fallacy active only when it attempts to maintain a status quo, as in my example of killing being natural behavior. Why? Because morality is exactly about the opposite - what the world ought to be which is NOT the way the world is.

However, morality must be grounded in something i.e. it has a basis from where our oughts originate. Isn't our desire for happiness and avoidance of suffering such a foundation? It is and from it all our oughts follow.

If (AvB) is an "is" statement, then consider this:
1. (AvB) ["is" statement]
2. ¬A ["is" statement]
2. ∴ B (1,2, disjunctive syllogism) ["ought" statement] — Nicholas Ferreira

I don't think your conclusion from 2 is valid. B would take the form "This is an ought statement" and that is an "is" statement.

Else, if (AvB) is an "ought" statement, then consider this:
1. A ["is" statement]
2. AvB (1, add.) ["ought" statement] — Nicholas Ferreira

For the same reason as above, AvB is an "is" statement.

Furthermore, if we can't make this derivation because they are from separate domains, different "kingdoms" of statements, then we couldn't derive "is" statements from "ought" statements too. But this argument shows that we actually can:
1. John ought to go to school
2. Kids and only kids ought to go to school
3. Therefore, John is a kid.
Is this wrong? — Nicholas Ferreira

I don't think the "is" and "ought" statements are different kingdoms when used within the context of formal logic. It's just that you cannot deduce an "ought" from an "is" because the "is" statement contains no "ought" information to uncover.

This is not necessarily true in reverse, since an ought statement presupposes a current state of affairs and therefore includes "is" information.

That said, I feel like you conclusion should be restated as John "must be" a kid.

Asserting the disjunction itself would be to assert an "is" statement. It says that it is true that either A is true or B is true. And unless both A and B are false, then the statement is true. — S

"you ought to realise this is ridiculous" is true.
Therefore, you ought to realise this is ridiculous.

But Hume never made the claim as it is attributed anyway. The way he put it is more so that if 'ought' does not appear in any premises, but appears in the conclusion, then the deduction is invalid, which is true for any term. Unsurprisingly, if one defines 'is' statements so as to include 'oughts', then his supposed law can have all the exceptions you like.

Hume famously closes the section of the Treatise that argues against moral rationalism by observing that other systems of moral philosophy, proceeding in the ordinary way of reasoning, at some point make an unremarked transition from premises whose parts are linked only by “is” to conclusions whose parts are linked by “ought” (expressing a new relation) — a deduction that seems to Hume “altogether inconceivable” (T3.1.1.27). Attention to this transition would “subvert all the vulgar systems of morality, and let us see, that the distinction of vice and virtue is not founded merely on the relations of objects, nor is perceiv’d by reason” (ibid.).

https://plato.stanford.edu/entries/hume-moral/#io

1. (AvB) ["is" statement]
2. ¬A ["is" statement]
3. ∴ B (1,2, disjunctive syllogism) ["ought" statement] — Nicholas Ferreira

Doesn't work for a couple different reasons.

First, ought statements are not true or false. They're not actually statements (in the sense usually used in philosophical logic, since statements are sentences that are true or false).

"AvB" is only an "is" statement if we parse it as "It is the case that either A is true or B is true."

Next you posit that A is false. Well, then AvB is false, because B has no truth value. (AvB is only true if either A or B are true.)

If you try to parse AvB as an "ought" expression (which makes little sense, really, but we could pretend that it does), then it has no truth value.

he disjunction AvB is either an "is" statement or an "ought" statement. — Nicholas Ferreira

Like @unenlightened said, there is no reason to accept this.

"It is raining outside or I should have bought some milk."

Is this an "is" statement or an "ought" statement?

I think it's just a nonsense statement.