Illustration of where the IS-OUGHT gap really lives

[Skepdick]

Logic (natural deduction) consists of to sets of rules.

Introduction rules: they introduce the terms that we are going to use
Elimination rules: they introduce the operations we are allowed to perform on our terms

Introduction: A B
Conjunction: A & B
Entailment: A, B ⊢ A & B

This is not the notation most logicians use. Most logicians use the Sylogism.

A B
-------
A & B

But there-in lies the crux.

A B <---- A is true, B is true.
------- <----- IS OUGHT GAP
A & B <-----A & B ought to be true.

But this is a non-sequitur. A and B need not be related in any meaningful way!
The AND-operator is a logical imperative. ALL operators are verbs - actions. Commands.

The logical operator ⊢ (entailment) defies the is-ought gap. Entailment is imperative, not declarative.

"Logic is imperative" is an IS statement.
"Logic is declarative" is an OUGHT statement. It's a value.

Philosophy has been doing it backwards all this time.

[Eodnhoj7]

Logic (natural deduction) consists of to sets of rules.

Introduction rules: they introduce the terms that we are going to use
Elimination rules: they introduce the operations we are allowed to perform on our terms

Introduction: A B
Conjunction: A & B
Entailment: A, B ⊢ A & B

This is not the notation most logicians use. Most logicians use the Sylogism.

A B
-------
A & B

But there-in lies the crux.

A B <---- A is true, B is true.
------- <----- IS OUGHT GAP
A & B <-----A & B ought to be true.

But this is a non-sequitur. A and B need not be related in any meaningful way!
The AND-operator is a logical imperative. ALL operators are verbs - actions. Commands.

The logical operator ⊢ (entailment) defies the is-ought gap. Entailment is imperative, not declarative.

"Logic is imperative" is an IS statement.
"Logic is declarative" is an OUGHT statement. It's a value.

Philosophy has been doing it backwards all this time.

The is/ought gap of logic is tautology declaration nothing more. What is derived from any ought statement is a definition of possibility. Logic cannot go beyond definition by nature.