Illustration of where the IS-OUGHT gap really lives
Posted: Thu Feb 20, 2020 1:06 pm
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.
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.