Think of it like this: Why is Gödel’s attack on ZFC and Peano Arithmetic so powerful...
Gödel’s Incompleteness Theorems are powerful because they revealed inherent limitations USING ONLY first-order logic. He showed that any sufficiently expressive, consistent system cannot prove all truths about arithmetic within itself… but with only numbers.
First-order logic is often seen as more fundamental because it has desirable properties like completeness and compactness, and its semantics are well-understood. In contrast, second-order logic, while more expressive, lacks these properties and relies on stronger assumptions...
According to EN, this is also because second order logic is entirely human made.So what is second-order-logic? The question itself is a question of second-order-logic. If you ask me what first order logic is… The question STILL is a question of second-order-logic.
First order logic are things that are clear as night and day. 1+1, what is x in x+3=4… these type of things.
Think of it like this: Why is Gödel’s attack on ZFC and Peano Arithmetic so powerful...
Gödel’s Incompleteness Theorems are powerful because they revealed inherent limitations USING ONLY first-order logic. He showed that any sufficiently expressive, consistent system cannot prove all truths about arithmetic within itself… but with only numbers.
First-order logic is often seen as more fundamental because it has desirable properties like completeness and compactness, and its semantics are well-understood. In contrast, second-order logic, while more expressive, lacks these properties and relies on stronger assumptions...
According to EN, this is also because second order logic is entirely human made.So what is second-order-logic?
The question itself is a question of second-order-logic.
If you ask me what first order logic is… The question STILL is a question of second-order-logic.
First order logic are things that are clear as night and day. 1+1, what is x in x+3=4… these type of things.