Post by Eugene 2.0 on Nov 21, 2020 13:09:44 GMT
One of Wittgenstein's logical reasoning that has its analogy in symbolic logic is the next one:
True judgement is implied by anything :: (x)(y)(Tx→.Ay→Tx)
Proof for a certain tautology:
p1) Tx :: Pa→Pa (axiom)
p2) (y)(Pa→Pa.→.Ay→.Pa→Pa )
p3) Pa→Pa.→.Ay→.Pa→Pa (UI)
p4) Ay→.Pa→Pa
C) Ay→.Pa→Pa
If each tautology is implied from anything, then either they're technical, or they don't play any role outside the logic.
I wonder what logic cannot imply true judgement or true statements?
On one hand, denying a formal system that can imply truth we could have the one ~ but, we would have a system that cannot impy the truth, but it would not be a system anymore...:
p1) ~(x – is a system.&.x – is what can imply truth)
p2) ~(x – is a system) v ~(x – is what can imply truth)
...on the other hand, we could use replication (="←" instead of "→") ~ then we would have no cause–reason analogy.
There is a question appears then: can we call logical a (formal) system that cannot imply truth?
True judgement is implied by anything :: (x)(y)(Tx→.Ay→Tx)
Proof for a certain tautology:
p1) Tx :: Pa→Pa (axiom)
p2) (y)(Pa→Pa.→.Ay→.Pa→Pa )
p3) Pa→Pa.→.Ay→.Pa→Pa (UI)
p4) Ay→.Pa→Pa
C) Ay→.Pa→Pa
If each tautology is implied from anything, then either they're technical, or they don't play any role outside the logic.
I wonder what logic cannot imply true judgement or true statements?
On one hand, denying a formal system that can imply truth we could have the one ~ but, we would have a system that cannot impy the truth, but it would not be a system anymore...:
p1) ~(x – is a system.&.x – is what can imply truth)
p2) ~(x – is a system) v ~(x – is what can imply truth)
...on the other hand, we could use replication (="←" instead of "→") ~ then we would have no cause–reason analogy.
There is a question appears then: can we call logical a (formal) system that cannot imply truth?