Thank you for this series, Professor. I am developing a domain-specific proof tree system and I am hoping to prove its soundness and completeness soon.
That’s right, logic is at bottom about good reasoning, which is an essential part of philosophy. Logic in CS tends to focus on more practical aspects, like computability, decidability and computational complexity. Also there’s interesting theoretical links between proofs & programs, as in the Curry-Howard isomorphism.
Proof by contradiction is a different proof strategy to proof by induction, but they’re often combined. Completeness is usually proved by contraposition, showing that unprovable arguments have counter-models.
Are you interested in taking philosophy further? If so, ask your lecturers about PhD study. If not, think about what kind of work makes you most happy, and then look for careers that involve that kind of thing. If you're still at uni, talk to the careers service.
Thank you for this series, Professor. I am developing a domain-specific proof tree system and I am hoping to prove its soundness and completeness soon.
Good luck!
Got a question? Leave me a comment below!
interesting that you teach philosophy. Do proof trees extend to philosophy aswell bc we were taught logic as part of computer science?
That’s right, logic is at bottom about good reasoning, which is an essential part of philosophy. Logic in CS tends to focus on more practical aspects, like computability, decidability and computational complexity. Also there’s interesting theoretical links between proofs & programs, as in the Curry-Howard isomorphism.
Would contradiction be a viable method of induction to prove soundness and completeness?
Proof by contradiction is a different proof strategy to proof by induction, but they’re often combined. Completeness is usually proved by contraposition, showing that unprovable arguments have counter-models.
Lovely vid!
(+ with what app do you write on? thanks!)
Thanks! The writing in the videos? That’s on Goodnotes on the ipad
@@AtticPhilosophy thanks! The background pic is really nice to read the writings :)
4:30 I thought contrapositives weren't equivalent in intuitionist logic, am I wrong about that?
That’s right - you can go from A->B to ~B->~A but not vice versa.
What to opt after ma. Philosophy with 60% aggregate ? Plz suggest.
Are you interested in taking philosophy further? If so, ask your lecturers about PhD study. If not, think about what kind of work makes you most happy, and then look for careers that involve that kind of thing. If you're still at uni, talk to the careers service.
lovely video, but please try to look at the camera
Thanks!
You really should ditch those horrible intros and outros