How to Derive New Rules in Natural Deduction | Attic Philosophy
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- เผยแพร่เมื่อ 24 ก.ค. 2024
- In this video, I show you how to derive new rules from old ones in natural deduction. This is part of a series of videos introducing the basics of logic. If there’s topics you’d like covered, leave me a comment below!
00:00 intro
00:44 The standard natural deduction rules
01:12 Modus tollens
03:46 Disjunctive syllogism
04:53 Repetition rule
06:26 Double negation elimination
07:27 Redundant rules
07:50 Explosion
08:56 Reductio ad absurdum
10:48 Indirect proof
11:40 Summing up
More on natural deduction:
Proofs in Logic: • How to do Natural Dedu...
Natural Deduction: • How to do Natural Dedu...
Rules for Natural Deduction proofs: • Rules for Natural Dedu...
Natural deduction examples: • Natural Deduction Proo...
Links:
My academic philosophy page: markjago.net
My book What Truth Is: bit.ly/JagoTruth
Most of my publications are available freely here: philpapers.org/s/Mark%20Jago
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Some people have made it so difficult to understand but you are one of few who actual knows how difficult concepts are made up of so many simple concepts.
Thanks, that's great to hear!
I have an exam on this topic in a week)) you are life savior
your videos helped to cover my syllabus in the upcoming exam of mine, thank you
your videos are very helpful. much thanks and respect!
Glad you like them!
You are a living god my lord. all the other philosophy channels on yt are so low quality and with terrible explanations. Somehow you were able to create entire series about logic in a way that made me completely understand it the first time i saw the video. Thank you so much
Thanks very much! For the record, there are other good TH-cam channels too!
@@AtticPhilosophy Do you know anyone who has any videos about number theory, binary relations and graphs?
@@diogopinheiro5337 I don't I'm afraid, but I'm sure they exist somewhere on TH-cam
Can you do more of these where we need to prove disjunctions or some negations? I feel those are the hardest ones to solve.
Please, Can you explain what scope of an assumption means in a layman terms? And what does it mean when we call an assumption "open assumption"?
Think of it like this. Assuming it will rain, I might take an umbrella. But on cancelling (or discharging) the assumption, I might not take an umbrella.
I’m trying to expand the language of predicate logic, and so I need to introduce some new inference rules, but I want to ensure that there are no redundancies. How would I do that?
There's 2 main approaches. A semantic approach is to consider, for each rule R in the system, a model for every axiom/rule except R. If there is one, then R isn't redundant. (So, think of each new non-redundant rule as ruling out some models.) Another approach is to use an automated theorem prover to show there are no derivations of any rule from the others.
Is it the case that Repetition can be proven by IR? If the assumption in line one of the proof is ~A, then that could immediately lead to proof of A by Falsum Introduction.
Yes, or more simply, using conjunction intro & elim. That’s also intuitionistically available.
Any clue on how to derivate material implication (ex: (p > q) to (~p v q); ~(p > q) to (p ^ ~q). I'm struggling to find examples online
Yes - assume the first and prove the second from that. For ~p v q I think you need to use indirect proof, assuming ~(~pvq) then getting a contradiction from those 2 assumptions.
Could you cover first order logic?
Yes, coming very soon! The next logic video - probably next week - will be Intro to First Order Logic
Hey mark could you give us more question about logic proofs?
What sort of thing are you after - like more homework-style logic problems to solve?
@@AtticPhilosophy yes, exactly