How to do Natural Deduction Proofs | Attic Philosophy
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- เผยแพร่เมื่อ 23 ก.ค. 2024
- Natural Deduction might be the simplest way to do proofs in logic. But how does it work? Let's find out!
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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!
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Literally didnt understand this for 5 weeks in uni, and just watching u for 10 mins was enough to complete my whole assignment....THANKYOU SO MUCH
Haha, glad it helped!
I am also in your shoes
Thanks for the video, combined with the Carnap textbook I am using for my philosophy class at college!
Hello from a freshman in California!
I’m approaching the topic of natural deduction proofs at the university. I didn’t know exactly how natural deduction works. But at the time when I came across your video of efforts to throw light on it, I kinda was starting to slowly but surely understand how it works. Thank you so so much. By the way, I subscribed your channel. 😊
Great! - new video coming tomorrow on making natural deduction easier, it might help you out
@Melis Aydin selamm, du hast ja auch paar andere videos kommentiert, drum wollt ich fragen wie’s bis jetzt läuft? passt alles gut, kommst du weiter? 🥹
@@zaetrus1682 Aleykum selam. Ja, bisher klappt es. Danke der Nachfrage. :)
@@mel.o.ayo-61 an welcher uni studierst du denn
This video is incredibly beautiful. Thank you for putting the time and effort to do the subject justice. Instantly made me a fan! God bless!
Thanks!
Wow I didn't expect to finally understand canceling in ND. You even used a different notation of ND than in my lecture (yours is much clearer).
There’s a few different ways to do it, it’s good to try them all & see what works for you. Glad this helped!
Well explained, thank you!
Hi great really helpful video on natural deduction, when will you release one with the natural rules as I'm struggling with it right now. Thanks.
Check back in about ... 12 minutes! Releasing at 2pm.
Great video as always! Any chance you’d be willing to do one about sequent calculi?
Absolutely - planning on a pan intro video in the new year.
Hi love your channel and may I ask a question:
If in set theory, I can create a relation which takes a set of elements which are propositions (like set a is a subset of set b) and map it to a set of elements containing “true” and “false”, then why is it said that set theory itself can’t make truth valuations?
I ask this because somebody told me recently that “set theory cannot make true valuations” Is this because I cannot do what I say above? Or because truth valuations happen via deductive systems and not by say first order set theory ?
Hello Professor, I am not that tech savvy and in this video, you recommend watching the video prior to this one. I noticed that your videos are not numbered. I can not find the video before this one. I did a search "how to proof natural deduction" and I ended up with this one as the starting. Thank you.
My mistake! I think it's this one: th-cam.com/video/CRDC9sVJaR0/w-d-xo.html
Sir ! first I want to thank you about your work, i have a question: what is the purpose of the logic course in an IT engineer student career, many thanks
Thanks! In IT engineering, you might cover logic gates (central to programming circuits), as well as logic in various programming courses. You use logic in most programming languages to combine conditions (with AND or OR), and to give if ... then ... else statements. Getting more advanced, you might look at logic programming languages (languages based on logic, like PROLOG), of functional languages like Haskell (based on type theory, a kind of logic). You might deal with knowledge representation in AI, which often involves using logic-based languages (again, like PROLOG, and its modern variants) .
Maaaaaaate. You're an absolute bloody legend. Cheers from Australia!
You're very welcome!
@@AtticPhilosophy Hello thanks for your videos, do you have a hint for me how to prove ~A↔ B, ~B ↔ C, ~C ↔ A ╞ λ ? I already used the Df rule but I still cannot see how to show that an absurdity follows... Help would be much appreciated... Thank you!
For this one, you can follow Modus Tollens-style reasoning: from A -> B and ~B, infer ~A. (Since MT usually isn't a basic rule, you need to go the long way around: assume A, infer B, contradiction, so ~A.) Given MT, you can reason like this: assume A, infer ~C; from ~C, infer B (MT-style); from B, infer ~A: contradiction. So (having assumed A) infer ~A. Infer B, then ~C, then A: contradiction (from no assumptions). That will be quite a long proof!
@@AtticPhilosophy thank you! That’s how I ended up doing it :D
@@kawaii_hawaii222 Great! Another way is using a different derived rule: from AB to (A&B)v(~A&~B) (i.e., both true or both false). That plus &-elimination quickly gets you to a contradiction.
Heyy really useful stuff. Just one question. Why are assumptions scoped? I mean, if the conclusion made in an inner scope reached to a conclusion that will be used in the outer scope, then might as well the assumption be usable in the outer scope. I'm not saying that "spilling" assumptions to the outer scope feels clean at all (feels like uncontrolled side-effects in programming), but just a thought.
Thanks! It's important to differentiate conclusions based on (in the scope of) assumptions from those that make no (or different) assumptions. Trivial example: assuming p, you can prove p, for any p. But you can't prove p without assumptions! Hope that helps.
@@AtticPhilosophy Yea I thought of this "spilling" of assumptions as just having a "global state", so each nested proof could count not only in its own assumptions but on previous assumptions made by previous inner proofs. Which is a larger version of what you're saying (if I understood correctly). And that's nasty since proofs would be context dependent, but had to ask anyways. Thanks for the (quick) answer!
nicely explained sir
Thanks!
Duuuuuuuddeeee I swear you are a fucking savior. Much love from India
Thanks! Glad it helped out.
Hi! I've always struggled with Natural deduction, vey helpful, for instance how to introduce new premises always feels a bit counterintuitive, and cancelling the premises always confuses me. Could you make a follow up on the rules and more on canceling the premises? anyways awesome video!
Hi! Have a look at the next 2 videos in this playlist, on the Natural Deduction rules and how to use them in some practise examples:
th-cam.com/play/PLwSlKSRwxX0pRuq6FU8DOvnl_v0RsF2VL.html
@@AtticPhilosophy oh! Thank you! Love the chanel btw, immediately subbed
Can you give real world example too?
Sure! Did you have something specific in mind?
What you call "conditional proof" is what Mathematicians (and many logicians) know as "deduction theorem"
They're related but slightly different things. Conditional proof is a proof rule, telling you want to may infer from what. The deduction theorem is actually a meta-theorem of many logics. It says that A proves B iff the conditional A->B is a theorem of that logic.
You proved an axiom jsjs