What is Entailment? | Symbolic Logic Tutorial | Attic Philosophy
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- เผยแพร่เมื่อ 5 ก.ค. 2024
- Entailment is one of the key concepts in all of logic. A good argument is one where the premises entail the conclusion, so if we can understand entailment, we'll have a good handle on what makes an argument good or bad.
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!
The series so far:
What is Logic? • What is Logic? | Symbo...
Intro to Propositional Logic • Propositional Logic | ...
Truth Tables • How to use Truth Table...
Entailment [this video!]
Equivalence [coming soon!]
Rewriting and Normal Forms [coming soon!]
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
Get in touch on Social media!
Instagram: / atticphilosophy
Twitter: / philosophyattic
#logic #philosophy #entailment
Your lessons are so helpful! I'm doing a logic course in university at the moment and you're a huge help. The lessons are always so clearly laid out and very easy to understand.
An underrated philosophy channel! Keep it up, thanks so much.
That's great to hear! I know how stressful logic courses can be at uni, so glad this has helped.
Hi! Your videos are so helpful. Keep up!
Thank you so much for this video, ive been so lost with entailment but now it makes sense!!!
Fantastic, glad it helped!
Very well explained.
AMAZING LESSONS!!!! CONGRATULATIONS!
Thanks!
20:14 my respect for you has increased so much , You have cleared my confusion 😭
Thanks! Glad it helped.
@@AtticPhilosophy There's one question , Deductive argument goes from general to specific and inductive argument from specific to general ... But will this always be the case?
finally I found a video that explains it perfectly. thank you for the video :)
Thanks!
Thank you
Great lesson. Thanks
Thanks!
the logic course we've all been missing. one emphasis i added for myself was that entailments rely on the validation of All propositions involved. like "premises entail conclusions" is contingent not only on specific premises, but also specific conclusions, which somehow felt unobvious after discarding the function(argument) notation in favor of "p entails c". i'm sure this is clear for many, but i felt a need to highlight this. thanks for having this exceptional course going! ps. i also wondered how "truism" relates to "tautology, logical truth and valid sentence". i assume it's just a term for their application in rhetoric.
my use of the word "conclusions" remained contentious even above. they were meant to denote separately evaluated premises, not conclusions implied by the other premises as conditions. my point instead was just that they need to share a same axiology. the disambiguation at the end of the video is a sticky one.
Thanks! I think 'truism' means something commonly understood to be true, like 'politicians lie', rather than anything to do with logic.
Thanks , keep up the great work
Thanks! I’ll try.
I have the same issue with you as I have with Agatha Christy. After I have finished one of her books I'm lost wondering which book to read next. Take your series on logic. I never did the subject at school so now in the autumnal glow of my late eighties I decided to give it a go. You have made it interesting and I'm bound to benefit largely but could you please put the videos in some sort of chronological order, please. I'd appreciate a list of titles that I could methodically work through from the start to the final video. NB Agatha presents the same problem but she isn't with us right now.
I'm looking to put some 'courses' together - guided playlists, eg, Logic 101, with videos following a (mostly) coherent progression. Bear with me!
That's the one! Much easy to understand. Why they make everything so confusing when it's barely even explained...
Thanks!
Would an objection (counterexample) towards “A → B iff A ⊨ B” be something like: “If a large dog is a dog then red is a color”?
Thanks for the suggestion! 'Red is a colour' isn't a logical truth, so in this case, A->B isn't valid and A doesn't entail B.
19:20 Okay so you’re telling me that this channel is named after the fact that he gives lectures from an attic and not from the region in Greece?
Didn’t know!
It's a terrible pun, I know ...
you are awesome
Thanks, I try!
How can I contact you for business enquiries
DM me on Twitter (@ in the description)
So "Entailment" to "=>" is what "Triple=" is to "".
Yes: A -> B is valid iff A entails B, and A B is valid iff A is equivalent to B.
What is about A ⇔ B |= A ∨ B.
In this one value of truth of AB is true but it is false for A ∨ B.
So what is the result
That’s not a valid entailment, AB allows both A,B to be false, but then AvB isn’t true.
i feel like i now have a better idea of what ⊧ is, but what about A⊧B vs A⊢B?
(sorry for abusing of your time but may i add the difference between the previous and A⊩B to this question?)
⊧ is semantic entailment: (in every valuation/model) if A is true, then B is true. ⊢ is about proof: B can be proved/derived from A. These are standard symbols with fixed meanings. ⊩ is sometimes used to speak about a sentence being true relative to a possible world, state, situation or whatever: s ⊩ A means that A is true relative to (world/state/situation) s. (Some people also use ⊧ for this.)