Natural Deduction for Quantifiers | Attic Philosophy
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- เผยแพร่เมื่อ 5 ก.ค. 2024
- In this tutorial video, we look at how to use the rules for quantifiers First-Order Natural Deduction. We'll go over examples in the next video: • Natural Deduction for ...
00:00 - Intro
00:33 - Recap
01:11 - Rules for PL
01:52 - Universal elimination
03:17 - Existential introduction
05:54 - Universal introduction
12:08 - Existential elimination
16:15 - Wrap up
Related videos:
Proofs in Logic • Proofs in Symbolic Log...
How to do Natural Deduction Proofs • How to do Natural Dedu...
Rules for Natural Deduction • Rules for Natural Dedu...
How to use Quantifiers • How to use Quantifiers...
If there’s a topic you’d like to see covered, leave me a comment below!
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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This is an EXCELLENT explanation of the Universal and Existential rules. THANK YOU for the clarity in your explanations!
Thanks!
thanks a lot I couldn't understand this from my textbook but it makes more sense now after watching your video
That's a win!
I am in college taking a Logic course. This video is very helpful and I’m immensely thankful for the work you do.
Glad you found it helpful! Good luck in the course.
Very straightforward. Great production!
Thanks! That's the aim.
Sooooooo bloody helpful
THANK YOU FROM THE BOTTOM OF MY HEART
Amazing channel! I’m in the middle of (re-)learning formal logic from the get-go and your videos are a major help, so thanks! :D
Greetings from Germany and keep up the great work :-)
Hi! Glad it's helping. Coming up soon: modal logic!
Absolutely! I've never seen such a powerful and along with it simple explanation. Literally, these videos could make my progress in FOL much much more quickly.
Insanely good video, tysm
Thanks!
Your explanation is FASCINATING! I am so grateful for you!
P. S. How are you? Why did you stop posting lectures? They are so amazing!
I wish you are okay. Thank you.
Thank you! I'm good thanks. I still post videos once a week, every Saturday, but not always on logic. I'm trying to cover broad philosophical topics as well as technical stuff on logic.
@@AtticPhilosophy Wish you all the best of the best! Among many other tutors - I am deadly serious - your channel is one of the most 100% hit about philosophy&logic.
I wish I had a tutor like you when I was studying phlosophy!..
Good luck! 💙💛
Could you please tell me where to find a video about pre-normal form?
Do you mean prenex normal form? That's when all the quantifiers appear that the front of a first-order sentence (or at the top of the syntax tree). I don't have one on this channel yet, but I'm sure you can find one by Googling!
Do we assume existentional import during Universal Elimination? Or do we perform it only when we know that the domain is NOT empty?
The domain is never empty, so we can always use universal Elim.
Hi Prof Jago. Does the deduction Px therefore ∃x Px count as an existential introduction?
Yes, that's it, so long as your system counts open sentences (like Px) as sentences capable of truth-values (under an assignment to variables). Under any assignment of an object to 'x', if it's P, then something is P, so Px entails ∃x Px.
@@AtticPhilosophy Thank you. Yeah, I noticed that ∃x Px can be thought of a concise way to write down Pe1 ∨ Pe2 ∨ Pe3... and so on, where the e1, e2, e3... are elements of the domain. Without the quantifiers, the formulas would be colossal. The universal quantifier is similar, but it uses conjunctions instead.
Right. This area has always been edgy but now it seems clear. "So let's imagine a bachelor, any bachelor. It turns out that he is unmarried." That's no surprise, because the element is predefined "in the argument" to have that property. But since I am not predefining the class membership of an ARBITRARY element BY definition, I am using only other information in the same universe of argument (arbitrary except for rules and assumptions), and obtaining the result of class membership "ex post facto", or a posteriori, out of the elements of the argument already in existence. It's parallel to propositional logic when making an assumption for conditional proof. The assumption of the antecedent IS the arbitrary factor there. Here, though, the assumption of a bare entity that represents "any" entity of the postulated member class, and then is demonstrated by no particular element already in existence (whose support is already not arbitrary since already given), simply cannot be any particular entity. In the universe of argument, that is any already-named entity.
On another tack, we are essentially interested in proving a negative at this point. No number of supporting instances will be enough unless it exhausts them all. When saying that all entities in class A are in class B, we are really saying there is no element in class A that is not in class B (if it's not in B, it's not in A). Every male is merely "on the cusp", definitionally, of being a bachelor. When I know, among an arbitrary group of males, that I can pick any male and confirm that he is unmarried, then of course that's just like saying they all are unmarried. It is the same level of certainty that closes the gap between counting all but one and finding out their status by counting all of them. If I create a "dummy" instance and I get the same result, I've really related two classes, and not just two members of two classes. I've in essence proven that if I were to pick any member of class A (is male) then I would have picked some member of class B (is unmarried).
But that is on par with defining a Bachelor to begin with. So really, we are saying that if some arbitrarily selected domain of elements meets a definition, then that domain acts as a perfect model of that definition. And therefore, in the universe of argument which includes that domain of elements, we can say that definition holds true and we can formally state it. It's the same as implication introduction but simply quantified in its details "atomically".
best stuff ever found