- 84
- 205 400
Lassonde Student
เข้าร่วมเมื่อ 13 มิ.ย. 2015
วีดีโอ
8.2 Soundness and Completeness in Predicate Logic
มุมมอง 9K8 ปีที่แล้ว
8.2 Soundness and Completeness in Predicate Logic
8.1 Examples of Interpretations of Formulae
มุมมอง 2.3K8 ปีที่แล้ว
8.1 Examples of Interpretations of Formulae
6.4 Continued
มุมมอง 1.5K8 ปีที่แล้ว
Table of Contents: 00:01 - Important Tools 00:31 - Examples 01:26 -
6.4 Alternate Equational Proof
มุมมอง 2.6K8 ปีที่แล้ว
Table of Contents: 04:21 - Example 05:56 - Important Tools 05:57 - Example
Introduction to Proofs in Predicate Logic
มุมมอง 2.6K8 ปีที่แล้ว
Introduction to Proofs in Predicate Logic
4.2 Axioms, Rules of Inference and Proofs in Predicate Logic
มุมมอง 6K8 ปีที่แล้ว
4.2 Axioms, Rules of Inference and Proofs in Predicate Logic
2.2-2.4 Introduction to Equational Proof
มุมมอง 4.2K8 ปีที่แล้ว
2.2-2.4 Introduction to Equational Proof
2.2-2.4 - Framework for Equational Style Proof
มุมมอง 4.3K8 ปีที่แล้ว
2.2-2.4 - Framework for Equational Style Proof
1.4 Rules of Inference and Theorem Calculation
มุมมอง 3.8K8 ปีที่แล้ว
1.4 Rules of Inference and Theorem Calculation
this seems very complicated
Thanking you after 9 years lol
I have a question in the length of a string segment. Since it was l(wx), we added 1. If it was l(wxy), since there are 2 elements that have been added to w, would the length become l(w)+2?
seems like the video overcomplicated it much like most videos out there.
How does one prove meta-theorems? Or do we just assume them to be true? Or are there meta-axioms and a meta-deduction system from which they are proved? In this video and in all mathematical logic books I've read, it seems that meta-theorems are "proved" by providing informal arguments in the natural language in an attempt to convince the reader, but shouldn't convincing and proving be two separate different things?
Umm, could you please explain the rest for people who cannot attend your class? This has over 5000 views at the time of commenting.
Great, now back to the kitchen
Noice.
May I ask a question: In Propositional and Predicate logic, what is the difference between a “structure” “interpretation” “model” “semantics” and “theory”?
saved my ds quiz thanks<3
This is not making it easier 😩😰😰
Trust the process!
it was helpful, thank you.
What is the textbook your following? Thanks
George Tourlakis Textbook
Hold on, why is a state by definition an infinite table as you say?
Because there are infinitely many possible variables. Example, p, q, r, s, p', q', r', s', p'', q'' .............
Hmm yeah the empty set proves all valid formulas, indeed that's like an important thing to grasp.. :) thanks :)
OMG! Thank you!
Wonderful video! Thank you for taking the time to make this video
Wait, what? "Mathematical truths are tautological truths"? How is 23 + 4 = 27 (a mathematical truth) a tautology? It's not true solely in virtue of its logical form... It might be a necessary truth, but how is it a tautology?!
Hey, would you say that it is ‘analytically valid’? I’m new to this terminology.
Some philosophers argue that mathematical truths are analytic, but this of course depends on what one means by "analytic" (which is often not clear). However, I believe that most philosophers do not think mathematics is analytic anymore, and accept that mathematics is what's called "synthetic a priori". Part of this has to do with the failure of the logicist program and how formalism in the philosophy of mathematics was falsified by Godel's Incompleteness Theorem. See this super short paper: Irving M. Copi The Journal of Philosophy, Vol. 46, No. 8 (Apr. 14, 1949), pp. 243-245
Just because something is what you call "true" does not mean it is a tautology. That is the point made by Veritas. 23 + 4 = 27 is a logical necessity, but it is not a tautology. On another note, this video was poorly put together and demonstrated that the majority of teachers in logic classes are mere bookworms who have done so much memorizing of terms and have made no real-life connections to the material they digest. They regurgitate their "knowledge" to students and have the utmost difficulty in helping them understand what everything means. I have never seen so many memorizers. PATHETIC.
@@onixz100 I can only find that paper at jstor and I can't afford to have acess to it, do you know another place where i can find it? I would be immensely grateful to you.
Is the set of universally valid formulas identical to the set of necessary truths? For example, "Necessarily, nothing is both red and blue all over." Would that be a logically valid?
No
No. Logical validity is formal. "It is not the case that there exists an x such that x is F and x is not-F" is a logical necessity, because the predicate 'is F' and the predicate 'is not-F' are *logically* contradictory. But "it is not the case that there exists an x such that x is B-all-over and x is R-all-over" is not a *logical* necessity, because the predicate 'B-all-over' and the predicate 'R-all-over' are not *logically* contradictory. That something cannot be blue-all-over and red-all-over is a *metaphysical* impossibility, but not a logical impossibility. To make the metaphysical impossibility into a logical impossibility, you would need a meaning postulate to the effect that "B-all-over" and "R-all-over" are incompatible.
No. That all bachelors are males is not valid/logically true, as there are some interpretations of the predicates ...is a bachelor and ...is a male in which some value of a variable, say x, is both an element of the set of bachelors but is *not* in the set of males. Ergo, there are some sentences that are necessarily true but not logically true. However, in my opinion, the converse holds.
your awesome teacher . i like your video .i need your help .i am stuck can you please help me in this question : Distinguish each of the following axioms as either Peano arithmetic or Presburger arithmetic with proper reason. 1. a×b (a + b) = (a×b) 2. a+ 1 = b + 1 → a = b please if its possible answer me within in one hour . kindly i am waiting for reply
Are you still waiting
@@AR-rg2en no ...... Thanks for reply after 4 years😊
@@learnwithsid2044 np
Bro has probably graduated now lol
did you figure it out bud
wouldn't ir be easier to not use 'Gamma u {A}', but instead {a1, ... ,a_n}? That way you would not need the operation and the statement would be easier to follow?
Not helpful
This was not helpful at all. Sad!
thanks, very clear!
thanks
very helpful! thanks
lol who's snoring in the background?
cant blame them
don't read news...try teaching us something...