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Crazy shit man. You gave me the why. All other teachers think i dont want to know the why.

27:21 Correction: Proof theory is a major branch of mathematical logic, which in contrast to model theory is not semantic but syntactic in nature. You shouldn't call a deductive system that. But the syntactic aspects of those systems are researched in the field of proof theory.

Thank you for explaining this better than my teacher

Absolute lifesaver !

COME BACK BROTHER!

only video i could find that i properly understood.

Are you gonna make any more videos by any chance?

I am stuck for Hilbret-style proof and looking where I lost. I can say your approach is a good one.

3 years later people still benefit from your efforts, thank a lot dude.

Hey love your channel and wish you would keep going!!!!! May I pose a few questions kind soul: Hey so here are the “soft” questions I have compiled. If anything is unclear just let me know! 1) Does naive set theory require attaching a logic to it to “work” or does logic require set theory to “work”? I am having trouble understanding the true nature of their relationship and they seem really connected during this first pass through some TH-cam videos. 2) With just naive set theory - no first order logic - can we make truth valuations? Can we even do anything at all in set theory without logic? 3) why is “first order logic” “fully axiomatizable”, but “independence-friendly first order logic” and “second order logic” isn’t? 4) Does this mean we can’t trust “independence-friendly first order set theory” and “second order logic” to always make true statements? If not, what consequences does it have if a logic isn’t fully axiomatizable? Thanks so much!

Hey 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 ?

woooow. I really had difficulty in understanding completeness and soundness and this video really helped me

Truly, you slayed this topic, i was struggling with natural deduction! underrated king! yaas

Very helpful vedio , thanks

Is the property of expressing arithmetic effectively (recursive computability of arithmetic) the same as expressive completeness?

Is this an alternative to fitch style?

Great vid, sad u got only 4k views , Your explanation could get you great returns if u aproach more common topics

Just brilliant, thank you.

THANK YOU

omg thank you!! your video really clarified everything I was confused with....

Can you give the example of logic in semantics that its not logic but make it then logical

Good work

Great video! I didn't understand the difference between the two types of turn tiles and soundness and completeness, u explained it so well.

I had a course that included proving some theorems using Coq and I really felt stupid. This series is a life saver, thank you very much and hope you're doing great!

very good

Astonishing, thanks so much for the summary.

I love the video style!

Thanks for your lecture. I have a question regarding soundness and completeness. When you say a logic must have the "soundness" property...but as far as I can see, it is not a property of the logic, but the deduction system. Would you mind elaborating more, please?

You're a life saver, thank you so much for this!

There are not so many videos on this subject, so I'm glad I stumbled upon this great vid. Thanks!

Hello Patrick, I found your videos so deep, clear and useful. It helps me a lot to learn about logic. Thank you

That's some great work you've done. Keep up:)

Thanks for this video! I'm doing a Masters in Cognitive Science and this helped me. You explain things very clearly.

I had no idea I was dealing with "vacously true" statements in the conditional truth tables. The "If-Then" are quite mysterious in its functioning in mathematics. In english, it hints at causality; In theorems, it hints at the truth of statement B holding; In Logic, it is truth-functional operation whose truth value is only on the truth of its parts, which is quite like transistors working. This video must be rewatched. Let's hope I can clear up what I see the next time I see an "If-Then" statement

Hi Patrick. I admire that you have taken the initiative to make these videos. I was overwhelmed emotionally in comparison to my small understanding of what "logic" is, which made me give more attention to you and felt great to have absorbed your insights. I would be continuing to the next lesson on Semantics for today. I am currently in my MSc. Mathematics program at Amrita Vishwa Vidyapeetham Coimbatore, and working on building my fundamentals. I see your last video was 7months ago; hope you can restart making videos again; its okay for me that you make a video every 2-3 weeks, because you rightly found out that some "core parts" of this subject can be take for granted elsewhere or not even looked at, which I feel is a crime against education, to withhold deep insights that can have an expansive impact on somebody else. Thank you for this video, once again though.

Excellent video - really enjoyed your style of expositing. If you get the time, please make some more detailed videos of proofs of completeness and soundness for propositional logic and maybe predicate logic. Perhaps you could make some videos on modal and other logics too? Bravo.

This was really helpful, thank you!

Hi Patrick

I think you will find that this can be done in Haskell using Monads