9. Logic Lecture: Symbolic Logic 7: Truth Trees

[@jordanzs521]

In ten minutes you explained this much better then my prof did in a hour and a half lecture! thanks so much, this helped me so much for my midterm coming up!

[@mari-bella]

YES SAME!

[@malaika6765]

14 years later and this vid is still saving grades 🙏

[@comadorejeff]

You just make two weeks of lectures make sense in 10 minutes, I can't thank you enough!

[@jessestanley4520]

This is excellent. I've got a midterm later today, and I would not have stood a chance without your work. Thank you kindly.

[@rashaobyat9511]

OMG... Thank you very much.. In 10 minutes you explained what my Prof was not able to teach me... All respect

[@Moze9116899]

I love when someone makes it this easy, Well done sir.

[@21978027737032]

this helped me so much and from 2010!! God bless Dr.Campbell

[@sunjz]

Thank you so much. No words to describe your kindness for making these videos to save lives.

[@atious]

you are really a very clear and efficient teacher. much genuine love for what's posted here.

[@petesorensenguitar]

Thanks for making this video, Jason. I think it would have been even more helpful if you had covered counterexamples and their ramifications, and also the application/purpose of truth tables (to test for validity, consistency/inconsistency of formulas, tautologies, or contradictions). You also forgot to mention that your conclusion was that the set was consistent! The video still helped me with my truth tables.

[@paulwilcox4564]

Thank you. This was a great refresher. I was worried you were going to run out of room there, but you made it!

[@drjasonjcampbell]

@sunjz thanks for the kind words: I'll carry that positive energy with me and work harder! :-)

[@dimitris5594]

You are a living legend, thank you so much

[@mariaBehlouli-cg4jw]

The video is 14 years old, but I benefited from it nonetheless. Thank you for your effort

[@drjasonjcampbell]

@kkallebb Yeah...I think I discussed it in an earlier video. I should have addressed it here again. if every branch closes the argument is valid.

[@gabrielleponceti3793]

A concise explanation of all the rules in one video!

[@ld8162]

Thank you very much. I know only a little english, but I understood mostly of your teaching. Well done!

[@drjasonjcampbell]

@mereshell :-) Thanks for watching.

[@himynameississy]

Thank you Dr. Campbell, this is very interesting and informative stuff and you present it in a very logical and well laid out manner. many of my current profs could learn a thing or two from you. thank you.

[@henryz0r]

Thankyou so much for this. I live in Australia, and they use different symbols for the if and only if, and if A then B. However, that wasn't a problem at all and I could clearly understand what you just said!

[@drjasonjcampbell]

@amjiva I agree that the benefit of the truth tree is the visual ability to see consistency and inconsistency.

[@nnathnn]

Thank you so much! Got an exam coming up and this was really useful :D

[@thepurgatorykids]

Thank you very much for the video-- you broke truth trees down to digestible form for me.

[@rivendell24sa]

I knew it wasn't really that hard, thanks for helping me see the light

[@drjasonjcampbell]

@dannyboy12357 if every branch closes the argument is valid. peace.

[@9jarry995]

Thank You so much dude! it has been way helpful than what is written in my logic book!

[@dailyhealthroutine]

thank you so much this video is so helpful. My books cannot explain thi sbut you did awesome job

[@MrLAduke12]

Great work man.

[@Saxton82]

tilda single arrow is vertical, not split...pre your rule in Lecture 6, Rule #8

[@syed--2023]

finally, an explanation that makes sense.

[@punkfacekilla7224]

Thank you for your video. It has been helpful.

[@Macrophantom]

Great video brother, this helped a lot!!

[@iasontzortzis9472]

Thanks for the amazing video its been very informative

[@TheFolkloreOfLore]

Absolutely GREAT lecture its was very helpful. Thank you! :-)

[@robertfrontino5330]

Super helpful. I hate this class at my university

[@Happen2Bme]

Now I can finish my homework....Thank you very much.

[@petesorensenguitar]

*forgot to list contingencies also since you can test for contingencies with truth-trees just like truth tables.

[@mari-bella]

this was so helpful, thank you so much!

[@izzylacroix4131]

I'm in 8th and our curriculum has college-level logic that makes my brain feel like a fried egg so thanks so much for posting this it really helps

[@drjasonjcampbell]

@drmeatontheface No problem! :-) good luck on the exam!!

[@drjasonjcampbell]

@himynameississy Thanks. Glad to help. Peace.

[@voldymore69]

only difference for my class is how my class symbolizes the iff differently thanks for the help

[@anonymousden]

This is very helpful! Thank you!

[@camilleklemetson7243]

This video was very helpful. Thank you.

[@drjasonjcampbell]

@9jarry995 ...no problem...gotta spread the knowledge...

[@erictobias3244]

Awesome Video

[@NoOneIsHereRightNow]

you are the best , man!

[@wensbane]

Shouldn't we negate the conclusion for this technique? I used another technique and the set is actually invalid since the premises can be true and conclusion false. I assumed that the conclusion is the iff statement.

[@christaflint]

videos 9 and 10 in the series are flip-flopped (9 should be 10 and 10 should be 9). Very helpful though!

[@subhashrawat7321]

Amazing ❤❤

[@kkallebb]

So, based on the truth tree, is the argument valid or not?

[@ProdigalSon222]

really helpful thank you appreciate it a lot!

[@chandulasenevirathna8176]

Thnx this vedio helped me a lot

[@masumabegamkhan4635]

It's really wonderful.

[@harvest_goon]

wonderful

[@niconikko]

I was listening through the flow when 2:34 happened

[@aradlevin4701]

perfect. thank you!

[@dannyboy12357]

so if all branches are closed the set is not valid?

[@saveUyghurs]

WATCH 8, 10 THEN 9!!

[@YoelFievelBenAvram]

If you're on the playlist, it's ordered wrong and you won't understand this. Watch 10 first and then come back to 9.

[@rithikrj3390]

Thank you sir :)

[@lowveykeyalove1]

Thank you!

[@oldboy9267]

did he negate the conclusion first?

[@gwinig11]

this vid helped a lot, good looking out bruh

[@GilinYahwehWizard108]

I thought you always negate the conclusion?

[@ballstoyou15]

Awesome thanks so much man :)

[@saypeachy52]

thank god for u

[@KaleidoArtspace]

hey why havent you taken the conlusion as false ??

[@EBHS230DE]

payal kohli he's checking consistency among statements, not an argument with a conclusion.

[@omfgfear]

akon

[@davidschwartzguitar]

You're very good at presenting this material, but you made a critical error in not negating the conclusion. The argument is actually invalid. If you do a truth table, you'll see that in the case where A is false, B is true, and C is true, you'll get true premises and a false conclusion. By negating the conclusion when doing a tree, you'll get an open branch. It might be a good idea to redo this video to prevent confusion, particularly since you've got a decent number of views.

[@signingsomething8560]

David Schwartz There is no error. He is checking for consistency, not validity. There is no argument to check for validity as there are no premises nor a conclusion, just a set of formulas. He is answering the question "Is this set satisfiable?" not "Is this argument valid?" (Though you're right, when we want to answer the latter we must negate the conclusion.)

[@davidschwartzguitar]

Signing Something Technically speaking, what he presented was indeed an argument; it just didn't have a context. We could fill in the variables with any sentences we want. For example: Bill is not at home (~A) If Bill is not at home, then he is at work (~A-->B) If Bill is at work, then he is in California (B-->C) Bill is either in California, or at home (CvA) Therefore, Bill is at home if and only if he is in California (AC) Right off the bat it should be apparent that this argument is invalid just by using intuition, and by doing a truth table or a proper truth tree (where the conclusion is negated) you can see there is a case where all the premises are true (consistent) and the conclusion is false. Since the presenter did the truth tree incorrectly, his conclusion would be that the argument is valid and inconsistent, which is wrong.

[@signingsomething8801]

David Schwartz Nope, it's not an argument (no matter the context) because there are no premises nor a conclusion. Simply being the last formula in a list or set of formulas does not automatically make the last formula a conclusion and the preceding formulas premises. Its status as a conclusion must be explicitly indicated somehow. This is often done by placing a "/" or "∴" before the formula we take to be the conclusion. (You did this in English with the addition of the word "therefore" on your last line. Take that word out and your list of sentences more closely approximates what we have in this video.) The set brackets he used "{ }" makes it even more clear that all we have is a set (and not an argument.)

[@signingsomething8801]

David Schwartz A quick add: He's answering the question "Can ~A, ~A→B, B→C, CvA, and A↔C all be true at the same? (i.e. is the set {~A, ~A→B, B→C, CvA, A↔C} satisfiable?)" He is not answering the question "Can we deduce A↔C if we are given ~A, ~A→B, B→C, and CvA?" Here's a cool link that I think might help clarify what's going on here: softoption.us/content/node/440

[@stynershiner1854]

It's not an argument. You can make it an argument, but you can make anything....anything. The statements were simply a grouping of different statements which he was checking for consistency.