A Crash Course in Formal Logic Pt 7c: Truth Tables for Arguments

[@perlizzel]

How is it that I can learn more from a crash course than a full online course? I don't have words for how grateful I am for your videos. I was for sure going to fail my course...but not any more!!! I get it now!!!! Thank you so much!!!!!

[@stefaniehafen4747]

I was having such a hard time in my online critical thinking class and literally an hour before my midterm, YOU JUST SAVED MY LIFE! The way you explain all of this detail is clear and to the point! I am so grateful I found your videos!

[@PhilHelper]

It's a pleasure to be of service. I hope that I can do the same help for other topics and classes.

[@Commissar]

PhilHelper You should definitely do a series on predicate logic! Thanks for all your help; you've been an indispensable aid!

[@PhilHelper]

Scott Miller I've got some of the predicate logic and other logic stuff prepared. Just doing epistemology first.

[@elghunk]

Scott Miller Agreed! And then Modal logic! Starting to think it is impossible to explain modal logic....at least from the books I have.

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I had to miss a couple lectures and was really worrying working on my homework and suddenly not understanding anything. This cleared up what I was looking for. Thank you so much for taking the time to make this!

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thank you, thank you. I really loved this video. your explanations are amazing!!!

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[@sophiadelogu627]

Best video tutorial on this subject

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[@amychan8233]

at 6:42, you say 5,6, 7 have true premises..how come 3 does not? I have a test on this tomorrow so if you could help clarify this for me that would be so appreciated! thank you!

[@PhilHelper]

Good eyes by you! I'm sorry to reply so late. I'm sure you did well on your test with skills like that! Notice that the argument is still valid on line 3 though. My apologies for not being more careful.

[@WhitbyStuff]

I've watched this on loop twenty times and I simply do not understand how the values for column F⊃~R is worked out. 5:32

[@karinajimenez8265]

me too dude

[@doll2400]

I know this is 3 years old but just in case anyone else comes across your comment, if the antecedent is false, the conclusion is true. But if the antecedent is true and the consequent is false, the conclusion is false. The truth values flip with the negation.

[@mollyoxy]

4:06 mad lad predicting the future

[@elghunk]

I would rather have seen more of the simpler arguments checked by a truth table than that monster in the end. It is rather scary....

[@PhilHelper]

True. I find that when students realize that the steps are all the same as for the simple arguments they can find it far less intimidating. When they beat a couple of "monsters" on their own, they rightly feel confident about anything.

[@jonathanscotti7145]

Your the man!

[@PhilHelper]

Training to be Batman :-)

[@malteeaser101]

How would you put this argument into SL argument? (If that is what it is called). *(I) All tigers are mammals* *(II) Tony is a tiger* *_____________* *Therefore, Tony is a mammal* I thought: *Let P = All tigers are mammals* *Let Q = Tony is a tiger* *Let K = Tony is a mammal* *P* *Q* *________* *K* or *P* *Q* *________* *(P & Q) --> K* I'm a bit confused. I was doing okay until truth tables and arguments. I've checked the truth tables and it says it is invalid. How the hell is that argument invalid? It was an example from this logician on KZbin.

[@PhilHelper]

+Controversy Owl Ah! Nifty example! You can't. Category logic can handle it just by rephrasing the second premise to say "All things identical to Tony are tigers." In order to get SL (as you put it, sentence logic) to handle it, sentence logic has to be expanded into quantified logic. I'll show you how in my next lectures. It's not hard. But it is an advancement on what we have now... To get simple SL to handle it we would have to cheat and rephrase the first premise..."If TONY is a tiger then Tony is a mammal." But the first premise really didn't mention Tony specifically (rather it alluded to him and all other things), so that's kind of a cheat by weakening the information content of the first premise just so that our logic here in SL can cover it. I'll try to remember to use your example when I finish constructing those more advanced lectures. Thanks.

[@malteeaser101]

PhilHelper Yeah, I saw another similar argument and they said the same as you. I thought about it and now I understand. I wrote down this other one and I think it ended up being valid, I'm doing it from memory, though: Let P = All tigers are mammals Let Q = Tony is a tiger Let R= Tony is a mammal P --> Q Q --> R ------- P --> R I actually think there is a special name for that? Like, a 'socratie' or something? (If x then y, if y then z, if z then n, etc. therefore, if x then z, if x then n, etc.) Anyway, thanks. I'm going to definitely subscribe! :)

[@PhilHelper]

The argument is valid, you are correct. Interestingly, in the second formulation of your argument with the conclusion (P&Q)>K you do not even need premises to prove that conclusion. See my video on proving logical truths. Either way, you are correct.

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