Does anyone feel like these kind of mental gymnastics are like equations? In that case, I'm not a fan of this kind of math lol. All I can deduce this is into is just standard sentences: Anyone who eats expired food--> gets sick. I ate expired food. Therefore, I get sick.
If the subscript is messing some people up, in my mind, writing out the contrapositive statement is really helpful. At the end of the day, we can only move from the left side of the arrow to the right. If we diagram that out clearly, I think it is difficult to go wrong
I remember taking a logic class in college and we used the negation symbol as this ~ and not the slash/. I think the slash is throwing me off in these lessons a little bit. Either way I am realizing that logic class actually helped me a lot.
At first I felt like some of these videos are super repetitive. Now I see that I never would have understood that if Luke is a Jedi and Jedi use the force that Luke uses the force.
Contradictorily
If Luke cannot use the force and Jedi use the force. Luke is not a Jedi.
so basically the form of the argument takes precedent over whether the argument is true or not (valid) to the real world. if the form of the argument is the same, the argument must be thought of as true. (right?)
@VenessaO77 It might be my lack of sleep and food, but what does "though of as true" mean? Other than that, I think you're correct. Determining the form of the argument is the most important thing when you're figuring out how to tackle it. If the argument states "All bears are pink. Luna is a bear, therefore she is pink" the argument is valid, just not true.
@Narmis The argument isn't valid in your example because being tall isn't necessary for being good at baseball (at least not according to your premise). So while knowing someone is tall is sufficient to know they play baseball, knowing someone plays baseball is not sufficient to know they are tall.
Instead, it would be
T ---> B (if one is tall, they must be good at baseball)
I dont really understand how we got Athena like where dod we just pull that out of and how is that in the slightest way related to proving the argument
It is just an example of the contrapositive. See the notes: If one is a Jedi, then one is a Force user. Athena is not a Force user. Therefore, Athena is not a Jedi.
"In the first argument, premise 2 identifies a member, Athena, and says that she fails the necessary condition, i.e., she doesn't use the Force, placing her outside the superset. The conclusion follows that therefore Athena must also fail the sufficient condition, i.e., she must be outside the subset and not be a Jedi"
Athena "exists" purely for the sake of argument: to satisfy-- or in this case, fail-- the necessary condition.
In a conditional argument, the purpose of the first premise in a syllogism is to establish a subset/superset relationship ("If one is a Jedi, then one is a force user").
The second premise dictates whether a particular person (or thing) is a member of the subset established by the first premise.
Athena doesn't necessarily have to exist "in real life" (if that is what you are asking)-- she exists within an isolated context, which is the syllogism itself. The key is to think very narrowly about what is being defined. Athena doesn't have to "come from" anywhere, she is just being used to prove (or disprove) membership in a given superset.
Take this classic syllogism for example:
All men are mortal
Socrates is a man
Therefore, Socrates is mortal
The second premise is telling us that Socrates is a member of the superset [mortal things]. From that premise, we can reasonably (and logically) conclude that Socrates is mortal, because he is a member of the superset established by the first premise
I often find myself confused as to how these concepts could be applied to the actual exam or exam questions- I understand that as a core course these videos are meant to lay a foundation but I would love to see more complex examples that reflect logical questions on the exam at the end of most videos to begin applying the concepts early on. It would help me understand why this is important and where I will be using it.
@danielamordonez Absolutely agree. There are LR questions which would have chain of causation (i.e. negations and contrapositives) and would conveniently skip a chain which we would later need to identify as a necessary assumption.
#feedback Some of the videos allow you to switch to full screen, fast forward, change the speed, etc. while other videos do not. I tried refreshing the page but that only worked once. Can this issue be resolved?
No, but you can create the visual yourself if you'd like. It's just to better organize the form of the argument and the relationship between different premises.
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69 comments
Does anyone feel like these kind of mental gymnastics are like equations? In that case, I'm not a fan of this kind of math lol. All I can deduce this is into is just standard sentences: Anyone who eats expired food--> gets sick. I ate expired food. Therefore, I get sick.
Makes sense mostly.
I wrote off me and contrapositives a looooong time ago, but this actually makes sense!!
If the subscript is messing some people up, in my mind, writing out the contrapositive statement is really helpful. At the end of the day, we can only move from the left side of the arrow to the right. If we diagram that out clearly, I think it is difficult to go wrong
A --> B
X = A
X --> B
is the same thing as
A --> B
/B --> /A
X --> /A
I remember taking a logic class in college and we used the negation symbol as this ~ and not the slash/. I think the slash is throwing me off in these lessons a little bit. Either way I am realizing that logic class actually helped me a lot.
If one prepares for the LSAT, then one is going to law school. Sarah is not going to law school; therefore, Sarah does not prepare for the LSAT.
LSAT→LS
s/LS
______
s/LSAT
All these math symbols are throwing me off
@SofiyaBerman yea im over all that, ill see how i fare
if one is a dancer, then one is an athlete.
D > A
Mike is not an Athlete
m^/A
________
m^/D
Therefore, Mike is not a dancer
If one eats a thousand donuts, then one must perform in the circus
TD>C
Nina did NOT perform in the circus
n^/C
------
n^/TD
Therefore, Nina did NOT eat a thousand donuts
At first I felt like some of these videos are super repetitive. Now I see that I never would have understood that if Luke is a Jedi and Jedi use the force that Luke uses the force.
Contradictorily
If Luke cannot use the force and Jedi use the force. Luke is not a Jedi.
Beginning to learn I am.
@fjnathaniel This is the way.
modus tollens
p-->q
~q
therefore ~p
so basically the form of the argument takes precedent over whether the argument is true or not (valid) to the real world. if the form of the argument is the same, the argument must be thought of as true. (right?)
@VenessaO77 It might be my lack of sleep and food, but what does "though of as true" mean? Other than that, I think you're correct. Determining the form of the argument is the most important thing when you're figuring out how to tackle it. If the argument states "All bears are pink. Luna is a bear, therefore she is pink" the argument is valid, just not true.
@kyorofan20 thought*
So is it fair to say that the conditional form represents a sufficient argument and the contrapositive form represents a necessary argument?
Everyone who is tall (T) is good at baseball (GB).
(T > GB)
S (s) is tall.
(s^T)
S is good at baseball.
(sGB)
C (c) is not tall.
(c/T)
C is not good at baseball.
(c/GB)
Is this right?
@Narmis The argument isn't valid in your example because being tall isn't necessary for being good at baseball (at least not according to your premise). So while knowing someone is tall is sufficient to know they play baseball, knowing someone plays baseball is not sufficient to know they are tall.
Instead, it would be
T ---> B (if one is tall, they must be good at baseball)
which can be arranged to:
/B ---> /T
so if....
/B ---> /T
and Maia (/B)
then
Maia (/T).
If one has supernatural powers, they've eaten a devil fruit. SP-->DF
Luffy has supernatural powers. l^SP
Luffy has eaten a devil fruit. l^DF
Contrapositive:
SP-->DF
Usopp does not have supernatural powers. u^/SP
Usopp has not eaten a devil fruit. u^/DF
All dogs like bacon
Kitty does not like bacon
Kitty is not a dog
Am i doing this right?
@kimwexler Yes!
Dog → Likes Bacon
Kitty /Likes Bacon
____
Kitty /Dog
All fishes stink
Sandy does not stink
Sandy is not a fish
Is this correct??
@Jcruzmed Yep! F->S, s^/S, therefore s^/F.
I'm not sure of anyone else has pointed it out, but is it fair to say that the contrapositive argument structure models that of "modus tollens"?
P1: All cats are annoying
P2: Peter is not annoyin
C: Peter is not a cat
All dogs are cute
Joe is not cute
Joe is not a dog
Premise 1: if a plant is a flower, then it is pretty.
Premise 2: the plant is not pretty.
Conclusion: the plant is not a flower
Is this correct ???
Looks good to me:
F→P
/P
------
/F
I dont really understand how we got Athena like where dod we just pull that out of and how is that in the slightest way related to proving the argument
It is just an example of the contrapositive. See the notes: If one is a Jedi, then one is a Force user. Athena is not a Force user. Therefore, Athena is not a Jedi.
"In the first argument, premise 2 identifies a member, Athena, and says that she fails the necessary condition, i.e., she doesn't use the Force, placing her outside the superset. The conclusion follows that therefore Athena must also fail the sufficient condition, i.e., she must be outside the subset and not be a Jedi"
Athena "exists" purely for the sake of argument: to satisfy-- or in this case, fail-- the necessary condition.
In a conditional argument, the purpose of the first premise in a syllogism is to establish a subset/superset relationship ("If one is a Jedi, then one is a force user").
The second premise dictates whether a particular person (or thing) is a member of the subset established by the first premise.
Athena doesn't necessarily have to exist "in real life" (if that is what you are asking)-- she exists within an isolated context, which is the syllogism itself. The key is to think very narrowly about what is being defined. Athena doesn't have to "come from" anywhere, she is just being used to prove (or disprove) membership in a given superset.
Take this classic syllogism for example:
All men are mortal
Socrates is a man
Therefore, Socrates is mortal
The second premise is telling us that Socrates is a member of the superset [mortal things]. From that premise, we can reasonably (and logically) conclude that Socrates is mortal, because he is a member of the superset established by the first premise
I often find myself confused as to how these concepts could be applied to the actual exam or exam questions- I understand that as a core course these videos are meant to lay a foundation but I would love to see more complex examples that reflect logical questions on the exam at the end of most videos to begin applying the concepts early on. It would help me understand why this is important and where I will be using it.
#feedback
I agree!
@danielamordonez Absolutely agree. There are LR questions which would have chain of causation (i.e. negations and contrapositives) and would conveniently skip a chain which we would later need to identify as a necessary assumption.
#feedback Some of the videos allow you to switch to full screen, fast forward, change the speed, etc. while other videos do not. I tried refreshing the page but that only worked once. Can this issue be resolved?
Question: How would I use this on the LSAT? They show visuals on the test?
No, but you can create the visual yourself if you'd like. It's just to better organize the form of the argument and the relationship between different premises.