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.
Correct you can tell by splitting them apart. For your first example you have T>S and S>B. the negation of both is /S>/T and /B>/S. which can be connected by /B>/S>/T.
Your second example has A>T and T>/S. The contra of both is /T>/A and S>/T which can be connected by S>/T>/A
I feel like the explanation is super wordy simply it is
a conditional statement
If one lives in NYC than they live in the USA
NYC → USA
Contrapositive just flip and slash
/USA → /NYC
so NOT in the USA than NOT in NYC
in a statement, the contrapositive is as follows
If one lives in NYC then one lives in the USA. Dave does not live in the USA. Therefore Dave does not live in NYC. As you can see from our contrapositive statement above this follows that exact form. This is valid.
I was thinking this too. I was actually confused that an additional person was brought in when it could've simply been if one does not live in the united states then they do not live in NYC.
Conditional Argument: If one lives in New York City, then one lives in United States.
When you want to find the Contrapositive you flip and negate. Why?
If we just negated without flipping it, it would say:
If one does not live in New York City, then one does not lives in United States.
This wouldn't make sense, because they can be in Los Angles, Texas. Just because they are not in New York, does not mean they can not be living anywhere else in United States.
But look if we negated and flipped what would happen:
If one does not live in United States, then one does not live New York City.
This would make sense because you cant be in New York without being in United states.
Does it remain that the Force is the necessary condition always, in that contrapositive relation? I just internalized that the left side of the arrow is the sufficient condition and the term on the right is the necessary, but when flipped in a contrapositive it seems like the necessary condition remains, i.e. in the argument /F --> /J, I read this as /F as the sufficient condition in this case, but the narrative above does not make that distinction clear for me at least, if someone knows can they clarify?
Yes it remains the same in terms of Force being the necessary condition. If I say "If not B then not A" then by default that means that B is the necessary condition because, as the claims says, not B equals not A, meaning you NEED B for A to happen. It doesn't matter if its A, B, C, D, E or whatever, if you say "if not THIS then not THAT" "THIS" will always be the necessary condition for "THAT".
So after seeing more lessons and reading other comments it seems things are not exactly as I had thought. Apparently the sufficient condition and necessary conditions are indeed swapped with "not B" now being the sufficient condition. It looks like when using "the arrow" the form is always "sufficiency -> necessity" no matter what. However, I searched online and I also saw that when doing a contrapositive "not B" becomes "negated necessary condition". So take it with a grain of salt.
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64 comments
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.
For chaining a contrapositive, I have created the following example:
If one is tall then one is smart if one is smart then they have a big brain (T --> S --> B)
Contra: If one does not have a big brain then one is not smart and therefore is not tall (/B --> /S --> /T)
and
If one is annoying then they talk a lot, if one talks a lot then they are not smart (A --> T --> /S)
Contra: If one is smart then they do not talk a lot, and they are not annoying (S --> /T --> /A)
Are these examples correct or incorrect? How does one create a contrapositive of a chain or is one unable to do so.
Thanks and let me know.
Correct you can tell by splitting them apart. For your first example you have T>S and S>B. the negation of both is /S>/T and /B>/S. which can be connected by /B>/S>/T.
Your second example has A>T and T>/S. The contra of both is /T>/A and S>/T which can be connected by S>/T>/A
I feel like the explanation is super wordy simply it is
a conditional statement
If one lives in NYC than they live in the USA
NYC → USA
Contrapositive just flip and slash
/USA → /NYC
so NOT in the USA than NOT in NYC
in a statement, the contrapositive is as follows
If one lives in NYC then one lives in the USA. Dave does not live in the USA. Therefore Dave does not live in NYC. As you can see from our contrapositive statement above this follows that exact form. This is valid.
I was thinking this too. I was actually confused that an additional person was brought in when it could've simply been if one does not live in the united states then they do not live in NYC.
I understood everything except when it came to introducing Formal Argument 2
Conditional Argument: If one lives in New York City, then one lives in United States.
When you want to find the Contrapositive you flip and negate. Why?
If we just negated without flipping it, it would say:
If one does not live in New York City, then one does not lives in United States.
This wouldn't make sense, because they can be in Los Angles, Texas. Just because they are not in New York, does not mean they can not be living anywhere else in United States.
But look if we negated and flipped what would happen:
If one does not live in United States, then one does not live New York City.
This would make sense because you cant be in New York without being in United states.
Does it remain that the Force is the necessary condition always, in that contrapositive relation? I just internalized that the left side of the arrow is the sufficient condition and the term on the right is the necessary, but when flipped in a contrapositive it seems like the necessary condition remains, i.e. in the argument /F --> /J, I read this as /F as the sufficient condition in this case, but the narrative above does not make that distinction clear for me at least, if someone knows can they clarify?
Yes it remains the same in terms of Force being the necessary condition. If I say "If not B then not A" then by default that means that B is the necessary condition because, as the claims says, not B equals not A, meaning you NEED B for A to happen. It doesn't matter if its A, B, C, D, E or whatever, if you say "if not THIS then not THAT" "THIS" will always be the necessary condition for "THAT".
So after seeing more lessons and reading other comments it seems things are not exactly as I had thought. Apparently the sufficient condition and necessary conditions are indeed swapped with "not B" now being the sufficient condition. It looks like when using "the arrow" the form is always "sufficiency -> necessity" no matter what. However, I searched online and I also saw that when doing a contrapositive "not B" becomes "negated necessary condition". So take it with a grain of salt.
All Canadians like Don Cherry's suits.
John doesn't like Don Cherry's suits.
John isn't Canadian.