@JoelKeenan yes they are. Go back to basic logic sections. If you’re a cat, you’re a mammal. If you’re not a mammal, you’re not a cat. In other words, it is necessary to be a mammal to be a cat.
@JoelKeenan A is sufficient for B. B is necessary for A. Being a cat is sufficient to be a mammal. Being a mammal is necessary to be a cat. If A is sufficient for B, then B is necessary for A. One implies the other.
Isn't the conclusion here false? The two premises are sufficient conditions. So just because /Jane is no happy, does not mean /sunny day. There could be many other sufficient conditions for her to be happy, birds singing is only one of them. Can someone help explain?
yea there could be many different ways that lead to Jane being happy, but you know that a sunny day at least guarantees her being happy, so if she isn't happy, you know at least that it isnt a sunny day -> not really saying anything about the other ways that could make her happy, just that her not being happy is ENOUGH to know that it isnt sunny~
This is breaking my understanding. How can I identify SA/NA confusion now? Is this only for causal logic? Do I need the "only if, if/then" phrases for it to be SA/NA confusion?
Hi :) We're chaining conditionals and then getting the contrapositive.
So, for our purposes Sunny Day- SD, Birds sing- BS, Jane Happy- J :)
If SD -> BS
If BS -> J :)
this tracks because the necessary condition for Sunny Day (Birds Singing) is ALSO a sufficient condition for Jane being happy. Then we can link a Sunny Day to Jane being happy.
So we have:
If SD-> BS -> J :)
With that chain we know that we can take out Birds Singing (which will make Jane Happy) because it's already confirmed to happen via Sunny Day:
If SD -> J :)
and then we just take the contrapositive!
If /J :) -> /SD
(side note, if this is confusing then forget I said anything, but it also makes it true that the birds are not singing, or /J :) -> /BS -> /SD
There is no sufficient/necessary confusion here. Let's break down the possible outcomes. Once the conditionals are chained as mentioned above we have a statement that looks like this, where SD = sunny day, BS = birds sing, and JH = jane is happy:
SD → BS → JH
accompanied by this contrapositive:
/JH → /BS → /SD
From this we know that:
A sunny day is sufficient to guarantee that Jane will be happy, and that Jane being happy is necessary whenever there is sunny day. Meanwhile Jane not being happy is sufficient to guarantee that it is not a sunny day, while it not being a sunny day is necessary for Jane to not be happy.
Therefore, we can validly infer that if Jane isn't happy, it isn't a sunny day, Since
What we cannot validly infer is: "It is not sunny, therefore Jane is not happy",. She could be, she could not, since there are potentially other sufficient conditions to trigger Jane's happiness outside of a sunny day (satisfying the necessary condition of the contrapositive tells us nothing about whether or not the sufficient condition is satisfied.)
We also cannot validly infer that it is a sunny day simply because Jane is happy, because said above there are potentially other sufficient conditions to trigger Jane's happiness.
Simply put: It not being sunny tells us nothing about whether or not it's Jane is happy, and Jane's happiness tells us nothing about whether or not it's sunny"
If you're still confused, I would recommend reviewing the lessons on sets and supersets, taking contrapositives, and chaining conditionals. For me in particular I found it extremely helpful to define sufficiency and necessity, with respect to sets and supersets, and then continue to relate those concepts back to one another, repeatedly making use of the circle diagrams that were used to introduce sets and supersets, being able to see the actual physical relationship of the sets is very helpful.
Keep in mind, here is a reason formal logic has been studied for thousands of years, and continues to draw confusion and ire: because it is truly difficult. People dedicate lives to studying these relationships, we need only a high level overview.
I am leaving a reply because it seems no one else has. This has helped me a bit. Normally, I look at formatting, topic, etc. So much more than what I need, and should be looking at.
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23 comments
oh man im scared
Oh no. I've been dreading this since the beginning. Parallel Flawed Reasoning, my nemesis....... we meet again.
Maaannnnn it feels good to see the words: "You made it! The final frontier" Woot woot... Making progress!
what's PF? parallel flaw?
I wanted a clear description on what this section is?
Similar reasoning of method or similar flawed reasoning method?
Parallel includes both valid and flawed parallel arguments right?
@CaseyLiu Yes, "Parallel" can involve a flawed argument (but most of the time it doesn't). "Parallel Flaw" always involves a flawed argument.
is there a problem here?
argument is one:
A -> B
/B
/A
but argument two is:
A<->B
/B
/A
if and only if is different from if? is this a flaw in the lesson or are they treated the same on the LSAT?
#HELP
@VincentPrestianni
this is a pretty important distinction I need to make for my test.
#support #help
@VincentPrestianni Can you point out where the second example uses "if and only if"? I see just "only if".
[This comment was deleted.]
@JoelKeenan yes they are. Go back to basic logic sections. If you’re a cat, you’re a mammal. If you’re not a mammal, you’re not a cat. In other words, it is necessary to be a mammal to be a cat.
@JoelKeenan A is sufficient for B. B is necessary for A. Being a cat is sufficient to be a mammal. Being a mammal is necessary to be a cat. If A is sufficient for B, then B is necessary for A. One implies the other.
Parallel reasoning has always been my Achilles heel. Lets see if we can make some magic happen.
I can already tell, this section is going to make me angry.
real
If the stimulus is flawed, I know the correct AC has to be flawed too, but does it have to be the same flaw?
For instance, let's say the stimulus overlooks a possibility. Would the correct AC also have to be overlooking a possibility?
update: nvm i didn't correctly <3
If it is a sunny day, birds sing.
If birds sing, Jane is happy.
So, if Jane is not happy, it’s not a sunny day.
Isn't the conclusion here false? The two premises are sufficient conditions. So just because /Jane is no happy, does not mean /sunny day. There could be many other sufficient conditions for her to be happy, birds singing is only one of them. Can someone help explain?
yea there could be many different ways that lead to Jane being happy, but you know that a sunny day at least guarantees her being happy, so if she isn't happy, you know at least that it isnt a sunny day -> not really saying anything about the other ways that could make her happy, just that her not being happy is ENOUGH to know that it isnt sunny~
This is breaking my understanding. How can I identify SA/NA confusion now? Is this only for causal logic? Do I need the "only if, if/then" phrases for it to be SA/NA confusion?
Hi :) We're chaining conditionals and then getting the contrapositive.
So, for our purposes Sunny Day- SD, Birds sing- BS, Jane Happy- J :)
If SD -> BS
If BS -> J :)
this tracks because the necessary condition for Sunny Day (Birds Singing) is ALSO a sufficient condition for Jane being happy. Then we can link a Sunny Day to Jane being happy.
So we have:
If SD-> BS -> J :)
With that chain we know that we can take out Birds Singing (which will make Jane Happy) because it's already confirmed to happen via Sunny Day:
If SD -> J :)
and then we just take the contrapositive!
If /J :) -> /SD
(side note, if this is confusing then forget I said anything, but it also makes it true that the birds are not singing, or /J :) -> /BS -> /SD
There is no sufficient/necessary confusion here. Let's break down the possible outcomes. Once the conditionals are chained as mentioned above we have a statement that looks like this, where SD = sunny day, BS = birds sing, and JH = jane is happy:
SD → BS → JH
accompanied by this contrapositive:
/JH → /BS → /SD
From this we know that:
A sunny day is sufficient to guarantee that Jane will be happy, and that Jane being happy is necessary whenever there is sunny day. Meanwhile Jane not being happy is sufficient to guarantee that it is not a sunny day, while it not being a sunny day is necessary for Jane to not be happy.
Therefore, we can validly infer that if Jane isn't happy, it isn't a sunny day, Since
What we cannot validly infer is: "It is not sunny, therefore Jane is not happy",. She could be, she could not, since there are potentially other sufficient conditions to trigger Jane's happiness outside of a sunny day (satisfying the necessary condition of the contrapositive tells us nothing about whether or not the sufficient condition is satisfied.)
We also cannot validly infer that it is a sunny day simply because Jane is happy, because said above there are potentially other sufficient conditions to trigger Jane's happiness.
Simply put: It not being sunny tells us nothing about whether or not it's Jane is happy, and Jane's happiness tells us nothing about whether or not it's sunny"
If you're still confused, I would recommend reviewing the lessons on sets and supersets, taking contrapositives, and chaining conditionals. For me in particular I found it extremely helpful to define sufficiency and necessity, with respect to sets and supersets, and then continue to relate those concepts back to one another, repeatedly making use of the circle diagrams that were used to introduce sets and supersets, being able to see the actual physical relationship of the sets is very helpful.
Keep in mind, here is a reason formal logic has been studied for thousands of years, and continues to draw confusion and ire: because it is truly difficult. People dedicate lives to studying these relationships, we need only a high level overview.
I love this new explanation! I am coming back to review foundations, and I saw this!
I am leaving a reply because it seems no one else has. This has helped me a bit. Normally, I look at formatting, topic, etc. So much more than what I need, and should be looking at.