I’m in a fantasy football league with friends. Quick refresher: you draft real players, set a lineup, and your team scores based on how those players do in real games.
This week Friend 1 was playing Friend 2. The score was 120 to 135. Friend 1 was down 15, and here is the kicker: he left his quarterback slot empty. Friend 2’s whole roster had already played, so 135 was his final score.
I told Friend 1, “If you want any chance to win, you need to start a QB.” Friend 2 jumped in and said, “Even if he adds a QB, that does not mean he will get 16 or more points.” I said, “Right, it is not a guaranteed win. But without a QB, there is zero chance.” That is the point. It is a necessary condition. A QB does not ensure victory, but no QB ensures defeat.
Shoutout to 7Sage. LSAT necessary assumptions can even help you talk trash with logic.
I don't understand how the jewels sentence is not necessary but it is sufficient. I get that it is not as narrowly tailored, but diamonds still fit into the category of jewels so that sentence still applies to them. I feel like the way this concept was explained went completely over my head. I understood everything until that point where it was sufficient but not necessary yet still applicable to diamonds because diamonds are jewels. Unless my problem is that I made the assumption that all diamonds are jewels.
THANK YOU for making a video for this section. I read the previous comments and it looks like this was a "read only" lesson that took 20 minutes to read
So, even though necessary conditions generally cast a wider 'net' (as the large circle with several sufficient conditions inside it) it actually needs to be more specific -- tailored -- to the argument than a sufficient assumption?
On the diamond question: another necessary assumption is that diamonds have any value at all. It is necessary for a diamond to have any kind of value in order for its value to be derived from aesthetic pleasure, yet it having any value at all is not sufficient for that argument we're referencing to be true. I think if we were to deny this necessary assumption, it would hurt the diamond-value argument even more than the example given here.
#feedback Why are there no examples for the must be true and negation tests? I would think that's handy information to have as part of a lesson before moving onto the questions.
The not-stated-fact here that makes this type of question more scary is that Necessary Assumption questions, according to the cheat sheet given to us, are 53% more numerous than the Sufficient Assumption questions :(
When applying the negation test, does it mean that negating the correct answer choice would render the conclusion impossible, or just that the premises would no longer support the conclusion? It makes more sense to me that it would mean that the negation of the answer choice would mean that the conclusion can absolutely no longer be drawn, but there's a few questions in the upcoming lessons where it seems like that isn't the case. Instead, it seems like if the correct answer choice weren't true, that the premises just no longer directly support the conclusion. However, negating the answer choice doesn't seem to preclude the possibility of other assumptions being made that could allow the conclusion to be drawn.
Does anyone have any tips for coming up with an answer in your head before looking at the answer choices? For example, should we hold the conclusion and think "what if conclusion is true, but..." or is this the wrong way to go about finding a loophole?
can someone give an example of using the negation test? i feel like i'm almost there with understanding it... if you contradict the answer choice and it makes the argument invalid, then that's the correct answer?
The lesson says "That assumption is said to be both sufficient and necessary. But often such distinctions do exist. An assumption can be just sufficient and not necessary. Or an assumption can strengthen an argument without being necessary."
Should it have said, "Or an assumption can strengthen an argument without being sufficient or necessary."
Or maybe it should have said "Or an assumption can be just necessary and not sufficient."
Perhaps I'm missing something here but the way it's written doesn't seem to highlight the distinctions very distinctly.
Where are the example questions on this intro page? This has been big for me in previous lessons. I noticed there weren't any in the last section either.
From my understanding, NA are types of questions that require the answer choice to be strongly true to reach the argument's conclusion. Through doing the Negation test if it destroys the argument then the answer choice is necessary for the argument to reach its conclusion. My concern on the other hand is when I am practicing the questions I get confused about if looking for the NA I am looking for new information OR it is finding gaps such as if something is said in the premise but the conclusion introduces something else. That is why I am getting the answers incorrect.
#feedback this takes way longer than 3 minutes to read and digest. I know it's not a huge deal, but I think it's important to provide accurate time predictions for sections. I've noticed this is a common theme for most reading lessons, that the time it takes to complete is underestimated.
In NA questions, we are being asked to identify how the author got to this point, with the argument as is. Ask yourself, "What is absolutely necessary to have gotten to this point?"
In SA questions, we are being asked to take the argument to the next level by adding to it something that would make it logically valid. Ask yourself, "What can we add to this to make it better?" so to speak
I don’t know if this is right, but my take on necessary assumptions is that they are logical implications of sufficient assumptions. By logical implications I mean the following: p logically implies q iff under all circumstances with which we are concerned, it is not possible for p to be true and at the same time for q to be false. Consider for example the following partial argument:
The moon is made of green cheese (Gm). So the moon is edible (Em).
The sufficient assumption would be that, for all things, if it is made of green cheese, it is edible (Ɐx Gx→Ex). This logically implies that, for most things, if it is made of green cheese, it is edible (ꟽx Gx→Ex), which in turn logically implies that, for some things, if it is made of green cheese, it is edible (Ǝx Gx→Ex). And it seems that this last existential claim does not logically imply anything further, so it constitutes a necessary assumption for the original partial argument. We can confirm this by showing that its negation (1), the premise of the original argument (2), and the conclusion (3) form an inconsistent set:
¬Ǝx Gx→Ex (1)
Gm (2)
Em (3)
Ɐx ¬(Gx→Ex) (4 from 1 by ¬Ǝ)
¬(Gm→Em) (5 from 4 by Ɐ)
Gm∧¬Em (6 from 5 by ¬→)
¬Em (7 from 6 by ∧)
⊥
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50 comments
I’m in a fantasy football league with friends. Quick refresher: you draft real players, set a lineup, and your team scores based on how those players do in real games.
This week Friend 1 was playing Friend 2. The score was 120 to 135. Friend 1 was down 15, and here is the kicker: he left his quarterback slot empty. Friend 2’s whole roster had already played, so 135 was his final score.
I told Friend 1, “If you want any chance to win, you need to start a QB.” Friend 2 jumped in and said, “Even if he adds a QB, that does not mean he will get 16 or more points.” I said, “Right, it is not a guaranteed win. But without a QB, there is zero chance.” That is the point. It is a necessary condition. A QB does not ensure victory, but no QB ensures defeat.
Shoutout to 7Sage. LSAT necessary assumptions can even help you talk trash with logic.
I don't understand how the jewels sentence is not necessary but it is sufficient. I get that it is not as narrowly tailored, but diamonds still fit into the category of jewels so that sentence still applies to them. I feel like the way this concept was explained went completely over my head. I understood everything until that point where it was sufficient but not necessary yet still applicable to diamonds because diamonds are jewels. Unless my problem is that I made the assumption that all diamonds are jewels.
THANK YOU for making a video for this section. I read the previous comments and it looks like this was a "read only" lesson that took 20 minutes to read
Klay Thompson scored 60 pts on 11 dibbles
Does the LSAT have a question type that requires sufficient and necessary?
Sometimes this guy has a weird way of explaining things
So, even though necessary conditions generally cast a wider 'net' (as the large circle with several sufficient conditions inside it) it actually needs to be more specific -- tailored -- to the argument than a sufficient assumption?
On the diamond question: another necessary assumption is that diamonds have any value at all. It is necessary for a diamond to have any kind of value in order for its value to be derived from aesthetic pleasure, yet it having any value at all is not sufficient for that argument we're referencing to be true. I think if we were to deny this necessary assumption, it would hurt the diamond-value argument even more than the example given here.
#feedback Why are there no examples for the must be true and negation tests? I would think that's handy information to have as part of a lesson before moving onto the questions.
The not-stated-fact here that makes this type of question more scary is that Necessary Assumption questions, according to the cheat sheet given to us, are 53% more numerous than the Sufficient Assumption questions :(
When applying the negation test, does it mean that negating the correct answer choice would render the conclusion impossible, or just that the premises would no longer support the conclusion? It makes more sense to me that it would mean that the negation of the answer choice would mean that the conclusion can absolutely no longer be drawn, but there's a few questions in the upcoming lessons where it seems like that isn't the case. Instead, it seems like if the correct answer choice weren't true, that the premises just no longer directly support the conclusion. However, negating the answer choice doesn't seem to preclude the possibility of other assumptions being made that could allow the conclusion to be drawn.
Does anyone have any tips for coming up with an answer in your head before looking at the answer choices? For example, should we hold the conclusion and think "what if conclusion is true, but..." or is this the wrong way to go about finding a loophole?
Thanks :)
can someone give an example of using the negation test? i feel like i'm almost there with understanding it... if you contradict the answer choice and it makes the argument invalid, then that's the correct answer?
#feedback I miss the videos!
The lesson says "That assumption is said to be both sufficient and necessary. But often such distinctions do exist. An assumption can be just sufficient and not necessary. Or an assumption can strengthen an argument without being necessary."
Should it have said, "Or an assumption can strengthen an argument without being sufficient or necessary."
Or maybe it should have said "Or an assumption can be just necessary and not sufficient."
Perhaps I'm missing something here but the way it's written doesn't seem to highlight the distinctions very distinctly.
Where are the example questions on this intro page? This has been big for me in previous lessons. I noticed there weren't any in the last section either.
Can someone explain the difference between necessary assumptions and sufficient assumptions?
can someone summarize what na questions are as simple as possible please thanks
It would be super helpful to include example question in many areas of this lesson so we can get it fully when reading.
From my understanding, NA are types of questions that require the answer choice to be strongly true to reach the argument's conclusion. Through doing the Negation test if it destroys the argument then the answer choice is necessary for the argument to reach its conclusion. My concern on the other hand is when I am practicing the questions I get confused about if looking for the NA I am looking for new information OR it is finding gaps such as if something is said in the premise but the conclusion introduces something else. That is why I am getting the answers incorrect.
#feedback this takes way longer than 3 minutes to read and digest. I know it's not a huge deal, but I think it's important to provide accurate time predictions for sections. I've noticed this is a common theme for most reading lessons, that the time it takes to complete is underestimated.
I see the difference like this:
In NA questions, we are being asked to identify how the author got to this point, with the argument as is. Ask yourself, "What is absolutely necessary to have gotten to this point?"
In SA questions, we are being asked to take the argument to the next level by adding to it something that would make it logically valid. Ask yourself, "What can we add to this to make it better?" so to speak
Please write a "Theory and Approach" lesson like this one, but for Sufficient Assumption 🥹
#feedback great lesson!
This was a good lesson.
I don’t know if this is right, but my take on necessary assumptions is that they are logical implications of sufficient assumptions. By logical implications I mean the following: p logically implies q iff under all circumstances with which we are concerned, it is not possible for p to be true and at the same time for q to be false. Consider for example the following partial argument:
The moon is made of green cheese (Gm). So the moon is edible (Em).
The sufficient assumption would be that, for all things, if it is made of green cheese, it is edible (Ɐx Gx→Ex). This logically implies that, for most things, if it is made of green cheese, it is edible (ꟽx Gx→Ex), which in turn logically implies that, for some things, if it is made of green cheese, it is edible (Ǝx Gx→Ex). And it seems that this last existential claim does not logically imply anything further, so it constitutes a necessary assumption for the original partial argument. We can confirm this by showing that its negation (1), the premise of the original argument (2), and the conclusion (3) form an inconsistent set:
¬Ǝx Gx→Ex (1)
Gm (2)
Em (3)
Ɐx ¬(Gx→Ex) (4 from 1 by ¬Ǝ)
¬(Gm→Em) (5 from 4 by Ɐ)
Gm∧¬Em (6 from 5 by ¬→)
¬Em (7 from 6 by ∧)
⊥