Note for anyone confused by the store and milk example:
That example is not intended to map onto whatever real life understanding you have about stores and milk. When we get a statement saying "If I go to the store, then I will buy milk," we have to analyze the meaning of that specific statement. And that statement means that if I go to the store, I am guaranteed to buy milk.
You might be thinking, "But I don't have to buy milk when I go to the store..." That may be the case in real life. But the statement "If I go to the store, then I will buy milk" does assert that I have to buy milk when I go to the store.
And, "If I go to the store, then I will buy milk" does not assert that the store is the only place that I can buy milk. It's entirely possible that whenever I visit a local farm, I buy milk. Or that I often buy milk from my neighbor. But, according to the statement, if I go to the store, I am guaranteed to buy milk.
This is why the statement is diagrammed like this:
Store → Milk
If I go to the store, the arrow points to what is guaranteed to happen: I will buy milk.
Does this depend on the language being used in the statement? What if the statement was: If I go to the store, I MIGHT buy milk. Does this change the relationship of sufficiency and necessity?
Yes, because "might" now means buying milk is no longer necessary. "If A, then B might happen" is no longer a conditional relationship. We can't say that A is sufficient to guarantee anything. And we can't say that B is necessary in order for A. Because it's possible for A to happen without B.
@bcn but its not though. Buying milk would be the superset and going to the store would be the subset. The lesson on group 1 indicators explains this quite clearly: the "If" in I go to the store is a sufficient indicator, meaning going to the store is a sufficient indicator for triggering buying milk.
@TheBigFatPanda The way you just explained this, broke the barrier that I had in understanding this concept. Thank you. I was starting to get really frustrated.
Using your examples, the direction of the arrows would be reversed, though:
Milk --> Store
Cat --> Mammal
That's how we'd represent "You must go to the store in order to buy milk" and "You must be a mammal in order to be a cat."
In other words, if someone bought milk, that guarantees they went to the store.
If something is a cat, that guarantees it's a mammal.
If you represent the arrow the other way around: "Store --> Milk", that would assert that anyone who goes to the store buys milk.
Note that the example in the lesson was "If store, then milk." That is intended to say that anyone who goes to the store buys milk. The example in the lesson isn't intended to be a description of anything from real life.
So to be clear, if we have "If store, then milk", that means store is a sufficient condition and milk is a necessary condition.
If we have "If milk, then store", that means milk is a sufficient condition and store is a necessary condition.
It doesn't matter whether in real life going to the store is required to buy milk; we're simply analyzing the meaning of the given statements.
Hi Kevin, I still need some clarifications regarding this.
So, to better understand I took this example and compared it to the New York/ USA example.
If I go to New York then I'll be in the USA
New York -> USA
sufficiency -> Necessity
If I go to the store then I will buy milk
store -> milk
sufficiency -> necessity
So I get the sufficiency part but what I'm still not understanding is the necessity aspect.
We know that being in the USA is necessary to being in New York, after all New York is inside of the USA. But with the milk example this is tricky because it is the milk that's inside of the store, not the other way around.
You NEED to go to the USA in order to visit New York.
But you do NOT NEED to buy milk in order to visit the store, actually is the other way around, you NEED to be in the store to buy milk.
I get that you mentioned that we are not supposed to look at it from the real world view, but even if its guaranteed that you will get milk by going to the store, I am still failing to see how it is a necessity to buy milk in order to be in the store.
I'll appreciate if you could clarify that. Thanks.
I think one of the downsides to using examples like the "If New York --> USA" statement is that it draws upon your own real-life understanding of the relationship between being in New York and being in USA. That's why it's easy to understand "being in USA" as necessary to "being in NY."
With the statement "If I go to the store, I will buy milk," however, this statement doesn't make sense in real life. Obviously in real life it's possible for me to go to the store and not buy milk. But let's just accept the statement as true, regardless of whether it maps onto our understanding of real life stores and purchases of milk.
"If I go to the store, I will buy milk."
This means if I go to the store, it must be the case that I will buy milk. It's impossible for me to go to the store and not buy milk.
What if you learn the following fact about me: I went somewhere, and I did not buy milk.
If I didn't buy milk...then that proves I didn't go to the store. Because if I went to the store, I had to buy milk. So if I didn't buy milk, you can conclude that I didn't go to the store.
This is the sense in which "buying milk" is necessary for the condition "I go to the store." The necessity is a reference to the truth of the conditions -- in order for "I go to the store" to be true, it must also be true that I will buy milk.
We're not saying that for us to be physically in the store, there's something about the physical presence of being in the store that requires us to also buy milk. We're just saying that the "state of the world in which I buy milk" is necessary in order for "the state of the world in which I go to the store" to be true.
Does that make sense? Here's another example. This statement is easy to conceptualize in terms of what's necessary:
"In order to get into law school, I must take the LSAT."
It's easy to see that taking the LSAT is necessary because we conceptualize the LSAT as one of the things we have to do to get into law school -- there's a big list of requirements and the LSAT is one of them.
But what about this:
"In order for the sky to be red, my neighbor's dog must bark loudly."
Here, my neighbor's dog barking loudly is necessary in order for the sky to be red. You might think...how does that make sense? Why does the sky bring red require my neighbor's dog to bark? There's obviously no real relationship between the color of the sky and my neighbor's dog barking.
However, given what the statement says, we know that if the sky is red, it must be that my neighbor's dog has barked loudly. And if my neighbor's dog hasn't barked loudly, the sky can't be red. This is the sense in which my neighbor's dog barking is necessary. The "state of the world in which my neighbor's dog has barked loudly" is necessary in order for the "state of the world in which the sky is red" to be true. "Necessary" is simply desribing a relationship between the truth value of various states of the world. It's not a comment on any kind of physical requirement or some kind of causal connection between the sky being red and the dog barking.
Keep in mind, that "In order for the sky to be red, my neighbor's dog must bark loudly" is not true in real life. But what matters is the meaning of the statement. If you analyze the meaning of the statement, without caring about whether it's true in real life, then you will see that the words in the statement express the idea that "my neighbor's dog must bark loudly" is necessary for "sky to be red."
Interesting. I think I got it now. So I am imagining a world where if I got to the store then I absolutely have to buy milk, regardless of what else I get or don't get, milk is a requirement, otherwise I cannot step foot inside the store, which would then mean that no milk equals no store. You're right. I was trying my best to not use real world logic in the exercise but what kept tricking me was the fact that the milk is inside the store, however that doesn't matter because buying milk in that world can simply be a requirement to enter the store, sort of like when going to a bar, if I sit at the bar then I must order a drink" so even if the drink is inside the bar, if you don't order it you can't sit in. So I imagined a world where buying milk is required to enter the store, which would then make milk necessary. Thanks Kevin, I get it now. Thanks for providing such an in-depth clarification.
@LiviaLSAT for me at least it feels more natural to use the dots because it allows me to hold more information. like if you introduce many subsets together "like cats ->mammals dogs->mammals" etc it can quickly add up and become complicated.
WOW. So, I studied on my own for the first LSAT I did and always saw this notation but constantly messed it up because I didn't know that the arrow itself had this rule. This is such a big clarity moment.
Since the store is sufficient in this sub/superset, then it is necessary to say "Every time I go to the store, I buy milk."
Since you can also buy milk elsewhere (farm, market, etc.) it means that just because you bought milk doesn't mean you went to the store, you could've acquired it elsewhere in this scenario, but if you went to the store, it is certain that you bought milk.
If an item(x) is a milk, it is guarenteed to be in a store( membership in milk is sufficient for membership in store).
If an item is a milk, it is sufficient to say the item is in the store.
If an item is not found within a store, it is impossible for the item to be milk (without membership in the necessary condition, membership in the sufficient condition is impossible)
If an item is found in a store, it is not sufficient to be a milk.( membership in the necessary condition(store) is not sufficient for membership in the sufficient condition(milk)).
In order for an item to be a milk, it is necessary for it to be in a store.( membership in the necessary condition(store) is necessary for membership in the sufficient condition(milk).
It is not necessary to be a milk in order to be in a store ( membership in the sufficient condition is not necessary for membership in necessary condition)
I think it would be like If one goes to the store, then one needs/buys milk. like the same sentence structure as the jedi example " if one is a jedi, then one is a force user"
Example: store → milk = If you went to the store (S) then you got milk (M).
- (S →): The left side of the implication (S, or going to the store) is the sufficient condition. This means if S occurs (you go to the store), it is sufficient to ensure that M (getting milk) follows under the context of this implication.
- (→ M): Viewing the right side of the implication (M, or getting milk) as the "necessary condition" in this framework means that M is necessary in the sense that it must occur if S has occurred. This is based on the assumption that if the sufficient condition is met, the occurrence of M is necessary to fulfill the truth of the implication S→M
In sum: The act of going to the store (S) is posited as a sufficient condition for obtaining milk (M). This implies that if the condition of going to the store is fulfilled (If S), the implication suggests that it guarantees the outcome of obtaining milk (then M). However, while going to the store ensures you will get milk within the logic of this statement, it is not stated as the only method of acquiring milk; other ways may exist, thus making it not a necessary condition for having milk.
I like how this lesson includes an alternative way of thinking of sufficient and necessary conditions as subset and superset -- this is a very important key that can easily allow arguments to be drawn out in sets (aka circles :) )
This will probably be explained in a future lesson I imagine, but I'd like clarification on what happens when the necessary condition is true instead of the sufficient.
I'll use the milk/store example since I think that's the one most of us are confused about. I'll also write it out to specify the premises and conclusion:
Premise 1: If I go to the store, I will buy milk.
Premise 2: I went to the store.
Conclusion: I bought milk.
And here the "Lawgic" version of Premise 1:
Store -> Milk
This might not make sense in our world, but in the world of this argument then if anyone ever goes to the store, they have to buy milk. I think this makes sense.
Now what if I change the argument to something like this:
Premise 1: If I go to the store, I will buy milk.
Premise 2: I bought milk.
Conclusion: I went to the store.
I want to say that this does not make sense/is not valid, because Premise 1 is unchanged that means that the Lawgic is still "Store -> Milk," and not "Milk -> Store." In English, this would mean that I could have gotten milk from anywhere, not just the store.
@aidanro2003 You're totally right! The necessary condition being true means nothing for the sufficient condition. The only other true logical statement you could get out of this is if you didn't buy milk, you didn't go to the store as we know if you went to the store you must have bought milk.
The reason i have trouble with the store -> milk example is because there simple isn't enough information. I read this as relating to what one gets when at the store, in which case milk -> store would be correct because i could get orange juice at the store, not milk
@epayne17 the point of the -> element is to show the conditional relationship present in the argument, not to provide context. Reading the sentence/argument provides you with the context to which we figure out how to use the -> to show the conditional relationship.
In this context, the "If I go to the store [subset], then I will buy milk [superset]." Therefore, store -> milk; try not to rely on your intuition about what you might get at the store. Only what is presented in the argument.
@epayne17 Part of this is also picking out those indicator words.
He says: If I go to the store, then I will buy milk. "If" is a sufficient condition indicator. He's not saying he could buy milk - he will buy milk if the condition (going to the store) is met.
@Livandthecats lol going to the store does not require milk. I'd argue it makes far more logical sense to say that for the most part buying milk requires going to the store. You simply cannot make the claim that he will buy milk if he goes to the store. He could buy literally anything else at that store.... Picture the store and milk as the circles visualization JY gives for relationships. The milk circle should logically lie within the store's bigger circle. This makes the store the proper necessary condition, not milk.
@epayne17 Yes, buying milk typically involves going to a store. However, the argument that is being presented is in fact that if he goes to the store, he will buy milk.
In this case going to the store is your sufficient condition/subset because it follows the indicator "if". It doesn't matter that realistically there's not many other places to buy milk (unless you live near dairy farms), the argument is presented in such a way that store is the subset and milk is the superset.
If it was phrased as "If I bought milk, then I've gone to the store" then your argument makes sense. But the argument has not been presented that way.
The way you listed all the "natural languages" in the exact same order as I learned my 2nd, 3rd, and 4th languages at 2:05 definitely caught my attention lol!
He's already using A for P and B for Q, but does anyone know if this will follow a more formal/classical logic language or a sentential logic language? Or neither and I'm just going to get really confused?
I think it's the other way around! The statement A --> B (if A then B) would be more accurately translated as B has to happen for A to happen. (B is the necessary condition that has to happen in order for A to be true.)
Exactly. The sentence structure is If A, then B. When diagramming it out,
It looks like B→A.
B is the sufficient condition; A is the necessary one. Example: If I go to the store, then I will buy milk.
If A, then B. Going to the store is necessary for buying the milk. The above would be diagrammed as Milk→Store. The lesson has it backwards, and it's confusing. Glad I'm not alone in that.
Yes, this is also my interpretation. A happening is sufficient to assume that B has happened already, because B is necessary for A to have happened. So if A happens, then B has also by definition happened
96 comments
Note for anyone confused by the store and milk example:
That example is not intended to map onto whatever real life understanding you have about stores and milk. When we get a statement saying "If I go to the store, then I will buy milk," we have to analyze the meaning of that specific statement. And that statement means that if I go to the store, I am guaranteed to buy milk.
You might be thinking, "But I don't have to buy milk when I go to the store..." That may be the case in real life. But the statement "If I go to the store, then I will buy milk" does assert that I have to buy milk when I go to the store.
And, "If I go to the store, then I will buy milk" does not assert that the store is the only place that I can buy milk. It's entirely possible that whenever I visit a local farm, I buy milk. Or that I often buy milk from my neighbor. But, according to the statement, if I go to the store, I am guaranteed to buy milk.
This is why the statement is diagrammed like this:
Store → Milk
If I go to the store, the arrow points to what is guaranteed to happen: I will buy milk.
Does this depend on the language being used in the statement? What if the statement was: If I go to the store, I MIGHT buy milk. Does this change the relationship of sufficiency and necessity?
Yes, because "might" now means buying milk is no longer necessary. "If A, then B might happen" is no longer a conditional relationship. We can't say that A is sufficient to guarantee anything. And we can't say that B is necessary in order for A. Because it's possible for A to happen without B.
If you get confused which goes at what side of the arrow, I remember it by "Start with Sufficient, Next is Necessary." S -> N
"If you don't like it, sue me. But first, you have to take the LSAT and get into law school so pay attention." that was unannounced lol
LOL
reading the comments below to look for some extra clarification but I see everyone seems lost as well.
Dear LittlePickleBigWorld,
I can explain how I understand the content. For me, this is how I am interpreting everything, given the Jedi example:
1. If one person is enough to assume (i.e sufficient enough) to be a jedi, then one is required to know how to use the force.
In the context of this example, the jedi is the subset & the force is the superset.
2 Luke, who is a member, is a Jedi.
That means that Luke has membership in the subset.
3 Therefore, Luke uses the force.
Because Luke has membership in the subset, it is required that he knows how to use the force.
so If I am... -> I must be ... ?
If I am a cat -> I must be a mammal
I think one way to understand the arrow, is that the arrow always points in the direction of certainty.
If I go to the store, I (must) buy milk).
Go to store -> buy milk.
Whereas you cannot say:
buy milk -> go to store. What if I got milk elsewhere?
@bcn but its not though. Buying milk would be the superset and going to the store would be the subset. The lesson on group 1 indicators explains this quite clearly: the "If" in I go to the store is a sufficient indicator, meaning going to the store is a sufficient indicator for triggering buying milk.
@TheBigFatPanda I see what you mean now.. this helps a lot; thanks for the clarification.
@TheBigFatPanda The way you just explained this, broke the barrier that I had in understanding this concept. Thank you. I was starting to get really frustrated.
This example doesn't make sense to me. This is what makes sense to me:
Store -> Milk
Mammal -> Cat
you have to go to the store to buy milk, but you dont have to buy milk if you go to the store.
just like how you have to be a mammal if you're a cat, but you dont have to be a cat if you are a mammal.
same! commenting to follow replies
Using your examples, the direction of the arrows would be reversed, though:
Milk --> Store
Cat --> Mammal
That's how we'd represent "You must go to the store in order to buy milk" and "You must be a mammal in order to be a cat."
In other words, if someone bought milk, that guarantees they went to the store.
If something is a cat, that guarantees it's a mammal.
If you represent the arrow the other way around: "Store --> Milk", that would assert that anyone who goes to the store buys milk.
Note that the example in the lesson was "If store, then milk." That is intended to say that anyone who goes to the store buys milk. The example in the lesson isn't intended to be a description of anything from real life.
So to be clear, if we have "If store, then milk", that means store is a sufficient condition and milk is a necessary condition.
If we have "If milk, then store", that means milk is a sufficient condition and store is a necessary condition.
It doesn't matter whether in real life going to the store is required to buy milk; we're simply analyzing the meaning of the given statements.
Hi Kevin, I still need some clarifications regarding this.
So, to better understand I took this example and compared it to the New York/ USA example.
If I go to New York then I'll be in the USA
New York -> USA
sufficiency -> Necessity
If I go to the store then I will buy milk
store -> milk
sufficiency -> necessity
So I get the sufficiency part but what I'm still not understanding is the necessity aspect.
We know that being in the USA is necessary to being in New York, after all New York is inside of the USA. But with the milk example this is tricky because it is the milk that's inside of the store, not the other way around.
You NEED to go to the USA in order to visit New York.
But you do NOT NEED to buy milk in order to visit the store, actually is the other way around, you NEED to be in the store to buy milk.
I get that you mentioned that we are not supposed to look at it from the real world view, but even if its guaranteed that you will get milk by going to the store, I am still failing to see how it is a necessity to buy milk in order to be in the store.
I'll appreciate if you could clarify that. Thanks.
I think one of the downsides to using examples like the "If New York --> USA" statement is that it draws upon your own real-life understanding of the relationship between being in New York and being in USA. That's why it's easy to understand "being in USA" as necessary to "being in NY."
With the statement "If I go to the store, I will buy milk," however, this statement doesn't make sense in real life. Obviously in real life it's possible for me to go to the store and not buy milk. But let's just accept the statement as true, regardless of whether it maps onto our understanding of real life stores and purchases of milk.
"If I go to the store, I will buy milk."
This means if I go to the store, it must be the case that I will buy milk. It's impossible for me to go to the store and not buy milk.
What if you learn the following fact about me: I went somewhere, and I did not buy milk.
If I didn't buy milk...then that proves I didn't go to the store. Because if I went to the store, I had to buy milk. So if I didn't buy milk, you can conclude that I didn't go to the store.
This is the sense in which "buying milk" is necessary for the condition "I go to the store." The necessity is a reference to the truth of the conditions -- in order for "I go to the store" to be true, it must also be true that I will buy milk.
We're not saying that for us to be physically in the store, there's something about the physical presence of being in the store that requires us to also buy milk. We're just saying that the "state of the world in which I buy milk" is necessary in order for "the state of the world in which I go to the store" to be true.
Does that make sense? Here's another example. This statement is easy to conceptualize in terms of what's necessary:
"In order to get into law school, I must take the LSAT."
It's easy to see that taking the LSAT is necessary because we conceptualize the LSAT as one of the things we have to do to get into law school -- there's a big list of requirements and the LSAT is one of them.
But what about this:
"In order for the sky to be red, my neighbor's dog must bark loudly."
Here, my neighbor's dog barking loudly is necessary in order for the sky to be red. You might think...how does that make sense? Why does the sky bring red require my neighbor's dog to bark? There's obviously no real relationship between the color of the sky and my neighbor's dog barking.
However, given what the statement says, we know that if the sky is red, it must be that my neighbor's dog has barked loudly. And if my neighbor's dog hasn't barked loudly, the sky can't be red. This is the sense in which my neighbor's dog barking is necessary. The "state of the world in which my neighbor's dog has barked loudly" is necessary in order for the "state of the world in which the sky is red" to be true. "Necessary" is simply desribing a relationship between the truth value of various states of the world. It's not a comment on any kind of physical requirement or some kind of causal connection between the sky being red and the dog barking.
Keep in mind, that "In order for the sky to be red, my neighbor's dog must bark loudly" is not true in real life. But what matters is the meaning of the statement. If you analyze the meaning of the statement, without caring about whether it's true in real life, then you will see that the words in the statement express the idea that "my neighbor's dog must bark loudly" is necessary for "sky to be red."
Interesting. I think I got it now. So I am imagining a world where if I got to the store then I absolutely have to buy milk, regardless of what else I get or don't get, milk is a requirement, otherwise I cannot step foot inside the store, which would then mean that no milk equals no store. You're right. I was trying my best to not use real world logic in the exercise but what kept tricking me was the fact that the milk is inside the store, however that doesn't matter because buying milk in that world can simply be a requirement to enter the store, sort of like when going to a bar, if I sit at the bar then I must order a drink" so even if the drink is inside the bar, if you don't order it you can't sit in. So I imagined a world where buying milk is required to enter the store, which would then make milk necessary. Thanks Kevin, I get it now. Thanks for providing such an in-depth clarification.
The arrow makes so much more sense to me, I am confused why circles and dots would ever be more beneficial
@LiviaLSAT for me at least it feels more natural to use the dots because it allows me to hold more information. like if you introduce many subsets together "like cats ->mammals dogs->mammals" etc it can quickly add up and become complicated.
WOW. So, I studied on my own for the first LSAT I did and always saw this notation but constantly messed it up because I didn't know that the arrow itself had this rule. This is such a big clarity moment.
CRAZY
why is there a store → milk in the sufficient → necessary condition?
What is it trying to say lol.
maybe also -- if it is a store, then it has milk..
• Sufficient Condition (Store): Being a store.
• Necessary Condition (Milk): Having milk.
I go to the store, I buy milk.
Since the store is sufficient in this sub/superset, then it is necessary to say "Every time I go to the store, I buy milk."
Since you can also buy milk elsewhere (farm, market, etc.) it means that just because you bought milk doesn't mean you went to the store, you could've acquired it elsewhere in this scenario, but if you went to the store, it is certain that you bought milk.
"store → milk"
what is this trying to say lol
#help (Added by Admin)
This is how I understood it,
If an item(x) is a milk, it is guarenteed to be in a store( membership in milk is sufficient for membership in store).
If an item is a milk, it is sufficient to say the item is in the store.
If an item is not found within a store, it is impossible for the item to be milk (without membership in the necessary condition, membership in the sufficient condition is impossible)
If an item is found in a store, it is not sufficient to be a milk.( membership in the necessary condition(store) is not sufficient for membership in the sufficient condition(milk)).
In order for an item to be a milk, it is necessary for it to be in a store.( membership in the necessary condition(store) is necessary for membership in the sufficient condition(milk).
It is not necessary to be a milk in order to be in a store ( membership in the sufficient condition is not necessary for membership in necessary condition)
#help - I was thinking the same thing! Can someone enlighten us?
I think it would be like If one goes to the store, then one needs/buys milk. like the same sentence structure as the jedi example " if one is a jedi, then one is a force user"
This is how I understood it:
Symbol: →
Meaning: If...then...
Example: store → milk = If you went to the store (S) then you got milk (M).
- (S →): The left side of the implication (S, or going to the store) is the sufficient condition. This means if S occurs (you go to the store), it is sufficient to ensure that M (getting milk) follows under the context of this implication.
- (→ M): Viewing the right side of the implication (M, or getting milk) as the "necessary condition" in this framework means that M is necessary in the sense that it must occur if S has occurred. This is based on the assumption that if the sufficient condition is met, the occurrence of M is necessary to fulfill the truth of the implication S→M
In sum: The act of going to the store (S) is posited as a sufficient condition for obtaining milk (M). This implies that if the condition of going to the store is fulfilled (If S), the implication suggests that it guarantees the outcome of obtaining milk (then M). However, while going to the store ensures you will get milk within the logic of this statement, it is not stated as the only method of acquiring milk; other ways may exist, thus making it not a necessary condition for having milk.
I think its saying if you're at a store, then there will be milk
Ground beef ---> type of meat
I like how this lesson includes an alternative way of thinking of sufficient and necessary conditions as subset and superset -- this is a very important key that can easily allow arguments to be drawn out in sets (aka circles :) )
Right? It helped me grasp these concepts much better.
This will probably be explained in a future lesson I imagine, but I'd like clarification on what happens when the necessary condition is true instead of the sufficient.
I'll use the milk/store example since I think that's the one most of us are confused about. I'll also write it out to specify the premises and conclusion:
Premise 1: If I go to the store, I will buy milk.
Premise 2: I went to the store.
Conclusion: I bought milk.
And here the "Lawgic" version of Premise 1:
Store -> Milk
This might not make sense in our world, but in the world of this argument then if anyone ever goes to the store, they have to buy milk. I think this makes sense.
Now what if I change the argument to something like this:
Premise 1: If I go to the store, I will buy milk.
Premise 2: I bought milk.
Conclusion: I went to the store.
I want to say that this does not make sense/is not valid, because Premise 1 is unchanged that means that the Lawgic is still "Store -> Milk," and not "Milk -> Store." In English, this would mean that I could have gotten milk from anywhere, not just the store.
@aidanro2003 You're totally right! The necessary condition being true means nothing for the sufficient condition. The only other true logical statement you could get out of this is if you didn't buy milk, you didn't go to the store as we know if you went to the store you must have bought milk.
This has been the most helpful part for me so far. That just finally clicked for me!
Can we not put "going to the store" as a superset and "buying milk" as a subset? It is sufficient for you to go to the store to buy milk.
@ConqueringLSAT I think since they are actions and not characteristics, it may be harder to distinguish in a question
The reason i have trouble with the store -> milk example is because there simple isn't enough information. I read this as relating to what one gets when at the store, in which case milk -> store would be correct because i could get orange juice at the store, not milk
@epayne17 the point of the -> element is to show the conditional relationship present in the argument, not to provide context. Reading the sentence/argument provides you with the context to which we figure out how to use the -> to show the conditional relationship.
In this context, the "If I go to the store [subset], then I will buy milk [superset]." Therefore, store -> milk; try not to rely on your intuition about what you might get at the store. Only what is presented in the argument.
@epayne17 Part of this is also picking out those indicator words.
He says: If I go to the store, then I will buy milk. "If" is a sufficient condition indicator. He's not saying he could buy milk - he will buy milk if the condition (going to the store) is met.
@Livandthecats lol going to the store does not require milk. I'd argue it makes far more logical sense to say that for the most part buying milk requires going to the store. You simply cannot make the claim that he will buy milk if he goes to the store. He could buy literally anything else at that store.... Picture the store and milk as the circles visualization JY gives for relationships. The milk circle should logically lie within the store's bigger circle. This makes the store the proper necessary condition, not milk.
@epayne17 Yes, buying milk typically involves going to a store. However, the argument that is being presented is in fact that if he goes to the store, he will buy milk.
In this case going to the store is your sufficient condition/subset because it follows the indicator "if". It doesn't matter that realistically there's not many other places to buy milk (unless you live near dairy farms), the argument is presented in such a way that store is the subset and milk is the superset.
If it was phrased as "If I bought milk, then I've gone to the store" then your argument makes sense. But the argument has not been presented that way.
in the "if i go to the store, i will buy milk", why is if i go to the store the sufficient? shouldn't that be necessary? please explain!!
@akhan1693 "if" is a sufficent condition indicator
I am excited to learn 'lawgic' as I think this will be really helpful for breaking down questions quickly! :)
Rugby Player > Person who runs the ball
Ballet --> Type of Dance
Basketball Player --> Person Who Can Dribble
@SheaStarrs Soccer Player --> Person Who can Dribble, thus it can never be Person Who Can Dribble --> BasketBall Player.
When he mentioned the abstract thought I immediately thought of an arrow like conditions. 🚶🏿♂️→buy milk 🏪
The way you listed all the "natural languages" in the exact same order as I learned my 2nd, 3rd, and 4th languages at 2:05 definitely caught my attention lol!
He's already using A for P and B for Q, but does anyone know if this will follow a more formal/classical logic language or a sentential logic language? Or neither and I'm just going to get really confused?
Update.... You will be very confused if you keep trying to use any sort of logic symbols you previously learned.
so if A then B.
A has to happen for B to happen
sufficient condition → necessary condition
Yes
I think it's the other way around! The statement A --> B (if A then B) would be more accurately translated as B has to happen for A to happen. (B is the necessary condition that has to happen in order for A to be true.)
Exactly. The sentence structure is If A, then B. When diagramming it out,
It looks like B→A.
B is the sufficient condition; A is the necessary one. Example: If I go to the store, then I will buy milk.
If A, then B. Going to the store is necessary for buying the milk. The above would be diagrammed as Milk→Store. The lesson has it backwards, and it's confusing. Glad I'm not alone in that.
Yes, this is also my interpretation. A happening is sufficient to assume that B has happened already, because B is necessary for A to have happened. So if A happens, then B has also by definition happened
Just to be clear, in your initial sentence "If A, then B", A is the sufficient condition and B is the necessary condition.
That would look like "A --> B".
So the statement "If I go to the store, then I will buy milk" would be diagrammed "Store --> Milk".