Something that confuses me is how do you know which goes in the bigger circle and which goes in the smaller circle? The diagram really helps me but I'm uncertain about which goes where.
@BrieV The key is figuring out which condition is sufficient and which is necessary. The sufficient is the smaller circle (subset), and the necessary is the bigger circle (superset). I just try to remember SS = Sufficient Small lol.
@billyg03 The example you shared is just another way of saying what I displayed in my example. The "x" are not negations, they are just a symbol for a variable "x".
For example, xA is not saying "not A". It's just saying "X is an A." So this can also be translated to the same statement I shared above: All As are Bs. X is an A. Therefore, X must also be a B.
@SarahShaver Yes, your argument is valid. It follows the valid logical form called "modus ponens" (If P. then Q. P. Therefore, Q). I learned the term modus ponens in philosophy, but it's also used in law too!! Modus ponens is latin for "the method of affirming".
@purplesunshine007 its so funny because youre the only other person ive ever seen use this form. i worked w a tutor once and i was like oh its like a math equation like they cancel each other out and he was like ... wtf are you talking about ?? I dont have a math brain by any means but these kinds of arguments reminded me of cancelling out two-sided equations lol
@bellaens18 I’m a philosophy graduate and that’s how we were talked to validate arguments in our logic class. In the back of the book was a list of rules like that one.
I think I struggle with the distinction between VALID arguments and TRUE arguments. If the Superset of "Ninjas" includes a subset of "Turtles", which includes "Donatello" then the argument is valid that donatello is a ninja, but it is not true that all turtles are ninjas. For the the argument to be both valid and true the subset would have to be TMNT.
@JeremyM I agree when I first began these questions I could not let go of the fact that they were untrue. It is getting easier now that the logic aspect is kicking in.
@HealthLaw@28 I do believe so, yes! It seems as if formal arguments say that a member of a smaller group (subset) are always a member of a larger group (superset). Then, it plugs in an example into this smaller group to create sufficiency for membership into this larger group.
For example, "I have a cat. All cats are cute. Therefore, my cat is cute." In this example, cats (the member in question) are a subset of things that can fit into the "cute" superset label; many more things can be cute, and cats are just one of them. Saying, "I have a dog. All dogs are cute. Therefore, my dog is cute," would provide an example of another statement that expands the umbrella of "cute" things. In both examples, membership in the subset - dogs/cats - is sufficient for membership in a larger, more-encompassing superset of cute things.
I hope this explanation was English and helped, even if only a little and even if a month late!
Does anyone else have days where they can't get any questions right? the drills are humbling me today. Im so scared im going to get to the test and be having one of those days
Another way to think of it: sufficiency guarantees necessity not the other the way around. Being a cat guarantees being a mammal but being a mammal doesn't guarantee being a cat.
@SarahSmile That is a good way of looking at it when there is a subset and superset relationship. However, it becomes a problem in a sufficiency and necessity causal relationship. For example:
A brain death is going to get you killed (body will stop) surely i.e. is sufficient for you to get killed. But that is not necessary for you to get killed. You can get killed in all sorts of ways kidney failure, cancer etc. Death does not require brain death.
This is an example of sufficient but not necessary. That is, sufficiency is not guaranteeing neccessity because maybe there are no necessary ways to get killed.
@Isra I think we’re using “necessary” in slightly different ways. In conditional logic, when we say X is sufficient for Y, we mean that Y is necessary for X. Meaning whenever X occurs, Y must occur. That doesn’t mean Y requires X in all cases. So brain death →death means that the occurrence of brain death guarantees “death” but “death” doesn’t necessarily guarantee that “brain death” occurred. Death could be the result of any other thing.
Premise 1: membership in a subset is sufficient for membership in a superset. Premise 2: X is a member of the subset. Conclusion: X is a member of the superset. Is that correct
@BreanaNunez Hi! I don't think is argument is valid.
Premise 1: If one is relaxing, they're watching tv. (Translation: If r -> tv)
Premise 2: Bre is watching TV. (Translation: B^TV)
You can't conclude that Bre is relaxing because watching TV is the necessary condition of the first premise or the "superset". This means that there are many other states that Bre or anyone could be in based on the first premise.
Another way to think about it is to think like this:
Premise 1: If one is in New York City, they're in the United States.
Premise 2: Bre is in the United States.
Based on the above logic, the conclusion would be: Bre is in New York. HOWEVER, we know that based on the premises/logic, Bre could be anywhere in the United States not just in New York.
To make the argument valid you would have to change the second premise to "Bre is in New York City" and then conclude "Bre is in the United States".
With the original argument, the same logic follows. You would have to change the second premise to "Bre is relaxing" and the conclusion to "therefore, Bre is watching TV" to make it logically sound.
You could also alter the first premise to say, "if one is watching TV, they're relaxing". Then the argument would be valid as it is.
for all of the formal logic people out there, this is is a simple argument form if you break it down into p and q. it would look something like: if p then q (p ->q), p, therefore q. this works because if the first half of a conditional statement is true (which we know it is because of the second premise, then the second half must be true in order for the statement (our original premise of if p -> q) to be true! idk if this helps anyone, but conceptually it works a lot better for me.
116 comments
All dromeosaurs are dinosaurs. Velociraptor is a dromeosaur, therefore Velociraptor is a dinosaur
A is B. C is A. therefore C is B
Right?
So it's just modus ponens?
Something that confuses me is how do you know which goes in the bigger circle and which goes in the smaller circle? The diagram really helps me but I'm uncertain about which goes where.
@BrieV The key is figuring out which condition is sufficient and which is necessary. The sufficient is the smaller circle (subset), and the necessary is the bigger circle (superset). I just try to remember SS = Sufficient Small lol.
i find it easier to see the relationship like this:
P: A --> B
P: A
C: B
(All As are Bs. X is an A. Therefore, X must also be a B.)
@billyg03 The example you shared is just another way of saying what I displayed in my example. The "x" are not negations, they are just a symbol for a variable "x".
For example, xA is not saying "not A". It's just saying "X is an A." So this can also be translated to the same statement I shared above: All As are Bs. X is an A. Therefore, X must also be a B.
7sage represents negations with "/"
Hope this helps!
im cooked
@studyever1234 Real
@studyever1234 YOU GOT THIS!
@studyever1234 take a symbolic logic class if you can, its very helpful for developing logical thinking skills
fat cats who sing the blues
Cats who sing the blues
Cats who sing
Cats
If Garfield is a fat cat who sings the blues, then we know he’s a cat who sings.
If Garfield is a cat, we don’t know if he sings.
If one is a cat, then one is a mammal.
Athena is a dog.
Athena is a mammal.
All animals who bark are dogs, Bradley barks therefore Bradley is a dog. Is this correct?
@SarahShaver
Given your premises, your conclusion is valid.
I think this could be a diagram of it.
@SarahShaver Yes, your argument is valid. It follows the valid logical form called "modus ponens" (If P. then Q. P. Therefore, Q). I learned the term modus ponens in philosophy, but it's also used in law too!! Modus ponens is latin for "the method of affirming".
if you find this confusing ur cooked lol
@Matt.bartos if one’s not cooked one doesn’t call others cooked.
If one’s cooked one calls others cooked.
“If you find this confusing ur cooked lol”
—Matt.bartos
if X then
Yif
Ythen ZTherefore, X then Z
@purplesunshine007 its so funny because youre the only other person ive ever seen use this form. i worked w a tutor once and i was like oh its like a math equation like they cancel each other out and he was like ... wtf are you talking about ?? I dont have a math brain by any means but these kinds of arguments reminded me of cancelling out two-sided equations lol
@bellaens18 I’m a philosophy graduate and that’s how we were talked to validate arguments in our logic class. In the back of the book was a list of rules like that one.
@purplesunshine007 thats so good to know, we think the same LOL
@purplesunshine007 I like this way of looking at it alot....
I think I struggle with the distinction between VALID arguments and TRUE arguments. If the Superset of "Ninjas" includes a subset of "Turtles", which includes "Donatello" then the argument is valid that donatello is a ninja, but it is not true that all turtles are ninjas. For the the argument to be both valid and true the subset would have to be TMNT.
@JeremyM I agree when I first began these questions I could not let go of the fact that they were untrue. It is getting easier now that the logic aspect is kicking in.
All Elephants are D1 Football players. Roxy is an elephant. Therefore Roxy is a D1 Football player.
Eating Buffalo Chicken Cheese Fries makes you a king. My friend ate Buffalo Chicken Cheese Fries. Therefor, my friend is a king.
@Super_Cookie doing LSAT practice everyday will get you a high score. I'm doing LSAT practice everyday. Therefor, I will get a high score
Question Anyone? As far as the logic equation for this lesson: is B always the superset, A always subset and X always the member/membership??
@HealthLaw@28 I do believe so, yes! It seems as if formal arguments say that a member of a smaller group (subset) are always a member of a larger group (superset). Then, it plugs in an example into this smaller group to create sufficiency for membership into this larger group.
For example, "I have a cat. All cats are cute. Therefore, my cat is cute." In this example, cats (the member in question) are a subset of things that can fit into the "cute" superset label; many more things can be cute, and cats are just one of them. Saying, "I have a dog. All dogs are cute. Therefore, my dog is cute," would provide an example of another statement that expands the umbrella of "cute" things. In both examples, membership in the subset - dogs/cats - is sufficient for membership in a larger, more-encompassing superset of cute things.
I hope this explanation was English and helped, even if only a little and even if a month late!
I am confused because this just seems a lot like logic games but I am going to review it until it makes sense
Does anyone else have days where they can't get any questions right? the drills are humbling me today. Im so scared im going to get to the test and be having one of those days
@KaraSwider Yep its day 5 for me
Please don't disrespect Luke!
@MRod It's ok, Star Wars and logical reasoning don't usually go hand in hand.
Another way to think of it: sufficiency guarantees necessity not the other the way around. Being a cat guarantees being a mammal but being a mammal doesn't guarantee being a cat.
@SarahSmile That is a good way of looking at it when there is a subset and superset relationship. However, it becomes a problem in a sufficiency and necessity causal relationship. For example:
A brain death is going to get you killed (body will stop) surely i.e. is sufficient for you to get killed. But that is not necessary for you to get killed. You can get killed in all sorts of ways kidney failure, cancer etc. Death does not require brain death.
This is an example of sufficient but not necessary. That is, sufficiency is not guaranteeing neccessity because maybe there are no necessary ways to get killed.
@Isra I think we’re using “necessary” in slightly different ways. In conditional logic, when we say X is sufficient for Y, we mean that Y is necessary for X. Meaning whenever X occurs, Y must occur. That doesn’t mean Y requires X in all cases. So brain death →death means that the occurrence of brain death guarantees “death” but “death” doesn’t necessarily guarantee that “brain death” occurred. Death could be the result of any other thing.
@SarahSmile I understand you now! tnx
Premise 1: membership in a subset is sufficient for membership in a superset. Premise 2: X is a member of the subset. Conclusion: X is a member of the superset. Is that correct
@VanillaCat yes!
Every conditional argument is valid? Does that also make every conditional argument true?
when you put it like this, it makes more sense.
Will the premises always be assumed true? like not all turtles are ninjas, but for the test we assume this is the case?
@SusanLeifker Oh lol it's the very next video
if one is relaxing, they're watching tv. Bre is watching TV. therefore bre is relaxing.
@BreanaNunez Hi! I don't think is argument is valid.
Premise 1: If one is relaxing, they're watching tv. (Translation: If r -> tv)
Premise 2: Bre is watching TV. (Translation: B^TV)
You can't conclude that Bre is relaxing because watching TV is the necessary condition of the first premise or the "superset". This means that there are many other states that Bre or anyone could be in based on the first premise.
Another way to think about it is to think like this:
Premise 1: If one is in New York City, they're in the United States.
Premise 2: Bre is in the United States.
Based on the above logic, the conclusion would be: Bre is in New York. HOWEVER, we know that based on the premises/logic, Bre could be anywhere in the United States not just in New York.
To make the argument valid you would have to change the second premise to "Bre is in New York City" and then conclude "Bre is in the United States".
With the original argument, the same logic follows. You would have to change the second premise to "Bre is relaxing" and the conclusion to "therefore, Bre is watching TV" to make it logically sound.
You could also alter the first premise to say, "if one is watching TV, they're relaxing". Then the argument would be valid as it is.
I hope this helps!
@BreanaNunezThis is actually known as affirming the consequent.
Finally had the light bulb moment for this section! Now let's see if I can connect the dots on PTs
for all of the formal logic people out there, this is is a simple argument form if you break it down into p and q. it would look something like: if p then q (p ->q), p, therefore q. this works because if the first half of a conditional statement is true (which we know it is because of the second premise, then the second half must be true in order for the statement (our original premise of if p -> q) to be true! idk if this helps anyone, but conceptually it works a lot better for me.