Why does "all cats are mammals" not get translated in lawgic to C^M since it is stating that all Cats are members of Mammals and not "If cat, therefore mammals"?
Is it necessary (no pun) to diagram as a subset versus an outright sufficient - necessary arrow for uniformity purposes? To be clear, instead of writing out gC, can I write this out as G---C, similar to how the first premise is written out as C---M?
I think this makes more sense after mapping out my own examples - someone correct me if I'm wrong here.
If rent goes down, then living conditions will improve for residents of 7Sage Apartments. Rent is going down for 7Sage Apartments, therefore living standards will improve for their residents.
This is not an argument that will require sets, as there are many different ways living conditions can improve. Saying in order for living conditions to improve, rent must go down doesn't work. It is fine to say that rent going down will improve living conditions, but that's not the whole story.
Rent is going down in 7Sage Apartments, which means residents' living standards will improve. JY is a resident of 7Sage Apartments. Therefore, his rent is going down and his living standards will improve.
This argument implies that there are sets being used, as it establishes JY as a member of a set (resident of 7Sage Apartments). The first argument doesn't establish membership for anything specific, it only contains a conditional relationship.
One thing I noticed about this example is that the claim "All cats are mammals. Garfield is a cat." doesn't appear on its surface to be a conditional relationship the way the second example with downtown restaurants does. Just a note for consistency since this example of "X is Y." has been used elsewhere to demonstrate when something ISN'T a conditional relationship. I guess that's the point J.Y. is trying to make here but it honestly just makes me more confused because intuitively you can tell these arguments are different in form.
It is so interesting to see conditional logic explained this way! I majored in Math and we were taught set and conditional logic in one of our core math courses (MATH 220: Mathematical Proofs). While it was taught in a slightly different way, it seamlessly applies to the LSAT.
Came here after getting 149.4.23 wrong. Did not find the answer explanation as to why C over B helpful. Came here. Also not helpful, as the difference between subsets/supersets and conditional logic is key in that answer choice and I need more help understanding. Revamping and making this lesson more thorough would be helpful. #feedback
Could it be helpful, for modus ponens (and other arguments hinging on a certain set of circumstances then setting into motion more circumstances) consider the reality presented by the premises to be the individual we are assessing, just like how we assess whether or not Garfield is a member of the cat set.
For example:
- If new restaurants open downtown, then quality of life will improve for downtown residents
New restaurants open downtown, therefore quality of life improves
is the same as
Reality is a member of the set of instances where new restaurants opened downtown, therefore quality of life improves for downtown residents.
or to use a different argument
- All cats are mammals
Garfield belongs to the set cat, therefore Garfield is mammal
is the same as
Garfield satisfies the condition of being a cat, therefore Garfield is a mammal
Is this thought experiment just confusing? In assessing the arguments from this perspective, how are sets and conditions any different. I don't really see how modus ponens and a categorical syllogism can be substantially different, unless the content of the argument is a factor in classifying the type of logic rather than just the base form. I am not a logician, so I really don't know.
Mmm... I disagree with this approach. I believe it is better to understand how these two arguments are different, since you rely on different methods to prove their validity. I use logical connectives for modus ponen/modus tollens and diagrams (circles and dots) for sets.
I'm still completely lost by using superscript and don't get why we have to over complicate this. I failed algebra a record number of times and the appeal of the LSAT was no math. Maybe I just need to reconsider my career plans.
i think i get it - but this sentence is really confusing me - i heard it in the video, and scrolled down to check if i heard right, but i'm not quite understanding the semantics of the following: "Why then do I conflate these two different types of arguments? Because I've never seen the LSAT create trap answers that trade on failing to make such a distinction." can anyone dumb this down for me?
So in a question where it asks what stated argument follows the format for the one stated above, is this essentially the choice you would choose? I hope this makes sense. #help
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62 comments
is it me or does he sound like he's talking faster?
All cats are mammals. Garfield is a cat. Therefore, Garfield is a mammal.
cats = C
mammals = M
Garfield = G
Cats --> Mammals
C --> M
Being a cat is sufficient to being a mammals but is not necessary.
Being a mammal is necessary to being a cat but is not sufficient.
Garfield is a cat, therefore he is also a mammal.
Premise 1: If the restaurant introduces chicken sandwiches, then sales will increase for the company.
Premise 2: The restaurant introduces chicken sandwiches to the menu.
Conclusion: Therefore, sales increase for the company.
I find the formal mathematics version of this more helpful to read for the Garfield example. It would be written as such:
For all generic things; if that thing is a cat then it is a mammal
Garfield is a cat
Therefore, Garfield is a mammal
Why does "all cats are mammals" not get translated in lawgic to C^M since it is stating that all Cats are members of Mammals and not "If cat, therefore mammals"?
couldve said theyre "lawgically equivalent" too har har
Is it necessary (no pun) to diagram as a subset versus an outright sufficient - necessary arrow for uniformity purposes? To be clear, instead of writing out gC, can I write this out as G---C, similar to how the first premise is written out as C---M?
I find this easier to track.
I think this makes more sense after mapping out my own examples - someone correct me if I'm wrong here.
If rent goes down, then living conditions will improve for residents of 7Sage Apartments. Rent is going down for 7Sage Apartments, therefore living standards will improve for their residents.
This is not an argument that will require sets, as there are many different ways living conditions can improve. Saying in order for living conditions to improve, rent must go down doesn't work. It is fine to say that rent going down will improve living conditions, but that's not the whole story.
Rent is going down in 7Sage Apartments, which means residents' living standards will improve. JY is a resident of 7Sage Apartments. Therefore, his rent is going down and his living standards will improve.
This argument implies that there are sets being used, as it establishes JY as a member of a set (resident of 7Sage Apartments). The first argument doesn't establish membership for anything specific, it only contains a conditional relationship.
I really hope this makes sense, lol!
One thing I noticed about this example is that the claim "All cats are mammals. Garfield is a cat." doesn't appear on its surface to be a conditional relationship the way the second example with downtown restaurants does. Just a note for consistency since this example of "X is Y." has been used elsewhere to demonstrate when something ISN'T a conditional relationship. I guess that's the point J.Y. is trying to make here but it honestly just makes me more confused because intuitively you can tell these arguments are different in form.
I am confused and would appreciate someone or a tutor explaining this/conditional arguments
Do you actually need to use this method?
Im glad i majored in philosophy, haha!
It is so interesting to see conditional logic explained this way! I majored in Math and we were taught set and conditional logic in one of our core math courses (MATH 220: Mathematical Proofs). While it was taught in a slightly different way, it seamlessly applies to the LSAT.
Until he explained how they were different. I assumed they were the same.
Came here after getting 149.4.23 wrong. Did not find the answer explanation as to why C over B helpful. Came here. Also not helpful, as the difference between subsets/supersets and conditional logic is key in that answer choice and I need more help understanding. Revamping and making this lesson more thorough would be helpful. #feedback
is this approach actually effective or not? How many people do this and how did it help you?
So far I am having extreme growing pains applying this method to solving LSAT questions ...
Could it be helpful, for modus ponens (and other arguments hinging on a certain set of circumstances then setting into motion more circumstances) consider the reality presented by the premises to be the individual we are assessing, just like how we assess whether or not Garfield is a member of the cat set.
For example:
- If new restaurants open downtown, then quality of life will improve for downtown residents
New restaurants open downtown, therefore quality of life improves
is the same as
Reality is a member of the set of instances where new restaurants opened downtown, therefore quality of life improves for downtown residents.
or to use a different argument
- All cats are mammals
Garfield belongs to the set cat, therefore Garfield is mammal
is the same as
Garfield satisfies the condition of being a cat, therefore Garfield is a mammal
Is this thought experiment just confusing? In assessing the arguments from this perspective, how are sets and conditions any different. I don't really see how modus ponens and a categorical syllogism can be substantially different, unless the content of the argument is a factor in classifying the type of logic rather than just the base form. I am not a logician, so I really don't know.
is it okay to think of the sufficient condition as the "why?" for the necessary condition?
I don't think mentioning the difference was necessary in the first place. Now my brain will start marking them different sort of..
Mmm... I disagree with this approach. I believe it is better to understand how these two arguments are different, since you rely on different methods to prove their validity. I use logical connectives for modus ponen/modus tollens and diagrams (circles and dots) for sets.
Is it just me or is he talking faster in this video lol
I'm still completely lost by using superscript and don't get why we have to over complicate this. I failed algebra a record number of times and the appeal of the LSAT was no math. Maybe I just need to reconsider my career plans.
i think i get it - but this sentence is really confusing me - i heard it in the video, and scrolled down to check if i heard right, but i'm not quite understanding the semantics of the following: "Why then do I conflate these two different types of arguments? Because I've never seen the LSAT create trap answers that trade on failing to make such a distinction." can anyone dumb this down for me?
I get it but I don't ! Been on this part of the course for a while now !
So from this example, is it likely that sometimes the necessary condition will also be the conclusion?
So in a question where it asks what stated argument follows the format for the one stated above, is this essentially the choice you would choose? I hope this makes sense. #help