I made a visualization (think Venn diagram) to help my brain absorb the concept of Most (or All) before Most not leading to valid conclusions. It helps me a ton.
wait okay okay after sitting w this for like ten minutes i think i get it. most almonds are grown in cali. most cali produce is exported to brazil. produce does NOT have to include almonds. cali produce can be avocados, apples, cherries, corn, wheat, blah blah blah and yes it COULD include almonds MAYBE but almonds also could be the ONE THING that is not included in "most" of cali's produce.
i appreciate the strategy of "lawgic" for the harder questions but as a writer/reader i sometimes find it much easier to think it through with words rather than symbols. the formula is nice, but it gets a little too "math-y" for me lol
@hannahhjh same, it's hard for me to translate to lawgic then back to english quick enough to meet the time limits for questions. the equation aspect helped in the earlier lessons but as they're getting more complicated, the symbols are confusing me more.
Most of America's almonds are grown in California.
Most produce from California is exported to Brazil.
Therefore, some almonds are exported to Brazil.
The problem here is that the premises don't guarantee the conclusion—just because "most" almonds are grown in California and "most" produce from California is exported to Brazil doesn't mean some almonds specifically are exported to Brazil. They could be eating the almonds domestically in CA and sending other produce to Brazil.
To make it valid you could say:
All of America's almonds are grown in California.
Most produce from California is exported to Brazil.
Therefore, some almonds are exported to Brazil.
Premise 1 guarantees that all almonds are grown in California.
Premise 2 states that most produce from California is exported to Brazil.
With these two premises, it's guaranteed that some almonds (because "most" produce from California is exported to Brazil) must be exported to Brazil.
OR another valid option:
All almonds grown in California are exported to Brazil.
@FranciscoLee I think it is correct because your drawing you conclusion from the fact the produce from the California element of the stem. A simpler way to look at it would be All implies most, so if all produce from Cali is almonds then also produce from California-m>almonds is also valid. So then just switch it around A-m>B and A-m>c
Remember: When two "most" statements are chained together, there are no valid conclusions to be drawn.
The ONLY instance in which two "most" claims can work together to draw a conclusion is when two "most" arrows come from the same set
A -m-> C
A -m-> B
____
C <-s-> B
Ex.
Most of USA's peaches come from Georgia. Most produce from GA is exported to Mexico. Therefore, some peaches are exported to Mexico.
A --m-> B --m-> C
____
A <-s-> C
This is NOT a valid conclusion; maybe, even though most USA peaches do come from GA, GA only produces 10% peaches and 90% other produce. So, those few, precious peaches stay in the US, while the rest is shipped out.
Ex.
Most of USA's peaches come from Georgia. Most of USA's peaches are exported to Mexico. Therefore, at least some of the peaches sent to Mexico are GA peaches.
I feel like this would make way more sense if we also were given a valid form of the argument.
So for this one, I think that would be:
Most of America's almonds are grown in California. Most of America's almonds are exported to Brazil. Therefore, some things (implied: produce) grown in California are exported to Brazil.
US almonds ‑m→ grown in California
US almonds ‑m→ exported to Brazil
_
grown in California ←s→ exported to Brazil
It may the case that some things [produce] grown in California are not exported to Brazil, and some things [produce] that are exported to Brazil are not grown in California.
This is invalid because even with two ‑m→ that leaves room for exclusion. Let’s say there are 70 almonds (produce) out of 100 that are grown in California and that 80 produce out of 100 produce is exported to Brazil. Produce is a big subset; it could be that 40 carrots and 40 blueberries get exported to Brazil and none of the almonds do. We can’t say that some almonds are exported to Brazil.
For me I think the big thing here wasn't quite the lawgic part of it, but the words "produce" and "almonds" aren't equivalent so to me I couldn't even make a chain
Every year America produces 100g of almonds, and 80g of these are grown in California. Every year 800 out of 1000 tons of produce from California are exported to Brazil. It just so happens that those 80g of almonds are in those 200 tons of produce not exported to Brazil but shipped to the Vatican so the Pope himself can chew them.
There's nothing stopping the first set being tiny but still fulfilling the "most requirement" while the second set being humongous and just so happens to neglect the first set. When looking at validity, every single possibility must be considered, even if there's just 1 scenario where it could be false, then it cannot be valid.
@SarahHolmes754 i get caught up in the words a lot, but drawing triple venn diagrams really helps me lol. a lot of the invalid arguments of this flaw section of the curriculum is based on the fact that the "B" bucket could be huge. Therefore, if only "some" or "most" of B are C, A could have a real good chance of never being in C, which is why those conclusions are invalid.
I think the reason A‑m→B‑m→C is invalid is because:
A→B→C sometimes we can say therefore A→C, but because in A‑m→B‑m→C a portion of A is in B and a portion of B is in C, we can not guarantee that the potion of A is the same in B. Yes, most of A is in B, but potions of B not in A can in be in C... So you can not draw A‑m→C.
However, A‑m→B and A‑m→C I think help clarify that A is in both B and C, rather than guessing that it is.
117 comments
I made a visualization (think Venn diagram) to help my brain absorb the concept of Most (or All) before Most not leading to valid conclusions. It helps me a ton.
https://drive.google.com/file/d/1rZBggqV3UVGhOvbiJo46cLWA5XUUwFFx/view?usp=sharing
Amazing work!! thank you :)
this rocks, thanks man
This is excellent thank you so much!
king.
Thanks SO much.
I am of great gratitude, thank you kind sir.
Thank you so much! This really helped me understand.
so helpful - THANK YOU!
Thanks. You're a legend.
This is great, thank you so much!
thank you!
Mans deserves noble peace prize
@mic.colman In 2026 and this still helps!
@mic.colman THANK YOU!!
@MorganWhite needed this, thank you
@MorganWhite Thank you! This was literally a lifesaver.
wait okay okay after sitting w this for like ten minutes i think i get it. most almonds are grown in cali. most cali produce is exported to brazil. produce does NOT have to include almonds. cali produce can be avocados, apples, cherries, corn, wheat, blah blah blah and yes it COULD include almonds MAYBE but almonds also could be the ONE THING that is not included in "most" of cali's produce.
i appreciate the strategy of "lawgic" for the harder questions but as a writer/reader i sometimes find it much easier to think it through with words rather than symbols. the formula is nice, but it gets a little too "math-y" for me lol
@hannahhjh This saved me, thank you! I agree having the examples written more thoroughly like you've done is extremely helpful.
@hannahhjh same, it's hard for me to translate to lawgic then back to english quick enough to meet the time limits for questions. the equation aspect helped in the earlier lessons but as they're getting more complicated, the symbols are confusing me more.
there are so many rules/reversal rules. Its overwhelming to distinguish them all
@kianamalek646
"It's overwhelming to distinguish them at the moment"
#feedback for all these invalid example I would like to see them turned into valid examples to better understand the formal arguments
Hoping this helps!
Most of America's almonds are grown in California.
Most produce from California is exported to Brazil.
Therefore, some almonds are exported to Brazil.
The problem here is that the premises don't guarantee the conclusion—just because "most" almonds are grown in California and "most" produce from California is exported to Brazil doesn't mean some almonds specifically are exported to Brazil. They could be eating the almonds domestically in CA and sending other produce to Brazil.
To make it valid you could say:
All of America's almonds are grown in California.
Most produce from California is exported to Brazil.
Therefore, some almonds are exported to Brazil.
Premise 1 guarantees that all almonds are grown in California.
Premise 2 states that most produce from California is exported to Brazil.
With these two premises, it's guaranteed that some almonds (because "most" produce from California is exported to Brazil) must be exported to Brazil.
OR another valid option:
All almonds grown in California are exported to Brazil.
Most almonds in America are grown in California.
Therefore, some almonds are exported to Brazil.
@liz.fenton10 Isn't this invalid because of "all before most"
"even if we drop everything from A set to B set, when the most scoops of members from B to C, it may or may not capture any As"
@bananerr I agree that even if we change the "Most" to "All" it still wouldn't be a valid argument.
My attempt would be:
All produce from California is almonds.
Most produce from California is exported to Brazil.
Some produce exported to Brazil are almonds.
sounds awkward but I'm hoping this is a valid argument!
@JacquelineMoon
produce from California>almonds
produce from California-m-> Brazil
-------------
Produce from Brazil <s> almonds
hahah a bit confusing to figure this one out
the form would look like
A>B
A-m->C
C<s>B ?
@FranciscoLee I think it is correct because your drawing you conclusion from the fact the produce from the California element of the stem. A simpler way to look at it would be All implies most, so if all produce from Cali is almonds then also produce from California-m>almonds is also valid. So then just switch it around A-m>B and A-m>c
Conc: B<s>C
Thus making it a valid conclusion.
I get it, the trap is that
A -m-> B
B -m-> C
A -s- C
A: America's almonds
B: Produce from California
C: Exported to Brazil
When it should be like this instead
A -m-> B
A -m-> C
B -s- C
So
Most of America's almonds are a product of California
Most of America's almonds are exported to Brazil
Some product of California is exported to Brazil
I need videos ;.;
@Heidi I agree!
Bro this is ridiculous why don't these lessons have videossss😣🤕😫
Trap 6: Attempting to chain "Most"s
Remember: When two "most" statements are chained together, there are no valid conclusions to be drawn.
The ONLY instance in which two "most" claims can work together to draw a conclusion is when two "most" arrows come from the same set
A -m-> C
A -m-> B
____
C <-s-> B
Ex.
Most of USA's peaches come from Georgia. Most produce from GA is exported to Mexico. Therefore, some peaches are exported to Mexico.
A --m-> B --m-> C
____
A <-s-> C
This is NOT a valid conclusion; maybe, even though most USA peaches do come from GA, GA only produces 10% peaches and 90% other produce. So, those few, precious peaches stay in the US, while the rest is shipped out.
Ex.
Most of USA's peaches come from Georgia. Most of USA's peaches are exported to Mexico. Therefore, at least some of the peaches sent to Mexico are GA peaches.
@JamieAAbrams
Continued:
USAp -m-> GA
USAp -m-> Mx
____
GA <-s-> Mx
This IS a valid conclusion
@JamieAAbrams I love your explanation because it shows how the verbiage should be for the statement to be valid. Thanks for the explanation!
I grasp the concept more with video lectures I'm not sure why this isn't the case for this giant section.
if this helps anyone!
@SundayMonday thank you
I feel like this would make way more sense if we also were given a valid form of the argument.
So for this one, I think that would be:
Most of America's almonds are grown in California. Most of America's almonds are exported to Brazil. Therefore, some things (implied: produce) grown in California are exported to Brazil.
US almonds ‑m→ grown in California
US almonds ‑m→ exported to Brazil
_
grown in California ←s→ exported to Brazil
It may the case that some things [produce] grown in California are not exported to Brazil, and some things [produce] that are exported to Brazil are not grown in California.
If this is wrong, let me know!
No videos??
I wish these had videos they really help me understand better
Ok here is my attempt:
Most slinky are toys, and most toys (these days) are electronic; therefore some slinky are electronic
@AlizaGGG This is a lot better than the example given in the course
Most A are B, which means that some A are not B. If some As don't have B. Then how can you validly assume that some A has C.
@Saint this was actually really helpful, thanks!
This is invalid because even with two ‑m→ that leaves room for exclusion. Let’s say there are 70 almonds (produce) out of 100 that are grown in California and that 80 produce out of 100 produce is exported to Brazil. Produce is a big subset; it could be that 40 carrots and 40 blueberries get exported to Brazil and none of the almonds do. We can’t say that some almonds are exported to Brazil.
yes, this is an invalid argument.
Because its using SOME and MOST, we cant say for sure that any one product is exported to Brazil.
For all we know, nuts as a whole are apart of the few products NOT exported to Brazil. Or maybe its everything but almonds.
Only if the stim said ALL products from Cali are exported, can we safely assume that SOME almonds are exported to Brazil.
@Sepshams Thank you! I couldn't figure this out.
For me I think the big thing here wasn't quite the lawgic part of it, but the words "produce" and "almonds" aren't equivalent so to me I couldn't even make a chain
@anamat ? Almonds-m->grown cali
Grown cali-m->go to Brazil
There's the chain. forget the produce.
@GordonGianadda ooo this is very helpful thank you
it would be helpful to have videos on these since they are common traps.
Yeah there's no way this section will take only 33 min.
I think of it as the last example:
Every year America produces 100g of almonds, and 80g of these are grown in California. Every year 800 out of 1000 tons of produce from California are exported to Brazil. It just so happens that those 80g of almonds are in those 200 tons of produce not exported to Brazil but shipped to the Vatican so the Pope himself can chew them.
There's nothing stopping the first set being tiny but still fulfilling the "most requirement" while the second set being humongous and just so happens to neglect the first set. When looking at validity, every single possibility must be considered, even if there's just 1 scenario where it could be false, then it cannot be valid.
Thank you so much it just clicked for me because of this
I've never been more confused and frustrated in my life. none of this makes sense and all the arguments seem valid to me ;(
@SarahHolmes754 i get caught up in the words a lot, but drawing triple venn diagrams really helps me lol. a lot of the invalid arguments of this flaw section of the curriculum is based on the fact that the "B" bucket could be huge. Therefore, if only "some" or "most" of B are C, A could have a real good chance of never being in C, which is why those conclusions are invalid.
Like I think it's easy to understand intuitively what is happening here, I just feel I some sort of drilling for it to actually become relevant to me
I think the reason A‑m→B‑m→C is invalid is because:
A→B→C sometimes we can say therefore A→C, but because in A‑m→B‑m→C a portion of A is in B and a portion of B is in C, we can not guarantee that the potion of A is the same in B. Yes, most of A is in B, but potions of B not in A can in be in C... So you can not draw A‑m→C.
However, A‑m→B and A‑m→C I think help clarify that A is in both B and C, rather than guessing that it is.
But I am not fully sure...