So pretty much its invalid because while there's the chance some almonds are exported to Brazil from CA it cant be proven with the info we were given, so saying yes or no would just be a 50/50 guess?
I think the bucket analogy might help here - but someone let me know if this is more confusing.
Say we have 4 of A, B, and C. If 3/4 As are in the B bucket, and 3/4 Bs are in the C bucket, SOME As being in C is not super likely. Maybe a few, but the boundary for some is greater than few. You could say "at least a few As are in C" and that would make more sense, but not "some" because that's not necessarily true.
Example: Most hummingbirds are brightly colored. Most brightly colored animals are poisonous. Therefore, some hummingbirds are poisonous.
Discarding intuition, we don't know that some hummingbirds are poisonous just because most brightly colored animals are. Hummingbirds are a smaller set than "poisonous brightly colored animals". We don't know if these two sets overlap in any meaningful way.
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.
My understanding is that Most before Most (A‑m→B‑m→C, Therefore: A←s→C) is not valid for two main reasons.
1. Most (51%-100%) includes all which means there is a world where you are making the much easier to understand all before most fallacy any time you say it.
Most (or all) NBA Basketball players are tall. Most tall people are not good at basketball. Therefore, some pro basketball players are not good at basketball INVALID
VS
Most NBA players are tall. ALL tall people are not good at basketball. Therefore, some pro basketball players are bad at basketball. VALID
2. You just lack enough information to bet your life on the fact that some of A are C. To use the above example, sure, some NBA basketball players might be not good at basketball, but I really doubt it. I would not bet my life on a 1v1 against the 'worst' player in the league.
You could come up with some crazy example of the third string guy who is only there because of who his dad is, or because of injuries, a player is not good right now... but you are bringing in a whole new set of premises that are no where in the presented argument.
TL/DR: Stop overthinking it, and accept that most can mean all. Don't think outside of the test question's box.
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.
Most almonds are made in California. Most produce in Califronia have worms inside them. Most almonds in Califronia have a worm inside them. but seeing that there isn't a clear connection that the produce includes any almonds, we can not strongly confirm that indeed any almond has a worm
In contrast:
VALID
Most almonds are made in California. Most almonds have a worm inside them. Most almonds made in California have a worm inside them. *
We can conclude that most almonds in California likely have a worm inside them.
Or would it be "some" almonds in California have a worm inside them?
So dumb mistake on my part, but I couldn't get it for a good 5 minutes because I kept thinking that when they said "Most Produce" they were talking about the almonds grown in California (referential), not produce as in vegetables of fruits. Sometimes these lessons are unnecessarily confusing.
I think I understand this based off of the example that they gave of the scooping. A‑m→B→C makes sense because if I take MOST As and scoop them into B and then ALL of B goes into C then of course most As are in C. But for this (A‑m→B‑m→C) if I scoop MOST As and put them in B then scoop MOST Bs and put them into C, there just is no guarantee that any of the As got into C. Our brains would like to say that they did, but logically we cannot make that assumption.
Most of America's almonds are grown in California. Most produce from California are exported to Brazil. Therefore, some almonds are exported to Brazil. ( saying most not all, so we CAN’T CONFIRM that some of the almonds are also the ones that are exported.)
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.
Why is it that this argument is invalid? Is it because some almonds might not necessarily be exported to Brazil because of the differences in sizes of the sets? #help
My issue is with linking conditionals. Making the assumption that Almonds → Produce and Produce ←s→ Almonds is a simple connection to make here because this is an introductory level fact pattern, but in disciplines that I am unfamiliar with this is extremely difficult!
When do we exponent the specific why isn't it aP? What would the question need to look like to be aP? I'm not looking for an explanation of:
All cats are black. Max is a cat. Thus, Max is black.
C→B
mC
_
mB
I understand that. I'm losing the plot in complex applications
I'm having a bit of a tricky time with the "most before most" arguments. Taking the example above, would this be considered a valid conclusion instead?
Most of America's almonds are grown in California. Most of America's almonds are exported to Brazil. Therefore, some almonds grown in California are exported to Brazil.
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...
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82 comments
No videos??
Is it wrong for me to be critical of thinking why produce should be only meaning almonds?
I get that context wise it should be referring to almonds, but to me the logic makes more sense if I don't confine it to almonds
So pretty much its invalid because while there's the chance some almonds are exported to Brazil from CA it cant be proven with the info we were given, so saying yes or no would just be a 50/50 guess?
I need videos ;.;
I think the bucket analogy might help here - but someone let me know if this is more confusing.
Say we have 4 of A, B, and C. If 3/4 As are in the B bucket, and 3/4 Bs are in the C bucket, SOME As being in C is not super likely. Maybe a few, but the boundary for some is greater than few. You could say "at least a few As are in C" and that would make more sense, but not "some" because that's not necessarily true.
Example: Most hummingbirds are brightly colored. Most brightly colored animals are poisonous. Therefore, some hummingbirds are poisonous.
Discarding intuition, we don't know that some hummingbirds are poisonous just because most brightly colored animals are. Hummingbirds are a smaller set than "poisonous brightly colored animals". We don't know if these two sets overlap in any meaningful way.
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.
Ok here is my attempt:
Most slinky are toys, and most toys (these days) are electronic; therefore some slinky are electronic
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.
My understanding is that Most before Most (A‑m→B‑m→C, Therefore: A←s→C) is not valid for two main reasons.
1. Most (51%-100%) includes all which means there is a world where you are making the much easier to understand all before most fallacy any time you say it.
Most (or all) NBA Basketball players are tall. Most tall people are not good at basketball. Therefore, some pro basketball players are not good at basketball INVALID
VS
Most NBA players are tall. ALL tall people are not good at basketball. Therefore, some pro basketball players are bad at basketball. VALID
2. You just lack enough information to bet your life on the fact that some of A are C. To use the above example, sure, some NBA basketball players might be not good at basketball, but I really doubt it. I would not bet my life on a 1v1 against the 'worst' player in the league.
You could come up with some crazy example of the third string guy who is only there because of who his dad is, or because of injuries, a player is not good right now... but you are bringing in a whole new set of premises that are no where in the presented argument.
TL/DR: Stop overthinking it, and accept that most can mean all. Don't think outside of the test question's box.
there are so many rules/reversal rules. Its overwhelming to distinguish them all
#feedback for all these invalid example I would like to see them turned into valid examples to better understand the formal arguments
Can someone explain this more please I'm confused as to why most before most works when split but not together :(
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!
Does anyone else have an example that might be easier to understand? I'm still struggling with these concepts!
Can someone help me with this possibility:
NON VALID:
Most almonds are made in California. Most produce in Califronia have worms inside them. Most almonds in Califronia have a worm inside them. but seeing that there isn't a clear connection that the produce includes any almonds, we can not strongly confirm that indeed any almond has a worm
In contrast:
VALID
Most almonds are made in California. Most almonds have a worm inside them. Most almonds made in California have a worm inside them. *
We can conclude that most almonds in California likely have a worm inside them.
Or would it be "some" almonds in California have a worm inside them?
So dumb mistake on my part, but I couldn't get it for a good 5 minutes because I kept thinking that when they said "Most Produce" they were talking about the almonds grown in California (referential), not produce as in vegetables of fruits. Sometimes these lessons are unnecessarily confusing.
I think I understand this based off of the example that they gave of the scooping. A‑m→B→C makes sense because if I take MOST As and scoop them into B and then ALL of B goes into C then of course most As are in C. But for this (A‑m→B‑m→C) if I scoop MOST As and put them in B then scoop MOST Bs and put them into C, there just is no guarantee that any of the As got into C. Our brains would like to say that they did, but logically we cannot make that assumption.
Most of America's almonds are grown in California. Most produce from California are exported to Brazil. Therefore, some almonds are exported to Brazil. ( saying most not all, so we CAN’T CONFIRM that some of the almonds are also the ones that are exported.)
Is that right?
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.
Why is it that this argument is invalid? Is it because some almonds might not necessarily be exported to Brazil because of the differences in sizes of the sets? #help
#help
My issue is with linking conditionals. Making the assumption that Almonds → Produce and Produce ←s→ Almonds is a simple connection to make here because this is an introductory level fact pattern, but in disciplines that I am unfamiliar with this is extremely difficult!
When do we exponent the specific why isn't it aP? What would the question need to look like to be aP? I'm not looking for an explanation of:
All cats are black. Max is a cat. Thus, Max is black.
C→B
mC
_
mB
I understand that. I'm losing the plot in complex applications
I'm having a bit of a tricky time with the "most before most" arguments. Taking the example above, would this be considered a valid conclusion instead?
Most of America's almonds are grown in California. Most of America's almonds are exported to Brazil. Therefore, some almonds grown in California are exported to Brazil.
AA--m-->GC
AA--m-->EB
AAEB
#help
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 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...