July 27, 2016 at 9:36 am #2309
Question about the lesson 18 American and Cheese drill. I don’t quite understand the “only those who love cheese are American” translation. The “are” in the statement implies to me that being American is necessary for loving cheese. I think I came to that conclusion because I translated the sentence to “only cheese lovers are American”. This, in my opinion, actually implies a biconditional where you are an American if and only if you are a cheese lover. This though is for sure conjecture. I haven’t studied formal logic in damn near a decade.
One thing I do remember though from back in the day is translating “unless” as “if not”. Makes sense and simplifies the logic some.
July 27, 2016 at 10:49 am #2310Mike KimKeymaster
These conditional wording issues can be very subtle and just a change or two here or there can totally flip the meaning — they are tough for pretty much everyone at first, but the good news is that there are only so many ways they can be written, and once you get the right mindset/systems they become much more manageable.
As I discuss in the Trainer, it can often be helpful to think of analogous situations (such as the “conditional mantras” mentioned on page 256) — you can have a few prepared in the back of your mind and whip them out when you need to in order to carefully evaluate a conditional statement —
Using the conditional mantras on 256, the equivalent statements would be:
“Only those who are at least sixteen are licensed drivers”
“Only those fish that are dead are eaten.”
For the first example — “Only those who are at least sixteen are licensed drivers”
Does this mean everyone at least sixteen is guaranteed to be a licensed driver? No.
Does this mean everyone who is a licensed driver is at least sixteen? Yes. So,
LD -> at least 16.
For the second — “Only those fish that are dead are eaten.”
Does this mean all dead fish are eaten? No.
Does this mean that if a fish was eaten, it was dead? Yes. So,
E -> D
Going back to our statement — “Only those who love cheese are American.”
This does not mean that all who love cheese must be American.
It does mean that if you are American, you must love cheese (you can also see, per this statement, that if you don’t love cheese, you can’t be American) —
So, we have A -> C.
Again, you want to be very careful in thinking about the exact conditional wording as given — even a small change to something like “the only people who love cheese are Americans” changes the conditional relationship.
Hope that helps — let me know if you have any follow-up — Mike
July 27, 2016 at 5:07 pm #2311
I got ya, man. Had to break it down to something physical: only those who are Houstonians are Texans. That statement doesn’t make any sense because you don’t have to be a Houstonian to be a Texan. However, “only those who are Texans are Houstonians” does make sense. You have to be from Texas to be from Houston.
Thanks for clearing it up for me, man. I know I shouldn’t really care about whether the statement makes sense, but I guess I could only make sense of the logic by hearing something that I can visualize with the same structure.
For sure helped, and thanks again,
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