Self-study
Since starting my practice drill I have seen soooooo many sentences in LR that feature the use of a Group 3 and Group 4 indicator in one sentence and truly cannot (see what I did there) figure out how to translate them into lawgic. Does anyone have any tips or loopholes on this?
Here's an Example:
"Major meteor impacts and mass extinctions cannot be consistently causally linked unless many mass extinctions have followed major meteor impacts."
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6 comments
I appreciate the other responses here, but your question is really about how to deal with two conditional indicators in one sentence. I think you have to start with translating "unless", even though with two conditional indicators present, "cannot" and "unless", you'd think you can start with either; here's why: consider this simple group 4 indicator statement:
Students cannot attend the prom if they are under 18.
Cannot is a group 4 indicator so:
Negate either idea and make it the necessary condition:
If under 18, then must not attend the prom. Or is contrapositive:
If attend the prom, then must be not under 18.
But now consider an exact analogy to your question:
Students cannot attend the prom unless they are 18 or older.
You’re right; there is a group 4 and group 3 indicator in the stem. But I can only see one way to proceed – address the “unless’ indicator first, or you can’t wind up with a conditional statement. So:
Negate sufficient to get:
If not 18 or older, then must not attend the problem. Or its contrapositive:
If attend the prom, then must be 18 or older.
If you try to solve this statement by addressing "cannot" first, it can't be done, I think, because the sentence's structure won't support it as long as "unless" is present.
This is probably a summary of what others may have said, but when I see these I say to myself: "Negation of the way things are --> unless..."
So, in your case, it would be: "Major meteor impacts & mass extinctions CAN be consistently causally linked --> many mass extinctions have followed..."
After I memorized that easy one liner, I never had a problem with these. I hope this helps! :)
Just adding my own strategy! I think of it like a distributive property in math (which I guess isn’t very helpful here, but can be super helpful for double negatives or and/or conditions!)
I take the phrase with ‘unless’, or the negated sufficient condition.
/(many mass extinctions follow major meteor)
Then I take the necessary condition.
cannot be causally linked consistently
aka, /causally linked consistently
So, altogether:
/many mass extinctions follow major meteor —> /causally linked consistently
Contrapositive:
causally linked consistently —> many mass extinctions follow major meteor
An important distinction is that in order for us to establish some sort of consistent causal link between major meteors causing mass extinctions, then AT LEAST SOME (or many) mass extinctions MUST follow major meteors. Or in other words, if we want to establish a causal relationship between the two phenomena, we need a specific observable repeated pattern.
My tip is when you see "unless" on the right side of the sentence, instead of translating as "if not", take contrapositive of the condition and it will be faster. Imagine the conditional arrow => strike through the "unless"! I will diagram the sentence you use as an example: (MMI <--> ME) => MMI before ME
The diagram in plain English: If Major Meteor Impact causally link to Mass Extinctions, then Major Meteor Impact occured before Mass Extinction (or "mass extinction have followed major meteor impacts).