Linda says that, as a scientist, she knows that no scientist appreciates poetry. And, since most scientists are logic...
ClaraEJanuary 24, 2020
Why can't you take the contrapositive of a quantifying statement?
by linkage I got
L - some - ~AP
and then deduced that to
AP - some - ~L
why is this not reversible? can someone explain what principle is behind this? it didn't seem like negation to me, I'd like to understand why this isn't valid but the video does not explain.
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Great question! I would avoid using the term contrapositive when working with quantifying statements. Contrapositives are strictly for conditional reasoning (sufficient and necessary.) I notice that a lot of people try to apply this logic to quantifiers, but it is not valid reasoning. Let's put an end to it here.
Your first statement is correct. L - some - not AP Who does this describe? The scientists. We know that most of them are logical and none of them appreciate poetry, so we can make this conclusion.
You then reversed and negated these terms, which is the right procedure for a conditional statement. I'll explain why it doesn't work here.
AP - some - not L
What do we know about a person who appreciates poetry? We can only say that this person is not a scientist. AP - - - -> not S
The reversed statement that you created forces us to make this connection:
AP - - - -> not S - - some - - not L
Here is the problem. What do we know about the population of non-scientists? Nothing. We only have information about scientists. We know that most scientists are logical, but we cannot say that some non-scientists are illogical.
Does that make sense?
ClaraEJanuary 25, 2020
Okay I think I understand, my issue is that I was trying to reverse the L - s - ~AP statement I deduced rather than reversing the original full linkage (L - s - S --> ~AP). Had I attempted to reverse the original linkage, I would have seen that it's invalid.
Can you confirm I've gotten the right takeaway from this? Essentially the lesson I've learned is that if you want to reverse a quantifying statement, you have to reverse the original linked statements, not merely the deduction you made from the linkage. Correct?
SkylarJanuary 26, 2020
@ClaraE,
The takeaway here is that quantifying statements (AKA some or most statements) can only be reversed. They cannot be negated. On the other hand, S->N statements should be both reversed and negated.
You refer to the statement "L - some - S -> not AP" as the "original linkage."
This statement can be simplified to "L - some - not AP." There is no issue in writing this shorter deduction as opposed to the entire linkage- in fact I would recommend this for clarity. The original linkage should be used to make this deduction rather than treated as its own new S->N statement.
The only thing we can do to the "L - some - not AP" statement at this point is reverse it, which would give us "not AP - some - L." Because this is a quantifying statement, there is no contrapositive or need to negate either side. We are done.
Does that make sense? Please let us know if you have any questions!
