Normal full-term babies are all born with certain instinctive reflexes that disappear by the age of two months. Becau...
AnthonyHJune 18, 2020
Why Not Answer E? Diagram help.
Hi! I watched the video explanation and noticed that the final answer choice (E) was hastily explained away as flawed without a diagram. Can someone diagram this to confirm what it would look like?
For answer E I diagrammed a contrapositive argument that seemed to match the structure in the stimulus and thus could not rule it out. Some Trees (ST) will shed their leaves annually (SLA). This tree has not shed its leaves (Not SL), and thus it it not normal (Not ST). Diagrammed as follows:
ST-> SLA
Not SLA -> Not ST
P: Not SLA
___
C: Not Normal (Not ST)
While the stimulus did not define what is considered normal, it did explicitly describe some tree (ST). I inferred this to mean that if you are NOT ST, you could be the following: 1) all trees, 2) most trees, 3) Anything that is NOT ST. Since "Not Normal" is included in anything that is Not ST, the argument as diagrammed in Answer E above would satisfy the contrapositive structure and could be considered the correct answer.
Could someone walk me through the logic on this one? Where did I go wrong?
Thank you!
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The problem here is that you attempted to diagram a sentence that actually does not have sufficient and necessary conditions. Rather, the first part of answer choice E is what we would call a "quantifier." Maybe you haven't reached that lesson yet, but it will make more sense when you get there.
Here is what a proper diagram would look like in this case:
Trees --- some --- SLA
We don't know if normal trees do this, most trees do this, or very few do this. We can only say that "some" trees do this. There is very little that we can conclude here, especially when we have no definition of normal.
While I respect the creativity here, your diagram does not draw a valid conclusion. You wrote:
ST ---> SLA
While it is true that some trees shed leaves annually, it is just as likely that some do not. So, how can we conclude with certainty that a given tree will shed its leaves annually? This is what your diagram is doing. You wrote ST for some trees, but we have no idea which trees. Therefore, we cannot draw the conclusion that it sheds leaves annually. If answer choice E had said,"all trees shed their leaves annually," then we could diagram:
T ---> SLA not SLA ---> not T
"All" gives us the certainty to do this, but "some" does not.
AnthonyHJune 19, 2020
Thanks for the response! This is very helpful. I'll definitely circle back to this question once completing the quantifier lesson. I really wanted to get the S & N subject ironed out before proceeding.
Could you further elaborate why you noted that this answer option does not contain sufficient and necessary conditions?
Answer E - "Because some types of trees shed their leaves annually and this tree has not shed its leaves, it is not normal."
I thought that since the word "Because" was used in the statement it triggered a cause and effect scenario which implied a need. The presence of a need should allow for us to diagram the relationship between the necessary condition for "some tree" (ST). In this case, shedding leaves annually is the necessary condition to be "some tree". The type of tree is unknown; and thus we cannot conclude the variety of tree that is being referenced. Luckily that isn't the conclusion being drawn.
We can, however, conclude that the tree in question has NOT shed its leaves because it is described explicitly in the answer, and thus meets the sufficient condition of the contrapositive argument i.e. Not SLA -> Not ST. From the sufficient can we not conclude necessary condition?
The tree in question, exists at the moment of observation, and is therefore NOT in the same "some tree" type that happens to sheds its leaves annually.
Our missing premise is then, what quantifies a tree as being normal. For now, it is simply the statement that this tree which is NOT some tree, is NOT normal.
Diagrammed as followed:
Not SLA -> Not ST
Not ST exists
Not ST-> Not Normal
___
C: Not SLA -> Not Normal
Transitive: Not SLA -> Not ST -> Not Normal
Please let me know if I'm off base here and then I'll happily move on. I'm sure there are plenty of other questions to tackle, but this one is bugging me.
In short, I'm treating "Some Trees" as a singular group that, in the absence of a quantifier, maintains its own vague identity and must be treated as a unit purely defined by the details provided - SLA.
Much appreciated,
Anthony
Brett-LindsayJuly 4, 2020
Hi @AnthonyH
While I haven't done the quantifiers section yet, I've noticed in the daily drills explanations that if we use a quantifier, then it's automatically not considered a sufficient and necessary statement.
"some" = 1 or more, possibly even "all"
So, "some types of trees" could be in the range from one type to every single type.
The fact that it could only be a single type (or even 99.9% of all types) makes it impossible for us to know whether shedding leaves is sufficient to be normal. After all, it would take only one exception for it to be insufficient to guarantee the outcome.
My understanding of sufficiency is that it must be 100% of the time because only then would the necessary condition (being normal) be guaranteed.
That's why this would be diagrammed as something like this:
SLA -some- normal (SOME trees shed leaves annually, making them normal) which would mean that normal -some- SLA (It is normal for SOME trees to shed their leaves annualy) because at least ONE tree does it.
Because quantifiers do not guarantee sufficiency or necessity, there is no implied direction. They have no corresponding contrapositive, so it's incorrect to use an arrow.
I'm really just thinking out loud here, partly to deepen my own understanding of these new concepts.
