The error most students make when reviewing their PTs

Audio Technica Guy
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The error most students make when reviewing their PTs

Postby Audio Technica Guy » Mon Jun 27, 2011 6:33 pm

One thing I have seen over and over again that impedes progress is the way students review their tests. Typically, best case scenario, a student looks at the correct answer, reads the explanations and thinks "oh, I see that now, okay." And then moves on. This isn't really helpful.

Here is how I advise reviewing your tests, so that it actually helps.

1) answer 4 questions:

i) What about the credited answer did I think made it wrong (if anything)?
ii) What attracted me to the wrong answer that obviously wasn't good?
iii) What made the right answer right?
iv) What made the wrong answer wrong?

2) Now do the problem over, making sure you take the right steps. It isn't enough to merely understand why you missed it, you have to retrace your steps and make yourself do it right. Do this like 4-5 times. Rewinding and making sure you know what you should have done for that question, step by step, no shortcuts. One thing that has been a common theme is students abstractly know how to do the problem, but doing it the right way just isn't a habit. You have to MAKE IT A HABIT.

Let me give an example:

Socrates was a man. All men are mortal. Therefore, Socrates was mortal.

This argument is flawed because it:

A) Assumes that just because two things are correlated that one must cause the other.
B) Fails to consider that Socrates may not have really been a man.
C) Takes for granted that what is true of men now was also true of men during Socrates' time.
D) Appeals to emotion without providing an actual justification for the conclusion
E) Provides no support for the conclusion aside from merely assuming it is true.

Let's assume you chose A. You chose A because you know that correlation does not equal causation and that's been an issue on problems you've seen before. However, you didn't really make sure that causation was actually an aspect of the original argument, which it wasn't. You eliminated the correct answer, C, because you didn't like the time aspect. Which is just kind of random and not really a reason at all.

i) you didn't really think about the correct answer and you just focused on time, and didn't really have a reason for eliminating it.
ii) you liked A because it mentioned causation.
iii) C is right because if men weren't necessarily mortal during Socrates' time, our argument falls apart.
iv) A is wrong because there is no aspect of causation in the original argument

Now the longer part.

first realize it is a flaw question. In this example it's easy enough to break down, we just have two premises:

p1) Socrates was a man
p2) all men are mortal
c) Socrates was mortal

The flaw here is that the conclusion is about what WAS the case, yet we have two premises, and only one of those is about what was the case. The other is about what is currently the case. So, we have a disconnect.

Attacking the answers:

A) There is no aspect of causation. Even though being a man might cause mortality, that's not what this argument is about. eliminate
B) The argument did consider this, it flat out stated that he was a man, as a matter of fact. You can't question premises. eliminate.
C) When it is saying that the argument takes something for granted, always think "would the argument fall apart if this wasn't true?" Here if what is true of men currently wasn't encessarily true of men in Socrates' time, then our argument clearly no longer works. So it seems that they took this for granted.
D) There simply is no appeal to emotion
E) This isn't a circular argument

Now make yourself do this at least three more times. It's about habit building. Making yourself go through the steps over and over so that it just becomes the way you do things. It doesn't matter if you "know" how to do a problem. All that matters on test day is what your habits are.

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SoPro
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Re: The error most students make when reviewing their PTs

Postby SoPro » Mon Jun 27, 2011 6:41 pm

Good thread, thanks.

ams
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Re: The error most students make when reviewing their PTs

Postby ams » Mon Jun 27, 2011 9:57 pm

I feel the need to bump this just for emphasis. Failing to thoroughly review answers is probably one of the top two mistakes I see in my new clients. Excellent post!

NaturalLawyer
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Re: The error most students make when reviewing their PTs

Postby NaturalLawyer » Mon Jun 27, 2011 11:54 pm

While I think your points are insightful and useful, I just don't see how your particular example is supposed to work.

The argument in the example was:
(1) Socrates was a man.
(2) All men are mortal.
So: (3) Socrates was mortal.

The correct flaw you say is that the argument "Takes for granted that what is true of men now was also true of men during Socrates' time."

But I just don't see how that flaw is being exhibited by the argument above. Is it because of (2)? But (2) is just equivalent to "Every man is a mortal."

Here is a similar argument:
(1) The figure that Mr. Popper drew on the board yesterday
was a triangle.
(2) All triangles have three sides.
So: (3) That figure that Mr. Popper drew on the board was three
sided.

It doesn't seem to me like a flaw that can pointed to in this argument is that the argument takes for granted that what is true of triangles now was also true of triangles yesterday. That doesn't appear to me to be a legitimate flaw. But if not, what makes this argument different from the Socrates argument?

We could, of course, attack the truth of one of the premises, e.g. that all men are mortal, or that Socrates was a man, but you suggested that you can't criticize premises on LSAT questions. (Is that really true? I didn't know that.)

But perhaps I'm just failing to see something.

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Re: The error most students make when reviewing their PTs

Postby Strange » Mon Jun 27, 2011 11:54 pm

Great thread

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suspicious android
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Re: The error most students make when reviewing their PTs

Postby suspicious android » Tue Jun 28, 2011 12:16 am

NaturalLawyer wrote:The argument in the example was:
(1) Socrates was a man.
(2) All men are mortal.
So: (3) Socrates was mortal.

The correct flaw you say is that the argument "Takes for granted that what is true of men now was also true of men during Socrates' time."

But I just don't see how that flaw is being exhibited by the argument above. Is it because of (2)? But (2) is just equivalent to "Every man is a mortal."

Here is a similar argument:
(1) The figure that Mr. Popper drew on the board yesterday
was a triangle.
(2) All triangles have three sides.
So: (3) That figure that Mr. Popper drew on the board was three
sided.



This is a very subtle flaw, and you were going in the right direction, but I think it's easy to breeze right past it since it seems like such a commonsense assumption.

We must accept the premises that "All men are mortal" and that "Socrates was a man", but notice that the first is a present tense statement while the second is past tense. It's logically possible that mortality is a quality of men now, but was not always so. If men used to be immortal but are mortal now, we would still say "all men are mortal." In that case, although Socrates was a man, we might have been a man back when men were immortal. Thus the premises could be true and the conclusion false, invalid argument. The correct answer points out that it makes the reasonable but not necessarily true assumption that what is true of men now used to be true of them in the past.

Now, I like this as an example of the flaw, but I would note that I doubt very much the LSAT would require people to recognize this continuity error in a context like this, since they typically seem to want you to make assumptions that are by commonsense standards actually true (e.g., the Earth rotates around the Sun, men weren't magically immortal thousands of years ago).

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Verity
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Re: The error most students make when reviewing their PTs

Postby Verity » Tue Jun 28, 2011 12:24 am

suspicious android wrote:Now, I like this as an example of the flaw, but I would note that I doubt very much the LSAT would require people to recognize this continuity error in a context like this, since they typically seem to want you to make assumptions that are by commonsense standards actually true (e.g., the Earth rotates around the Sun, men weren't magically immortal thousands of years ago).


+1. This kind of a question would probably be flagged and removed from the scoring of the test if it somehow made its way in (and it wouldn't).

It's almost always the case that the LSAT does not require special outside knowledge, but LSAC does want you to know some very basic common-knowledge stuff. Ex: A question about the towns Vertigon and Vorso on the planet Veris must be answered only with the information given. However, a question that asks about different gun law standards in New Jersey and California will probably require you to at least consider the possibility that their gun laws might be different, which in turn requires you to know that states can have different gun laws. That's common-knowledge stuff. There is no common knowledge regarding Vertigon, Vorso, or Veris.

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Re: The error most students make when reviewing their PTs

Postby NaturalLawyer » Tue Jun 28, 2011 12:50 am

I see that the the second premise, "All men are mortal" is stated as in the present tense. But so is my analogous argument which went:

(1) The figure that Mr. Popper drew on the board yesterday
was a triangle.
(2) All triangles have three sides.
So: (3) That figure that Mr. Popper drew on the board was three
sided.

So is it also a flaw that the above argument is taking it for granted that what is true of triangles now was also true of triangles yesterday? After all, (2) makes a statement in the present tense as well.

Or how about the following argument:
(1) Mr. Popper wrote the number 5 on the board yesterday.
(2) The number 5 is a prime number.
So: (3) Mr. Popper wrote a prime number on the board yesterday.

Is a flaw in this argument also that it is taking for granted that what is true of the number 5 now, is true of the number 5 yesterday? After all, (2) is a statement that uses a present tense verb, while (1) is written using a past tense verb.

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Re: The error most students make when reviewing their PTs

Postby Verity » Tue Jun 28, 2011 12:55 am

NaturalLawyer wrote:I see that the the second premise, "All men are mortal" is stated as in the present tense. But so is my analogous argument which went:

(1) The figure that Mr. Popper drew on the board yesterday
was a triangle.
(2) All triangles have three sides.
So: (3) That figure that Mr. Popper drew on the board was three
sided.

So is it also a flaw that the above argument is taking it for granted that what is true of triangles now was also true of triangles yesterday? After all, (2) makes a statement in the present tense as well.

Or how about the following argument:
(1) Mr. Popper wrote the number 5 on the board yesterday.
(2) The number 5 is a prime number.
So: (3) Mr. Popper wrote a prime number on the board yesterday.

Is a flaw in this argument also that it is taking for granted that what is true of the number 5 now, is true of the number 5 yesterday? After all, (2) is a statement that uses a present tense verb, while (1) is written using a past tense verb.


We get the "was" problem. It's been resolved.

TL;DR Yes and no.

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EarlCat
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Re: The error most students make when reviewing their PTs

Postby EarlCat » Tue Jun 28, 2011 1:20 am

The triangle and prime number examples aren't analogous to the mortal men example because the the premises "All triangles have three sides" and "The number 5 is a prime number" are definitional premises (did I just make up a word?). In other words, triangles and prime numbers are not fluid things. They are what they are by definition. But, one might argue, men evolve and may change in character throughout the ages. Thus, whether a premise considers men in the past, present, or future might be relevant to whether a conclusion about them is flawed even though the same can't be said about triangles and prime numbers.

On the other hand, if men were once immortal, where are these men now? If they've died, that fact calls into question their immortality.

Then again, perhaps not.
http://www.youtube.com/watch?v=SnJt9p-sHho

In any event, I don't think LSAC is going down this road anytime soon. :mrgreen:

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Re: The error most students make when reviewing their PTs

Postby Verity » Tue Jun 28, 2011 1:27 am

EarlCat wrote:The triangle and prime number examples aren't analogous to the mortal men example because the the premises "All triangles have three sides" and "The number 5 is a prime number" are definitional premises (did I just make up a word?). In other words, triangles and prime numbers are not fluid things. They are what they are by definition. But, one might argue, men evolve and may change in character throughout the ages. Thus, whether a premise considers men in the past, present, or future might be relevant to whether a conclusion about them is flawed even though the same can't be said about triangles and prime numbers.

On the other hand, if men were once immortal, where are these men now? If they've died, that fact calls into question their immortality.

Then again, perhaps not.
http://www.youtube.com/watch?v=SnJt9p-sHho

In any event, I don't think LSAC is going down this road anytime soon. :mrgreen:


I think you mean tautology (with respect to the triangle example), as opposed to "definitional" premises. Both examples are also technically apodictic.*

*EDIT, FTFM
Last edited by Verity on Tue Jun 28, 2011 11:18 am, edited 1 time in total.

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Re: The error most students make when reviewing their PTs

Postby EarlCat » Tue Jun 28, 2011 1:41 am

Verity wrote:I think you mean tautology (with respect to the triangle example), as opposed to "definitional" premises. The triangle example is also technically apodictic, and the #5 example is assertoric. Look it up.

Potato Potahto :wink:

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Re: The error most students make when reviewing their PTs

Postby Jeffort » Tue Jun 28, 2011 2:07 am

Just for the hell of it I looked up "men" in a few online dictionaries to parse the second premise properly in the context of the argument. One of the web sites had a box in the result, it said "why did you search for men?" and displayed a list of suggested external web pages it thought I might be interested in viewing. A few of the links were for gay oriented web resources. Then I refreshed this thread and Verity had posted the word assertoric (yes, it's a real word).

I laughed, cried and scratched my head as I remembered all the wonderful things I learned in UG humanities class lectures about Socrates and the predilections of other 'great' ancient philosophers.

Gutter/toilet humor, especially with word association always gets me :D

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Re: The error most students make when reviewing their PTs

Postby NaturalLawyer » Tue Jun 28, 2011 7:43 am

[On a side note to Verity: I think the proposition: "The number 5 is a prime number." is also an apodictic proposition. While it is true that it is not part of the definition of the number 5 that it is a prime number, it is still necessarily true (in the sense of broadly logical necessity) that the number 5 is a prime number. That is to say, there is no possible world in which the number 5 is not a prime number. But perhaps you can correct me about my understanding of assertoric/apodictic propositions.]

I do agree that my examples use statements that involve the definition of terms.

But then wouldn't the flaw in the original Socrates example be about the truth of premise 2, namely, "All men are mortal"?
We might argue, "No! That statement is not necessarily true -- perhaps in the future (or perhaps there have been in the past) some men are immortal!"
(Incidentally, as a Catholic I take this to actually be the case! :-)

I suppose my only real point was that the flaw is not to be located in noticing that there is a tense shift but in the truth of the premise 2 itself.

[And to Jeffort: I didn't mean for you to be led to porn sites! Sorry about that man.]

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Re: The error most students make when reviewing their PTs

Postby Verity » Tue Jun 28, 2011 11:28 am

NaturalLawyer wrote:[On a side note to Verity: I think the proposition: "The number 5 is a prime number." is also an apodictic proposition. While it is true that it is not part of the definition of the number 5 that it is a prime number, it is still necessarily true (in the sense of broadly logical necessity) that the number 5 is a prime number. That is to say, there is no possible world in which the number 5 is not a prime number. But perhaps you can correct me about my understanding of assertoric/apodictic propositions.]

This is true. That's what happens when you drink six Coronas and TLS after midnight.

I do agree that my examples use statements that involve the definition of terms.

But then wouldn't the flaw in the original Socrates example be about the truth of premise 2, namely, "All men are mortal"?
We might argue, "No! That statement is not necessarily true -- perhaps in the future (or perhaps there have been in the past) some men are immortal!"
(Incidentally, as a Catholic I take this to actually be the case! :-)

"All men are mortal" is assertoric, and cannot be apodictic unless we know for sure that "men" includes "dead men," which would clash with the definition of "mortal," which means "subject to death." This is also where the common knowledge expectation may come into play, where we should know that men do not lose their mortality, or become "immortal" while they are still alive. Luckily, you can rest assured that you will never see the "Is Socrates mortal?" question on the LSAT.

I suppose my only real point was that the flaw is not to be located in noticing that there is a tense shift but in the truth of the premise 2 itself.

Yeah, I think this is way too loaded to resemble a real LSAT question. They make you recognize tense shifts and unwarranted assumptions, but this is taking it to a whole new extreme that wouldn't appear on the test.

[And to Jeffort: I didn't mean for you to be led to porn sites! Sorry about that man.]

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Re: The error most students make when reviewing their PTs

Postby EarlCat » Tue Jun 28, 2011 2:56 pm

NaturalLawyer wrote:I suppose my only real point was that the flaw is not to be located in noticing that there is a tense shift but in the truth of the premise 2 itself.

What about the following?

Joe took an apple from the barrel.
All the apples in the barrel are red.
Therefore, the apple Joe took was red.

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Re: The error most students make when reviewing their PTs

Postby NaturalLawyer » Tue Jun 28, 2011 3:19 pm

EarlCat wrote:
NaturalLawyer wrote:I suppose my only real point was that the flaw is not to be located in noticing that there is a tense shift but in the truth of the premise 2 itself.

What about the following?

Joe took an apple from the barrel.
All the apples in the barrel are red.
Therefore, the apple Joe took was red.


Nice example. I'm not sure. The central question really is the meaning of the second premise: "All the apples in the barrel are red." Perhaps we can disambiguate the proposition into:
(2a): Every apple that has existed, exists, and will exist in the barrel, are red.
(2b): All the apples in the barrel at this present moment, are red.

If (2) is interpreted as (2b), then the argument is invalid since the premises can be true and the conclusion be false.

But if (2) is interpreted as (2a), then the argument is valid.

And I do think that the fact that the verb itself is present tense doesn't settle the matter since we can say something like: "Every president of the United States has the power to start a war."

The question is: should (2) be taken as (2a) or (2b)? I think people can mean either when they state (2).

So in the same way perhaps: "All men are mortal." can be taken as either:
(a) "Every man that has existed, exists, and will ever exist, are mortal." or (b) All the men that exist at this present moment, are mortal.

But here it does seem to me like anyone who makes the statement: "All men are mortal" means (a) rather than (b).

I think this is getting into some difficult areas within the philosophy of language which, I must admit, I haven't studied much of.

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Re: The error most students make when reviewing their PTs

Postby Verity » Tue Jun 28, 2011 3:34 pm

EarlCat wrote:
NaturalLawyer wrote:I suppose my only real point was that the flaw is not to be located in noticing that there is a tense shift but in the truth of the premise 2 itself.

What about the following?

Joe took an apple from the barrel.
All the apples in the barrel are red.
Therefore, the apple Joe took was red.


Could make a funny assumption question. It would follow if we assume that there were more red apples in the barrel before Joe took his, and no apples have been taken since he took his.

Could also make a good flaw question. The argument is flawed because it takes for granted that what is now true of the apples in the barrel was also true before Joe took his apple.

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Re: The error most students make when reviewing their PTs

Postby EarlCat » Tue Jun 28, 2011 4:17 pm

NaturalLawyer wrote:Nice example. I'm not sure. The central question really is the meaning of the second premise: "All the apples in the barrel are red." Perhaps we can disambiguate the proposition into:
(2a): Every apple that has existed, exists, and will exist in the barrel, are red.
(2b): All the apples in the barrel at this present moment, are red.


I think limiting the premise to all apples in the barrel rather than all apples pushes it in to the 2b camp, because we would expect the contents of a barrel (a temporary holding place) to change over time.

In other words, "All apples are red" is more readily interpreted as all apples for all time (though it could also be interpreted as only apples in the present). But "All apples in the barrel are red" appears to be only a momentary observation.

What if we changed from inanimate apples to people?

Joe was in the waiting room.
Everyone in the waiting room is tall.
Joe is tall.

Or

Socrates was a man.
All men watch ESPN.
Socrates watched ESPN.

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Re: The error most students make when reviewing their PTs

Postby NaturalLawyer » Tue Jun 28, 2011 7:07 pm

EarlCat wrote:
NaturalLawyer wrote:Nice example. I'm not sure. The central question really is the meaning of the second premise: "All the apples in the barrel are red." Perhaps we can disambiguate the proposition into:
(2a): Every apple that has existed, exists, and will exist in the barrel, are red.
(2b): All the apples in the barrel at this present moment, are red.


I think limiting the premise to all apples in the barrel rather than all apples pushes it in to the 2b camp, because we would expect the contents of a barrel (a temporary holding place) to change over time.

In other words, "All apples are red" is more readily interpreted as all apples for all time (though it could also be interpreted as only apples in the present). But "All apples in the barrel are red" appears to be only a momentary observation.

What if we changed from inanimate apples to people?

Joe was in the waiting room.
Everyone in the waiting room is tall.
Joe is tall.

Or

Socrates was a man.
All men watch ESPN.
Socrates watched ESPN.


Your point about the barrel is a nice thought. I think it would also apply to your Joe and Waiting Room example.

But the Socrates and ESPN example is interesting since I don't think we mean to restrict the scope of its application to just one moment but we mean for it to extend through a certain stretch of time. (Though not indefinitely since at one point ESPN didn't exist!)

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Re: The error most students make when reviewing their PTs

Postby suspicious android » Tue Jun 28, 2011 7:26 pm

NaturalLawyer wrote:But the Socrates and ESPN example is interesting since I don't think we mean to restrict the scope of its application to just one moment but we mean for it to extend through a certain stretch of time. (Though not indefinitely since at one point ESPN didn't exist!)


This is part of the whole confusion. Natural languages like English all have some degree of ambiguity. What we "meant" is not really relevant, what we said is what counts.

"All men watch ESPN."

This, and pretty much all the arguments discussed, have a problem in that the scope of the sentence could be fairly interpreted in different ways. Just because we know that ESPN has only existed for the last 30 years doesn't mean it definitely means that it only applies to men now. It could be taken to mean that by definition, a man is a thing that watches ESPN. If that were true the conclusion would follow. It could also be taken to mean that currently, all things that are men have the quality of being ESPN watchers. In that case, the conclusion wouldn't follow. Since there's at least one interpretation wherin the premises are true yet the conclusion false, it is an invalid argument.

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Re: The error most students make when reviewing their PTs

Postby EarlCat » Tue Jun 28, 2011 10:34 pm

suspicious android wrote:Since there's at least one interpretation wherin the premises are true yet the conclusion false, it is an invalid argument.


Presumes without providing justification that what is true of all men today was true for all men in the past?

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Re: The error most students make when reviewing their PTs

Postby suspicious android » Tue Jun 28, 2011 10:43 pm

EarlCat wrote:Presumes without providing justification that what is true of all men today was true for all men in the past?


Sounds good to me.. but I'm skeptical at this point how persuasive it will be.




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