Premise and Conclusion Analysis Drill #3

[marxowski]

Not sure if I'm barking up the wrong tree here, but in the explanation of this question (on p40) it states that "Ameer has asserted that at least one of the two tests will be cancelled...", however the question states that the said that "...either the midterm is cancelled or the final is cancelled." This to me reads that one or the other but not both will be cancelled, ultimately rendering this a strong argument.

A: M or F will be cancelled (but not both)
T: M and F might be cancelled
Authority of T > A
A is probably incorrect

Thoughts?

[Nikki Siclunov]

Hey marxowski,

Thanks for your question. The "either/or" construction is indeed somewhat confusing, especially since its logical meaning deviates somewhat from the way we normally use it IRL.

In logic, "either/or" does not preclude the possibility of both! if I tell you that I'll either have a cookie or a brownie, I am not committing myself to choosing only one of these two pastries. I can choose to have both as well. However, I won't go hungry: I will definitely eat at least one of them.

To reiterate, "at least one of C or B" is functionally equivalent to "either C or B." This is diagrammed as:

NOT C B

NOT B C

As you can see, the occurrence of either C or B means nothing: to conclude otherwise would be to make a Mistaken Negation. However, the non-occurrence of either C or B requires the occurrence of the other. Hence, at least one of C or B must occur.

To preclude the occurrence of both C and B, we need to state, "either C or B, but not both." This is what you did in your interpretation of the argument.

Let me know if this makes sense!

[jt1234]

This is on page 56 of the 2014 edition of the Logical Reasoning Bible.

Conclusion: Ameer is probably incorrect

Premise: If Ameer is correct, either the midterm is cancelled or the final is cancelled
Premise: But the professor said in clas last week that she is considering cancelling both test and instead having students submit a term paper
Premise: Because the professor has final authority over the class schedule and composition.

The reasoning for it being a weak argument is that "no evidence is presented to contradict Ameer's assertion, so there is no reason to conclude that Ameer is probably incorrect (this would be a much better argument if the conclusion stated instead that he 'might be incorrect.')."

I am confused as to how it would be better argument if the conclusion stated that he might be incorrect. If the professor chooses to cancel both tests, wouldn't Ameer still be correct in that the truth value of his statement "Either the midterm is cancelled or the final is cancelled" still holds?

Does substituting with "might be incorrect" make it a better argument because ""might be incorrect" accounts for some outside event that could cause the professor to not cancel both tests?

Please help and thank you!

[Lucas Moreau]

Hello, jt1234,

The difference between "might be incorrect" and "probably incorrect" matters a great deal! Ameer "might be" incorrect because the professor still has a chance of choosing to cancel neither test. That would make Ameer incorrect, by the contrapositive of the first premise.

There's no reason to say "probably incorrect", though. Ameer has a non-zero chance of being incorrect, which is all that "might be incorrect" means. Any chance of being incorrect would make that true. Saying "probably incorrect" implies that his chances of being incorrect are high, at least more than half - that's what "probably" means, more probable than not! And there's no evidence to show what Ameer's chances of being incorrect are, since we don't know what the odds are of the teacher deciding one way or another.

Hope that helps,
Lucas Moreau

[jt1234]

That definitely helps clarify things. Thank you so much Lucas!

[RickMiranda]

Hi

I'm trying to understand the rationale, explained in Pg.56, behind the argument being weak.

Premise1: If Ameer is correct, either the midterm OR the final is cancelled.
[Note on this Premise]: Not quite sure what to make of the fact that this sentence is written in the present tense for something that will occur in the future, as apposed to, either the midterm or the final WILL BE cancelled. Not sure why question was written as "[either/OR IS cancelled]"

Premise2: The professor said...that she is considering canceling both tests...
Note: I can see that she is "considering". However, in my mind I automatically gave the professor's thoughts more weight than Ameer. Is this an example of bringing in outside biases or information into the argument?

Premise3: The professor has final authority over the class schedule.

Conclusion: Therefore, Ameer is probably incorrect

The explanation states that this is a weak argument because there is no evidence to contradict Ameer's assertion...

I guess the point is that there IS evidence to contradict the Professor's assertion, since she said that she is "considering" canceling both, whereas with Ameer, he is either correct or he isn't....

Any explanation here would be helpful. Thanks.

[Steve Stein]

Hi Rick,

Thanks for your message. In that one, Ameer thinks that one of those two tests is going to be cancelled.

The teacher is considering cancelling both.

So would this prove Ameer wrong? Not really...as you alluded to, "considering" tells us that the decision hasn't even been made. The professor controls the schedule, but it''s not clear that the professor will do anything that contradicts Ameer's prediction. As such, we cannot conclude that Ameer is probably incorrect, so this is a weak argument.

I hope that's helpful! Please let me know--thanks!

~Steve

[RickMiranda]

Ok, I think that helps Steve. Thanks.

[IgnesFatui]

Hi,

While working through the mini drill questions in Ch. 2 of the 2018 LR Bible, I encountered difficulty in understanding the difference between certain probability indicators. For example, the answer key states that for question #3 of the premise and conclusion analysis drill (p. 71) "this would be a much better argument if the conclusion stated instead that "he might be incorrect" versus probably incorrect. I just don't see much of a difference between might (which I interpret to mean "may or may not be true") versus "probably" (which I interpret to mean "likely"). Doesn't "might" fall under the scope of probability determined by the word "probably"? Is not something that might happen also likely to happen? Any answers or insights would be much appreciated.

Here is the stimulus for reference:

If Ameer is correct, either the midterm is cancelled or the final is cancelled. But the professor said in class last week that she is considering cancelling both tests and instead having students submit a term paper. Because the professor has final authority over the class schedule and composition, Ameer is probably incorrect.

Thanks in advance,
Monique

[Dave Killoran]

Hi Ignes,

Thanks for the question! You've actually defined these correctly, but incorrectly concluded that the difference is small or inconsequential: it's not! "Might" suggests that something could happen but is uncertain, which could be as low as a 0% chance of something happening. On the other hand, "probably" means that the chances of it happening are greater than 50%. So, while they overlap, they are very different in terms of force being used.

If that still feels uncertain, think about the difference in meaning between statements such as:

• I might go to the store tonight.
  
  and
  
  I'm probably going to the store tonight.

The LSAT will test you repeatedly on your ability to discern small differences such as these, so it's good to lock in on it now

Thanks!