logical reasoning

Logical Reasoning Questions Answered: What are Mistaken Reversals and Mistaken Negations?

what-s-that-1527433Lucy K. reached out to me with some questions about Logical Reasoning and asking for resources on mistaken reversals and mistaken negations. Here's what I told her about these terms and whether they're important when studying for the LSAT. Lucy K.: I'm working on a review of conditional reasoning right now. Do you have any resources on mistaken reversals? And also mistaken negations? I just worked through the LRB chapters on Weaken and Must Be True questions. The Weaken practice problem set went better than the Must Be True problem set, but I want to review them both. Right now I've been noticing that Weaken questions, compare/contrast dialogue between two speakers, // reasoning, principle, sufficient assumption, and flaw questions are LRs I've tended to get wrong.

I've noticed that I tend to get weirded out by long arguments, arguments with lots of formal logic, and some of the science/nature arguments (I always think I don't know what this jargon-word means, or I'm not an architect, biologist, anthropologist, et cetera, what if I'm missing something about a scientific process, or I think it would be great to diagram this LR question as I see the logic words, but I'm really scared that I'd diagram it wrong and/or am debating which abbreviations to use). I would like to practice these more.

Nathan: Oh dear. "Mistaken reversals"... "mistaken negations"... they're one and the same. I'm sorry you even have those two terms in your head, because you really don't need them. This is just something that LSAT dorks say when they want to impress someone. Logically, it's the exact same flaw. All you really need is the big picture. One example should suffice.

Premise: If you're eaten by a shark, then you're dead.

Mistaken reversal: Everyone who's dead was eaten by a shark. This is stupid because there are a lot of other ways to die. Like maybe a flock of rabid turkeys pecks you to death. Or whatever. Point is, it's obviously stupid. And believe it or not, this simple, obvious flaw is the LSAT's favorite thing to test. It's on every single LSAT.

Mistaken negation: If you're not eaten by a shark, then you're not dead. See, that's a slightly different statement but it's logically identical and it's stupid for the exact same reason. What about the rabid turkeys? What about all the other ways to die? This, again, is the LSAT's most common flaw.

Formally, the two flaws are contrapositives of one another. I suppose there is a technical difference in the form of the flaw, but it's simply not important enough of a distinction for you to bother knowing two different names for them. The terms "mistaken reversal" and "mistaken negation" have never appeared on the LSAT. Only in LSAT books. But not in my LSAT books, because I don't want you to waste your time on irrelevant technicalities.Generally, I am not in love with Powerscore's Logical Reasoning Bible for exactly this reason. It focuses on too many trees, so unsuspecting readers often miss the forest. It's not technically wrong (at least not often) but it's far too technical. Students come away thinking that the LSAT is harder than it really is.

Learn more about my LSAT prep class and how they can help you conquer the LSAT.

Image Credit: Adam Ciesielski via freeimages

Thou Shalt Pay Attention to the Type of LSAT Question

question-mark-1238622No matter what type of question you're looking at on the LSAT Logical Reasoning section, it's critical that you argue with what you're reading. But that's only half the battle. Once you've argued with the speaker, and made sure you've comprehended what they're saying, it's critical to figure out what kind of question you're dealing with. There's no point in looking at the answers until you know what you're looking for. This Commandment applies to all sections, but particularly to the Logical Reasoning. I'm shocked when a student says, "I didn't pick A because it seemed too strongly worded," on a Sufficient Assumption question. Sufficient Assumption questions love strongly stated answers! Stop being so formulaic, forget everything you learned from whatever gimmicky LSAT book you read before this, and pay attention to what the question is asking. You are smart enough to figure this out. Read every word on the page, figure out what they are asking, and answer the question. If you're not open to the possibility that you're smart enough to do this, then you really shouldn't even attempt it. I believe in you.

Here are examples of what various "question stem" wordings sound like for any given type of question.

FLAW:

-- Which one of the following most accurately describes a way in which the reasoning above is questionable? -- The reasoning in the argument is flawed because the argument -- Which one of the following most accurately describes a flaw in the reasoning above?

WEAKEN:

-- Which of the following, if shown to be a realistic possibility, would undermine the argument? -- Which one of the following, as potential challenges, most seriously calls into question evidence offered in support of the conclusion above? -- Which one of the following, if true, most seriously weakens the support for the arguments conclusion?

STRENGTHEN:

-- Each of the following supports the arguments reasoning EXCEPT: -- Which of the following, if assumed, most helps to justify the reasoning above? -- Which one of the following, if true, most strengthens the columnist’s reasoning?

SUFFICIENT ASSUMPTION:

-- Which one of the following, if assumed, would allow the conclusion above to be properly drawn? -- The conclusion drawn follows logically from the premises if which of the following is assumed? -- The conclusion is properly inferred if which one of the following is assumed?

NECESSARY ASSUMPTION:

-- Which one of the following is an assumption on which the argument depends? -- The argument makes which one of the following assumptions -- Which one of the following is an assumption required by the argument?

MUST BE TRUE:

-- Which one of the following must be true if the statements above are correct? -- The above statements, if true, most strongly support which one of the following? -- Which of the following is most strongly supported by the information above?

MAIN CONCLUSION:

-- Which one of the following most accurately expresses the arguments conclusion? -- Of the following, which one most accurately expresses the conclusion drawn above?

AGREE/DISAGREE:

-- “Robert” and “Sarah” have committed to disagreeing on which of the following? -- “Beth’s” and “Carmen’s” statements provide the most support for the claim that they would disagree about whether -- The dialogue most strongly supports the claim that “Chris” and “Joe” disagree about which one of the following?

EXPLANATION:

-- Which one of the following, if true, contributes most to an explanation of the puzzling situation described above? -- Which of the following, if true, most helps to resolve the apparent discrepancy above? -- Which one of the following, if true, contributes to a resolution of the apparent paradox?

IDENTIFYING A GUIDING PRINCIPLE:

-- Which one of the following principles best justifies the above actions? -- Which one of the following principles is best illustrated by the information above? -- The reasoning above conforms most closely to which one of the following propositions?

APPLYING A PRINCIPLE GIVEN:

-- Which one of the following would be a proper application of the principle stated above? -- Of the following, which one conforms most closely to the principle illustrated by the situation described above? -- Which one of the following best illustrates the proposition above?

COMPLETE THE ARGUMENT:

-- Which one of the following most logically completes the argument? -- The conclusion of the argument above is most strongly supported if which one of the following completes the argument? -- Which one of the following most reasonable completes the argument?

STRATEGY OF ARGUMENTATION:

-- Which one of the following most accurately describes the method of reasoning used in the argument? -- “Which of the following most accurately describes the role played in the Philosopher’s argument by the claim that “…” -- The editorial undermines the conclusion of the causal argument by

MATCHING PATTERN:

-- Which one of the following arguments is most similar to the reasoning in the argument above? -- The reasoning in the argument above is most paralleled by the argument that there is -- In which one of the following is the pattern of reasoning most similar to that in the Doctor’s argument?

MATCHING FLAW:

-- Which one of the following arguments exhibits flawed reasoning most similar to that exhibited by the argument above? -- Which one of the following exhibits both of the logical flaws exhibited in the arguments above? -- The flawed pattern of reasoning in which of the following most closely resembles the flawed pattern of reasoning in the actor’s argument?

This post is excerpted from "Introducing the LSAT” (available on Amazon). Please drop me a line in the comments, or at nathan@foxlsat.com.

Learn more about my LSAT prep class and how they can help you conquer the LSAT.

Image Source: freeimages

Q and A: Should You Diagram Logical Reasoning Questions?

tools-673837-mA student recently asked me whether I recommend diagramming Logical Reasoning LSAT questions. I'm asked this a lot, so I wanted to answer it here for anyone who is wondering the same.

Student: Firstly, I have all of your books, and I think they're great! I never thought I'd be actually laughing out loud while studying for the LSAT! :)

I've noticed that in your Logical Reasoning (LR) explanations, you rarely diagram the questions. I'm just wondering what your general opinion is on diagraming/using formal logic to answer some of the questions. I find that as I get into the late teens-and into the twenties, the questions get more convoluted and generally harder to follow/keep in my head. In your explanations, I've noticed that you solve these problems by just using the stimulus - but some of these the questions are so dense that I find it difficult to keep the main points in my head (especially for Inference questions and SA questions with a lot of conditional logic).

I want to tackle these questions in the most efficient way possible. So do you think I should practice diagramming, or is that a waste of time? What's the best approach? And do you have any specific diagramming techniques?

Nathan: Thanks for writing! I'm glad you've enjoyed my books. If you have a chance to write me a review, the phrase "laughing out loud while studying for the LSAT" would go an awful long way. No pressure, of course.Your question about diagramming on the Logical Reasoning section is a common one.

You should diagram only when necessary for understanding the argument. What type of question you're dealing with is irrelevant. What's relevant is whether or not a diagram is the only way to understand the argument itself. If you understand the argument, don't diagram. If you don't understand the argument, but you can re-read it and now you understand, then good, don't diagram. If diagramming won't help you understand the argument (like if it is very long, or has rules that don't follow a clear "if->then" or "only if" or "unless," etc. pattern, then don't diagram. If you suck at diagramming, then don't diagram.

Diagram if you can't understand any other way, and if diagramming will actually help. Otherwise don't.

Your practice test scores will clearly indicate whether or not you're ready for the December LSAT. If you want a 165, and haven't gotten a 165 on a practice test, then I'd bet against you getting a 165 on the December LSAT. On the other hand, if you had achieved a 165 on an actual LSAT, strictly timed, then I would clearly bet for scoring a 165 on the December 2014 LSAT. No need to speculate. Instead, get back to work and make it happen. If you're not ready, you can always withdraw.

Hope that helps. Good luck!

Learn more about my LSAT prep classes and how they can help you conquer the LSAT.

Photo credit: konarska via freeimages