Formal logic

Formal arguments tend to be simple, straightforward, and extreme.

Example:

Everyone in Manhattan lives in NYC. Everyone in NYC lives in New York State. Therefore, everyone in Manhattan lives in New York State.There are no assumptions here - it's mathematical, and the evidence fully justifies the conclusion.

Represented in symbols, we can therefore say:

Manhattan -> NYC. NYC -> NYS. Therefore, Manhattan -> NYS.

Change the topic to something about climate change or morality, and you've got one of the few formal logic questions in Logical Reasoning. (See my post a few weeks back on 15 Common Logical Reasoning Topics for more on that). Most formal logic on the LSAT happens in Logic Games.

On the LSAT, of course, it might not be that simple. The argument above could be phrased as follows:

If you live in Manhattan, then according to accurate, yet decades-old, government records, you must live in NYC. However, if you're in New York State, then you may or may not be in NYC. On the other hand, if you're in NYC, then you must live in New York State.I included the 2nd sentence as filler just to make the argument more difficult to understand. Although it's more casual and wordy than the formal logic version, this doesn't mean it's easier.

The two versions above are identical. It's not necessary to represent it in symbols, but it can sometimes help.

Informal logic

Informal arguments are much more common on the LSAT. They tend to be complex and contain unstated assumptions.

Example:

Some people in New York State aren't famous. However, because I live in NYC, I ride around Manhattan in limos and hang out with celebrities. Therefore, I'm famous by association.This can't be diagrammed as neatly, the evidence doesn't fully justify the conclusion (by a long shot), and a lot of other things also need to be true in order for the conclusion to logically follow.

Logic IS mathematical. Diagram the above tautology using a Venn Diagram. Draw a large circle for NYC. Draw a smaller circle entirely inside to represent Manhattan. Draw a larger circle entirely encompassing NYC (and necessarily, Manhattan) to represent New York State. It becomes simple to verify the conclusion.

ReplyDeleteDespite what Caleb said below, your suggestion helped me TONS! Sometimes it just takes another way to look at it to understand it.

DeleteErid- that would be the simple, mathematical formal logic that this post describes.

ReplyDeletePost: "This is mathematical and simple."

You: "Nuh uh! Logic IS mathematical! See?"

Me: "Um... right. That's what he just said."

Draw a large circle with "people who comment without reading this post" above it and then put a picture of you in it.

PS Ha! My verification word was "defake." Google's on to you, Erid.

You don't have to be a jerk, Caleb. If you don't have something useful to say, don't say anything.

ReplyDeleteErid, tell your mom to use her real name if she's going to post on here.

ReplyDeleteMom- contrapositive: I did say something, so I had something meaningful to say.

Sort of.

Steve,

ReplyDeleteThank you for all your work. It has greatly aided my LSAT prep. I was hoping you'd be able to clarify how one would go about diagramming (the contrapositive as well) the following kind of if/then statement:

"If I fall down, then I will scream or cry."

Thank you

I won't scream and cry if I don't fall down

DeleteI was going over this post and I wanted to take a shot at D's question

ReplyDeleteIf I do not scream and cry then I did not fall down.

-S and -C -> -FD

Two things:

ReplyDeleteFirst, Caleb you are immature and annoying.

Second, Alana, your English version is wrong. The correct way of putting it is "If I do not scream OR cry, then I did not fall down" or to be more precise: If I failed to either scream or cry, then I didn't fall down.

Your way would lead to the conditional that if I did not both scream and cry, I didn't fall. That would mean you could still do one or the other (but not both) and it would necessarily lead to "didn't fall," but that's incorrect. The real proposition (as you stated in representative form) is that you must neither scream or cry; you can't do either of those, in order for "didn't fall" to be the necessary condition.

Side point: Steve, if even formal logic problems come to me quickly and fairly easily naturally (without diagramming) should I continue it that way or try to incorporate diagramming with the idea that maybe one day my intuition will fail me?

ReplyDeleteP.S. one more thing --Alana's mistake is just one more reason why the sort of analysis Kaplan, Powerscore, and some other big companies use can be misleading for the average student. They tell you to simply switch "and" with "or" and "or" with "and" to make contrapositives of those conditionals. Well guess what--that works for superficial diagrams, but the core understanding has to come along too if you are going to really crack open the LSAT. And the core understanding is actually more intuitive and easy to learn in my opinion. At the very least these companies should make sure the students realize that the and/or switching doesn't work for the English version of the relationships. I'm sure the testmakers could have an English answer choice that would easily capture a lot of these students who don't have the fuller grasp.

ReplyDeleteCan you give another example where the translation doesn't always alternate and/or? I've been using that method on practice tests and it seems to work, so I'm worried there's something I'm missing. Alana's contrapositive really looks right to me.

DeleteTotal amateur here, but what Anonymous @7:03 was saying is that the English written-out version of Alana's contrapositive was incorrect; however, the diagram was correct.

DeleteI think Caleb's comment was entertaining and I needed that to keep me awake.

ReplyDeleteCaleb you made me giggly guts.

ReplyDeleteCaleb, thanks very much for the post. I was wondering if you have a suggestion as to how one can think about and accordingly diagram better comparisons. Say we have an argument "To manufacture hard drive X is more expensive than hard drive Y. However, using hard drive X is cheaper than hard drive Y because hard drive X uses very little energy and lasts longer when compared to hard drive Y". How do we diagram this please? Do we have an automatic contrapositive of this? Generally, how can we better relate categories via the diagrams? I am generally having trouble with inferences and when it comes to comparisons I get even more lost. Thanks, John

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