Q14 - Historian: Leibniz, the seventeenth-century

[sbuzzetto10]

I correctly chose E on this one, but what makes B incorrect? Is it because even if someone else independently discovered calc before both of them, that doesn't necessarily mean that they knew about it or used it at all? Sometimes it's hard to decide what's actually necessary and what just sounds necessary!

[noah]

Sometimes it's hard to decide what's actually necessary and what just sounds necessary!

So true!

This question is asking for a necessary assumption. Let's ID the core:

The conclusion is that Lieniz and Newton each independently discovered calculus.

Why? What's the premise? It takes a bit of digestion, but the premises boil down to this:

Liebniz published his version of calculus before Newton, and didn't receive any real help (regardless of some people who disagree). Also, Newton had been using those ideas for at least a decade before Lieniz published his. All of that boils down to the idea that they didn't help each other.

There are some serious gaps here! For one, just because Liebniz published his ideas in year X doesn't mean he didn't tell Newton about it beforehand. Similarly, we never learn that either character actually discovered calculus. Perhaps they didn't help each other, but who is to say that the fact these two guys didn't help each other means they each discovered calculus? Maybe their wives did and they stole the work (independently of each other, of course ).

(E) hinges on this assumption - we have to assume that neither of them learned crucial bits of calculus from someone else.

(A) is about who Liebniz told before publishing it. It's a problem of Liebniz told Newton, but it might be OK if he told someone else.

(B) This is quite tempting! It sure seems that the negation of this - a third person independently discovered calculus - would destroy the argument. But it doesn't! So what if a third person independently discovered it? As long as neither Newton or Liebniz used that discovery to "discover" calculus, it's not a problem. Apparently this argument accepts the idea that multiple people can independently discover an idea.

(C) is irrelevant - we don't care about what Newton believed about Liebniz.

(D) is also tempting - it sounds like it's saying "neither learned calculus from the other" but it doesn't! It says that neither knew that the other had discovered a version of calculus. Knowing that someone had developed something doesn't mean you know what the thing is.

Read this: I've discovered a new website: gooble! What do you now know?

You know I've discovered a wesite, but you don't know what it's about. Furthermore, perhaps they both discovered calculus years before Liebniz published anything. So what if they each knew that the other had discovered calculus - they both might still already discovered it!

[efd628]

Can someone provide the Logical negation for (E)

E reads:

Neither Newton nor Leneiz learned crucial details about calculus from some third source.

To logically negate a conditional statement, negate the necessary condition right?

so is it correct to re-write E as:

If you are newton or leibniz you did not learn crucial details about calculus from some third source.

negation is:

if you are newtown and leibniz you did learn crucial details about calculus from a third source. (not independently)

[ohthatpatrick]

You can negate any statement by simply prefacing it with “It is not true that ____”.

So negating (E) is saying “It is NOT true that Neither N nor L learned crucial details about calculus from some third source”.

Can you rephrase that?

I would say “At least one of them learned crucial details about calculus from some third source”.

Well if that’s true, it severely weakens the conclusion that they each independently discovered calculus.

(E) is not a conditional statement, unless you’re really working hard to make it one.

Is this a conditional statement? “It didn’t rain today”.

No, unless you really want to make it one:
If it is today —> then it didn’t rain.

That’s just silly, though. That’s not making the test EASIER to digest.

So I’m not sure why you’re trying to make (E) seem like a conditional, when it’s just a statement of fact.

You might be remembering that “neither / nor” sometimes appears in conditional rules.

(for example “If Sally is selected, neither Bob nor Gary can be selected”). But the “neither / nor” doesn’t itself make something a conditional.

However, to address your concern / confusion, you do NOT negate either side when you’re negating a conditional. You are negating the arrow; i.e. you’re saying “There is NOT some inflexible connection between these two ideas”.

This is most easily demonstrated with an ALL statement, which can be symbolized as a conditional.

All girls like Justin Bieber.

negated: NOT all girls like Justin Bieber (at least some girls DON’T like Justin Bieber)

Seen conditionally, we’d have:
Girl —> like Justin Bieber

The negation isn’t saying that “all girls DON’T LIKE Justin Bieber”. It’s just saying “being a girl does NOT guarantee me that you like Justin Bieber.

I almost never find that we need to negate a conditional, so it’s really a moot point for 99.9% of LSAT.

You’re probably remembering that when we want to FIGHT / WEAKEN a conditional, we’re looking for an example in which we HAVE the Sufficient but DENY the Necessary.

But again, the point of that is not to show that the Sufficient ALWAYS leads to ~Necessary. It’s just to show that there are exceptions. It’s just to argue that “It is NOT the case that the Sufficient always leads to the Necessary”.

Hopefully I haven’t made things more confusing.

[olaizola.mariana]

I missed this question because I read "independently discovered" as meaning that they made the discovery independently OF EACH OTHER. I now see that the sentence actually meant independent as in "without outside help." Is this correct?

However, it seems we can't rule out (A) unless we assume, as noah does, that Leibniz did not share calculus with Newton before publishing. But how can we assume this???

[ohthatpatrick]

A correct answer to Necessary Assumption can be tested with the
Negation Test: if negated, it should ruin/severely weaken the argument.

For the most part, ruining/weakening an argument means giving ourselves a way to argue against the conclusion.

In this case, we'd need a way to argue that "L and N did NOT each discover calculus all by himself."

negated-(A)
Leibniz DID tell someone about calculus prior to publishing his version of it.

Okay, does that allow us to argue that L and N did NOT each independently discover calculus?

Not really. If I discovered calculus, I'd totally be bragging to my friends as I worked on publishing my actual work.

You're taking that idea and adding your own idea that the person who was told by Leibniz was in fact Newton.

It doesn't say that.

If (A) said "L did not tell Newton about calculus many years prior to publishing his version of it", then you have yourself a tasty answer.

Meanwhile,
negated (E)
Either N or L (or both) learned some crucial details about calculus from some third source.

Okay, well that concretely, with no added assumptions, allows us to argue that N and L did NOT, each, discover calculus all by himself.

Hope this helps.

[ohthatpatrick]

A correct answer to Necessary Assumption can be tested with the
Negation Test: if negated, it should ruin/severely weaken the argument.

For the most part, ruining/weakening an argument means giving ourselves a way to argue against the conclusion.

In this case, we'd need a way to argue that "L and N did NOT each discover calculus all by himself."

negated-(A)
Leibniz DID tell someone about calculus prior to publishing his version of it.

Okay, does that allow us to argue that L and N did NOT each independently discover calculus?

Not really. If I discovered calculus, I'd totally be bragging to my friends as I worked on publishing my actual work.

You're taking that idea and adding your own idea that the person who was told by Leibniz was in fact Newton.

It doesn't say that.

If (A) said "L did not tell Newton about calculus many years prior to publishing his version of it", then you have yourself a tasty answer.

Meanwhile,
negated (E)
Either N or L (or both) learned some crucial details about calculus from some third source.

Okay, well that concretely, with no added assumptions, allows us to argue that N and L did NOT, each, discover calculus all by himself.

Hope this helps.

[scarlettng0623]

I am confused with B.

It's possible that multiple persons can discover calculus. However, it says "prior to Newton and Leibniz." If we negate this answer choice, it would invalidate the conclusion.

Thoughts?

[aaronwfrank]

Sometimes it's hard to decide what's actually necessary and what just sounds necessary!

So true!

This question is asking for a necessary assumption. Let's ID the core:

The conclusion is that Lieniz and Newton each independently discovered calculus.

Why? What's the premise? It takes a bit of digestion, but the premises boil down to this:

Liebniz published his version of calculus before Newton, and didn't receive any real help (regardless of some people who disagree). Also, Newton had been using those ideas for at least a decade before Lieniz published his. All of that boils down to the idea that they didn't help each other.

There are some serious gaps here! For one, just because Liebniz published his ideas in year X doesn't mean he didn't tell Newton about it beforehand. Similarly, we never learn that either character actually discovered calculus. Perhaps they didn't help each other, but who is to say that the fact these two guys didn't help each other means they each discovered calculus? Maybe their wives did and they stole the work (independently of each other, of course ).

(E) hinges on this assumption - we have to assume that neither of them learned crucial bits of calculus from someone else.

(A) is about who Liebniz told before publishing it. It's a problem of Liebniz told Newton, but it might be OK if he told someone else.

(B) This is quite tempting! It sure seems that the negation of this - a third person independently discovered calculus - would destroy the argument. But it doesn't! So what if a third person independently discovered it? As long as neither Newton or Liebniz used that discovery to "discover" calculus, it's not a problem. Apparently this argument accepts the idea that multiple people can independently discover an idea.

(C) is irrelevant - we don't care about what Newton believed about Liebniz.

(D) is also tempting - it sounds like it's saying "neither learned calculus from the other" but it doesn't! It says that neither knew that the other had discovered a version of calculus. Knowing that someone had developed something doesn't mean you know what the thing is.

Read this: I've discovered a new website: gooble! What do you now know?

You know I've discovered a wesite, but you don't know what it's about. Furthermore, perhaps they both discovered calculus years before Liebniz published anything. So what if they each knew that the other had discovered calculus - they both might still already discovered it!

"Apparently this argument accepts the idea that multiple people can independently discover an idea."

If that were the case, then the negation of E wouldn't affect the conclusion. So this is wrong.

[ohthatpatrick]

The issue at hand is the truth value of the conclusion (as well as the relevance of the evidence that got the author there).

The court is hearing the case of "Whether or not Newton and Leibniz each independently discovered calculus".

Which of these ideas better helps us argue that they did NOT independently discover calculus:
negated-(B): Someone else independently discovered calculus prior to when Newton and Leibniz purportedly did.

negated-(E): Newton and/or Leibniz learned crucial details about calculus from some other source.

(B) has no effect on the issue at hand. If you're trying to assess whether Bob and Eddie each were able to build a car by themselves, it makes no difference whether Lisa built a car by herself a long time ago.

(E) does have an effect. If you're trying to assess whether Bob and Eddie each were able to build a car by themselves, it makes a big difference whether Bob and/or Eddie got crucial help about building a car from someone else.

[esthertan0310]

Hello

In plain English, what's wrong if either Newton or Leibniz learned crucial details about calculus from third sources? What if Newton's source is different from Leibniz' source?

Thanks in advance

[JosephV]

Hello

In plain English, what's wrong if either Newton or Leibniz learned crucial details about calculus from third sources? What if Newton's source is different from Leibniz' source?

Thanks in advance

You have to read very, very closely for the LSAT.

Answer choice (E) says that neither Newton nor Leibniz learnt essential stuff about calculus "from some third source." The word used is source - in the singular! This means that (E) is ruling out the possibility that both discovered calculus with the help of the same person.

With this understanding of (E) go ahead and apply the Negation Test. You get: At least one of them - either Newton or Leibniz, or possibly both - discovered calculus with a third person's help. (NOTE that the proper negation of "either.... or...." is "at least one", not "both," as Patrick points out below.)This sentence completely destroys the conclusion of the stimulus that "Leibniz and Newton each independently discovered calculus."

If the negated (E) were true, then Leibniz and Newton would be "connected", so to speak, through this third person who taught them both, i.e. their discoveries of calculus would not be independent.

[ohthatpatrick]

Awesome post!

Quick correction: negating "neither L nor N got info from a third source" wouldn't be "BOTH of them got it from a third source", it would be "AT LEAST ONE of them got it from a third source".

Since the conclusion is claiming that "EACH of them discovered it independently", we're doing plenty of damage just by establishing that "AT LEAST ONE of them got help".

If you got essential information about calculus from someone, then you did not discover calculus independently.

[JosephV]

Thanks Patrick.

The correction is very helpful and well-received! I'll edit my prior post to reflect it.