Mistaking sufficient condition for necessary, and vice-versa Forum

[theoretics]

Is there a difference between 'mistaking the sufficient condition for the necessary condition' and 'mistaking the necessary condition for the sufficient condition'? I can sort of see a difference, but I feel like it could be phrased either way and still be the same flaw.

[pkraft1]

the difference is what the argument is utilizing. For example,

if a then b.

b

therefore a.

mistakes a necessary condition for a sufficient condition because it utilized what is actually a necessary condition as a sufficient condition.

On the other hand,

if a then b

not a

therefore not b.

mistakes a sufficient for a necessary.

[Germaine]

Is there a difference between 'mistaking the sufficient condition for the necessary condition' and 'mistaking the necessary condition for the sufficient condition'? I can sort of see a difference, but I feel like it could be phrased either way and still be the same flaw.

mistaking the sufficient condition for the necessary condition = it's a sufficient condition, and you wrongly thought it was a necessary
mistaking the necessary condition for the sufficient condition = it's a necessary condition, and you wrongly thought it was a sufficient

think of it this way:

I mistook my dog for an intruder = it was my dog, and I wrongly thought it was an intruder (not: it was an intruder, and I wrongly thought it was my dog)

[Jeffort]

Is there a difference between 'mistaking the sufficient condition for the necessary condition' and 'mistaking the necessary condition for the sufficient condition'? I can sort of see a difference, but I feel like it could be phrased either way and still be the same flaw.

The explanations from pkraft1 quoted below are correct and my explanations build on his examples.

Depending on which materials/source you're using for prep (which company's class or books), there are easy to remember shorthand labels/descriptions for these two different common flawed uses of conditional premises.

premise A --> B (If A then B, All A's are B's, etc.)
This flawed reasoning method/pattern/utilization: B is true, therefore A must be true

is mistaking the necessary condition for the sufficient condition.

In the LSAT prep world this flawed method of reasoning is commonly called invalid/incorrect/mistaken reversal since the reasoning method using the conditional premise to arrive at the conclusion reverses the conditional premise in a logically invalid way by treating it as if the premise established B --> A rather than A --> B. Hence, the flawed reasoning improperly reversed the conditions from their valid sufficient vs. necessary positions/mistakenly assumed that the sufficient/necessary relationship between the conditions is the reverse of what the premise established.

same premise A --> B
Flawed reasoning method/pattern/utilization: A is false, therefore B must be false

is mistaking the sufficient condition for the necessary condition.

In the LSAT prep world this flawed method of reasoning is commonly called invalid/incorrect/mistaken negation since the reasoning method using the conditional premise to arrive at the conclusion negates both sides of the conditional premise relationship in a logically invalid way by treating it as if the premise logically established ~A --> ~B. That flawed negation of both conditions while leaving them in the same diagrammatic sufficient and necessary condition places in the arrow diagram is the contrapositive of conditional premise B --> A, the flawed reversal of the given A--> B conditional relationship premise.

Under the premise, condition 'A' being true is sufficient to guarantee that B must also be true, but the premise by itself DOES NOT exclude the possibility that there could be other sufficient conditions that could also guarantee that B must be true other than condition 'A' being true. Thus, this flawed method of treating the sufficient condition 'A', (which guarantees that condition 'B' must be true), as if it also establishes that the sufficient condition 'A' being false guarantees that necessary condition 'B' must also be false invalidly assumes/mistakes/treats the sufficient condition 'A' as if it's a necessary condition for B to be able to be true because the premise ( A --> B ) only establishes that 'A' is a sufficient condition, not a necessary condition for condition 'B' to be true.

Sufficient conditions are called 'sufficient' because when you know the condition is true, it's enough to logically GUARANTEE that the necessary condition must also be true, whereas knowing that a necessary condition of a conditional relationship is true isn't enough to guarantee anything about the absolute logical truth (must be true or must be false) of the other condition in the relationship. Knowing that a necessary condition is true only establishes that the sufficient condition is possible/could be true, but logically doesn't guarantee anything absolute/must be true/must be false about the sufficient condition in the relationship.

Hope this isn't overly confusing. The foundations and concepts behind logically valid vs. invalid conditional reasoning methods usually take a little bit of time, practice and review to get familiar and comfortable with for most people during the important learning LSAT concepts/building your LSAT knowledge foundation phase of prepping for the test.

With standard conditional premises (not formal logic premises that use quantifiers Most or Some), an easy way to think about and remember their logically valid uses/valid methods of using them to establish logically correct conclusions vs. flawed ways they're frequently used to produce invalid/illogical/flawed conclusions is that you can only make a valid must be true inference/conclusion from a conditional premise when you know either one of two things: that the sufficient condition is true or that the necessary condition is false.

(You may already know this stuff, so feel free to disregard if so, I'm just trying to be thorough since I have no idea where in your prep journey you are.)

Since every standard conditional premise also implicitly establishes that the contrapositive of it is also a valid premise, a really easy way to remember when you can draw a valid MUST BE TRUE conclusion from conditional premises is that you can only make an absolute must be true/must be false conclusion about an element from a conditional premise when you know that the sufficient condition is true, meaning that the condition on the side the arrow points away from (the left side if you always draw your arrow diagrams with the arrow pointing to the right).

Premise: A --> B
contrapositive: ~B --> ~A

The contrapositive that's implicitly true/valid from every standard conditional premise is simply formed by both REVERSING AND NEGATING both conditions, so the valid implicit contrapositive of the original premise is ~B --> ~A.

With the original premise and its contrapositive properly diagrammed,
A --> B
~B --> ~A

you only need to and should only look at the left side of the diagrams to determine the valid must be true conclusions that can be drawn from the premise. If you know/are told that/it's established that a condition on the left side of the arrow diagram is true, then it must be true that the condition on the right side must be true. Knowing that a necessary condition (the ones on the right side of the arrow diagrams) is true doesn't allow you to conclude anything absolute (must be true or must be false) about the sufficient condition(s) on the other side/left side of the arrow diagram of the conditional premise.

If you diagram conditional premises and the contrapositive of each, you only need to focus your attention on the left side/sufficient condition side of the diagrams to quickly know what valid conclusions are supported/established by those premises when combined with other facts about which conditions are true or false (other premise(s) or info in answer choices that tell you certain condition(s) are true or false).

With the example A --> B conditional premise, knowing that the necessary condition of either the original premise or it's contrapositive is true (the conditions on the right side of the arrow diagrams) doesn't guarantee anything absolute about the truth of the sufficient conditions on the left side of the diagrams. So, knowing that necessary condition 'B' is true or that condition 'A' is false (necessary condition '~A' in the contrapositive), doesn't guarantee/establish whether the other/sufficient condition is true or false. If 'B' is true, it only supports the conclusion that condition 'A' COULD BE TRUE, but also leaves open the possibility that 'A' could be false. If 'A' is false (~A), 'B' could be true or could be false since knowing that a necessary condition is true does not guarantee anything absolute about the logical truth (for sure true or for sure false) of the sufficient condition in the conditional relationship.

----

In a nutshell:

mistaking a necessary condition for a sufficient condition = LSAT prep world labels invalid/incorrect/mistaken reversal of the explicitly given conditional premise.

mistaking a sufficient condition for a necessary condition = LSAT prep world labels invalid/incorrect/mistaken negation of the explicitly given conditional premise.


I hope this helps clear things up. Feel free to ask for clarification or anything since conditional reasoning is used in some complex/tricky ways in many LR questions of various question types including must be true, most strongly supported, strengthen, weaken, describe the flaw, sufficient assumption, necessary assumption, parallel reasoning and principle question types.

the difference is what the argument is utilizing. For example,

if a then b.

b

therefore a.

mistakes a necessary condition for a sufficient condition because it utilized what is actually a necessary condition as a sufficient condition.

On the other hand,

if a then b

not a

therefore not b.

mistakes a sufficient for a necessary.

[Clearly]

Slight reassurance though, the two have only appeared opposite each other on maybe 3 flaw questions ever. I'm pretty good at these things and even I have the thought process of "look for a conditional answer" rather than a specific phrasing until I see both, then I'd go back and think it through.

[Jeffort]

Slight reassurance though, the two have only appeared opposite each other on maybe 3 flaw questions ever. I'm pretty good at these things and even I have the thought process of "look for a conditional answer" rather than a specific phrasing until I see both, then I'd go back and think it through.

ehh, there's actually more than three when you include ones where they offer both flaws as AC's but only phrase one of them in these ways using obvious straightforward conditional keywords language but use totally different vocabulary and phrasing to describe the other conditional flaw, such as by describing it like 'it takes for granted that xyz blah blah blah' or 'presumes without justification that xyz' or 'fails to consider that xyz' using substantive wording about the subject matter elements in the argument to disguise from skimming that it's describing a conditional reasoning flaw.

Although the most noticeable/memorable questions that offer both flaws as AC's on flaw questions appeared on older tests, the tactic is still alive and well.

LSAC did it again very recently on PT70 with an easy flaw Q (early in the section as #3 where people assume the Qs are easy so tend to rush and be less careful!) where the argument is simple and easy to understand that clearly makes a basic conditional reasoning flaw of one of these two types where the trap AC uses the clear cut 'treats a necessary...sufficient' easy to recognize conditional flaw description language that jumps out when skimming to trap/steal a point from people and phrased the CR as 'it takes for granted...[substantive language]' that you have to seriously consider and think about a little to realize is properly describing the conditional flaw made in the stimulus rather than the obviously describing a conditional flaw, but the wrong flaw trap AC. It works effectively to pick pocket that easy point from some test takers that skim a bit and aren't as meticulous on the questions early in LR sections for pacing purposes, the stats on the various online PT scoring utilities reflect that.

Since LSAC used that tactic again recently and it apparently worked, I wouldn't get complacent on the issue and assume it's unlikely to happen again.

[theoretics]

Slight reassurance though, the two have only appeared opposite each other on maybe 3 flaw questions ever. I'm pretty good at these things and even I have the thought process of "look for a conditional answer" rather than a specific phrasing until I see both, then I'd go back and think it through.

ehh, there's actually more than three when you include ones where they offer both flaws as AC's but only phrase one of them in these ways using obvious straightforward conditional keywords language but use totally different vocabulary and phrasing to describe the other conditional flaw, such as by describing it like 'it takes for granted that xyz blah blah blah' or 'presumes without justification that xyz' or 'fails to consider that xyz' using substantive wording about the subject matter elements in the argument to disguise from skimming that it's describing a conditional reasoning flaw.

Although the most noticeable/memorable questions that offer both flaws as AC's on flaw questions appeared on older tests, the tactic is still alive and well.

LSAC did it again very recently on PT70 with an easy flaw Q (early in the section as #3 where people assume the Qs are easy so tend to rush and be less careful!) where the argument is simple and easy to understand that clearly makes a basic conditional reasoning flaw of one of these two types where the trap AC uses the clear cut 'treats a necessary...sufficient' easy to recognize conditional flaw description language that jumps out when skimming to trap/steal a point from people and phrased the CR as 'it takes for granted...[substantive language]' that you have to seriously consider and think about a little to realize is properly describing the conditional flaw made in the stimulus rather than the obviously describing a conditional flaw, but the wrong flaw trap AC. It works effectively to pick pocket that easy point from some test takers that skim a bit and aren't as meticulous on the questions early in LR sections for pacing purposes, the stats on the various online PT scoring utilities reflect that.

Since LSAC used that tactic again recently and it apparently worked, I wouldn't get complacent on the issue and assume it's unlikely to happen again.

Hrms.. Thanks for your explanations! As I understand it, then, the two errors may be phrased thusly:

Mistakes sufficient for necessary = Treats something sufficient as necessary = The argument mistakenly assumes that failing to satisfy a sufficient condition implies the falsity of the necessary condition.

Mistakes necessary for sufficient = Treats something necessary as sufficient = The argument mistakenly assumes that satisfying a necessary condition implies the truth of the sufficient condition.

I feel like I have a better grasp of what the two conditional fallacies mean and how they are different from each other because of the explanations on this thread. That said, how does LSAC try to evade talk of sufficient and necessary conditions with substantive language? I remember PowerScore talking about how it's difficult for the test to not use those words. Is it through synonyms such as 'a factor that would be enough to prove a claim as true' for sufficient conditions and 'what needs to be true' for necessary conditions? Are there other variations I should be aware of?

[Jeffort]

That said, how does LSAC try to evade talk of sufficient and necessary conditions with substantive language? I remember PowerScore talking about how it's difficult for the test to not use those words. Is it through synonyms such as 'a factor that would be enough to prove a claim as true' for sufficient conditions and 'what needs to be true' for necessary conditions? Are there other variations I should be aware of?

Using synonyms for 'sufficient' and/or 'necessary' is one tactic the test writers sometimes use to write AC's phrased in the same common/generic abstract ways to describe these flaws we're discussing in this thread/that are in our above posts.

A few commonly used synonyms for necessary: essential, required, needed, prerequisite
A few commonly used synonyms for sufficient: enough, adequate, suffices, ample, ensures, justifies

The test writers also sometimes use significatly different phrasings than the two we're discussing to describe these two flaws that usually include one or more common conditional indicator words and/or phrases such as 'only', 'nothing but/nothing other than', 'unless', etc.

For example: The argument fails to establish that a condition under which another must be true is the only condition under which the other condition can be true.

What I mean by substantive flaw description AC's are ones that are not generic abstract descriptions of the flawed methods like the two phrasings we're discussing, but instead ones that describe the flaw in less/non abstract ways that includes the subject matter elements involved in the argument. These are typically phrased in two common ways: 'fails to establish that...' or 'assumes/presupposes without justification that...' or 'fails to consider the possibility that...'

Invalid negation/mistaking sufficient for necessary conditional flaw argument:

If an account holder takes their paycheck to a teller at a branch of the bank, then the paycheck will be deposited into the persons account. John did not take his paycheck to a teller at a branch of the bank he has an account with, therefore John's paycheck was not deposited into his account with the bank.

Substantive examples of how the flaw could be described:

'fails to establish that taking ones paycheck to a teller at the bank is the only way to deposit the money into ones account with the bank.'

or

'fails to consider the possibility that one might be able to deposit their paycheck into their bank account without taking it to a teller at a branch of the bank.'

or

'assumes without justification that there is no other way to deposit ones paycheck into ones account than taking it to a teller at a branch of the bank'

or

'fails to establish that one cannot deposit their paycheck into their bank account unless they take it to a teller at a branch of the bank'

or

'presumes without warrant that one can only deposit their paycheck into their account at the bank if they take it to a teller at a branch of the bank'

There are plenty of other similar paraphrases the test writers can and/or have used to describe these two conditional flaws using the various different ways conditional relationships can be phrased/described.

Do these clarify what I meant by substantively phrased flaw Q AC's?

The LSAT test writers are masters of paraphrase and frequently use the flexibility of the English language to write answer choices (and/or parts of arguments/the stimulus) in cryptic ways as one of many methods to make certain questions harder/higher difficulty level. The test writers are very skilled professionals at taking simple ideas that can be expressed in clear cut easy to understand layman's terminology/language and instead phrasing them in mind bending cryptic ways. They intentionally do this in part to test your reading and grammar skills and repeatedly use certain forms of confusing phrasings (like double negatives or backwards-speak phrased sentences) because much of the language the laws and cases you'll have to read and learn in law school are written in similar confusing cryptic language phrasings.

[theoretics]

Ahh, I see what you mean. So, here are some of my interpretations of your stimulus and ACs. Let me know if I'm on the right track.

Original argument: teller > deposit; (John) not teller > not deposit

This argument mistakenly assumes that failing to satisfy the sufficient condition implies the falsity of the necessary condition, i.e., assumes the conditional to be [not teller > not deposit], which can also be written as [deposit > teller]. On my paper, I would have written these out as the mistaken assumptions.

"fails to establish [deposit > teller; the mistaken assumption]"

"fails to consider [not teller > deposit; a logical negation and counter-argument to the mistaken assumption]"

"assumes without justification [deposit > teller]"

"fails to establish [deposit > teller]"

But the last AC threw me in for a loop. Presumes with warrant? I had only seen the construction 'presumes without warrant.' And the conditional statement that that last AC refers to seems to be the original statement of [teller > deposit]. I'm having trouble seeing how the argument presumes this when the argument seems to mistakenly interpret this statement.

[Jeffort]

Ahh, I see what you mean. So, here are some of my interpretations of your stimulus and ACs. Let me know if I'm on the right track.

Original argument: teller > deposit; (John) not teller > not deposit

This argument mistakenly assumes that failing to satisfy the sufficient condition implies the falsity of the necessary condition, i.e., assumes the conditional to be [not teller > not deposit], which can also be written as [deposit > teller]. On my paper, I would have written these out as the mistaken assumptions.

"fails to establish [deposit > teller; the mistaken assumption]"

"fails to consider [not teller > deposit; a logical negation and counter-argument to the mistaken assumption]"

"assumes without justification [deposit > teller]"

"fails to establish [deposit > teller]"

But the last AC threw me in for a loop. Presumes with warrant? I had only seen the construction 'presumes without warrant.' And the conditional statement that that last AC refers to seems to be the original statement of [teller > deposit]. I'm having trouble seeing how the argument presumes this when the argument seems to mistakenly interpret this statement.

Oops, that was a typo in the last one. Fixed it to what it was supposed to say 'presumes without warrant...' Sorry, wrote that up late last night and overlooked that major typo! Good catch!

However, the assumption it describes is [deposit --> teller] since it's an 'only if' statement (only if = necessary condition) where the 'only' and 'if' are just split apart in the phrasing with substance in between but the meaning of the sentence is the same as a paraphrase that keeps 'only if' together as a phrase with none of the substance in between those two words.

'presumes without warrant that one can only deposit their paycheck into their account at the bank if they take it to a teller at a branch of the bank'

is the same thing as saying (and is another good example of one tricky way the test writers sometimes use their mastery of paraphrasing to trip people up/make questions harder by phrasing a conditional in an easy to misinterpret way):

'presumes without warrant that one can deposit their paycheck into their account at the bank only if they take it to a teller at a branch of the bank'

Yeah, given your examples/descriptions you've totally got it/are on the right track.

An interesting useful concept these examples also help illustrate is that the same flaw/unwarranted assumption can be described either as something the argument assumes/presumes without warrant/justification or as something that the author fails to consider, and that those two forms are basically just opposites of one another/two sides of the same coin.

In terms of describing flaws in flaw Q answer choices, what the argument fails to consider is something that is either the logical or extreme opposite of the unwarranted assumption of the argument. Meaning that whatever the unwarranted/flawed assumption is (for any type of flaw), the test writers can write the CR in either form: by stating what the flawed assumption is, or by stating that the argument failed to consider something/a possibility that contradicts the unwarranted assumption. Both the logical opposite (its logical negation, same way you negate answers for necessary assumption questions) of the unwarranted assumption and the extreme/polar opposite of the assumption contradict the flawed/unwarranted assumption by showing that it's something that could be false, hence pointing out a specific hole in the reasoning of the argument. The logical or extreme opposite of whatever the unwarranted assumption is are both valid ways to describe the flaw using 'fails to consider the possibility that...' phrasing.

With answer choices that describe flaws in 'assumes/presumes...' form, if you're not sure about an answer choice you can also use the negation technique to test it, just like how you can use the negation technique with necessary assumption questions to test AC's since flaw Q's where the CR is written in 'assumes...' form are the same thing as necessary assumption questions!

[theoretics]

That's a clever and interesting AC! Looking back on it, I can see how it could be reworded to make more sense that way. In my head, though, I wouldn't have thought to phrase it in terms of 'only if' (although I can see how that's the legit method), I would have translated it to 'presumes without warrant that [the only way] one can deposit their paycheck into their account at the bank [is] if they take it to a teller at a branch of the bank.' Another reason why it pays to not blindly follow indicator words (curses, LSAT!).

Much thanks and appreciation for your clarifications, Jeffort!

[Jeffort]

That's a clever and interesting AC! Looking back on it, I can see how it could be reworded to make more sense that way. In my head, though, I wouldn't have thought to phrase it in terms of 'only if' (although I can see how that's the legit method), I would have translated it to 'presumes without warrant that [the only way] one can deposit their paycheck into their account at the bank [is] if they take it to a teller at a branch of the bank.' Another reason why it pays to not blindly follow indicator words (curses, LSAT!).

Much thanks and appreciation for your clarifications, Jeffort!

Glad my posts are helpful!

And yeah, blindly following conditional indicator words will ensure that you get some/most of the highest difficulty level conditional reasoning based questions wrong since the test writers intentionally write some of them in tricky grammatical ways where just blindly following the conditional indicator words out of the full context sentence meaning will produce a misinterpretation of the conditional relationship(s) and likely lead you to eliminating the CR and thinking a trap answer is logically correct.

There's also a deeper level of tricky evil conditional relationships phrasing the test writers occasionally use that are much nastier/trickier than the last one above with the split 'only if' that really warrant the 'damn you LSAC bastards!' notion.

The nastiest/most tricky way the test writers occasionally do this to construct high difficulty level questions is with nested conditional statements/relationships, such that one conditional relationship is nested within another conditional relationship. The various ways nested conditional relationships can be phrased are/can be pretty mind bending until you get good at recognizing them and figuring out how to break them down properly.

Nested conditional relationships can be hard to recognize and are tricky to interpret correctly since several conditional indicator words are usually used in the same sentence, making it difficult to properly determine which elements each of the words is referring to so that it's easy to get confused about which conditions are sufficient vs. necessary. They can also be very confusing since nested conditional relationships are usually (but not always) expressed in a single compound sentence that's actually expressing two conditional relationships rather than just one.

To see an example and deep discussion of a high difficulty question that involves a nested conditional statement and other tricky conditional relationships phrasing, check out this thread where we discussed another question from PT70 and nested conditionals at length. After you check out that LR question and/or the thread, feel free to up the ante on profane words to describe the test writers! lol

http://www.top-law-schools.com/forums/v ... &p=7674032

[ltowns1]

I feel like I'm growing so much. I looked on the link that Jeffort gave and I read the thread. From the mintue I read Jeffort's initial post I was like "oh ok I know exactly what to do on this".Just for a word of encouragement to theoretics...don't worry with time you'll get it without much of a problem, especially on flawed questions. I got a question for you guys on stregthen/weaken questions on conditions. If the stimulus contains a conditional but the conclusion doesn't, what should be my first step generally. (Assuming that the conditional is a part of the core)

Example:I'm at home watching the national championship game. If Duke wins, i will be happy. Therefore, I will throw a party.

Which answer most supports the argument?

My initial thought would be to look for weakness in the sufficient condition, but I guess it's not necessarily limited to that.

Assumption 1: I'm assuming Duke wins and as a consequence I will throw a party, assumption 2: becoming happy is sufficient for throwing a party. From this analysis could look at both the sufficient and necessary condition of the sentences, but I usually tend to look for a gap in the sufficient condtion at first. Csn anyone give me some rules of thumb when dealing with conditional reasoning in a stregthening/weakening argument?

As a side not I just happened to stumble on a stregthen except question today PT 33 section 1, #20 that just happens to be an actual example of what I'm talking about

[KDLMaj]

People like to over complicate this stuff sometimes.

Here's the deal: when you're dealing with flaw answer choices, NEVER leave vague terms vague. That's what gets people into trouble.

So if the answer choice says "Mistakes a sufficient condition for a necessary condition", you need to ask yourself what the sufficient was in the stim and what the necessary was. If you plus those specifics into the vague terms, and it doesn't describe the argument, it's wrong.

This is true for ALL flaw answer choices.

When the LSAT gives you both:
1) Mistakes a sufficient condition for a necessary condition
2) Mistakes a necessary condition for a sufficient one

They're just testing your ability to handle vague language- not some overarching concept. I'm guessing that's your real trouble here.

[Clearly]

People like to over complicate this stuff sometimes.

Here's the deal: when you're dealing with flaw answer choices, NEVER leave vague terms vague. That's what gets people into trouble.

So if the answer choice says "Mistakes a sufficient condition for a necessary condition", you need to ask yourself what the sufficient was in the stim and what the necessary was. If you plus those specifics into the vague terms, and it doesn't describe the argument, it's wrong.

Disagree