Necessary Assumption issue Forum

[timmydoeslsat]

In the context of a necessary assumption, sometimes it is true that a necessary assumption will also be sufficient for an argument to be valid. Such as this instance:

P ---> T
_____________
P ---> ~H

The necessary assumption here would be [T---> ~H] which is also sufficient in this case.

However, I would like to discuss this construct:

P ---> T ---> ~C
______________
P ---> ~H

Here we could have two different sufficient assumptions.
(1) [T ---> ~H]
(2) [~C ---> ~H]

Since we have two different ways of making this argument valid, my question would be what is the necessary assumption in this argument.

I will repeat myself as it seems that a majority of my threads do not answer the question posited: What is the necessary assumption of the second argument.


To me, I believe that the [T --->~H] connection is necessary given the evidence presented. Either you go from ~T --->~H or you go from ~C --->~H....either case will have T being led to ~H.

[MLBrandow]

timmydoeslsat,

Are you assuming that there must be only one necessary assumption, or that if given two possible choices, one must be preferred over the other?

Perhaps it is necessary that ~C --> A --> B --> Φ --> ~ψ and ~7 --> either or but not both AND --> ~H.

Is this THE necessary assumption? Is it preferrable over (1) or (2) or both?

[dooood]

I would help out but your avatar frightens me

[timmydoeslsat]

timmydoeslsat,

Are you assuming that there must be only one necessary assumption, or that if given two possible choices, one must be preferred over the other?

Perhaps it is necessary that ~C --> A --> B --> Φ --> ~ψ and ~7 --> either or but not both AND --> ~H.

Is this THE necessary assumption? Is it preferrable over (1) or (2) or both?

There can be multiple necessary assumptions.

With the evidence given, what is the necessary assumption? Your example still shows that indeed C--->~H is occurring, no matter the intermediate conditions it takes to get there.

[MLBrandow]

timmydoeslsat,

My point is that if this is a valid chain of logic, then each conditional must independently be true, and each, in turn, are necessary.

I think it represents a misunderstanding to assert that there must be some prevailing necessary assumption, or that one must be more necessary than the other.

As you say, there can be multiple necessary assumptions.

Both (1) and (2) that you mention can be necessary assumptions. It is not the case that one has to be true and the other false, or even either of them must be true.

It might be the case that:

(3) P --> A --> ~H

You're right in that both (1) and (2) would be sufficient to draw the conclusions, but there could be many other necessary assumptions. Only one of (1) and (2) would be necessary (although both could be true), but asking which one serves no practical purpose.


edit:

The necessary assumption here would be [T---> ~H] which is also sufficient in this case.

This is actually an invalid statement. What you mean is: "A necessary assumption here could be [T---> ~H] which is also sufficient in this case.

[timmydoeslsat]

It seems very practical to me. If it is true that T can lead us to ~H, then it is not necessary for ~H to lead us there.

There can be multiple necessary assumptions, but they cannot address the same issue.

However, it does seem necessary for T to lead us to ~H.

[timmydoeslsat]

To support my contention that each assumption is not necessary, I will let you read LSAT Blog's analysis from a prior thread, about the exact same problem.

The reason is that a necessary assumption always needs to be the case in order for an argument to work (the conclusion follow), but a sufficient assumption is just that - sufficient to make the argument work (the conclusion follow), but not all sufficient assumptions are required in order for the argument to work (for the conclusion to follow).

In other words, the correct answer to sufficient assumption questions is often something that does not actually need to be true, but if it is true, will fully justify the conclusion. (Note that many answers to sufficient assumption questions are broader than the argument.)

Take, for example, PrepTest 35 (Oct 2001), Section 1, Question 22 (p226 in Next 10).

Evidence: C -> NOT T -> NOT P
Evidence: P -> T -> NOT C
---
Conclusion: P -> NOT H

While H -> C is sufficient to guarantee the conclusion, it's not required in order to do so. Even if H didn't require C, information from the evidence could still, in combination with a sufficient assumption, guarantee that P required NOT H.

What if we learned that T required NOT H, or that H required NOT T? In combination with the statement that P -> T, the conclusion would still follow from the evidence (even if H didn't require C).

(It's possible that LSAC would disregard the T -> NOT C statement when considering how to make the evidence + sufficient assumption lead to the conclusion - stimuli often contain information that serves as filler and is irrelevant in guaranteeing the conclusion.)

So LSAT Blog disagrees with your analysis that both are required, which is my point.

My question to you or anyone in this thread, is what would indeed by a necessary assumption of that argument?

[airbud]

Be sure not to confuse something that is "sufficient" for the conclusion to be true and something that is "necessary" for the conclusion to be true. Maybe you already have these concepts nailed down, but I feel like it's worth addressing before getting wrapped around a specific question.

Take "If A, then B". A is the sufficient condition and B is the necessary condition (yes, I know you know, I'm not trying to insult your intelligence). A is "sufficient", because if we know A, then we automatically know B. A is enough (sufficient) to know B for sure. B is only necessary for A. In other words, if we know that ~B, then we know for sure that ~A. Without B, we cannot have A. That's the essence of a condition being necessary.

Say an LSAT stimulus simply states that "Steve is an excellent tennis player". If the question stem were to ask "What assumption is necessary for the conclusion to be drawn" vs "The following enables the conclusion to be properly drawn if...", you're being asked two totally separate questions. The former is asking you to provide a premise that is necessary for the conclusion to be true, while the latter is asking you to provide a premise that is sufficient for the conclusion to be true.

A satisfactory response to the "necessary" question might be "Steve can hit the tennis ball over the net". This is necessary because IF IT'S NOT TRUE, there's no way the conclusion can be true. A satisfactory response to the "sufficient" question might be "Steve just won Wimbledon", because if we know this, we know for sure that Steve is an excellent tennis player.

I bring this up because there are many cases where you'll be asked to provide the sufficient condition, and then an incorrect A/C is given with something that is only necessary for the argument (or vice versa). I've been caught too many times mixing this up, so I'd hate for you to do the same!

[timmydoeslsat]

P ---> T ---> ~C
______________
P ---> ~H

What would be a correct answer to a question stem asking for a necessary assumption of that argument?

My take would be that [T---> ~H] is necessary.

The [~C --->H] is not not necessary.

[thestalkmore]

I am 12 years old and what is this?

[MLBrandow]

timmydoeslsat,

I don't understand what you mean at all now.

You're arguing that one is required, and that both are required, and that neither are required.

Both (1) and (2) that you mention can be necessary assumptions. It is not the case that one has to be true and the other false, or even either of them must be true.

Seeming necessary is not the same thing as actually being necessary.

You are assuming that because either of two possibilities WOULD be sufficient, that one of them MUST be necessary, and that's just not the case.

If you're asking for someone to validate your reasoning error, you might be here a while, given that it has the disadvantage of not being true.

[timmydoeslsat]

Is there a necessary assumption involved in this construct?

P ---> T ---> ~C
______________
P ---> ~H

If somebody asked you this question, which I am doing, what would it be? I, of course, see two ways we can make the argument's conclusion follow, but is there something that is necessary for it? (I don't know how many different ways I can ask the same question)

[timmydoeslsat]

timmydoeslsat,

I don't understand what you mean at all now.

You're arguing that one is required, and that both are required, and that neither are required.

OK, first I want to clarify that just because those 2 statements are sufficient, I am not assuming that this is the reason one must be necessary for the argument.

Second, instead of me giving my opinion, I will ask yours. Can you give me a necessary assumption to that argument.

[MLBrandow]

timmydoeslsat,

Based on what you wrote, if the conclusion is true, then there must indeed be a necessary (but unknowable) assumption(s) required by the argument. This is why sufficient assumptions always qualify the question by including "if established/true/etc."

There is nothing to disqualify (1) (2) (3) or the very long chain I made up from being correct, or from any of them precluding requirement from any of the others. All we can say is that one or all of these COULD be necessary, and that is not the same as saying that any or all of them MUST be necessary.

And while this would be a fine sufficient assumption question, this doesn't resemble a necessary assumption LSAT question at all. You're asking for an answer to a question that doesn't have a knowable answer, and you're assuming one of a few possible ones must be true.

And while there certainly have existed necessary assumption LSAT questions whereby the answer choices are both necessary AND sufficient, none are in such a form as you write.

A question like this has never nor will ever appear on the LSAT.

[jigglebottom]

I have four legs
Therefore, I am a dog.

Necessary assumptions: I am not an amphibian, I am not a cat, I am not a table
Sufficient assumption: all things that have four legs are dogs

[thestalkmore]

Timmy why don't you do full length PTs?

[dowu]

[sintacs]

Is there a necessary assumption involved in this construct?

P ---> T ---> ~C
______________
P ---> ~H

If somebody asked you this question, which I am doing, what would it be? I, of course, see two ways we can make the argument's conclusion follow, but is there something that is necessary for it? (I don't know how many different ways I can ask the same question)

i would think the necessary assumption would simply be ~C--->~H. I don't see any brackets in the original so I dont think something like:
[T--->~C]--->~H is the necessary assumption. it seems like you could break it up into: P--->T; T--->~C; ~C--->~H(this is your assumed);
.: P--->~H
it's been a while since my Logic classes so i dont remember specific rules.

[suspicious android]

Is there a necessary assumption involved in this construct?

P ---> T ---> ~C
______________
P ---> ~H

Necessary assumption:
Ǝ(X)[(P -->X) & (X --> ~H)]

(there exists at least one X such that if P, then X and if X, then not H.)

[dowu]

Is there a necessary assumption involved in this construct?

P ---> T ---> ~C
______________
P ---> ~H

Necessary assumption:
Ǝ(X)[(P -->X) & (X --> ~H)]

(there exists at least one X such that if P, then X and if X, then not H.)

Damn, I kind of miss symbolic logic..

Too bad I got a B in it. I should have taken it when I was a junior so that I could have taken it more seriously.

[thestalkmore]

Is there a necessary assumption involved in this construct?

P ---> T ---> ~C
______________
P ---> ~H

Necessary assumption:
Ǝ(X)[(P -->X) & (X --> ~H)]

(there exists at least one X such that if P, then X and if X, then not H.)

[jas1503]

Is there a necessary assumption involved in this construct?

P ---> T ---> ~C
______________
P ---> ~H

Necessary assumption:
Ǝ(X)[(P -->X) & (X --> ~H)]

(there exists at least one X such that if P, then X and if X, then not H.)

Lol'd

[jas1503]

I have four legs
Therefore, I am a dog.

Necessary assumptions: I am not an amphibian, I am not a cat, I am not a table
Sufficient assumption: all things that have four legs are dogs

Thanks for this!

[timmydoeslsat]

And while this would be a fine sufficient assumption question, this doesn't resemble a necessary assumption LSAT question at all. You're asking for an answer to a question that doesn't have a knowable answer, and you're assuming one of a few possible ones must be true.

And while there certainly have existed necessary assumption LSAT questions whereby the answer choices are both necessary AND sufficient, none are in such a form as you write.

A question like this has never nor will ever appear on the LSAT.

And there is your answer for why I asked. I have not seen this asked on the LSAT and I am curious as to what the answer would be.

I have been given an answer, and it is all I wanted: there is not a necessary assumption that we can prephrase from the construct I provided.

Thanks to everyone for helping.

[MLBrandow]

timmydoeslsat,