Understanding of Sufficient and Necessary Conditions + Lawgic

GUDETAMA

Hello. I have been having some trouble with actually solidifying my understanding of the meaning of Sufficient Conditions and Necessary Conditions as I found the information provided in the core curriculum in regard to the topic to be a bit vague. I seem to always get confused and lack confidence when I have to deal with a conditional relationship in an argument because I just take the Premises of the argument to mean the Sufficient Condition and the Conclusion of the argument to mean the Necessary Condition. If someone can please clarify it for me or correct my understanding of this it would be much appreciated.

Also I have been having some difficulty with knowing when exactly to diagram Lawgic. Are we only supposed to diagram when we see words from Group 1-4 of the Sufficient and Necessary Condition indicators?

General Structure of Conditional Statements: Sufficient Condition --> Necessary Condition
Sufficient Condition
- If satisfied or is true the Sufficient Condition guarantees/triggers/implies the Necessary Condition
- While a certain Sufficient Condition (X) is a one way to trigger the Necessary Condition it does not mean that it is the only way but rather it is only one way that we know of to trigger the Necessary Condition (as it is possible that there are other Sufficient Conditions that may trigger the Necessary Condition or the one we know of is possible to be the only one, without any other information we cannot tell for sure)
Necessary Condition
- Must be true in order for the Sufficient Condition to be true (the Necessary Condition is required for the Sufficient Condition to be true?)
- Necessary Conditions (at least when diagramming using Universal Quantifiers/Complete Subsumption) encapsulate the Sufficient Conditions
- Without Necessary condition you cannot have the Sufficient Condition
- With the truth of the Necessary Condition you cannot conclude anything about the Sufficient Condition

Bumblebee

Hi!
With regard to your first question about Sufficient and Necessary conditions, you shouldn't think automatically that the premises are the sufficient condition and the conclusion is the necessary condition.

Actually, the speakers/authors of arguments in LR usually assume that their premises are sufficient for their conclusion, when it is not the case. In flaw/weaken questions, it is our job to weaken/find the flaw in such arguments by pointing out that the premises aren't sufficient for the conclusion.

For example, let us consider this argument:
Premise: Larry ate chocolate ice cream.
Conclusion: Larry must be happy.

The flaw of this argument is that it assumes that Larry's consumption of chocolate ice cream is sufficient to make him happy. In other words, the argument assumes that eating chocolate ice cream necessitates happiness. But there is no reason to make such an unwarranted assumption because there is no support for that assumption.

Now, if we are answering a Sufficient Assumption question, the correct answer choice would say: "Eating chocolate ice cream necessitates happinesss".

So premises are not automatically sufficient conditions nor are conclusions necessary conditions. But, when we are searching for Sufficient Assumptions for an argument, we usually look for a conditional statement that puts the premise in the sufficient condition and the conclusion in the necessary condition. This is because we need a conditional statement that connects the premise to the conclusion.
I am guessing that you meant something like this when you wrote that you equate premises with sufficient conditions and conclusions as necessary conditions.

I hope this made sense!

About your second question regarding diagramming conditional statements, you don't need to draw diagrams every time you see an indicator. That would be too much or unnecessary under time pressure.

But for the sake of practicing, I recommend practicing drawing out diagrams for conditional statements until you are super fast at it and it becomes intuitive to you.

But when you are in the full PT phase, you may find that you don't need to diagram conditional logic for all questions. If you practice regularly, you may find that it is possible to do some simple contrapositives and chaining in your head. For some curve breaker MBT questions, it may be necessary to digram conditional logic, but simpler questions don't require diagramming.

AudaciousRed

@"L.S.A.T." said:

For example, let us consider this argument:
Premise: Larry ate chocolate ice cream.
Conclusion: Larry must be happy.

The flaw of this argument is that it assumes that Larry's consumption of chocolate ice cream is sufficient to make him happy. In other words, the argument assumes that eating chocolate ice cream necessitates happiness. But there is no reason to make such an unwarranted assumption because there is no support for that assumption.

Now, if we are answering a Sufficient Assumption question, the correct answer choice would say: "Eating chocolate ice cream necessitates happinesss".

So premises are not automatically sufficient conditions nor are conclusions necessary conditions. But, when we are searching for Sufficient Assumptions for an argument, we usually look for a conditional statement that puts the premise in the sufficient condition and the conclusion in the necessary condition. This is because we need a conditional statement that connects the premise to the conclusion.
I am guessing that you meant something like this when you wrote that you equate premises with sufficient conditions and conclusions as necessary conditions.

Well said!

The other factor in figuring out if something is necessary or sufficient is to practice those group words. Know that "if a, then b" a is sufficient and b is necessary. Or that "must" creates a condition of necessary. "When John goes to school, he must use the bus" So, if he's going to school ---> he's on the bus. Now, he could be on that bus for any number of other reasons: field trips, public transit, etc. And it has nothing to do with school. But if he's going to school, he HAS to be on that bus. He can't take a car or anything else to get there. No bus, no school. Memorizing those key words in the CC is extremely helpful to figuring out how it all should be aligned.
For more complex items, say, several premises and a conclusion, we have to ask how the premises connect to that conclusion. Maybe they don't connect directly. Maybe something is missing. If we realize something is missing, we can mentally figure out how it could connect. Like L.S.A.T. said. Larry ate ice cream. Larry is happy. How did ice cream mean happiness? We need something like "When Larry eats ice cream, it makes him happy". Looking for and realizing there are gaps is extremely helpful in answering many types of LR questions.
Now, say we get "Larry is happy". Can we assume he ate ice cream? No. He could be happy because he just got RedDead2 for his birthday. But if he eats ice cream, happiness occurs. Larry is never bummed out by ice cream.
A way that helps me is that you can always go forwards when things are positive, but it has to go backwards if it's negative.
Larry ate ice cream, ice cream makes him happy, so Larry is happy. a-->b-->c but if C is negated (John is not happy), we get c-->b-->a (John is not happy, ice cream didn't make him happy, so Larry did not eat any ice cream). If you think about it only being able to go one direction for positive and the other for negations, it's very helpful.

As far as looking for the conclusion... find the thing that everything else seems to support. Can that statement be supported by everything else? No? Then that's not your conclusion. Your conclusion could be the first line, in the middle, or at the end. I want to say that you are correct that the conclusion becomes the necessary, and the premises are your sufficient. However, it's not so much like a-->d, b-->d, c-->d. Let's say we have this:

A rare type of American bird eats wild walnuts. But walnuts are disappearing from American forests. These American birds should be placed on the endangered species list.

In this instance, we are missing something that could strengthen the argument. How do we get from A bird eats walnuts for food -> walnuts, their food, are disappearing --> birds should be on endangered species list? There's no connection between walnuts (their food) and the list. Something like "rare animals who have their food supply threatened should be placed on the endangered species list." Now we get "birds eat walnuts for food -> walnuts/food disappearing --> disappearing food endangers them --> birds should be on endangered list" Even more basic, we need to make the assumptions like "if birds can't find their food, they die", "rare animals that die are endangered" and that "being endangered puts you on the list".
A way to weaken the argument might be "The birds also eat corn, which is abundant." Well, now we don't necessarily need walnuts, which was the whole reasoning for them being on the endangered species list. We have cast doubt on the birds' need to be on the endangered list if they have plenty of food, right? Sure, the birds might still need to be on the endangered list, for any number of reasons. But we have poked holes in the argument that a lack of walnuts are what causes the birds to be on the list.

Anyway, I hope this helps.
Ya'll feel free to call my reasoning out. It's already been a long week! LoL