More random questions that I ask about the LSAT Forum

[secretad]

What all does a correlation include? I know it's definition is that two things may occur together without one causing the other, but does a correlation also include random chance? I assume that it does include it.

My other question is regarding assumptions, necessary assumptions that is. It is my understanding that even valid arguments that are perfect and airtight. Isn't this true?

[Jeffort]

Correlation refers to having data that proves certain things are associated with each other in terms of existing at the same time, in the same place, or in the same circumstances as each other. Basically, facts that co-exist in some time, place, circumstance. It also includes negative associations. A negative correlation would be a finding such as 'whenever thing A is true, thing B is false'.

Correlations are important for cause and effect reasoning purposes in terms of trying to figure out whether or not there is a causal relationship between things that have been observed to correlate. A correlation between two or more things can be the result of random chance(meaning no cause and effect relationship between them), but could also be evidence of a cause and effect relationship.

It is flawed reasoning to jump to a cause and effect conclusion merely because two things correlate since it could be due to random chance or could also be because there is some 3rd factor that causes both of the things to occur that have been observed to correlate. However, it is still evidence showing that a causal relationship MAY exist because correlation is necessary for a true cause and effect relationship to exist, you just cannot conclude C&E for sure (or more or less likely to be true) without more information.

Your second question about necessary assumptions is unclear.

[secretad]

Thanks for the explanation on the first part. The second part of my question can be better looked at this way. Could you ever have an argument without any necessary assumptions? Even your most basic argument....

A->B
B->C
Therefore, A->C

Although this argument is valid, it still requires necessary assumptions such as there not being a premise A->-C because that unstated premise would kill the argument. My assumption is that every single argument has necessary assumptions.

[suspicious android]

Thanks for the explanation on the first part. The second part of my question can be better looked at this way. Could you ever have an argument without any necessary assumptions? Even your most basic argument....

A->B
B->C
Therefore, A->C

Although this argument is valid, it still requires necessary assumptions such as there not being a premise A->-C because that unstated premise would kill the argument. My assumption is that every single argument has necessary assumptions.

The statements "A --> C" and "~(A --> ~C)" are logically identical, so you proposed necessary assumption is actually just a restatement of the conclusion. So it is not an assumption of the argument, it is an inference. Assumptions are always premises, that is, they must support the conclusion.

Similarly, restatement of a previous premise does not count as an assumption.

Generally, formal logic arguments are fairly easy to construct without necessary assumptions. It's only in informal arguments (using regular language) that end up having numerous necessary assumptions.

[secretad]

You misread the necessary assumption. I said if a then not c.

[suspicious android]

You misread the necessary assumption. I said if a then not c.

Eh, I didn't misread anything. You said "it still requires necessary assumptions such as there not being a premise A->-C." That is to assert that A --> ~C is not true, that is to say ~(A -->~C).

~(A --> ~C) is logically identical to A --> C. They are the same statement.

[secretad]

You misread the necessary assumption. I said if a then not c.

Eh, I didn't misread anything. You said "it still requires necessary assumptions such as there not being a premise A->-C." That is to assert that A --> ~C is not true, that is to say ~(A -->~C).

~(A --> ~C) is logically identical to A --> C. They are the same statement.

I do not understand your use of parentheses and negations. Let me just ask this in a different way.

B -----> C
B
-----------------
C

Isn't a necessary assumption of that argument B ------> -C does not exist.

[suspicious android]

I do not understand your use of parentheses and negations. Let me just ask this in a different way.

B -----> C
B
-----------------
C

Isn't a necessary assumption of that argument B ------> -C does not exist.

Okay, I see where the misunderstanding is. Parenthesis can be used to set off a statement.

~A --> B means if it's not an A it must be a B. However, that is completely different from the statement "it's not true that if A then B" which can be diagrammed as ~(A --> B), where the "~" means "not", and describes the phrase "A --> B." Anyway, enough of that.

In your argument when you assert that B --> C you are at the same time asserting that it's not true that B --> ~C is true. Those statements are really the same thing. Those two statements are logically identical, asserting one is the same as asserting either or both. Since it's already inherently true, it's not an assumption. Assumptions by definition are unstated premises. Although your statement "B --> ~C does not exist" must be true, that doesn't make it a necessary assumption. There is a literally infinite number of statements that must be true for any given argument, but they are not all assumptions. For example, in any argument whatsoever, "X or ~X" must be true, but it is not a necessary assumption unless you stretch the definition of "necessary assumption" to things like "the ordinary rules of logic hold for this agument."

[secretad]

Thanks for the clarifications. How about this question. Can an argument be valid and have necessary assumptions, which obviously were never stated. I realize that stating an unstated premise is a form of strengthening an argument so that implies it is not a valid argument because you cannot strengthen a valid argument.

[suspicious android]

Thanks for the clarifications. How about this question. Can an argument be valid and have necessary assumptions, which obviously were never stated. I realize that stating an unstated premise is a form of strengthening an argument so that implies it is not a valid argument because you cannot strengthen a valid argument.

Depends on how strict you are about validity. For the puposes of the LSAT, you can geneally go ahead and take commonsense assumptions for granted, e.g., squares have four sides, the Earth is a sphere, that sort of thing. But in formal logic you are usually only taking explicit premises into account.

[secretad]

Thanks for taking the time to help me answer some nagging questions. When you have the question stems involving necessary assumptions, are those arguments invalid before the necessary assumptions are stated. And even with perhaps a necessary assumption being stated, it could still be an invalid argument because it may have more necessary assumptions that must be stated. Is my thinking correct?

[suspicious android]

Thanks for taking the time to help me answer some nagging questions. When you have the question stems involving necessary assumptions, are those arguments invalid before the necessary assumptions are stated. And even with perhaps a necessary assumption being stated, it could still be an invalid argument because it may have more necessary assumptions that must be stated. Is my thinking correct?

Yep, all necessary assumption questions involve arguments that are invalid, and there can be an infinite number of necessary assumptions to some arguments. Same for sufficient assumption questions.