Need some help :( (first post) Forum

[voodoo_child]

[Let's use the symbol "=/=>" to denote "doesnt cause", and "=>" to denote "causes"]

Let's assume the relationship : X => Y (X leads to Y)

then one of the assumption behind this causality is that Y shouldnt cause X i.e. the effect shouldnt cause "cause" In other words, Y =/=> X....Equation 1 (I am using concepts from LR Bible)

Secondly, another assumption that can be made is that when there is no cause (~X) then effect shouldnt happen (~Y). In other words, ~X => ~Y. ....Equation 2 (I am using concepts from LR Bible)



Now, if we take contrapositive of Equation 1, CONTRAPOSITIVE (Y =/=> X ), we get ~X =/=> ~Y which is completely different from Equation 2 (i.e. ~X => ~Y) ....

Both the equations are assumptions. While one says ~X doesnt cause ~Y, the other one says ~X causes ~Y. I am lost
I know that I am being mistaken somewhere. Not sure where.

Can you please help me?

[lawgod]

Nope. I can't.
I haven't a clue what you're talking about.

[cogitoergosum]

[Let's use the symbol "=/=>" to denote "doesnt cause", and "=>" to denote "causes"]

Let's assume the relationship : X => Y (X leads to Y)

then one of the assumption behind this causality is that Y shouldnt cause X i.e. the effect shouldnt cause "cause" In other words, Y =/=> X....Equation 1 (I am using concepts from LR Bible)

Secondly, another assumption that can be made is that when there is no cause (~X) then effect shouldnt happen (~Y). In other words, ~X => ~Y. ....Equation 2 (I am using concepts from LR Bible)



Now, if we take contrapositive of Equation 1, CONTRAPOSITIVE (Y =/=> X ), we get ~X =/=> ~Y which is completely different from Equation 2 (i.e. ~X => ~Y) ....

Both the equations are assumptions. While one says ~X doesnt cause ~Y, the other one says ~X causes ~Y. I am lost
I know that I am being mistaken somewhere. Not sure where.

Can you please help me?

Okay, you are wrong in equation 2. You cannot deduce the statement if not x then not y (what you refer to as Equation 2) from the initial conditional statement if x then y (what you refer to as Equation 1). That is what is enabling you to draw contradictory statements.

Think about it like this: if I say If he is a conservative then he will vote republican, you cannot deduce from the fact that he is not a conservative that he did not vote republican. Maybe he's a libertarian who finds the republican more agreeable, or maybe he's a democrat who is terribly disappointed with his party and is voting republican out of spite, etc.

If indeed the LR Bible makes the statement you made above, I would guess they are saying, for LSAT LR purposes, that a suggestion of causation is made weaker when the effect happens without the cause, and implies that there are other causes sufficient to create the effect. Be careful with it though, this is not a sound logical move, just a "rule of thumb" or something.

All you can do with a conditional statement is infer from knowledge of the cause's occurrence that the effect occurs (from he is a conservative that he votes republican), or from knowledge that the effect does not occur that the cause does not (from he did not vote republican to he is not a conservative). On its own, knowledge that the cause does not occur, or that the effect does occur does not allow you to make ANY further deductions.

Hope that helps, good luck!

[ExpectLess]

[Let's use the symbol "=/=>" to denote "doesnt cause", and "=>" to denote "causes"]

Let's assume the relationship : X => Y (X leads to Y)

then one of the assumption behind this causality is that Y shouldnt cause X i.e. the effect shouldnt cause "cause" In other words, Y =/=> X....Equation 1 (I am using concepts from LR Bible)

Secondly, another assumption that can be made is that when there is no cause (~X) then effect shouldnt happen (~Y). In other words, ~X => ~Y. ....Equation 2 (I am using concepts from LR Bible)



Now, if we take contrapositive of Equation 1, CONTRAPOSITIVE (Y =/=> X ), we get ~X =/=> ~Y which is completely different from Equation 2 (i.e. ~X => ~Y) ....

Both the equations are assumptions. While one says ~X doesnt cause ~Y, the other one says ~X causes ~Y. I am lost
I know that I am being mistaken somewhere. Not sure where.

Can you please help me?

Causality and conditional statements are two different things.

You can look at a causal relationship as a conditional one--for example, if I said A causes B, it's also true that if A, then B.

But conditional statements don't necessarily imply causation--for example, if I said if it rains in the afternoon, then I must have watched a movie that morning. It raining in the afternoon certainly wasn't the cause for me watching a movie in the morning. That's one thing about causal relationships, that there's a temporal relationship between the two. (By definition, the cause must precede the effect. The sufficient condition does not have to temporally precede or follow the necessary.)

Contrapositives apply to conditional statements. You can't take a contrapositive of this "=/=>" notation of yours, because the statement "Y doesn't cause X" is not conditional. You're conflating the two concepts, and you're generally not going to have to translate a causal relationship into a conditional one. Think of causal relationships as one thing (keeping in mind what causation implies and doesn't imply), and conditional relationships (where you can take a contrapositive) as another.

[cogitoergosum]

Also, your use of contraposition isn't correct. This is also causing confusion for you.

The contrapositive of equation 1 is going to be ~Y -> ~X. If I'm reading it right, you stated it as Y -> X. Again, given the conditional statement X -> Y you can't correctly deduce anything from the fact that Y occurs.

I'm repeating myself, but this is really the bottom line on conditional reasoning, and SUPER important on the LSAT:

If you have the conditional statement X -> Y, you can only deduce two things. 1. Given X, you can deduce Y, and 2. Given ~Y you can deduce ~X.

Any other deduction such as ~X therefore ~Y, or Y therefore X, is incorrect and will cost you points.

Good luck.

[ExpectLess]

All you can do with a conditional statement is infer from knowledge of the cause's occurrence that the effect occurs (from he is a conservative that he votes republican), or from knowledge that the effect does not occur that the cause does not (from he did not vote republican to he is not a conservative). On its own, knowledge that the cause does not occur, or that the effect does occur does not allow you to make ANY further deductions.

Careful with this--the statement "If he is a conservative then he will vote republican," does NOT imply by itself that his being a conservative had anything to do with his voting republican. This statement is just showing a conditional relationship between the two, NOT a causal one.

[cogitoergosum]

True, the Conditional statement does not imply the antecedent CAUSED the consequent.

EDIT: only that its occurrence is sufficient to make the consequent necessary.

EDIT: which would seem to make the distinction irrelevant for LSAT purposes, but maybe I'm missing something...

[ExpectLess]

True, the Conditional statement does not imply the antecedent CAUSED the consequent.

EDIT: only that its occurrence is sufficient to make the consequent necessary.

EDIT: which would seem to make the distinction irrelevant for LSAT purposes, but maybe I'm missing something...

The distinction is very relevant but rarely tested. You can think of causality as a more specific version of a conditional statement. The cause's occurrence is sufficient to imply the necessary, but causality by definition implies a few more things as well--that the cause precedes the effect, etc.

[cogitoergosum]

http://www.readbookonline.net/readOnLine/22891/

[locthebloke]

"If he got drafted, then he went to war"
D---->W

The sufficient condition (D), is an indicator that the necessary condition (W) occured. However, the presence of a necessary condition does not necessarily mean the sufficient condition occured, *though it could have*. Hopefully the next example makes this clear

"If he went to war, then he got drafted"
W---->D

Does that sound right? No, if he went to war he could have enlisted, or he could have gone as a convict for some kind penal regiment. This shows that the presence of your necessary condition does not mean your given sufficient condition had to occur. The above example is the "mistaken reversal".

"If he did not get drafted, then he did not go to war"
/D---->/W
Again does this sound right? No, again, he could have gone to war by enlistment, etc. This is the "mistaken negation"

"If he did not go to war, then he did not get drafted"
/W---->/D

This is the contrapositive, and it makes more sense. Chances are, if you never went to war beign drafted was something you never went through. This makes more sense formally. (Actually, it makes me realize my example probably wasn't the best. In a real world perhaps a person who got drafted didn't go to war because they went to Canada or the war ended before they shipped out, BUT I hope this makes some sense. It seems like you're having problems with contrapositives and such so I just figured I would do my best at a review...

[cogitoergosum]

Expectless raises good points - you can't infer causation from a conditional statement, and cause is understood to precede the effect, which isn't necessarily the case with a conditional statement.

With that being said, I wouldn't get too worried about other distinctions between C&E and conditional reasoning. C&E isn't, strictly speaking, a logical concept, but rather a commonsensical one. There are conventions regarding C&E, namely the two above that could possibly be tested and should be acknowledged, but other than that, you can consider elements in a causal relationship in terms of a conditional statement with no loss.

So if X causes Y, you can deduce Y from X, and ~X from ~Y, just like you could from the conditional statement X -> Y.