The Domino Effect: Sufficient vs. Necessary

[Mark Yerrid]

I was with my tutor on Satuday. He gave me a very 'visual' way of looking at "chain relationships with S/N conditions. A light went off...I was feeling cocky, then when I arrived home; I forgot it. I recall his analogy of long chain relationships as having a "DOMINO EFFECT". So, if anyone with a score higher than 170 can answer this; I will heed your advice if you can try and decipher what he meant. Here is what we talked about:

A B C D E F G.

So, If A then B, if B then C, if C then D, if D then E, if E then F, if F then G.

We all undertand that. Also, we can say that A G (If A, then G).

We can say too, IF NOT G...then NOT A.

My issue?

My issue is, he described it as "If something falls to the RIGHT, ALL things FALL to the RIGHT (in regard to the chain relationship).

Vice Versa, IF something FALLS to the LEFT, ALL things fall to the LEFT.

He was referring to the conditions in the statements.

So if we had A B C D E F G and say E (could not be, or was not to be and we had a slash through it); I assume that all things LEFT (A,B,C,D) would be negated? But too, F&G could be negated if we canceled out E. See, I forgot what he meant--totally. And if we slashed "E"....and all things to the left are then negated, what happens to F and G?

[Dave Killoran]

Hi Mark,

In my reply to your other question I mentioned some resources to help you out with conditional reasoning. They will help with the type of idea you ask about in this post as well That said, let's look at the question you asked about.

So if we had A B C D E F G and say E (could not be, or was not to be and we had a slash through it); I assume that all things LEFT (A,B,C,D) would be negated? But too, F&G could be negated if we canceled out E. See, I forgot what he meant--totally. And if we slashed "E"....and all things to the left are then negated, what happens to F and G?

You are correct about A, B, C, D, and E: If E does not occur, then nothing to the left of E can occur, and A, B, C, and D cannot occur (this is the contrapositive at work). What happens to F and G? We don't know, and they can either occur or not occur. As I referenced in my other answer to you, when the sufficient condition does not occur (in this case, that is when E does not occur), then anything can happen with the necessary conditions (F and G in this case). So, F can occur, but does not have to occur, and the same holds for G.

Thus, for example, if we had a Must Be True question, a correct answer could state that one or more of A, B, C, and D do not occur. But any answer choice that referenced F or G would be wrong, because nothing must occur with those two variables (this assumes the answers are all along the lines of "F does not occur" etc).

It sounds like you are pretty close to understanding this, and both your questions actually revolve around the same type of understanding of how conditions work. So, I think you'll get this concept locked down pretty soon.

Please let me know if that helps. Thanks!

[Mark Yerrid]

Dave.

Thank you. Yes, it helps. However, what if, for example, A was negated from that line of variables.

A B C D E F; and A was negated at the beginning of the construct.

The reason I am belaboring this point is because Adam told me that everything falls to the right if something is negated on the very left of the conditional statements(canceled out "/").

I hope this makes sense. Thank you again for your previous emails. They are very helpful.

Mark

[Dave Killoran]

Hi Mark,

I think you may have misunderstood Adam. If A is negated, the sufficient condition is not met, and thus we have no idea what happens with B, C, D, etc. They could occur or not occur.

They way it works is that if somethings occurs on the left, then everything to the right also occurs (this is the chain reaction where you just follow the arrows); if something does not occur on the right, everything to the left does not occur (this creates a series of contrapositives).

In this instance, something on the left did not happen, and at that point nothing is known (and the same would be true if something on the right did occur--anything could occur to the left).

Please let me know if that helps. Thanks!

[Mark Yerrid]

Dave,
you had me 100% until the last sentence:

[i]In this instance, something on the left did not happen, and at that point nothing is known (and the same would be true if something on the right did occur--anything could occur to the left). [/i]

My understanding of (and the same would be true if something on the right did occur--anything could occur to the left) would mean the only thing to happen on the right (a-b-c-d-e); we;ll take c for sake of argument; if this is negated.... a&b cannot happen. We then don't know about D or E which ARE to the right of C. So when you state that 'if something on the right did occur--anything to the left could occur. That's the issue: What, if anything, COULD occur on the left.

I am sure I did misunderstand Adam. He is an exceptional tutor.

Thank you.
Mark

[Nikki Siclunov]

Let me jump in real quick.

In the conditional chain you gave as an example, you can only move "forward" (i.e. make deductions) if you have evidence that a particular sufficient condition has been met; you can only move "backwards" if you have evidence that a particular necessary condition has NOT been met. Thus:

A B C D E

Let's say C occurs. We know immediately that D and E must also occur, because C is a sufficient condition for D, and D is a sufficient condition for E. When it comes to A and B, however, we don't know much. They could occur, because a necessary condition for their occurrence (i.e. C) has been met. But they don't need to occur.

What if C does NOT occur? Because C is a necessary condition for B, B cannot occur (and neither can A). However, in this case you cannot move "forward" because the failure to satisfy a sufficient condition for D and E does not render their occurrence impossible. They could occur, but do not need to occur.

Now, what if you have a more complex chain in which one of the terms is already negated?

A B C NOT D E

In that case, if D does not occur, we know automatically that E occurs (because NOT D was a sufficient condition for E to occur). However, we cannot make deductions to the left of NOT D. On the other hand, if D does occur, by the contrapositive we know that A, B, and C do not occur (but we cannot make inferences about E - E could occur, but does not need to).

[Mark Yerrid]

Thank you. This is fantastic information.