Very strong correlation and bi-conditionals

audeamus300

Hi guys, hope you all are doing well!

I'm wondering if a strong correlation like "the more X, the less Y" could be diagrammed as a bi-conditional (e.g. "The more history a person knows, the less likely that person likes history"). Also, is "the more X, the less Y" logically equivalent to "the less Y, the more X"?

How about "As x increases, Y decreases"? Can this be diagrammed as a bi-conditional? (e.g. "As one's knowledge of history increases, one's love for history decreases")

Thanks!
P.S. I have nothing against history lol. I just happened to modify a few sentences from PT61.2.24

jmarmaduke96

Hi!

That is a very interesting question, although I am inclined to say no, just because of the nature of biconditionals. Obviously, in a biconditional A is both sufficient and necessary for B.

I think it will make more sense if we pull the biconditional apart, just for the sake of clarity, and look at it as two conditionals. (A ---> B ) and (B ---> A).

In your example, "The more X the less Y" - "The more X" would be the "A" item, and "the less Y" would be the "B" item. I think you could plausibly understand the conditional going forward, if you have progressively increasing amounts of X, Y must then decrease in turn. For example, the more I study for the LSAT the less I get PT scores that I don't like. The inverse does not have to be true though. In other words, B ---> A does not follow. Just because I suddenly am getting many fewer PT scores that I dislike, it does not follow that I must be studying more. Perhaps my fragile ego can't handle another bad PT so I am just finding all the answers before I take the PT and inputting them so that I feel warm and fuzzy inside when I grade the PT. Obviously, that is a silly example, but I think it illustrates the fact that "the more X the less Y" probably cannot be properly understood as a biconditional.

The same goes for your other example. "As one's knowledge of history increases, one's love for history decreases." The conditional can be read forwards, my knowledge of history goes up and thus my love for it must come down. However, if my love of history has come down, maybe that is because I had a terrible history teacher that made me hate the subject. Because the teacher was so horrible, he/she did not teach me anything. So, just like with the first example, it seems very plausible that A ---> B, but not that B ---> A. Therefore, the biconditional does not follow.

There might be certain examples where very strong correlations could possibly be diagrammed as biconditionals, but not as a general rule of thumb.

I hope this helps!

audeamus300

@jmarmaduke96 Thanks for the thorough explanation! That makes a lot of sense. So you wouldn't say that "the more X, the less Y" is logically equivalent to "the less Y, the more X," correct?

I guess I was confusing it with a different layout of correlation like below, which I think are logically equivalent. (Can you confirm that they are?)
"The more hate you have, the less friend you have."
"The more love you have, the more friend you have."

Thanks!

Edit: Maybe "logically equivalent" is too strong. How about "inferable"?

jmarmaduke96

@audeamus300 of course! happy to help!

With respect to the different type of correlation that you were speaking about, I want to be careful about the terminology. Typically, on the LSAT, an inference is something that must be true or otherwise follows necessarily. What you have in your correlation example is basically "the more A you have, the less B you have," and therefore "the more /A you have the less /B you have." I do not think that such a reversal qualifies as an inference on the LSAT. Logically, it amounts to essentially sufficiency/necessity confusion.

So, while the reverse of the correlation may be supported, that is dependent upon the unique context and the specific ideas that are correlated with one another. I don't think that it is something that can be inferred as a general rule of thumb. Does that make sense?

Maybe with more specific examples we could find some certain contexts that would give some guidelines as to when the support for such a reading of a correlation would be the strongest, but I don't know of what they would be off the top of my head.

I hope this helps, feel free to hit me if you have any other questions or if this doesn't make sense!

EddieM

I think a big issue here is the difficulty of putting together the conditional "true/false" with the matters of degree indicated by "the more" and "the less." If you say, "the more you know about history, the less you love history," there certainly is a positive if/then that you can take from it: if you know about it more, then you love it less. But as I read it, it's not only that relationship that you can take away; you can also get a bunch more relationships of degree: If you know about it a lot more, then you love it a lot less, right? I think that's how it'd work if you graphed it. (When I think about "the more bananas you eat -> the fewer oranges you eat," I imagine a huge increase of bananas eaten meaning a huge decrease in oranges eaten, whereas an much smaller increase in bananas eaten would mean a correspondingly small decrease in oranges. But so wouldn't that also translate to statements of degree here, in this qualitative matter?)

If so, then the initial steps would seem easy enough, as "a moderate amount of additional knowledge" would seem to be imply "a moderate amount less love" and perhaps even the same with "a bit more knowledge" and "a bit less love." But what happens when you get decreasing knowledge? Would that imply more love? I am really not sure. If you were to graph this as a linear relationship, and increasing knowledge meant decreasing love, then this would indeed be true--as you moved backwards on that graph, every bit less knowledge would mean a bit more love. If so, then I think what you'd be looking at here indeed not only a biconditional, but a zillion little biconditionals of degree--a little less knowledge means a little more love, a ton less knowledge means you are absolutely infatuated with it, etc.

I think I disagree with @jmarmaduke96's argument. Sure you could conceivably imagine someone liking history less NOT because they study more but instead because they dislike their teacher, but does a statement such as "the more you know about history, the less you like history" allow for that possibility? Perhaps if it were just "an increase in knowledge is sufficient for a decrease in love of history," but I think that "the more... the less" is far more expansive than that because of its implied relationships of degree. To my mind, "the more... the less" would indicate that you simply cannot dislike history less without seeing a corresponding increase in knowledge. And that would indicate something like a billion little biconditionals...

But I'm afraid I might be totally wrong. Perhaps we need some #help?

audeamus300

@EddieM Hmm, I see your point. In a linear relationship, for example, y = x, each variable needs to correspond to a change in the other variable in order to satisfy the equation (i.e. the relationship). And what's more, you only need to know how one variable behaves to figure out how the other variable will behave. If x is the # of apples and y is the # of oranges, and we know we have 10 apples, we expect our oranges to be 10. And vice versa. In cases like this, you'll have zillions of bi-conditionals (i.e. any point that lies on the line).

So I think the issue here is if "the more X, the more Y" will constitute a linear relationship (and maybe we might need some context clues in the stimulus that would give some guidelines). Same goes with "As X increases, Y increases." If it does constitute a linear relationship, I think it's fair to say that they have a bi-conditional relationship (as to @EddieM 's post). If not, then not necessarily (as to @jmarmaduke96 's post).

EddieM

@audeamus300 Yes, that's what I'm thinking!

EddieM

I just realized I think another critical thing is whether or not it says “all other things being equal...” first. If it does, then definitely not necessarily a linear relationship. But if it doesn’t, I don’t see how it could be anything other than linear.