That isn't the complete definition.
Again, no, it's not. You keep choosing words from the definition and claiming that somehow, those words prove your point but they don't. A direct correlation, measured by Pearson's r and used in the studies I quoted, is an expression of linear correlation (not quadratic, or cubic, or exponential, etc.). When two variables have a linear relationship, it means that they rise and fall together in a constant ratio. That's why the equation they yield is one of direct proportionality.
No, it isn't, and there's no "imply" about it--that's the definition of a directly proportional relationship. You say I found the right definition, but it doesn't seem like you read it.
Sorry, but this is going nowhere. I understand what you are insisting, but it simply does not work that way in practice. You can't draw perfect correlations from empirical data. You can only draw significant correlations. However, regardless of what correlation you draw, the regression equation that you end up with is always a linear equation, an expression of direct proportion.
Here is the graph of two variables that are linearly (directly) correlated.

Here is the graph of two variables in direct proportion.

Here is a graph of a simple regression analysis, in which the resulting equation is not derived from a perfect correlation, but the equation of the graph is nonetheless a linear equation that plots the two variables in direct proportion.

Yes. Your analogies are all kinds of wrong.
Really? How is my analogy wrong? You said using known level of education to predict intelligence of an individual is a "gross misuse of statistics." I explained that in medicine, some variables (such as blood chem results, gender, etc.) are used to predict the risk that a single patient would have a specific disease. Education is to "some variables" as intelligence is to "risk of disease." That's my analogy. If you can accept the latter, why can't you accept the former?
You are suggesting that if we only now someone's intelligence, we can reasonably predict their level of educational attainment, and conversely that if we know someone's level of educational attainment we can reasonably predict their level of intelligence.
Yes, that's how correlation works. If the correlation is significant, we can predict one variable in terms of the other using an equation that expresses a direct proportionality between them. You still fail to grasp that I am not talking about causality here. If you give me a person and tell me his educational attainment, I can use the results from the studies I quoted (if I had them) to predict what that person's IQ likely is. Similarly, you can give me the IQ of the person, and I will simply reverse the formula and predict his educational attainment.
However, if you give me a person's educational attainment and have me predict his IQ, and then you have him take a higher degree (thereby raising his educational attainment), and then ask me to predict his IQ again, there is no guarantee that his IQ would rise because while the two variables are highly correlated and the equation used to predict one in terms of the other expresses them in direct proportion, causality is not implied.In brief: Most dumb people don't pursue Ph.Ds. That doesn't mean all or even most smart people do.
That's your unfounded inference of causality. I have mine too (higher intelligence makes people pursue higher degrees). However, this has nothing to do with the topic on direct correlation implying direct proportionality.