Convergent validity of reflective indicators

[BenLien]

In the book complementing the SmartPLS software (A Primer on Partial Least Squares), we are advice to asses the convergent validity with reflectively measured constructs.
The actual measures listed under "convergent validity" are AVE and indicator reliability. But convergent validity is the extent to which a measure correlates positively with alternative measures of the same construct. The loadings used to asses indicator reliability are the correlation between the latent variable and a standardized indicator. But the LV is constructed from the indicators (including the one where we asses the loading). In this respect we are not assessing whether the indicator are correlated with alternative measures of the same construct, but how it correlates with a LV made up partly by the indicator we asses. How can it then be justified to say that we are assessing convergent validity by looking at the indicator reliability?
I also find it confusing that we asses validity by a reliability measure (indicator reliability)?
Best
BenLien

[jmbecker]

Some researchers think that the construct and the indicators are so different that assessing the loadings (correlations between construct and indicators) is a form of convergent validity. Other researchers do think like you and think that using the own indicators cannot assess convergent validity (I would agree with you). However, traditionally, the first view has often been advocated and I think the authors of the book (I am not part of the authors) refer to some extend to this more traditional view.