Would it be possible to apply $(\lambda x.\lambda y. x)$ to the argument $y$? It seems to me that this must not be possible as it would give a different answer if applied to a constant, call it $\alpha$ and $y$. Namely:
$(\lambda x.\lambda y. x) \alpha = \alpha$
$(\lambda x.\lambda y. x)y = \lambda y.y$
I am afraid that I might be making considerable mistakes but this is only the case because I have been studying $\lambda$-calculus for just one day.
Thank you very much in advance for your comments and suggestions.