In lambda calculus the fixed point combinator is defined as: $$Y=\lambda f \cdot(\lambda x \cdot f(x x))(\lambda x \cdot f(x x))$$
It is very easy to see how $Yg =g(Yg)$ for any $g$ by using $\beta$-reduction.
At the same time I wonder what is the meaning of $Yg$ when $g=\lambda x.x+1$, a fuction without fixed point. I need somebody to explain me that please.
I know that the fixed point combinator is related to the Curry paradox which proves that the lambda calculus as a deductive system is inconsistent. Does this inconsistency has to do with the case I wrote above?