On first sight, an intuitive way of understanding proposition 4, part I, of Spinoza’s Ethics, is the following:
For all x and for all y, if not x=y, then either (there is a z and a z' such that z is an attribute of x and not of y and z' is an attribute of y and not of x) or (there is a w and a w' such that w is a mode of x and not of y and w' is a mode of y and not of x).
However, Jarrett presents an argument against it:
A formidable difficulty with such a formulation, however, is that the strategy that Spinoza employs in proving Proposition (v) is to argue that satisfaction of the second disjunct stated in I, iv, is never sufficient to show that x and y are distinct, if they are substances. If (iv) were correct, then, Spinoza's argument for I, v would disbar us from holding that if x and y are substances and there is a mode of x which is not a mode of y (or vice versa), then x is distinct from y. But then (∃x)(∃y)(∃z)(Mzx &-Mzy) & x = y)[with Mxy = “x is a mode of y”] would be consistent. (Charles Jarrett, The Logical Structure of Spinoza’s Ethics, pp.32-33)
Can anyone explain Jarrett’s argument in a bit more detail? In its condensed form, it is not really clear to me what he wants to say here.