Spinoza has separate definitions for 'attribute' (1d4) and 'mode' (the substance's affections) (1d5). In (1p4) Spinoza claims that
Duae aut plures res distinctae, vel inter se distinguuntur ex diversitate attributorum substantiarum, vel ex diversitate earundem affectionum.
That is, two or several distinct substances, are distinguished by either different attributes, or by different affections. The next proposition, (1p5), claims that
In rerum natura non possunt dari duae aut plures substantiae ejusdem naturae sive attributi.
The term 'rerum natura' no doubt refers to Lucretius' De rerum natura, and means existence, the nature of things, the world as we know it, or something along these lines. The term 'substantiae naturae', is identified with 'attributi'. That is, Spinoza seems to be stating that that the nature of a substance is encoded in its attributes. More accurately, he saying that for a substance to have the same nature as another substance, means that they have the same one attribute. This is a literal translation of
plures substantiae ejusdem naturae sive attributi.
(attributi is the singular genitive of attributum, a neuter noun).
The following question then naturally suggests itself:
From (1p4), one may logically deduce that that there exist two distinct substances that only differ in their affections, but have the same attributes. However, from (1p5), it logically follows that there do not exist distinct substances that have the same attributes.
So, what does Spinoza really mean? Or maybe one should not read Spinoza's geometric method the way one reads Euclid?
