P15: Any thing can be the accidental cause of Joy, Sadness, or Desire.

Dem.: Suppose the Mind is affected by two affects at once, one of which neither increases nor diminishes its power of acting, while the other either increases it or diminishes it (see Post. 1). From P14 it is clear that when the Mind is afterwards affected with the former affect as by its true cause, which (by hypothesis) through itself neither increases nor diminishes its power of thinking, it will immediately be affected with the latter also, which increases or diminishes its power of thinking, i.e. (by P11 S), with Joy, or Sadness. And so the former thing will be the cause of Joy or Sadness—not through itself, but accidentally. And in the same way it can easily be shown that that thing can be the accidental cause of Desire, q.e.d.

Cor.: From this alone—that we have regarded a thing with an affect of Joy or Sadness, of which it is not itself the efficient cause, we can love it or hate it.

Dem.: For from this alone it comes about (by P14) that when the Mind afterwards imagines this thing, it is affected with an affect of Joy or Sadness, i.e. (by P11 S), that the power both of the Mind and of the Body is increased or diminished. And consequently (by P12), the Mind desires to imagine the thing or (by P13 C) avoids it, i.e. (by P13 S), it loves it or hates it, q.e.d.

Schol.: From this we understand how it can happen that we love or hate some things without any cause known to us, but only (as they say) from Sympathy or Antipathy. And to this must be related also those objects that affect us with Joy or Sadness only because they have some likeness to objects that usually affect us with these affects, as I shall show in P16. I know, of course, that the Authors who first introduced the words Sympathy and Antipathy intended to signify by them certain qualities of things. Nevertheless, I believe we may be permitted to understand by them also qualities that are known or manifest.