 Once again, even this strong modal conclusion is not equivalent to full-blown necessitarianism regarding infinite modes. Even if every existing infinite mode necessarily exists, could there have been other infinite modes as well? I am not aware of any texts in which Spinoza explicitly rules this out, but it is easy to imagine what he would say. Non-actual infinite modes do not exist necessarily, or else they would actually exist, on the plausible assumption that necessity entails actuality (□p → p). So, for reductio, consider a non-actual possible world, w*, that contains Sophia, one of these extra, non-actual infinite modes. What is the manner of Sophia’s dependence on substance? Spinoza’s discussion of infinite modes suggests that Sophia must, by definition, follow from God’s absolute nature (either immediately or mediately). If so, then Sophia follows from the absolute nature of God in w*, on the assumption that true definitions express necessary truths. But in that case, the modal transfer principle will apply to Sophia in w*, in which case Sophia’s existence is necessary. However, again assuming that necessity entails actuality, Sophia would not be a non-actual infinite mode after all, pace our initial assumption. QED.