“Let no one ignorant of geometry enter” (Plato)

Plato doesn’t mean here that a prerequisite for learning philosophy is math, rather Mathema means what is eminently learnable, and so we speak of polymaths.  For, in order for me to encounter the triangle as the figure that it is, I must have the rule before my mind’s eye of an enclosed figure with three straight sides.  In order to encounter the triangle in its specificity, the mind must apply the rule of either equilateral, scalene, isosceles, or right triangle. 

Plato says one of the ways of seeing the immortality of the soul is through recollection, that the mind knows some ideas prior to experience that makes experience possible, that would in later philosophy be called the a priori.  But what is recollection?  Last time I gave the example of Justice, in that when we learn about justice we do not invent the concept out of whole cloth, but rather when we hear LGBTQ+ rights cry out for the violence being done by the traditional definition of marriage, in deconstructing and reconstructing the definition to be less violent we un-cover what justice is and always was – just that it was hidden. We don’t invent Justice as a concept but “re-cognize” it. Plato argues that this capacity to recognize Justice when we “see” it and realize we have un-covered Justice suggests the immortal mind always knew it but had forgot.

How does this relate to the immortality of the soul?  There is a debate in philosophy between empiricists and rationalists as to whether all knowledge comes via the senses, or rather that there are innate ideas in the mind that didn’t come via the senses.  For instance, the degree of language acquisition in humans seems hard to explain through learning alone.  In terms of innate ideas, in order to be able to intelligibly encounter this being as the being it is, it must already be “recognized” generally and in advance as a being, i.e., with respect to the constitution of its Being.  Heidegger points out Plato gives the example in the Sophist in critique of Antisthenes that the dog is not just a “this here,” but is already being made intelligible by an understanding of Einai, Being, choris, separate from, ton allown, the others, and kath auto, in itself.  I encounter the dog as a “not me,” for example.  To be particular is clearly a universal characteristic of things. If we look more closely, then, we realize that these particular things are in each case this, this door, this piece of chalk, this here and now, and not those of Classroom 6 and not the ones from last semester.  Also, we could not have the experience of beings that we do unless we had in view such things as variation/equality by the mind’s eye in order to encounter various things; a view of sameness/contrariety to encounter ourselves as self-same in each case; a view of symmetry and harmoniousness allow us to arrange and construct things; etc.

If there are these innate ideas that are not derived from experience but make experience possible/intelligible, the question is how these ideas got there?  One traditional answer is God may have put some them there (eg. Descartes’ analysis of his idea of God, he discovers that it is innate, since it is neither adventitious nor factitious. It is not adventitious (or sensory), since he has had no sensory experiences of God (i.e., he has never seen, heard, felt, smelt, or tasted God).  Nietzsche answered this by pointing out a lizard may hear a rustling in the leaves, but not a gunshot close to it, so every creature is going to circumscribe the world of its experience in different ways, and so the way humans do it tell us about human physiology, not immortal minds.