Essentially Not

While telling the salamander's tale, Richard Dawkins launches into a critique of Essentialism and what he calls the discontinuous mind. I am broadly sympathetic to that critique, but armed with 100 plus pages of very elementary category theory, I have to say that Dawkins view is also naive.

Essentialism enters the picture because it forms a key creationist argument that Dawkins wants to demolish. What about that last common ancestor of both cat and dog, asks the lawyer, was it cat or dog? By way of answer, Dawkins tells him about a couple of pairs of ring species, in each case there is an uninhabitable zone surrounded by a habitable zone. At one end of the ring zone there are two distinct but closely related species, but as you go around the ring each grades continuously into the other.

Essentialists, as Mayr calls them, or "discontinuous minds" as Dawkins styles them, seem to have a lot of trouble with this notion of gradation. The Abortion debate is a classic example invoked by Dawkins. The abortion absolutists see no difference between a 1 day old embryo and an infant born alive. Oddly enough, there is a variant of this on each side of the debate, with pro-choicers unwilling to concede that a six or eighth month fetus is different from that same embryo. To Dawkins (and to me)both views are absurd. Those eight or sixteen undifferentiated cells are clearly not a person and the eighth month fetus is clearly well on the way to personhood.

Dawkins seems to regard essentialism as a sort of mental defect, but at one level, I think he is wrong. He concedes the value and necessity of classifications, but wants to insist that nature isn't like that. Made dangerous with a little category theory, I want to say that we need to recognize that the map from the big set of all animals to the little set of species is a retract from the big set, so that in some sense the ideal exemplars exist as fixed points in the big set of all animals. The mistake that the essentialists make is in thinking that the retract is an isomorphism, which it isn't.

No doubt, though, essentialism is dangerous in biology. Physics, though is a different matter. Elementary particles really are ideal objects. Every electron is exactly like every other electron, except in where it happens to be at the moment, and everything is made of just a few such ideal elements.