Classical Platonism, which identifies Determinants with certain sorts of structural universals, holds that the instantiation of a structural universal is the achievement of an end, and 37 With the relata highlighted, the relational property of METHANE would be best named with the following predicate: ... HAVING A PART THAT INSTANTIATES CARBON AND HAVING A SECOND PART THAT IS DISTINCT FROM THE FIRST PART, WHICH INSTANTIATES HYDROGEN WHILE BEING BONDED TO THE FIRST PART, AND HAVING A THIRD PART THAT IS DISTINCT FROM BOTH THE FIRST AND THE SECOND PARTS, WHICH INSTANTIATES HYDROGEN WHILE BEING BONDED TO THE FIRST PART, AND HAVING A FOURTH PART THAT IS DISTINCT FROM EACH OF THE FIRST, SECOND, AND THIRD PARTS, WHICH INSTANTIATES HYDROGEN WHILE BEING BONDED TO THE FIRST PART, AND HAVING A FIFTH PART THAT IS DISTINCT FROM EACH OF THE FIRST, SECOND, THIRD, AND FOURTH PARTS, WHICH INSTANTIATES HYDROGEN WHILE BEING BONDED TO THE FIRST PART.
that the instantiation of its involved universals is the achievement of the end’s constitutive means. According to Classical Platonism, a structural universal is an end to which the involved universals are constitutive means, and a structural universal is necessarily connected to the universals it involves because an end is only achieved when its constitutive means are achieved as well. According to Classical Platonism, the involvementrelation is that of constitutive means.38
Intuitively, constitutive means can be thought of as steps in a procedure that, logically, cannot be skipped. Our example will be the procedure of COUNTING FROM ONE TO TEN, with respect to the steps of COUNTING FROM FIVE THROUGH SEVEN.
First, there are lots of ways to count from to ten: one can vocalize the words, “one, two, three...” or write them; one can have a machine do the counting or one can read the words “one, two three...” off of a page. There are many different ways to count from one to ten. Each of these ways, in turn, consists in different steps. When counting from one to ten verbally in English, for instance, one of the steps is pronouncing the word “one,” and another is verbally pronouncing the word “two,” and so on.
There are a myriad of ways to count to ten, but no matter how one does it, one cannot successfully count from one to ten without also successfully counting from five through seven. Without counting from five through seven, then, one cannot be counting from one to ten; one would be skipping necessary steps. Counting from five through seven, then, is a kind of logically necessary means for counting from one to ten. No matter what one’s physical technology, in
38 The view of properties as ends goes back to Plato, and was arguably maintained by Aristotle, for whom essences were teleologically unified: “If we wanted to grasp the species of animals, we should first of all determine the organs which are indispensable to every animal, as for example some organs of sense and the instruments of receiving and digesting food, such as the mouth and the stomach, besides organs of locomotion.” Politics 1290b25-30, emphasis added. On Aristotle and structural universals, see Loux (2006) and Scaltsas (1994).
other words, one cannot logically count from one to ten unless one completes certain intermediate steps.
On the Classical Platonist Account, being involved in a structural universal is just being a necessary step for a certain end. To illustrate, consider again the universal HOUSE CAT LIFE #17. According to Classical Platonism, HOUSE CAT LIFE #17 is something that cats do; it is an end whose achievement makes something a cat with a specific sort of life. Rather than being part of a cat, HOUSE CAT LIFE #17 is an end.
To answer the question of what involvement is, consider again the end of HOUSE CAT LIFE #17. This end is a structural universal. To achieve that end, a cat must achieve certain means, including having four cat legs, having a cat tail, having a cat brain, and so on. Each of these means, in turn, is correlated with a structural universal: BEING A LEFT CAT FORELEG, BEING A CAT TAIL, BEING A CAT BRAIN, and so on. The cat achieves the means to CAT LIFE #17 exactly when its parts achieve the ends of BEING A LEFT CAT FORELEG and the like. The relationship of involvement, therefore, is that of being a constitutive means, or a means whose achievement just is part of the end’s achievement. BEING A CAT BRAIN is among the constitutive means to achieving CAT-HOOD; CAT-HOOD is the constitutive end of BEING A CAT TAIL, BEING A CAT BRAIN, and the like.
Critics may suspect that the difference between treating properties as ends and treating them as something else--parts, say--is merely verbal, but this is not so. By treating the
involvement relation as the teleological relation between means and ends, Classical Platonism avoids all the problems faced by the standard solutions. Here’s how.