[This is just a preliminary exercise written no more than a month after I started really getting interested in philosophy. It should not be taken as a definitive statement of any kind of independent discovery; I had read very little in the way of primary literature at the time of this writing, and I'm sure there's plenty else that's been written on this basic metaphysical topic.]
All generalities, those being classes into which particulars are grouped as members, seem to be themselves members of one of two main types:
Observed, a posteriori generalities; for instance: “All fish have scales.” If there were no such thing as a fish, this generality would not exist.
Basic, irreducible, a priori generalities. These can include (a) mathematical and (b) moral generalities. These are not dependent on the existence of certain specified externals, although such externals can be (and, apparently in the case of moral generalities, must be) used for illustrative purposes to express such a generality. More on that later.
Now, what is the essential difference between these two types? Type 1 generalities have the property of having to be stated as a tautology when reduced to their essence. Returning to the example statement of “All fish have scales,” let’s increase our precision in that statement (the act itself of which will be illustrative of the point at hand). In fact, all fish do not have scales: sharks and their ilk (class Chondrichthyes) are fish that do not have scales. Another class within the “fish” grouping (Osteichthyes) does include scales (as well as a bone skeleton, jaws, and paired fins, gill openings, and nostrils). Now, when we say that fish with the aforementioned characteristics are subsets of the generality known in zoology as Osteichthyes, we are in fact stating a tautology: the class Osteichthyes, by definition, contains fishes with those characteristics, and no fish without them. We can see by extension to other possible examples that all such observed generalities end up being stated as tautologies.
In contrast, Type 2 generalities, not being dependent on externals, are not essentially tautological. For instance, given the generality “murder is immoral,” it seems clear that the general class “immoral” is not dependent on the possibility of murder in order to be real. Nor does the classification “immoral” depend on an enumeration of all possible immoral acts; which specific externals may fall under the classification “immoral” in any given setting is dependent on the nature of the given set of externals, which in turn is essentially independent of the classes “moral” and “immoral.” For instance, in some possible world, (say, ours but very far in the future, where presently-unimagined technology presents new dilemmas) there may, due to the character of externals in that world, be some possible act which is not possible in the world we know now, and yet could be considered “moral” or “immoral.” Likewise, mathematical truths and generalities can be applied to externals; e.g., 2 + 2 = 4 is illustrated by the fact that when I buy two apples and two oranges, lo and behold, I have four pieces of fruit. Where mathematical and moral generality-truths seem to differ is that there exist mathematical truths, which can be stated in syntax consistent with other mathematics, to which no relation to externals as we know them can be found; non-applied and non-applicable abstract mathematics is a very real and well-established science. Moral application to possible worlds is up to the imagination, and it seems to be a daunting task for the imagination to discover moral principles not already known based on our given set of externals. What moral and mathematical truths have in common is that they are used in such a way that no possibility is left for a proviso that there may be an instance in which such generalities do not hold. Contrast that with the fish example, where the fish-with-scales classification would not exist if there were no such thing as a fish (or scales!).
So, Type 2, nondependent, irreducible, a priori generalities are obviously ontologically superior to, and will preferentially be appealed to over, those of Type 1.
Originally written October 2003 Last updated: Sunday, August 15, 2004; 7:11 pm CDT
