Logical and Spiritual REFLECTIONS
Book 3.In Defense of Aristotle’s Laws of Thought
Chapter 12.A formal logic of change
I have in the past, following Aristotle and Darwin, proposed three forms of change for logical consideration. Namely:
a)Alteration, stated as “X gets to be Y”, meaning that something is characterized as X and not Y at one time and as X and Y at a later time. This is intended to imply that, while remaining X for the whole time under consideration, the individual thing concerned is successively not Y then Y. This signifies a mere change of attributes (not Y to Y), without essential change (X constant).
b)Mutation, stated as “X becomes Y”, meaning that something is characterized as X (and not Y) at one time and as Y (and not X) at a later time. This is intended to imply that the individual thing concerned does not remain X or Y for the whole time under consideration, but is successively X then Y (these two being different, or incompatible, characterizations). This signifies metamorphosis or essential change (X to Y), insofar as the thing concerned is here defined by its being X or Y.
c)Evolution, stated as “Xs evolve to Ys”, meaning thata setof things is characterized as Xs (and not Ys) at one time,gives rise to another setof things characterized as Ys (and not Xs) at a later time. Note well the intended implication here that the individuals subsumed under the classes X and Y are all different entities, although there is a significant causal relation between them. For instance, in the evolution of a living species, the earlier individuals (the Xs) are no longer present at the later stage (among the Ys), but they are their biological ancestors.
The first two forms of change can be expressed in terms of each other. “X gets to be Y (after not being Y)” can be stated as “X + notY becomes X + Y”; and conversely, “X becomes Y” can be stated as “Something gets to be notX + Y (after being X + notY)”. This is pointed out to show that the differentiation between changes of attribute and essence are relative, depending on what one focuses on as the substratum of change: in the case of alteration, the substratum is specifically the label “X”, whereas in the case of mutation, it is more vaguely “some thing”.
While the first two forms of change are found in Aristotelian logic, the third form did not become fully formulated (in Western philosophy) till Darwin and after. Evolution is often confused with mutation, but they are clearly very different logical forms, note well. Two very different kinds of subsumption are involved.
Mutation concerns anindividualentity, which persists from its early state (X) to its later state (Y); in the plural (i.e. some or all X become Y), this form refers to many entities but still as individuals. Evolution distinctively refers to groups, so that the individuals referred to at the beginning of the change (Xs) arenotthe same as those referred to as the end of it (Ys). Implied in the latter case is, not only a qualitative change in the same individuals, but more thoroughly a change of individuals. Nevertheless, note well, the two sets of individuals are causally related in some way, i.e. there is still acontinuityof sorts between them; this is why we say that one set has evolved into the other.
These three forms of change seem to cover all our ordinary discourse concerning change. On the surface, that analysis of change seems unassailable; but as we shall now see, it is possible to radically criticize it.