One common notion of the identity of an object or a class of objects emerges out of understanding similarities and dissimilarities between properties. This is more or less based on comparing one object with other objects in its environment. A reformulated definition of
universals as offered by Socrates (see above §1.1 page 14) is obtained in this manner. The form of this definition shows clearly how an understanding of this notion of identity depends on the operation of negation. It is common practice to interpret this notion of identity in terms of a class—the property shared by a class of objects. This is more or less the same thing as what the type stands for in a type-token relation. Therefore, let us call this notion
of identity type-token identity.
We are however interested in highlighting another notion of identity, that has become rather central to science, including mathematics. This notion of identity occurs in almost every discipline of science and is so predominant that it would be rather surprising to know how little this notion is employed in characterizing scientific knowledge. We would like therefore to give full attention possible in explicating the epistemological significance of this identity as well as its logical relation with inversion.
This identity, unlike the other, does not emerge out of the persistence of a quality
in object/s, it emerges out ofchange orvariability orflux ortransformation . . . of object/s.
This identity refers to theinvariant pattern of variation by capturing thesubstanceof change.
Right from antiquity the problem of explaining transforming properties of things has been a riddle, which ultimately finds consolation in this special notion of identity. We will call this
vital notion invariant identity or simplyinvariance, though it is also known by several other
names, such as equivalence.
We can find examples of invariance abundantly throughout quantitative science. Detailed discussion with further characterization and illustrations will be found throughout the following text. Therefore we shall be content with two simple examples here. Motion is usually regarded as a property of things. However, science deals with it as if it is in itself an object, because a scientist is not interested in the object that is moving or the kind of
object that is moving, but motion per se. Galileo—as a true scientist—was interested in the
substance of motion, and the notion of inertia and acceleration have thus became the first invariant properties of motion to be discovered. How inertia became a parameter of motion will be elaborated in the case-studies.
Weight can be characterized as a measure of quantity of matter of an object. How- ever, the weight of the same object may change from place to place, hence it is variable. Therefore weight cannot be regarded as a satisfactory measure for quantity of matter by
a scientist due to its variability. The discovery of mass as an invariant identity for a spe-
cific quantity of matter solved the problem. Likewise almost every measurable dimension of science has a corresponding invariance.
176 Chapter 6. Inversion
We are not very certain about whether this identity is the same as Leibniz’s notion of theidentity of indiscernables. We have therefore decided to develop the notion independently to avoid confusion. Another reason for doing so is that we are going to essentially link this notion of identity with inversion. This linkage to the best of our understanding has precedence
only in modern mathematics and in thegenetic epistemology of Jean Piaget. It may also be
pointed out that anticipation of this notion of identity can be found in the writings of Ernst Cassirer, Emile Meyerson and Herman Weyl. However, we cannot at the moment either trace the history or explicate clearly the affinities or differences of this special notion with those of other thinkers, except with Piaget. In Piaget, more than anyone else, the notion acquires a very special significance specially in the context of generation, as well as its connection with inversion.
There is another notion of identity in which philosophers have shown a lot of interest. An object might undergo changes or variations in one or more than one property over a period of time. Take for example, water, which may appear in different shapes, different states like vapor, ice, etc. Despite these changes one or more property of objects may remain unchanged.
The Aristotelian name for such properties is theessential property, as against theaccidental
properties that are taken to be contingent. This notion of identity continues to enjoy attention
even to this day.20
Kripke would interpret this kind of identity as that property of an object which it will have in all possible worlds, and therefore such identities are asserted by using
necessary orapodictic modality, as againstpossible orproblematic modality.21 Since scientific knowledge is also regarded to be about the essences of things, this notion of identity of things has been regarded as a significant notion of identity of scientific concepts despite a number of philosophical problems. All natural kind terms are regarded as of this variety. Since it is easy to recall this notion of identity by the term ‘natural kind’, let us call this variety of
identity of things as thenatural-kind-identity.
We will regard invariance and natural-kind-identity as two distinct notions based
on the interpretations given, and this distinction is indeed very vital for understanding the nature of scientific knowledge. Natural-kind-identity, as stated above, is that ‘portion’ or that
aspect of an object or an individual that is unchanging in its history. In the case of a class
of objects it is that commonness obtained after excluding all contingencies. On the other
hand invariant identity is about the essence of achanging property of an object. Since most
natural-kindentities are members of ataxon,22 they are obtainable as a result of taxonomic
20
Modern essentialists like Kripke, Putnam etc., have attempted to defend a version of essentialism.
21
S. Kripke 1972,Naming and Necessity inSemantics of Natural Language, ed. by Donald Davidson and Gilbert Harman 1972.
22
systematization. Invariance, on the other hand, ‘refers’ to the essence of a property, rather
than an individual. In other words, invariance is properly attributable only to attributables
of an object. Therefore, we think, the two notions, natural-kind-identity and invariance are significantly different, though both are very useful in characterizing scientific knowledge.