Identity is an axiomatic, primitive concept and therefore cannot be defined. It will here be explained with the help of examples.¹

A statement of the form ‘S₁ is identical to S₂’ – formally, S1 ≡ S2 – presupposes the possibility of S₁ and S₂ being distinct entities, or a contrast with a statement to the effect that two entities are not the same. The statement may be motivated by S₁ and S₂ having been perceived in different places or at different times, so that their identity is realized secondarily.

Of special interest in linguistics is the identity of a sign S₁ of language L₁ with a sign S₂ of language L₂. It presupposes that L₁ and L₂ are in a genetic or loan relationship. In the clearest case, they are an earlier phase P₁ and a later phase P₂ of the same language (this condition, again, presupposing the concept of identity). Then for S₂ to be diachronically identical with S₁ means that S₂ is S₁ despite any changes that S₂ may have undergone in linguistic change.

As a simple example, consider the pair of words from Latin and French displayed in Diagram 1:

Although we recognize both phonological and semantic differences between the two words, we also recognize them to be diachronically identical.

Now assume a stretch of time including phases P₁ and P₂. If the distance between P₁ and P₂ is sufficiently long, the instantiation of our sign at P₂ may be more like another sign that existed at P₁ than its own instantiation at P₁. For an example, consider the relationship between Latin erat and French était, as visualized in Diagram 2:

French était is not diachronically identical with Latin erat. Instead, the latter was replaced, at some point, by what had been Latin stabat, while erat itself dropped out of use. Now the function or meaning of French était is as much similar to the function or meaning of Latin erat as is possible in two different linguistic systems. Thus, erat is not identical with était although the significata are (nearly) identical, while stabat is identical with était although the significata differ. The conclusion here is that identity of the significatum is not a necessary condition of diachronic identity.

The other side of the coin is visualized in Diagram 3.

Here Latin /kor/ is not diachronically identical with French /kor/ despite the near identity of the significantia. Instead, the predecessor of French /kor/ is Latin /korpus/, despite the difference between the significantia. The conclusion here is that identity of the significans is not a necessary condition of diachronic identity.

All of this goes to show that diachronic identity of linguistic signs cannot be reduced to some notion of similarity, be it of the significans or of the significatum. Instead, it is simply identity of a sign with itself over time, where ‘identity’ and ‘time’ are axiomatic notions of the theory.

From a heuristic point of view, the situation is a bit different. The notion of diachronic identity of a linguistic sign is basic for the notions of replacement and renewal. A linguist must be able to recognize the identity of two signs across space and time when he encounters them. The axiomatic theory does not support him in this. Instead, he takes recourse to a similarity relation of the two signs in question regarding their expression, their content or their distribution. However, this is just heuristics. Since identity cannot be defined, it cannot be proved, either.

¹ The present text incorporates a slightly modified quote from Lehmann 2004, section 2.3.

Lehmann, Christian 2004, „Theory and method in grammaticalization“. Zeitschrift für germanistische Linguistik 32(2 [2005]): 152-187. [download]