"1. Indexes, as in x₁, x₂, x₃ ... x_n; chair₁, chair₂, chair₃ ... chair_n; Smith₁, Smith₂, Smith₃ ... Smith_n, etc. The role of the indexes is to produce indefinitely many proper names for the endless array of unique individuals or situations with which we have to deal in life. Thus, we have changed a generic name into a proper name. If this indexing becomes habitual, as an integral part of our evaluating processes, the psycho-logical effect is very marked. We become aware that most of our "thinking" in daily life as well as in science is hypothetical in character, and the moment-to-moment consciousness of this makes us cautious in our generalizations, something which cannot be easily conveyed within the Aristotelian structure of language. A generic term (such as "chair") deals with classes and stresses similarities to the partial exclusion or neglect or disregard of differences. The use of the indexes brings to consciousness the individual differences, and thus leads to more appropriate evaluation, and so eventually "perception," in a given instance. The harmful identifications which result from the older language structures are often prevented or eliminated, and they may become supplanted by more flexible evaluations, based on a maximum probability orientation."
— Alfred Korzybski, The Role of Language in the Perceptual Processes.

In mathematics, indexes are useful to discriminate elements of a set. These elements have common characteristics, symbolised by a same name. The indexes make it possible to differentiate each one of these elements.

Example:

In general semantics, we use indexes with a similar aim. Our goal is to individualise the elements of a set, so as to point out their differences to us, differences that the Axristotelian law of identity very often makes us forget. The use of indexes enables us to take into account the first premise ("is not"), at least at the descriptive level (first verbal level).

Examples:

We can thus say "Chair₁ is not chair₂", "Smith₁ is not Smith₂", "Time_Smith is not time_Brown", etc.

Whenever you use indexes, try to find some of the differences between the objects considered.