If […] it proves impossible to substitute the equivalents of a symbol for that symbol in some of its occurrences, we dinstinguish those occurrences by giving the symbol a distinctive raised number. For instance, 'N –s = N: paper + -s = paper'; and 'papers' can be substituted for 'paper' in most environments. However, we cannot substitute 'N –s' for the first 'N' in this very equation: we cannot substitute 'papers' for the first 'paper' and then add '–s' again ('papers' + '-s'), as this equation would seem to indicate. We therefore write 'N ¹ –s = N ²' and state that wherever 'N ²' occurs we can substitute for it any 'N ¹' or another 'N ²', while for 'N ¹' we can only substitute any member of 'N ¹' (never 'N ²' ). Then it becomes impossible to construct a sequence 'papers' + '-s', since 'paper' is 'N ²' and '–s' is added only to 'N ¹'.
- Harris (1946), a pag.170

The procedure in assigning these raised numbers which indicate uni-directional substitutability is in essence as follows: we assign raised ¹ to each class symbol, say 'X', when it first appears. Next time the 'X' appears in an equation, we assign it the same number ¹ if the equivalents of this 'X' can be substituted for 'X ¹' in every equation which has so far been written. If the new 'X' cannot be substituted for all the preceding 'X ¹' we number it 'X ²'. If we later obtain an 'X' which cannot be substituted for all the preceding 'X ¹' or 'X ²', we will number it 'X ³', and so on.
- Harris (1946), a pag.170

On the left-handside of the equations, each raised number will be understood to include all lower numbers (unless otherwise noted). Thus in 'TN ² = N ³' we have not only 'the men' ('N ²') equalling 'N ³', but also 'the man' ('N ¹'). Any 'N ¹' can be substituted for the 'N ²' on the left side. On the right-hand side, however, each number indicates itself alone: 'N ³' on the right can only substitute for another 'N ³', and 'N ¹́́́́́́́́́́́́́́́́́́́́́́́́́́́́́́́́́́́́́́́́́́́́́́́́́́́́́́̓̓̓,²' for an 'N ¹' or an 'N ²'.
- Harris (1946), a pag.170