John Leslie on the Origins of Number

The following quotation is from John Leslie's book Philosophy of Arithmetic (Edinburgh, 1820). We give the quotation because it is interesting to see how an excellent mathematician like Leslie might be thinking about the origin of number at the beginning of the 19th century. However, we do not think that numbers would arise in the way that Leslie suggests:

The idea of number, though not the most easily acquired, remounts to the earliest epochs of society, and must be nearly coeval with the formation of language. The very savage, who draws from the practice of fishing or hunting a precarious support for himself and family, is eager, on his return home, to count over the produce of his toilsome exertions. But the leader of the troop is obliged to carry father his skill in numeration. He prepares to attack a rival tribe, by marshalling his followers; and, after the bloody conflict is over, he reckons up the slain, and marks his unhappy and devoted captives. If the numbers were small, they could easily be represented by very portable emblems, by round pebbles, by dwarf shells, by fine nuts, by hard grains, by small beans, or by knows tied on a string. But to express the larger numbers, it became necessary, for the sake of distinctness, to place those little objects or counters in regular rows, which the eye could comprehend at a single glance; as, in the actual telling of money, it would soon have become customary to dispose of rude counters, in two, three, four, or more ranks, according as circumstances might suggest. The attention of the reckoner would then be less distracted, resting chiefly on the number of marks presented by each separate row. ...

These simple arrangements would, on their first application, carry the power of reckoning but a very little way. To express larger numbers, it became necessary to renew the process of classification; and the ordinary steps by which language ascends from particular to general objects, might point out the right path of proceeding. A collection of individuals forms a species; a cluster of species makes a genus; a bundle of genera composes n order; a group of orders constitutes a class; and an aggregation of classes may complete a kingdom. Such is the method indispensably required in framing the successive distribution of the almost unbounded subjects of Natural History.

In following out the classification of numbers, it seemed easy and natural, after the first step had been made, to repeat the same procedure. If a heap of pebbles were disposed in certain rows, it would evidently facilitate their enumeration, to break down each of these rows into similar parcels, and thus carry forward the successive subdivision till it stopped. The heap, so analysed by a series of partitions, might then be expressed with a very few low numbers, capable of being distinctly retained. The particular system adopted for this decomposition would soon become clothed in terms borrowed from the vernacular idiom.

JOC/EFR October 2016

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