The development of counting in mathematics required similar attributes to those which resulted in the formation of numbers. The process of counting stems from our ability to percieve an object as being separate from others. Thus we are able to recognize that repeated objects, while having the same form and size, are in fact distinct and separate from one another; likewise for a group of many objects of varying form and size.
While the ability to count stems from the notion of individualism, what does it actually mean to count? Counting means to assign each object in a group a label. That is, counting may be thought of as placing each object within the group in a one-to-one correspondence with a label. Both counting and numbers require the constructing of a one-to-one correspondence relationship; be it between objects from different groups or an object and a label. Indeed, this highlights the intimate association that exists between numbers and counting. Counting is simply determining how many objects are in the set. This is equivalent to determing the number of a set, where the number used in this context is simply an adjective used to describe the set.
We count by assigning each object in a group a label. However, if we use labels that are not in a definite order or tell us nothing about how many objects there are, then we have not counted at all. This alludes to an extremely important, yet subtle aspect of the nature of counting: the labels we use must contain within them the information telling us how many objects there are in a set. If the labels we use do not inherently contain this information, then we have not counted.
Our very early ancestors counted using the very primitve technique of: "one, two, many". A single object was recongised as a individual being, seperate from othes and was given the name "one" (meaning single). Likewise, two objects were given the name "two" (one more than one) since it was recognised that placing one object with one other gave two objects. However, more than two objects were given the name "many". While there was a recognition that a set consisted of more than two objects, there was no mechansim in place to permit the counting of these sets. In light of this, one wonders whether our early ancestors were really counting at all. They had adjectives in place to describe sets of one or two (one more than one) objects, but it appears that (at a fundamental level) they did not have a true understanding nor appreciation for the art of counting. Other civilisations had adjectives for three (one and two) and four (two and two), but again could count no higher. However, we know counting to be an unbounded process; there is no upper bound or limit to which we can count. For these civilisation which had a definite limit to which they could count, we can only conclude that they did not have a complete understanding of the counting process that we have today.
