Counting Criteria

Gelman and Gallistel (1978) list three criteria that formally define the process of counting. They are:

  1. The one-to-one principle

    2. Each item in a set (or event in a sequence) is given a unique tag, code or label so that there is a one-to-one correspondence between items and tags. No item or tag may be omitted, nor conversely used more than once. In pacemaker-accumulator models of counting (see section VI), the code or tag is equivalent to the current value of pulses in the accumulator or in working memory. In the neuronal filtering model, the tag corresponds to the particular numerosity detector that has been activated.

  2. The stable-order principle

    3. The tags or labels must always be applied in the same order (e.g. 1, 2, 3, 4 and not 3, 2, 1, 4). This principle underlies the idea of ordinality – that the label "3" stands for a numerosity greater than the quantity called "2" and less than the amount called "4". In counting models (see section VI) this ordering of tags is achieved by the progressive accumulation of pulses, or the increasing thresholds that must be crossed for different numerosity detectors to be activated.

  3. The cardinal principle

    4. The label that is applied to the final item represents the absolute quantity of the set.

    Two other principles generally apply but are not fundamental to the process of counting. These are:

  4. The abstraction principle

    5. Any types of items may be counted (e.g. birds in a flock or windows in a building).

  5. The order-irrelevance principle

The order in which the items themselves are tagged is irrelevant. (If we want to count the number of flowers in a bunch, it does not matter which one we label "1", which we label "2", etc.)