Full Idea
It has been proposed (on the basis of observations) that young children have three innate principles of counting - one-to-one correspondence of number to item, stable order for numbers, and cardinality (which labels the nth item counted).
Gist of Idea
Children may have three innate principles which enable them to learn to count
Source
Alvin I. Goldman (Phil Applications of Cognitive Science [1993], p.60)
Book Reference
Goldman,Alvin I.: 'Philosophical Applications of Cognitive Science' [Westview 1993], p.60
A Reaction
I like the idea of observed patterns as central (which is the one-to-one principle). But the other two principles are plausible, and show why pure empiricism won't work.