About Cardinal Numbers and Cardinal Number Comprehension

Abstract

In this theoretic article we discuss cardinal numbers and what it means to grasp or comprehend cardinality and a cardinal number value. We discuss details that require a clarification of these concepts. We find inspiration partly from mathematics and our point of departure is cardinal numbers in mathematics. A thought experiment identifies some ideas that appear central for what we may mean by grasping a cardinal number value. These ideas are embodied in the concept which we call cardinal number comprehension. Cardinal number comprehension is related to, but not equivalent to, concepts like numerical magnitude understanding and the approximate number system. We argue that cardinal number comprehension is mainly embraced by two principles which we call number-to-set separation and number separation. Futhermore, cardinal number conception is linked and organized in relation to concepts like counting and different forms of subitizing.