Peter Simons has been rather alone in the modern philosophy of mathematics to argue that the natural numbers should be regarded as properties of multitudes or collections. This paper, however, sides with Simons, but it modifies his property view by adding the notion of imposed collection boundaries and accepting fictional collections. Although partly inspired by the Husserl of Philosophy of Arithmetic, Simons dismisses Husserl's talk of psychological acts of collective combination, but this paper saves them by dressing them in modern cognitive clothes. Hereby, a reasonable partially constructivist notion of the natural numbers emerges. ***** The most naive opinion is that according to which a number is something like a heap, a swarm in which the things are contained lock, stock and barrel. Next comes the conception of number as a property of a heap, aggregate, or whatever else one might call it. Frege, Review of Dr. E. Husserl's Philosophy of Arithmetic (Frege 1972 [1894], 323) 1 This view is also argued for by (Yi 1998). He presents it by criticizing the relational account in (Bigelow 1988). He is aware of Simons as a forerunner, but in a long footnote (25) he complains about ambiguities in (Simons 1982a). I find him over-complaining. About Yi, see also footnote 12 below. 2 My trope accepting realism is best defended in (Johansson 2014a) and my view of fictions in (Johansson 2010). 3 Of course, noted by Simons: "The history of the philosophy of mathematics during the golden years of 1879-1939 hardly ever mentions Husserl" (Simons 2010, v).