The degree-of-presence concept, accompanying that of the wavefunction-reality postulate, is introduced and studied in two ways. To begin with, an incomplete exposition of the present author's views is given. Subsequently, a short historical and philosophical review of answers to the question about the meaning of indeterminate individual-system probabilities is presented from the literature. It is done in the form of a carefully selected collage of quotations mostly with polemic comments by the present author and with further elaboration of his point (...) of view. The advocated notion of ‘degree of presence’ generalizes the intuitively most easily acceptable idea of ‘delocalization’ in wavelike behavior of a quantum system. (shrink)