only a property of a plurality or that everything which we have defined as *infinite* is only called so because, and in so far as, we discover a property in it which can be regarded as an infinite plurality. Now it seems to me that is really the case. (§10.)

Collections, multitudes, pluralities, series, quantities
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At the beginning of *Paradoxes of the Infinite*, Bolzano very precisely and thoroughly explains the basic notions in §§3 - 9. Nearly the same explanations can be found in the *Theory of Science* in §§82 - 86. The basic notion is “*a collection* of certain things or a whole consisting of certain parts,” which are connected by the conjunction “and”.

Bolzano had dealt with the concept of *collections* before, and there has been considerable professional discourse about his idea. (Simons 1998), (Rusnock 2000), (Behboud 1998), (Krickel 1995). This primarily concerns the question of whether we should interpret the objects contained in a collection as elements or as parts thereof. Peter Simons shows that Bolzano’s collections cannot be equated even with Cantor’s sets, nor can they serve as a basis for mereology, the study of parts and wholes, as Franz Krickel has proposed, but that 