Plenitudinous

A fourth and final version of the third strategy, developed independently (and somewhat differently) by Balaguer (1995, 1998a) and Linsky & Zalta (1995), is based on the adoption of a particular version of platonism called plenitudinous platonism (Balaguer also calls it full-blooded platonism, or FBP, and Linsky and Zalta call it principled platonism). ❋ Balaguer, Mark (2009)

Kerry writes that she favors “A culture of liberty [that] would . . . beget [a] raucous, plenitudinous hodgepodge” of different subcultures. ❋ Unknown (2009)

Linsky & Zalta respond to this by arguing that plenitudinous platonism (or in their lingo, principled platonism) is knowable a priori because it is required for our understanding of any possible scientific theory: it alone is capable of accounting for the mathematics that could be used in empirical science no matter what the physical world was like. ❋ Balaguer, Mark (2009)

Since plenitudinous platonism, or FBP, says that there are mathematical objects of all possible kinds, it follows that if FBP is true, then every purely mathematical theory that could possibly be true (i.e., that's internally consistent) accurately describes some collection of actually existing mathematical objects. ❋ Balaguer, Mark (2009)

Linsky & Zalta develop plenitudinous platonism by proposing a distinctive plenitude principle for each of three basic domains of abstracta: abstract individuals, relations (properties and propositions), and contingently nonconcrete individuals (1995, 554). ❋ Balaguer, Mark (2009)

One might object here that in order for humans to acquire knowledge of abstract objects in this way, they would first need to know that plenitudinous platonism is true. ❋ Balaguer, Mark (2009)

One alleged benefit of this plenitudinous view is in the epistemology of mathematics. ❋ Linnebo, Øystein (2009)

In Linsky and Zalta's version of plenitudinous platonism, the mathematical entity that is postulated by a consistent mathematical theory has exactly the mathematical properties which are attributed to it by the theory. ❋ Horsten, Leon (2007)

In Balaguer's version, plenitudinous platonism postulates a multiplicity of mathematical universes, each corresponding to a consistent mathematical theory. ❋ Horsten, Leon (2007)

It is enough for your LogoBox to draw plenitudinous attention. ❋ Unknown (2006)