Are there objects that are "thin" in the sense that not very much
is required for their existence? Frege famously thought so. He
claimed that the equinumerosity of the knives and the forks
suffices for there to be objects such as the number of knives and
the number of forks, and for these objects to be identical. The
idea of thin objects holds great philosophical promise but has
proved hard to explicate. Oystein Linnebo aims to do so by drawing
on some Fregean ideas. First, to be an object is to be a possible
referent of a singular term. Second, singular reference can be
achieved by providing a criterion of identity for the would-be
referent. The second idea enables a form of easy reference and
thus, via the first idea, also a form of easy being. Paradox is
avoided by imposing a predicativity restriction on the criteria of
identity. But the abstraction based on a criterion of identity may
result in an expanded domain. By iterating such expansions, a
powerful account of dynamic abstraction is developed. The result is
a distinctive approach to ontology. Abstract objects such as
numbers and sets are demystified and allowed to exist alongside
more familiar physical objects. And Linnebo also offers a novel
approach to set theory which takes seriously the idea that sets are
"formed" successively.
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