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A Nominalist Alternative to Reference by Abstraction.

Gareth Rhys Pearce1

  • 1Faculty for Philosophy University of Vienna Universitätsstraße 7 Vienna 1010 Austria.

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Summary
This summary is machine-generated.

Nominalists can avoid Øystein Linnebo's argument for abstract objects by rejecting reference-based abstraction (RBA). This paper offers an alternative explanation, using mereology to achieve abstraction without abstract objects.

Keywords:
nominalismphilosophy of mathematicsreference by abstractionthin objects

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Area of Science:

  • Philosophy of Mathematics
  • Metaphysics
  • Ontology

Background:

  • Øystein Linnebo's book 'Thin Objects' (2018) proposes a hierarchy of abstract objects using dynamic abstraction.
  • Linnebo's argument relies on reference-based abstraction (RBA) principles.
  • Nominalism opposes the existence of abstract objects.

Purpose of the Study:

  • To provide a nominalist response to Linnebo's argument for abstract objects.
  • To challenge the sufficiency of reference-based abstraction (RBA) principles.
  • To offer an alternative explanation for abstraction without positing abstract objects.

Main Methods:

  • Analysis of Linnebo's deductive and abductive arguments for RBA.
  • Critique of the deductive argument as unsound.
  • Development of a nominalist counter-argument to the abductive case for RBA.
  • Exploration of mereological methods as an alternative to RBA.

Main Results:

  • Linnebo's deductive argument for RBA is found to be unsound.
  • Linnebo's abductive argument for RBA is prima facie plausible, requiring a nominalist response.
  • Abstraction, even in challenging cases like "reference to ordinary bodies," can be achieved via mereology, bypassing RBA.

Conclusions:

  • Nominalists can reject Linnebo's conclusion by denying the sufficiency of RBA.
  • Mereological approaches offer a viable alternative for achieving abstraction without abstract objects.
  • The paper presents a novel nominalist strategy against arguments for abstract objects.