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Pluralities, counterparts, and groups.

Isaac Wilhelm1

  • 1National University of Singapore, 3 Arts Link, Block AS3, #05-22, Singapore, 117570 Singapore.

Philosophical Studies
|January 18, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a new theory of groups, defining them as pluralities existing at a single time. It utilizes counterpart theory for modal and temporal group properties, similar to stage theory for objects.

Keywords:
Counterpart theoryGroupsPluralitiesSocial metaphysics

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Area of Science:

  • Philosophy of Mathematics
  • Metaphysics
  • Logic

Background:

  • Existing theories of groups often lack a robust framework for their temporal and modal properties.
  • Stage theory provides a precedent for analyzing objects based on temporal stages and counterparts.

Purpose of the Study:

  • To formulate a novel theory of groups grounded in pluralities and counterparts.
  • To develop a counterpart-theoretic semantics for modal and temporal statements concerning groups.
  • To establish an analogy between the proposed group theory and the stage theory of material objects.

Main Methods:

  • Defining groups as pluralities of entities existing at a specific time.
  • Employing counterpart theory to address modal, temporal, and coincidence properties of groups.
  • Drawing parallels with the stage theory's approach to material objects.

Main Results:

  • A formal theory of groups is presented, where groups are understood as temporal slices or pluralities.
  • Counterpart-theoretic semantics are established for modal and temporal claims about groups.
  • The theory aligns with stage theory in its treatment of entities existing at single times.

Conclusions:

  • The proposed theory offers a unified framework for understanding groups, their temporal existence, and modal characteristics.
  • This approach provides a novel perspective on group ontology by leveraging pluralities and counterparts.
  • The analogy with stage theory highlights the utility of counterpart semantics in metaphysical analysis.