dorsal/arxiv
View SchemaOn the Persistence of Particles
| Authors | Jeremy Butterfield |
|---|---|
| Categories | |
| ArXiv ID | physics/0401112 |
| URL | https://arxiv.org/abs/physics/0401112 |
| DOI | 10.1007/s10701-004-1943-4 |
Abstract
This paper is about the metaphysical debate whether objects persist over time by the selfsame object existing at different times (nowadays called `endurance' by metaphysicians), or by different temporal parts, or stages, existing at different times (called ` perdurance'). I aim to illuminate the debate by using some elementary kinematics and real analysis: resources which metaphysicians have, surprisingly, not availed themselves of. There are two main results, which are of interest to both endurantists and perdurantists. (1): I describe a precise formal equivalence between the way that the two metaphysical positions represent the motion of the objects of classical mechanics (both point-particles and continua). (2): I make precise, and prove a result about, the idea that the persistence of objects moving in a void is to be analysed in terms of tracking the continuous curves in spacetime that connect points occupied by matter. The result is entirely elementary: it is a corollary of the Heine-Borel theorem.
{
"annotation_id": "96f08eb4-1a03-4195-b5ca-805c2ad7b07d",
"date_created": "2026-03-02T18:00:49.118000Z",
"date_modified": "2026-03-02T18:00:49.118000Z",
"file_hash": "533b6f13fe9055fcb94527c3d1bdc421de5b95ccd76bc8ed890623708c41072f",
"private": false,
"record": {
"abstract": "This paper is about the metaphysical debate whether objects persist over time\nby the selfsame object existing at different times (nowadays called `endurance\u0027\nby metaphysicians), or by different temporal parts, or stages, existing at\ndifferent times (called ` perdurance\u0027). I aim to illuminate the debate by using\nsome elementary kinematics and real analysis: resources which metaphysicians\nhave, surprisingly, not availed themselves of. There are two main results,\nwhich are of interest to both endurantists and perdurantists.\n (1): I describe a precise formal equivalence between the way that the two\nmetaphysical positions represent the motion of the objects of classical\nmechanics (both point-particles and continua).\n (2): I make precise, and prove a result about, the idea that the persistence\nof objects moving in a void is to be analysed in terms of tracking the\ncontinuous curves in spacetime that connect points occupied by matter. The\nresult is entirely elementary: it is a corollary of the Heine-Borel theorem.",
"arxiv_id": "physics/0401112",
"authors": [
"Jeremy Butterfield"
],
"categories": [
"physics.class-ph",
"physics.gen-ph"
],
"doi": "10.1007/s10701-004-1943-4",
"title": "On the Persistence of Particles",
"url": "https://arxiv.org/abs/physics/0401112"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "5581fce0-f2ea-4fae-bff3-5bc7b988db45",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}