Endurantism and Temporal Gunk

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Endurantism and Temporal Gunk

• Andrew Bacon,
• Oxford University

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What is endurantism?

• A thesis about concrete particulars and how they
  persist through time.
• The endurantist holds that at any given instant
  of time physical objects exist wholly in the
  sense that they, and all their parts, exist at
  that time.

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Central tenets of endurantism

• Physical objects are three dimensional.
• Physical objects only have spatial parts.
• Identity statements about objects at different
  times is to be interpreted as strict identity.
• Physical objects are not extended in the temporal
  dimension.

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Perdurantism

• On the other side of the fence we have
  perdurantism. Perdurantists believe that
• Physical objects are four dimensional worms
  (think Donnie Darko). It is sometimes called
  worm theory.
• Identity statements across time are loose in the
  sense that you only need to ostensively pick out
  different parts of one object to make an identity
  assertion.

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Temporal parts and Endurantism

• Endurantists will typically claim that an object
  has different parts at different times.
• Example on the 19th of May 1536 Anne Boleyn had
  a head, but on the 20th she did not.
• These are not temporal parts in the traditional
  sense, all the endurantist is committed to is
  that it was the case that Anne Boleyn had a head

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Whats the difference?

• Perhaps the best way to explain the difference is
  to say that Perdurantists believe four
  dimensional entities, and Endurantists in three
  dimensional entities.

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• Is this necessary?
• Surely an endurantist could believe in many (even
  infinitely many) spatial dimensions, or even many
  temporal dimensions.

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Endurantism as a necessary truth

• Claim Endurantism, if true at all, is
  necessarily true.
• It is a claim about the nature of physical
  objects and time.
• It ascribes a certain characteristic to an
  ontological category. If something falling under
  this category exists, then it must have this
  feature.

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Structure of argument

• If endurantism is true, it is necessarily true
• There are possible worlds with certain exotic
  space times.
• In these worlds endurantism is false.
• Therefore endurantism is false. (contrapositive
  on 1.)

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Mereology 1

• First order language.
• Only non logical symbol ?
• x ? y is to be read as x is a part of y

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Mereology 2

• For convenience introduce the defined symbols
• Overlap x ? y ? ?zz ? x ? z ? y
• Disjoint x ? y ? x ? y
• Proper Part x lt y ? x ? y ? x y

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Axioms 1

• Reflexivity
• ?x x ? x
• Anti-symmetry
• ?x?yx ? y ? y ? x ? x y
• Transitivity
• ?x?y?zx ? y ? y ? z ? x ? z

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Axioms 2

• Supplementation
• ?x?yy ? x ? ?zz ? y ? z ? x
• Product
• ?x?yx ? y ? ?z?ww ? z ? w ? x ? w ? y
• Sum
• ?x?y?zx ? z ? y ? z ? ?z?ww ? z ? w ? x ? w
  ? y

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Axioms 3

• If we want an even stronger mereology add the
  fusion axiom schema.
• Unrestricted Fusion
• ?x? ? ?!y?zz ? y ? ?x? ? x ? z
• For any well formed formula ? with no free
  occurrences of y or z

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Atoms and Gunk

• Definition Call something an atom iff it has no
  proper parts
• Definition Call something gunky iff all its
  parts have proper parts.

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Axioms 4

• Atoms
• ?x?yy ? x ? ?zz lt y
• Gunk
• ?x?yy ? x ? ?zz lt y

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Atoms and Gunk

• Atoms says that every thing is made up of atoms
  simples which have no proper parts.
• Gunk says that there are no atoms, everything is
  made up of gunk, which in turn is made up of more
  gunk and so on and so forth turtles all the
  way down.

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Can we prove these assertions from preceding
axioms?

• Atoms and Gunk are both independent of standard
  mereology.
• Consider two models for Atoms take sets of
  points in Euclidean 3-space and subset as
  parthood, our atoms will then be the singleton
  sets. For Gunk take the non-empty open sets in
  Euclidean 3-space and subset as parthood.

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Is gunk possible?

• Gunk passes three great tests for possibility
• Logically possible (we can provide a model for
  it, it is consistent).
• Conceivable (it is frequently discussed in
  mereological literature.)
• Physically serious (Leibniz thought our
  space-time was gunky!)

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Gunky space-time

• The obvious way to interpret the existence of
  gunk would be for the structure of space-time to
  be gunky. This idea dates back to the stoics, and
  can also be found in the writings of Whitehead.

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• To imagine gunky space-time we think in terms of
  the model given earlier non-empty open sets of
  space-time points.

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Topological digression

• A set X in 3-space is said to be open iff for all
  x ? X, we can find a ? ? R, such that B?(x) ? X
  where B?(x) is a sphere of radius ? gt 0 with
  centre x, called the epsilon ball around x.

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Come again?

• This basically says that no matter how close to
  the edge of the region you get, there is always
  room to wiggle in all directions and stay within
  the region.
• It also means an open set is a region of space
  without a skin or a boundary. If an open set
  did contain its boundary then if you were on the
  boundary there would be some directions in which
  you could not wiggle.

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A little observation

• Lemma A non empty open set in n-dimensional
  space is extended in all n dimensions.
• Proof Let X be a non empty open set. Since X is
  non empty it contains an element, x. By the
  openness property X contains an n-dimensional
  ball around x. (i.e. you can wiggle about in all
  dimensions around x and stay inside X). Therefore
  X is n-dimensional.

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In terms of gunky space-time?

• This means that if space-time is gunky then all
  regions (parts) of space-time are four
  dimensional (discounting the null object).

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The Argument

• Physical objects have spatial parts
• If physical objects have spatial parts, they
  overlap with space-time.
• All parts of space-time are four-dimensional (by
  lemma).
• Therefore, physical objects will have
  four-dimensional parts (and hence temporal parts).

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Objections

• Endurantists treat time as fundamentally
  different from space.
• Argument makes essential use of 4D talk.

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Temporal Gunk

• Suppose we respect the endurantist notion of time
  and focus just on the possibility of temporal
  gunk.
• We can let space can be gunky or have atoms, it
  doesnt matter.
• Question is endurantism consistent with such a
  possibility?

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Problems

• For a physical object, x, the endurantist claims
  that at any instant t, x is wholly present at t.
• But if time were gunky there would be no
  instants! (only periods or intervals of time)

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How do we phrase the endurantist position in gunk
time?

• Merricks suggests we analyse x is wholly present
  at t as all of xs parts exist when time t is
  present
• Firstly there are problems with the notion of
  present in gunky time. If the interval (a, b)
  is present, why is it that intervals contained in
  or containing (a, b) are not present. Perhaps
  there is no unique present? These matters seem to
  pose problems for presentism or even the
  possibility of gunk time depending on your
  sympathies

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How do we phrase the endurantist position in gunk
time?

• Secondly, if we run Merricks analysis on
  intervals it sounds like were committed to
  temporal parts.
• all of xs parts exist when interval (a, b) is
  present
• Lastly, if these kinds of analysis fail, then the
  notion of time indexed properties breaks down
  completely for the endurantist.

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What next for the endurantist?

• Two strategies suggest themselves naturally
• Deny the possibility of temporal gunk.
• An interesting response would be to deny that
  physical objects have spatial parts.

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The second option

• Simons discusses the possibility of extended
  simples. (Get references off me later.)
• That objects and space-time do not overlap also
  seems to be entailed by relationism about
  space-time.

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Conclusion

• Whether or not such theories will stand up to
  scrutiny is an open question, however, for those
  of us who cannot stomach this rather radical
  notion of extended simples, there are few options
  but to accept temporal parts.

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References

• Hawley, Katharine, 2004, Temporal Parts,
  Stanford Encyclopedia Of Philosophy
• Heller, Mark, 1984, "Temporal Parts of
  Four-Dimensional Objects", Philosophical Studies,
  46 323-334.
• Lewis, D. K., 1991, Parts of Classes, Oxford
  Blackwell.
• Merricks, Trenton, 1994, "Endurance and
  Indiscernibility", Journal of Philosophy, 91
  165-84.
• Needham P., 1981, Temporal Intervals and
  Temporal Order, Logique et Analyse 24 4964.
• Simons, Peter, 1987, Parts A Study in Ontology,
  Oxford Clarendon.
• Simons, Peter, 2004, Extended Simples A Third
  Way Between Atoms and Gunk, The Monist 87
  371-84
• van Benthem, J, 1983, The Logic of Time,
  Dordrecht Reidel (1991)
• Whitehead A.N., 1929, Process and Reality, New
  York Macmillan