A Divine Ontology

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A Divine Ontology

• by Robert Michael

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Axioms

• The Bible is truth.
• Abstract objects exist.

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Abstract and Concrete Objects

• Concrete Objects
• Rocks
• Trees
• Buildings
• Chairs

• Abstract Objects
• Blue
• Addition
• 13
• 13 is prime

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Definitions

• The distinction between necessary and contingent
  truth is as easy to recognize as it is difficult
  to explain to the skeptics satisfaction.
• - Alvin Plantinga

• The Way of Example
• The Way of Negation
• The Causal Inefficacy Criterion
• The Non-Spatiality Criterion

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Causal Inefficacy Criterion
Definition - An abstract object is any thing
which does not have causal power.

• Example Rocks can break things, red does
  nothing.

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Causal Inefficacy Criterion

• Problems
• What does it mean to take part in causal order?

Example Rocks vs. The Pythagorean Theorem
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Non-Spatiality Criterion

• Definition - An abstract object is any thing
  which does not occupy space or time.

• Example Consider the difference
• between the letter A and this
• particular manifestation of the
• letter A.

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Non-Spatiality Criterion

• Problems
• Due to Heisenbergs Uncertainty Principle an
  electron may be considered an abstract objects.
• Impure sets may be regarded as concrete objects.

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PRPs As AOs

• Property A characteristic of an object.
• Relation A property which holds for two or more
  objects.
• Proposition An expression with an associated
  truth value.

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Sets as Abstract Objects

• Properties as sets
• The Cantorian view of number regards cardinality
  of sets as the definition of integers.

• The number 3 can be thought of as a set
  containing exactly 3 members.

• Thus sets enter our ontology as numbers.

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The Existence of Sets

• Sets as a mental activity of collection.

• Sets as a collection activity on Gods part.

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The Problems With Sets

• Russells Paradox
• Consider the set of all sets which do not contain
  themselves. Is this set a member of itself?
• NO? Then it must contain itself because of the
  definition of the set.
• YES? Then it cannot contain itself because of the
  definition of the set.

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The Problems With Sets

• Example
• Consider the barber who shaves men if and only if
  they do not shave themselves
• Does the barber shave himself?

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The Problems With Sets

• Does this place restrictions on God?
• If sets are a collecting activity on Gods part,
  and the set of all sets which do not contain
  themselves cannot be created, then is God still
  omnipotent?

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Solutions

• 1) Our knowledge is limited.
• I will destroy the wisdom of the wise, and will
  bring into nothing the understanding of the
  prudent (1 Cor. 119)
• Can a mortal ask questions which God finds
  unanswerable? Quite easily, I should think. All
  nonsense questions are unanswerable. How many
  hours are there in a mile? Is yellow square or
  round? Probably half of the questions we ask
  half our great theological and metaphysical
  problems are like that
• - C. S. Lewis

Accepting that God is omnipotent even in the face
of this paradox is only as trouble as accepting
His triune nature or the fact that a holy God can
love sinful creations.
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Solutions

• 2) Some of the limits which we think are placed
  upon God are not so much limits as they are
  simply not in His divine nature.
• We do not consider God to be feeble simply
  because He cannot sin. Sin is defined to be that
  which is not Holy and God is the definition of
  Holiness.
• In the same way we cannot consider a perfectly
  rational God to be feeble simply because He, in
  His very nature, will not conceive of irrational
  or nonsensical thoughts.

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Necessity vs. Contingency

• Definitions
• Necessary An object is necessary if it exists
  and could not have failed to exist.
• Contingent An object is contingent if it exists
  but could have failed to exist.
• Contingent Upon An object is contingent upon
  something else if it depends upon something
  outside of itself for its existence.

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Necessity vs. Contingency

• Are abstract objects necessary or contingent?
  Furthermore, are abstract objects created by God?
• Howell Bradley contend that God either does or
  does not create abstract objects and that there
  are problems for both positions.

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God Does Not Create AOs

• The Sovereignty Problem
• If abstract objects are uncreated, then God is
  just one more thing in a sea of uncreated objects.

• The Uniqueness Problem
• If abstract objects are uncreated, then Gods
  aseity is no longer unique.

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God Does Not Create AOs

• The Heresy Problem
• For by Him all things were created things in
  heaven and on earth, visible and invisible,
  whether thrones or powers or rulers or
  authorities all things were created by Him and
  for Him - Col. 116 (emphasis added)
• According to the Non-Spatiality Criterion,
  abstract objects are things that are
  invisible, so according to Col. 116, God
  created them.

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God Does Create AOs

• The Coherence Problem
• If abstract objects have always existed, and
  could not have even failed to exist, it does not
  make sense for them to have been created.

• The Freedom Problem
• If abstract objects are necessary, then God could
  not have helped but create them. Thus, God does
  not have free will.

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Solutions

• Suppose that abstract objects are not necessary.
• This obviously solves both the freedom and
  coherence problem.
• Refine the meaning of necessity.
• This allows abstract objects to be necessary, but
  will help to solve the freedom problem.
• Rethink Gods eternal nature.
• Understanding that God may exist eternally in a
  different manner than do abstract objects will
  help make His creation of them more coherent.

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Solutions

• Why do we even regard AOs as necessary?
• Though they may feel necessary in our world and
  reality, our world and reality are not necessary.

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Solutions Freedom

• Redefine necessity
• Perhaps AO are necessary because God created them
  to be so, and not that He created them because
  they are necessary.
• Example Gods holiness

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Solutions - Coherence

• Necessity still feels like a problem
• No matter what definition we use, abstract
  objects still feel like a problem.

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Solutions - Coherence

• What does it mean to exist eternally?
• God existed before He created our order

• What does creation mean?
• We tend to think of creation as having a place in
  time, but God when did God create time?

• Creation as continual Sustenance
• The Son is the radiance of Gods glory and the
  exact representation of His being, sustaining all
  things by His powerful word.
• - Hebrews 13 (emphasis added)

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A Proper Cornerstone

• Every discipline must be framed by a theological
  perspective otherwise these disciplines will
  define a zone apart from God, grounded literally
  in nothing.
• - John Millbank, Radical orthodoxy

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Works Cited

• Howell, Russell and James Bradley, eds. 2001.
  Mathematics in a Postmodern Age A Christian
  Perspective, Grand Rapids, MI Wm. B. Eerdmans
  Publishing Co.
• Lewis, C.S. 1961. A Grief Observed. New York, NY
  HarperCollins Publishing, Inc.
• Plantinga, Alvin. 1974. The Nature of Necessity.
  Oxford, UK Oxford University Press
• Milbank, John, Catherine Pickstock and Graham
  Ward, eds. 1999. Radical Orthodoxy, London,
  Routledge Press.
• Abstract Objects. 2001. Stanford Encyclopedia
  of Philosophy. http//plato.stanford.edu/entries/a
  bstract-objects/