A neoingardenian ontology of situations

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A neo-ingardenian ontology of situations

• Pawel Garbacz
• Catholic University of Lublin
• Poland

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A neo-ingardenian ontology of situations

• Primitive notions
• Axioms
• Formalism
• Comparisons

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Primitive notions

• Object
• Situation
• (state of affairs)
• Parthood
• Occurence
• Representation

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Primitive notions

• LANGUAGE
• REALITY

George W. Bush is a wise president of the USA.
George W. Bush is a wise president of the USA.
George W. Bush
George W. Bush is a president of the USA.
George W. Bush is wise.
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Primitive notions

• sentence
• REPRESENTS
• situation
• OBTAINS IN (IS PART OF)
• situation

object OCCURS IN
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Primitive notions Situations

• Ontology
• A situation is an entity which unfolds
• some object.
• A situation is an entity which reveals
• the ontic structure of an object which
• occurs in it.

• Semantics
• A situation with respect to a language
• L is an ontic representation of an
• atomic sentence ? from L.

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Primitive notions Situations

• To nominalise situations or not to nominalise?
• Nominalise, but be careful!

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Primitive notions Situations
George W. Bush is a wise president of the USA.

• LANGUAGE
• INTENTIONAL
• WORLD
• REALITY

That George W. Bush is a wise president of the
USA.
That George W. Bush is a wise president of the
USA.
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Primitive notions Situations

• INTENTIONAL SITUATIONS
• They are heteronomous.
• Every sentence creates an intentional situation.
• There are no ontological regularities among
  intentional situations.

• REAL SITUATIONS
• They are autonomous.
• Some sentences do not represent any real
  situation.
• There are some ontological regularities among
  real situations.

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Axioms

• ASSERTED PRINCIPLES
• REJECTED PRINCIPLES
• ??? PRINCIPLES

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AxiomsAsserted

• (2.1) Every (real) situation is possible.
• (2.2) If a sentence ? represents a situation x
  and a situation y, then xy.
• (2.8) If a situation x obtains in a situation y,
  then every object occurring in x occurs in y as
  well.
• (2.10) If X is the set of all situations in which
  only o1, o2, , on occur, then there is a
  situation which is the least upper bound of X
  with respect to the relation of obtain in.

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AxiomsRejected

• (2.3) If a sentence ? represents the situation
  x, then there is a situation represented by the
  sentence It is not the case that ?.

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Axioms???

• (2.7?) If a sentence ? represents a situation x
  and a sentence ? represents a
• situation y, then there is a situation
  represented by the sentence ? and ?.

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AxiomsWhy are negations not (genuine)
representational sentences?

George W. Bush is not Polish.
George W. Bush is American.
George W. Bush is German.
George W. Bush is Russian.
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AxiomsAre conjunctions representational
sentences?

• A possible world is a maximal ideal of situations
  in the set of all situations.
• A set X of situations is an ideal of situations
  iff
• (i) every part of every situation from X belongs
  to X,
• (ii) for every pair x, y of situations from X,
  the join of x and y belongs to X.

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AxiomsWhat is relation?

• George Bush George W. Bush
• Geroge Bush is 70 years old. George W. Bush is
  50 years old.
• George Bush is 6 feet tall. George W. Bush is
  7 feet tall.
• George Bush knows English, George W. Bush
  knows English.
• German, and Russian.
• ... ...
• ... ...

The relation between George Bush and George W.
Bush
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AxiomsWhat is relation?

• (2.10) If X is the set of all situations in which
  only o1, o2, , on occur, then there is a
  situation which is the least upper bound of X
  with respect to the relation of obtain in.

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Formalism

• ltS, O, ?, Ogt
• (i) S?O?,
• (ii) ??S?S,
• (iii) lt ?\,
• (iv) O S ? ?(O).

Set of objects
Set of situations
Situation parthood
Object(s) in situation
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FormalismAuxiliary definitions

• X?Y ? ?x?X ?y?Y x?y.
• At(S) x?S ??y?S yltx.
• S(o) x?S o?O(x).
• IS(o1, o2, , on, W) x?W O(x)o1, o2, ,
  on.

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Formalism ltS, O, ?, Ogt

• (C1) The relation ? is a partial order.
• (C2) W??,
• where W is the set of all maximal ideals in
  ltS, ?gt
• (C3) S?W.
• (C4) If x?y, then O(x)?O(y).
• (C5) ?x?S O(x)??.
• (C6) ?o?O S(o)??.
• (C7) If IS(o1,, on, W)??, then ?y?W ysup?
  IS(o1,, on, W).

• ?
• ? 2.1 and 2.7
• 2.1
• 2.8
• definition of situation
• definition of situation
• 2.10

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FormalismHow expressive is it?

• structure of object in world
• range of object in world
• intrinsic structure of object in world
• intrinsic range of object in world
• existence of object
• essence of object

• ltS(o)?W, ?(S(o) ?W) gt
• sup S(o)?W
• ltIS(o, W), ?IS(o, W)gt
• sup IS(o, W)
• W(o) W?W S(o)?W??.
• x?Ess(o) ? ?W?W(o) x?IS(o, W).

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FormalismDependence

• An object o1 strongly depends on an object o2 in
  a possible world W iff
• o1 exists in W and S(o1)?W?S(o2)?W.
• An object o1 partially depends on an object o2 in
  a possible world W iff
• o1 exists in W and (S(o1)?W)?(S(o2)?W)??.
• An object o1 weakly depends on an object o2 in a
  possible world W iff
• o1 exists in W and S(o1)?W?S(o2)?W.
• An object o1 strongly (partially, weakly) depends
  on an object o2 iff o1 strongly
• (partially, weakly) depends on o2 in every
  W?W(o1).
• An object is strongly (weakly) independent in O
  iff it does not weakly (strongly)
• depend on any other object from O.

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FormalismExtensionalist NIOSO

• (C9) If x?At(S) or y?At(S), then xy ? ?z (zltx ?
  zlty).

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FormalismLeibnizian NIOSO

• (C9) If ?W?W (S(o1)?WS(o2)?W), then o1o2.
• (C10) If S(o1)?WS(o2)?W??, then o1o2.

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ComparisonsRepresenting and truthmaking

• REPRESENTATION
• One sentence represents at most one
• situation.
• Tautologies do represent.
• Existential generalisations do not represent.

• TRUTH MAKING
• One sentence is made true by more than one truth
  maker.
• There are no truth-makers for tautologies.
• (Some) existential generalisations have
  truth-makers.

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ComparisonsWhy do existential generalisations
not represent?

John runs quickly.
Someone runs quickly.
Someone does something quickly.
Someone does something somehow.
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ComparisonsNIOS and mereology

• SSP
• (i) that John runs quickly
• (ii) that John runs
• Not iii.
• There is no situation iii such that
• iii?i
• and
• iii and ii do not overlap.

• General Axiom of Sum