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Ontology

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					Ontology
                  Ontology
   Ontology is the study of existence.
   Epistemology: Necessarily, for any person
    S and proposition p, S knows that p if and
    only if (iff)                .
   Ethics: Necessarily, for any act-token A, A
    is right iff            .
   Ontology: Necessarily, for any x, x exists
    iff            .
                          Ethics
   Right                          Wrong
       Ryan’s teaching class          Ryan’s failing a
       Hud’s taking a nap              student for no good
       Ned’s eating a snack            reason
                                       Hud’s skipping the
                                        department meeting
                                        without an excuse
                                       Ned’s stealing snacks
                                        out of greed
                         Ontology
   Does Exist                  Does Not Exist
       Mars                        Vulcan
       NYC                         Atlantis
       Pedro Martinez              Sidd Finch
       Oxygen                      Phlogiston
       Secretariat                 Pegasus
                   Ontology

   For any x, x exists iff it is physical.
   For any x, x exists iff it has causal powers.
   For any x, x exists iff               .
   There are no negative cases!
                          Ethics
   Right                          Wrong
       Ryan’s teaching class          Ryan’s failing a
       Hud’s taking a nap              student for no good
       Ned’s eating a snack            reason
                                       Hud’s skipping the
                                        department meeting
                                        without an excuse
                                       Ned’s stealing snacks
                                        out of greed
                         Ontology
   Does Exist                  Does Not Exist
       Mars                        Vulcan
       NYC                         Atlantis
       Pedro Martinez              Sidd Finch
       Oxygen                      Phlogiston
       Secretariat                 Pegasus
                  Ontology

   There are some things that don’t exist.
   There are some things that          iff
    there exists some things that           .
   There exists some things that don’t exist.
   Some things that exist don’t exist.
                 Summary

   Ontology is not an attempt to analyze
    existence.
   Ontology is an attempt to say what kinds
    of things exist.
                  Ontology

   Things that exist
       Earth
       Mars
       …
       Spot
       Fido
       …
                      Ontology

   Things that exist
       Physical objects
                      Ontology

   Things that exist
       Physical objects
       Space ?
       Species ?
       Numbers ?
Quine on Ontological Commitment

   W.V.O. Quine (1908-2000)
   The Quinean Approach to Ontology:
       Begin with a true sentence of natural language.
       Translate that sentence into the language of first-
        order logic.
       The ontological commitment of the original sentence
        are whatever has to exist for the translations to be
        true.
   Example: Some dogs chase cats.
                Three Examples

   Some numbers are even.
       (âx) (Nx & Ex)
   Some species are endangered.
       (âx) (Sx & Ex)
   There is a region of space separating you
    and I.
       (âx) (Rx & Sxab & (†y) (Ry ¨ (y=x)))
                      Ontology

   Things that exist
       Physical objects
       Space ?
       Species ?
       Numbers ?
                      Ontology

   Things that exist
       Physical objects
       Space û
       Species û
       Numbers û
                     Problems

   The average American family has 1.8
    children.
       (âx) (Ax & Cx & (†y) (Ay ¨ (y=x)))
   The winged-horse does not exist.
       (âx) (Wx & ~Ex & (†y) (Wy ¨ (y=x)))
                     Ontology

   Things that exist
       Physical objects
       Space
       Species
       Numbers
       The average American family !
       The winged-horse !
                Paraphrase
   The average American family has 1.8
    children.
   The total number of children in American
    families divided by the total number of
    American families equals 1.8.
   The winged-horse does not exist.
   It’s not the case that there is something
    that is a winged-horse.
                   Paraphrase
   There is a region of space separating you
    and I.
       (âx) (Rx & Sxab & (†y) (Ry ¨ (y=x)))
   You and I are spatially separated.
       Sab
   Some numbers are even.
       (âx) (Nx & Ex)
   ???

				
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