1. Ontology

2. Ontology Ontology is the study of existence. Ontology is the study of existence. Epistemology: Necessarily, for any person S and proposition p, S knows that p if and only if (iff). 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. Ethics: Necessarily, for any act-token A, A is right iff. Ontology: Necessarily, for any x, x exists iff. Ontology: Necessarily, for any x, x exists iff.

3. Ethics Right Right Ryan’s teaching class Ryan’s teaching class Hud’s taking a nap Hud’s taking a nap Ned’s eating a snack Ned’s eating a snack Wrong Wrong Ryan’s failing a student for no good reason Hud’s skipping the department meeting without an excuse Ned’s stealing snacks out of greed

4. Ontology Does Exist Does Exist Mars Mars NYC NYC Pedro Martinez Pedro Martinez Oxygen Oxygen Secretariat Secretariat Does Not Exist Does Not Exist Vulcan Atlantis Sidd Finch Phlogiston Pegasus

5. Ontology For any x, x exists iff it is physical. 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 it has causal powers. For any x, x exists iff. For any x, x exists iff. There are no negative cases! There are no negative cases!

6. Ethics Right Right Ryan’s teaching class Ryan’s teaching class Hud’s taking a nap Hud’s taking a nap Ned’s eating a snack Ned’s eating a snack Wrong Wrong Ryan’s failing a student for no good reason Hud’s skipping the department meeting without an excuse Ned’s stealing snacks out of greed

7. Ontology Does Exist Does Exist Mars Mars NYC NYC Pedro Martinez Pedro Martinez Oxygen Oxygen Secretariat Secretariat Does Not Exist Does Not Exist Vulcan Atlantis Sidd Finch Phlogiston Pegasus

8. Ontology There are some things that don’t exist. There are some things that don’t exist. There are some things that iff there exists some things that. There are some things that iff there exists some things that. There exists some things that don’t exist. There exists some things that don’t exist. Some things that exist don’t exist. Some things that exist don’t exist.

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

10. Ontology Things that exist Things that exist Earth Earth Mars Mars … Spot Spot Fido Fido …

11. Ontology Things that exist Things that exist Physical objects Physical objects

12. Ontology Things that exist Things that exist Physical objects Physical objects Space ? Space ? Species ? Species ? Numbers ? Numbers ?

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

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

15. Ontology Things that exist Things that exist Physical objects Physical objects Space ? Space ? Species ? Species ? Numbers ? Numbers ?

16. Ontology Things that exist Things that exist Physical objects Physical objects Space û Space û Species û Species û Numbers û Numbers û

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

18. Ontology Things that exist Things that exist Physical objects Physical objects Space Space Species Species Numbers Numbers The average American family ! The average American family ! The winged-horse ! The winged-horse !

19. Paraphrase The average American family has 1.8 children. 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 total number of children in American families divided by the total number of American families equals 1.8. The winged-horse does not exist. The winged-horse does not exist. It’s not the case that there is something that is a winged-horse. It’s not the case that there is something that is a winged-horse.

20. Paraphrase There is a region of space separating you and I. There is a region of space separating you and I. ( â x) (Rx & Sxab & ( † y) (Ry ¨ (y=x))) ( â x) (Rx & Sxab & ( † y) (Ry ¨ (y=x))) You and I are spatially separated. You and I are spatially separated. Sab Sab Some numbers are even. Some numbers are even. ( â x) (Nx & Ex) ( â x) (Nx & Ex) ??? ???