True Stories

1. True Stories Barry Smith (IFOMIS/Buffalo) Jonathan Simon (NYU)

2. What is truth? • for contingent judgments • (empirical judgments, judgments not true as a matter of necessity, not judgments about numbers or other abstracta) http://ontology.buffalo.edu

3. What is truth? • First approximation: • Truth is correspondence to reality • Strategy thus far: use analysis of the idea of truthmaking to carve out a rigorous notion of correspondence as a relation between truthmakers and truthmakers http://ontology.buffalo.edu

4. Beyond tinkering • The proponents of truthmaker-theory have been running about, tinkering with definitions and counterexamples, like a bunch of epistemologists. • A methodological self-examination is in order: which question are we trying to answer when we try to figure out what the truthmakers for truths are? http://ontology.buffalo.edu

5. The important task • is not conceptual analysis of the notion of truthmaker. Who cares? It’s a term of art. • Rather its about carving a realist theory of truth that goes beyond the mere metaphor of ‘correspondence’ http://ontology.buffalo.edu

6. Truthmaker arguments cut no ice • any particular account of truthmaking rests on tenets denied by its enemies; • thus no argument for a certain ontological posit, on the basis of a truthmaker theory, could withstand a modus tollens countermove by someone skepticial with respect to the relevant ontological posit http://ontology.buffalo.edu

7. Factualism, Meinongianism, etc. • If one’s ontological theory entails that there are truthmakers even for negative truths about the non-existence of unicorns, then so be it. http://ontology.buffalo.edu

8. But here • we shall focus our energies on accounts appealing only to types of entities for which we have independent reasons to believe that they exist • (recognizing that there are still contestable cases e.g. involving tropes, universals, ...) http://ontology.buffalo.edu

9. Thus no facts, states of affairs, ... • It is unclear how states of affairs can help us to understand instantiation relations. Why isn’t there more mystery, rather than less, when we must explain such relations by means of an extra, gerundive entity? http://ontology.buffalo.edu

10. In particular no negative facts • Why are negative facts so nasty: • Mary is red – all the parts exist, we can see how this fact is carved out within reality • Mary is not green – here not all the parts exist • Mary is not a cardinal number • Mary is not a golden mountain • Mary is not Cicero http://ontology.buffalo.edu

11. Against Deflationism • These pessimistic remarks need not lead to deflationism, the view that the meaning of the truth predicate is exhausted by the disquotational schema T. http://ontology.buffalo.edu

12. Against Deflationism • There may be several true biconditionals for any given truthbearer, some more contentful than others. • Tarskians are interested in true biconditionals of the form • S is true iff p http://ontology.buffalo.edu

13. But there are also ontologically contentful truth conditions of the form:p iff x exists http://ontology.buffalo.edu

14. Armstrong’s rejoinder • Rejecting truthmaker maximalism implies the need for two theories of truth • Since truthmaker maximalism is false we need at least two theories of truth in any case http://ontology.buffalo.edu

15. Aristotle end of methodological preamble http://ontology.buffalo.edu

16. How to understand the relation • between Amundsen’s flight and the truth that Amundsen flew to the North Pole • First answer: in terms of necessitation • x necessitates p =: x exists and (that x exists entails that p) http://ontology.buffalo.edu

17. xNp =: E!x & (E!xÞp) • John is a necessitator for: ‘John exists’. • In every possible world in which John exists, ‘John exists’ is true http://ontology.buffalo.edu

18. Necessitation • This neurological event in John’s head necessitates ‘John has a headache’ • (if this event, exists then John has a headache) • Accidents do not migrate • Necessity here includes physical or material necessity http://ontology.buffalo.edu

19. Necessitation is a bridge from Reality to Judgment • If reality is such and such a way, • then: necessarily, this judgment is true http://ontology.buffalo.edu

20. Two difficulties for the identification of truthmaking with necessitation • 1. Restall’s refrigerator • If truthmakers are just necessitators, • then every contingently existing entity is a truthmaker for every necessary truth • Restall’s refrigerator, in particular, is a truthmaker for Goldbach’s conjecture. http://ontology.buffalo.edu

21. 2. John’s funeral • Entailment is transitive. • Thus if x is a necessitator for some contingent truth p, and if p entails q, • then x is a necessitator also for q. • John’s funeral, in particular, is a truthmaker for ‘John is dead’ • Breaks no truthmaking backward in time constraint http://ontology.buffalo.edu

22. There are other malignant necessitators • God wills p • God’s willing act thereby necessitates p • (For Malebranche, all necessitation is of this sort.) • But God’s act of willing is typically not a truthmaker for p http://ontology.buffalo.edu

23. John’s funeral and God’s Necessitating Will break the locality constraint • A truthmaker is a necessitator that belongs to the ontological orbit of the objects referred to in the judgment No truthmaking-at-a-distance http://ontology.buffalo.edu

24. Solution • to block the transitivity of entailment in • xNp =: E!x & (E!xÞp) • impose some factor of relevancebetween x and p http://ontology.buffalo.edu

25. Portions of reality necessitate judgments • Blanche is shaking hands with Mary http://ontology.buffalo.edu

26. Judgments project on portions of reality • Blanche is shaking hands with Mary http://ontology.buffalo.edu

27. Our goal: understanding correspondence between reality and judgment • Blanche is shaking hands with Mary http://ontology.buffalo.edu

28. Projection • Think of a judgment as a searchlight • Everything that falls within the beam of the searchlight is relevant to the truth of the judgment http://ontology.buffalo.edu

29. A Portion of Reality http://ontology.buffalo.edu

30. Cartographic Hooks http://ontology.buffalo.edu

31. Die Projektion • 3.12 ... der Satz ist das Satzzeichen in seiner projektiven Beziehung zur Welt. • 3.13 Zum Satz gehört alles, was zur Projektion gehört; aber nicht das Projizierte. http://ontology.buffalo.edu

32. A Map 3.13 Zum Satz gehört alles, was zur Projektion gehört; aber nicht das Projizierte. http://ontology.buffalo.edu

33. Satz und Sachverhalt language a r b names simple objects world http://ontology.buffalo.edu

34. projection Satz und Sachverhalt language a r b world http://ontology.buffalo.edu

35. Projection • a truthmaker for a given judgment should be part of that portion of reality upon which the judgment is projected • (roughly: it should fall within the mereological fusion of all the objects, qualities and processes to which reference is made in the judgment) http://ontology.buffalo.edu

36. The Theory of Projection as Dual of Necessitation http://ontology.buffalo.edu

37. Projection: A Bridge from Judgment to Reality • DP xPp := p Ù (p Þ E!x) • xPp := x is part of that on which p projects • All true judgments p of the form ‘x exists’ will satisfy xPp. http://ontology.buffalo.edu

38. (John’s death) is part of the projection of (‘John’s funeral occurred’). • But not • (John’s death) necessitates (‘John’s funeral occurred’). http://ontology.buffalo.edu

39. (John’s funeral) necessitates (‘John’s death occurred’). • But not: • (John’s funeral) is part of the projection of (‘John’s death occurred’). • Projection can be used to block malignant necessitators http://ontology.buffalo.edu

40. How put projection and necessitation together to define truthmaking? • x makes p true =: xPp and xNp • xTMp =: p (E!x  p) http://ontology.buffalo.edu

41. x TM p =: p  (E!x  p) • works for existential judgments like ‘David exists’: • David is a necessitator for my judgment and is projected by my judgment http://ontology.buffalo.edu

42. This definition blocks malignant necessitators • Restall’s refrigerator is not even a candidate truthmaker for Goldbach’s conjecture. • God’s Necessitating Will is not part of the total projection of ‘John is kissing Mary’. • John’s funeral is not a truthmaker for (though it is a necessitator of) ‘John is dead’. http://ontology.buffalo.edu

43. E!(John’s funeral)  E!(John’s death) http://ontology.buffalo.edu

44. If, against the Humeans, • there can be dependence relations connecting disjoint individuals, then • If x makes p true and E!x  E!y, then y makes q true • will yield counterexamples to the locality constraint http://ontology.buffalo.edu

45. If x makes p true and p  q, then x makes q true • This account of truthmaking partitions the world into equivalence classes of co-entailing propositions http://ontology.buffalo.edu

46. If x makes ptrue and E!x  E!y, then y makes p true • The entities in reality are partitioned into equivalence classes on the basis of the mutual dependence between x and y • The ontologically basic judgments are partitioned into equivalence classes in exactly corresponding fashion. http://ontology.buffalo.edu

47. “Truthmaker Realism” (AJP, 1999) • sought to exclude these problem cases by modifying the formula: • x TM p =: p  (E!x  p) • Here we accept the problem cases and explore what happens if we consider biconditionals of the sort • p iff E!x http://ontology.buffalo.edu

48. Logically basic judgments • F(a) • R(a,b) • S(a,b,c) • ... • a is colourless • colourless(a) • coloured(a) http://ontology.buffalo.edu

49. Ontologically basic judgments • = judgments whose sole demand on reality is that some individual exists: • ‘Superman is real’, ‘I exist’, ‘This redness exists’ • but also: ‘Socrates is mortal’ (because Socrates is necessarily mortal – it suffices, for the given judgment to be true, that Socrates exists, and it suffices, for Socrates to exist, that the given judgment be true) http://ontology.buffalo.edu

50. Definition • p is ontologically basic = it would have a truthmaker, were it true: • OB(p) := p(px(E!(x) p)) http://ontology.buffalo.edu