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

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

2 2 What is truth? for contingent judgments (empirical judgments, judgments not true as a matter of necessity, not judgments about numbers or other abstracta)

3 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

4 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?

5 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’

6 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

7 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.

8 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,...)

9 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?

10 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

11 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.

12 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

13 13 But there are also ontologically contentful truth conditions of the form: p iff x exists

14 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

15 15 Aristotle end of methodological preamble

16 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)

17 17 xNp =: E!x & (E!x  p) John is a necessitator for: ‘ John exists ’. In every possible world in which John exists, ‘ John exists ’ is true

18 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

19 19 Necessitation is a bridge from Reality to Judgment If reality is such and such a way, then: necessarily, this judgment is true

20 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.

21 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

22 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

23 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

24 24 Solution to block the transitivity of entailment in xNp =: E!x & (E!x  p) impose some factor of relevance between x and p

25 25 Portions of reality necessitate judgments Blanche is shaking hands with Mary

26 26 Judgments project on portions of reality Blanche is shaking hands with Mary

27 27 Our goal: understanding correspondence between reality and judgment Blanche is shaking hands with Mary

28 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

29 29 A Portion of Reality

30 30 Cartographic Hooks

31 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.

32 32 A Map 3.13 Zum Satz gehört alles, was zur Projektion gehört; aber nicht das Projizierte.

33 33 Satz und Sachverhalt arb language world names simple objects

34 34 Satz und Sachverhalt arb language world projection

35 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)

36 36 The Theory of Projection as Dual of Necessitation

37 37 Projection: A Bridge from Judgment to Reality DPxPp := p  (p  E!x) xPp := x is part of that on which p projects All true judgments p of the form ‘ x exists ’ will satisfy xPp.

38 38 (John ’ s death) is part of the projection of ( ‘ John ’ s funeral occurred ’ ). But not (John ’ s death) necessitates ( ‘ John ’ s funeral occurred ’ ).

39 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

40 40 How put projection and necessitation together to define truthmaking? x makes p true =: xPp and xNp xTMp =: p  (E!x  p)

41 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

42 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 ’.

43 43 E!(John’s funeral)  E!(John’s death)

44 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

45 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

46 46 If x makes p true 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.

47 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

48 48 Logically basic judgments F(a) R(a,b) S(a,b,c)... a is colourless colourless(a)  coloured(a)

49 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)

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

51 51 An ontologically basic judgment is true iff it is made true (™) aTMp := p  (E!(a)  p) or, if you like: a makes p true on our world iff: 1. p is true on our world and 2. p is true on all and only those worlds on which a exists.

52 52 Truthmaker maximalism holds, by definition, only for ontologically basic judgments Armstrong: All judgments are ontologically basic

53 53 Truthmaking, as defined for ontologically basic judgments, a starting point for an ontologically robust theory of truth conditions. Ontologically basic judgments will play a role similar to that of basis vectors in a vector space, with other judgments built up out of these

54 54 Note: a natural language judgment is ontologically basic independently of its logical regimentation.

55 55 Relation between ( OB ) and (™) every judgment with a truthmaker is ontologically basic, and every judgment that is ontologically basic and true has a truthmaker. No necessarily false judgment can be ontological basic

56 56 Truthmaker Maximalism Every true judgment is made true by something in reality Truthmaker Realism Every true judgment is associated with some necessary and sufficient ontologically characterized condition that is satisfied by reality

57 57 True stories Such an ontologically characterized condition we call a true story. A judgment has a true story only if it is true (otherwise we speak of what its true story would be) The true story for an ontologically basic judgment is: a truthmaker for this truth exists.

58 58 There is a true story for every truth For every truth there is a true story that could be told given enough knowledge and patience True stories are not artefacts of language or cognition – they do not need to be told They are out there in the world independently of how we speak about it (Compare the way in which a judgment has its place in logical space independently of our being aware of this fact)

59 59

60 60 The Ontologically Basic ‘John exists’ ‘Socrates is mortal’ ‘Socrates is not a cardinal number’.

61 61 ‘Socrates is not a handshake’ Note that there are different judgments which may be expressed by the same English sentence (1)  !x (Socrates(x)  ~Handshake(x)) (2) ~  !x (Socrates(x)  Handshake(x)) (3) ~Handshake(Socrates) (1) are (3) ontologically basic

62 62 (1)  !x (Socrates(x)  ~Handshake(x)) is true at a world iff Socrates exists there and false otherwise. (2) ~  !x (Socrates(x)  Handshake(x)) is true at every world. (3) ~Handshake(Socrates) is true at all worlds where Socrates exists, and not evaluable at other worlds – it functions like an indexical assertion (‘That elephant is hungry’) – an utterance which does not reach the starting gate for having meaning when there is no elephant to be designated

63 63 A false ontologically basic judgment is a judgment which is true necessarily if and only if something exists which does not actually exist, but which could exist. To avoid quantifying over non-actual possibilia we can conceive the matter in terms of rigidly designating descriptions which happen not to designate

64 64 ‘D(x)’ is a rigidly designating description :=   x (D(x)   (  y(D(y)  x = y))) Example: ostensive ‘that’: ‘being a person composed of that sperm and egg’ (has no referent if the relevant sperm and egg do not combine)

65 65 Negations of Ontologically Basic Judgments Assume that Patch is a dog. Then, ‘Patch is not a dog’ is necessarily false. If on the other hand, Patch is a cat, then ‘Patch is not a dog’ will be ontologically basic. Remember: No judgment is both ontologically basic and necessarily false.

66 66 ‘Patch is not a dog’ Here a single sentence type is divided between two families of token judgments Again: logical form is not a guide to ontological form

67 67 ‘That is a kiss of Mary by John’, said while pointing, is ontologically basic. It indexically refers to a specific event, call it k, an instance of the universal kissing (baiser) existentially dependent on both John and Mary. Here ‘that’ functions rigidly, like a proper name. The truth of the judgment implies the existence of k, just as the existence of k implies the truth of the judgment.

68 68 A judgment ‘John is kissing Mary’ can support a similar analysis as ontologically basic. Not however when said while musing speculatively from afar E!(k) would entail its truth, but this truth does not entail that k exists Many ordinary attributions once standardly regimented as logically atomic are ontologically complex. (They host an implicit existential quantifier.)

69 69 ‘John is not kissing Mary’ is not ontologically basic. The worlds on which ‘John is not kissing Mary’ is true are: all and only the worlds on which there exists no event which is a present-moment kissing of Mary by John.

70 70 ‘John is not kissing Mary’ There is no object whose existence is precisely what a world needs in order for such a negative judgment to be true – such a judgment is a matter of there not existing anything satisfying a certain description

71 71 ‘There is a rabbit’ is true at a world if and only if there is some rabbit there. But there is no particular rabbit whose existence is necessary and sufficient for the truth of the judgment. Thus it is not the case that Harvey, your favorite pet rabbit, makes it true that there is a rabbit.

72 72 ‘All ravens are black’ is true at a world if and only if every raven there is black. Which of all possibly existing ravens must be black therefore changes from world to world. Thus, we see again that there is no particular entity (no specific congregation of ravens) whose existence is necessary and sufficient for the truth of the given judgment.

73 73 Compound ontologically non-basic judgments If p is the negation of q, and q is ontologically basic, then the true story for p is the condition that no truthmaker exists for q. If p is the disjunction of q and r, and q and r are both ontologically basic, then the true story for p is the condition that either a truthmaker for q exists, or a truthmaker for r exists. Etc.

74 74 In general, however, judgments are not logical compounds of ontologically basic judgments No algorithm to decide whether a judgment is ontologically basic. Tarskians in the same boat – their recursive accounts of truth in terms of satisfaction only work for regimented languages, and then there is no recipe for moving from a natural- language sentence to its regimentation

75 75 Some Cases

76 76 Positive singular existentials ‘John exists’, ‘Ba’al exists’ Judgments in this group are true if and only if the entity to which existence is attributed does in fact exist.

77 77 The true story of ‘John exists’ is: ‘John exists’ has a truthmaker.

78 78 Negative singular existentials ‘Pegasus does not exist’ properly to be analyzed as featuring disguised rigid definite descriptions (satisfied by the same entity in every possible world where they are satisfied)

79 79 The true story of ‘Pegasus does not exist’ is: ‘Pegasus exists’ does not have a truthmaker.

80 80 Predications of necessary intrinsics and necessary internal relations ‘John is a man’, ‘This experience is mine’, ‘That event is a kissing’ ‘Patch is not a man’, All of these cases (when true) are ontologically basic. (If one is a man, then one is necessarily a man; an experience of mine is necessarily an experience of mine; a kissing event is necessarily a kissing event – that kiss could not have been a football game or an armadillo; Patch is necessarily not a man)

81 81 ‘George and Jeb are brothers’ This is an assertion of a necessary internal relation, namely that of brotherhood. Since origins are essential, George and Jeb are necessarily brothers (provided that both of them exist). Judgments of this category are then analogous to ontologically basic judgments but have plural truthmakers, all of which must simultaneously exist on a world when the judgment is true.

82 82 The true story for ‘George and Jeb are brothers’ is: George and Jeb both exist.

83 83 Standard predications in the category of accident Examples: ‘John is hungry’, ‘John is running’. The first case involves the existence of a quality of being hungry, the second of a process of running, both existentially dependent on a certain substantial bearer The judgments are in effect existentially quantified and assert the existence of some state, quality or process satisfying a certain description

84 84 The true story of ‘John is hungry’ is: There exists a present state of being hungry on the part of John.

85 85 The true story of ‘John is running’ is: Some process exists, which is a present running on the part of John.

86 86 Standard external relational judgments ‘John is kissing Mary’, ‘Mary is slapping John’. These cases, too, involve an event whose existence necessitates the truth of the relevant judgment. But what is entailed by the truth of these judgments is only that an event of the given sort exists. Such judgments are existential generalizations of ontologically basic judgments.

87 87 The true story of ‘John is kissing Mary’ is: Some event exists, which is a present kissing of Mary by John.

88 88 Standard contingent negations ‘John is not hungry’, ‘John is not kissing Mary’. Assumption: special entities are not required to account for how the world is when something fails to be the case. If there is no golden mountain, then there does not need to be some other entity whose existence entails that this is true. All that is needed is that there be no golden mountain.

89 89 The true story of ‘John is not hungry’ is: There is no presently existing state which is a being hungry on the part of John. Sometimes judgments state their true stories transparently (Tarski-style deflationists say that this is always so).

90 90 The true story of ‘John is not kissing Mary’ is: There is no event which is a present kissing of Mary by John

91 91 Totalizer judgments ‘Everyone is hungry’, ‘No one is kissing’. The true story for ‘Everyone is hungry’ is: For every actual human being [in the context determined by the token judgment at issue], there is a present state of being hungry of that human being.

92 92 The true story for ‘No one is kissing’ is: There is no event which is a present kissing of any actual human beings [in the context determined by the token judgment at issue].

93 93 Contingent intrinsic predications, internal relational judgments ‘John is two meters tall’, ‘Jones is in Thailand today’, ‘Mary’s arm is a part of Mary’s body’, ‘John is taller than Mary’. For ‘John is kissing Mary’ we have a process of kissing But what could motivate us to hold that there are parthood-processes, or tallness- processes?

94 94 Processes could not have been otherwise than they actually are If the Titanic had sunk an hour later than it did, then the process referred to by the description ‘the sinking of the Titanic’ would have been a different entity from the process that is in fact referred to by that description

95 95 Objects vs. their lives Objects like people and oceanliners are such that their lives could have been filled with different processes than those which actually did occur. John had oranges for lunch, but he could have had bananas instead.

96 96 So, is it a contingent matter that a certain process is a part of a certain life? No: what is contingent is not that this process was a part of that life but rather that this particular extended process (John’s life), having yesterday’s eating-of- oranges incident as a part, was John’s life.

97 97 John’s life = the maximal process in which John is the exclusive or principal participant John’s life is existentially dependent on John – John’s life could not have been if John had not been. But the converse is not true: John could have lived differently. His life would then have been a different entity; John would still have been himself.

98 98 Lives are key to the true stories for judgments like ‘John is in Thailand’ among the essential properties of John’s life are its spatial location and material composition at every instant during which it is occurring.

99 99 The true story of ‘John is two meters tall’ is: There is an entity which is the now-slice of John’s life, and its maximal spatial span is two meters (This last clause will then be ontologically basic, with its truthmaker being the now-slice of John’s life).

100 100 The true story of ‘Jones is in Thailand today’ is: There are entities which are the today-slice of Jones’ life, and the today-slice of Thailand’s life, and the today slice of Jones’ life is located in a spatial region which is a part of the spatial region in which the today-slice of Thailand’s life is located

101 101 The true story of ‘Mary’s arm is a part of Mary’s body’ is: There are entites which are the now-slice of Mary’s arm’s life, and the now-slice of Mary’s life, and the former is a part of the latter.

102 102 The true story of ‘John is taller than Mary’ is: There are entities which are the now-slices of John and Mary’s lives, and the maximal spatial span of the former is greater than that of the latter.

103 103 Synchronic identity attributions ‘Cicero is Tully’, ‘Cicero is not Nero ’,‘The Morning Star is the Evening Star’. The judgment that the thing named by ‘Cicero’ is identical to the thing named by ‘Tully’ is a posteriori but necessarily true (existential presuppositions granted). It is contingent that each of those names denotes its corresponding denotatum. But it is necessary that that denotatum is the same as itself.

104 104 ‘Cicero is not Nero’ is likewise necessary: It is contingent that these names denote what they do, but that those respective denota are non-identical is necessary.

105 105 The true story of ‘Cicero is Tully’ is: The entity named by both ‘Cicero’ and ‘Tully’ exists.

106 106 The true story of ‘Cicero is not Nero’ is: Cicero and Nero exist.

107 107 ‘The Morning Star is the Evening Star’ Here the judgment involves non-rigid designators. These terms could have retained their meanings and yet failed to be co-referential. ‘The Morning Star is the Evening Star’ asserts that there is an individual satisfying both (definite) descriptions. It is true whenever there is an x such that x is the Morning Star and x is the Evening Star.

108 108 Let us assume that x is the Morning Star just when there is a certain sequence of events MS characterizing the life of x. Likewise x is the Evening Star just when a suitable series of events ES characterizes the life of x. The true story of ‘The Morning Star is the Evening Star’ is then: Something x exists, whose life features both an MS sequence and an ES sequence. But if we use this sentence to make an identity judgment rigidly or de re, then its true story would be: Venus exists.

109 109 Logical truths ‘Every thing either is a human or is not a human’, ‘It is not the case that some thing is a human and is not a human’ Their true story is, we might say, the empty story: they entail no ontological posits whatsoever, as there is no condition that the world must satisfy when they are true. (Wittgenstein: “A tautology has no truth- conditions, since it is unconditionally true.”)

110 110 Truth and meaning Some hold that these truths are true in virtue of their meaning; but true stories, and talk of how the world must be if a certain judgment is true, come after meaning is fixed. (Token judgments bring the meanings of the corresponding expressions in their train.)

111 111 Our job is to elucidate the ontological posits implicit in true judgments Logical truths are not contingently true, and they specify no ontological conditions. However: if one is of the opinion that it is possible that nothing exists, one could maintain that: The true story of ‘Every thing either is a human or is not a human’ is: Something exists.

112 112 Alethic modalities ‘If something is a man, then it is necessarily a man’, ‘If something is a kissing event then it is necessarily a kissing event’, ‘Necessarily, if Socrates exists then he is a man’, ‘Socrates is a truthmaker for the judgment, “Socrates is a man”’ If we are right that there is a difference between metaphysical and logical necessity then we owe an account of the true stories for truths stating, e.g. that it is necessary that Socrates is a man, provided that he exists. (Metaphysical necessities de re, logical truths de dicto ?)

113 113 ‘Socrates is human’, ‘All green things are extended’ seem to specify non-trivial features of Socrates and green things

114 114 So pick your view Modal actualism Combinatorialism Real potentialities, dispositions, capacities Etc.

115 115 Truthmaker assertions One subclass of the necessary truths is ontologically basic. These are the true assertions to the effect that a given truthmaker relation obtains x TM p is true, then x TM ‘x TM p’ Thus the true story for x TM p is: x exists.

116 116 FIN

117 117 We mention that it is the work of a theory of language and meaning, not of a theory of truth, to specify the sense in which truths must correspond or refer to reality.

118 118 in particular, the problems with using token judgments and defining true stories as having so much to do with judgments. Ie a true negative has as its true story the existence of some other judgment which lacks a truthmaker.... who makes this judgment? For 'grass is not infrared' to be true it doesnt seem that anyone ever needed to make the judgment 'grass is infrared'

119 119 And that even if we had found a reasonably elegant view, which we didnt. so thats why im just saying we should look at necessarily true biconditionals. We surpass deflationists just by saying that you get interesting ones sometimes, and these may still have a good deal to do with truth, so truth isnt exhausted by the trivial T schema. but we arent committed to any specific ontology on this basis either.

120 120 even if we used platonic propositions, theres still issues here because intuitvely the existence of any proposition hasnt got much to do with the way the world is when 'grass is no infrared' is true... the true story should involve primarily grass and colors... second there are the existence issues, trying to make sense of these things like a doesnt equal b, what happens when a exists but b doesnt, and all of that crap. The details got really messy, and it wasnt very interesting because i think we were already down the wrong track, so the messiness probably wont lead to any interesting sort of impossibility proof.

121 121 then there were the issues with making true stories for general truths sound in any way 'built up' out of true stories for 'simpler' truths. That turned out also not to work. But again, as I said, my skepticism now is that anything trying to give a specific schema for truthmakers or true stories, that could force me to make any ontological decisions (that works in some onotlogical theories and not others) could be for that reason be rejected modus tollens by someone holding an opposing ontological view.

122 122 Hochberg’s Complaint A pair (a, b) will necessitate a  b only when in fact a  b. This does not mean that we ‘presuppose’ the non-identity. It means that certain implications of the relevant logical form are necessary, where others are downright false. The world decides. We presuppose nothing except a notion of real, non-syntactic necessity.

123 123 Hochberg’s Claim There can be no coherent notion of necessitation which has a, b necessitate a  b but does not have c, d necessitate c  d just when c =d

124 124 Of course the entailment is not a logical truth. But there are necessary truths that are not logical truths. (Cf. Husserl, Kripke)

125 125 Realist hunter-gatherer ontology vs. syntactic amusement Because Hochberg conceives of necessity as in every case logical (syntactic?), he thinks we must be getting necessitation by playing games with rules for names. So he says we disallow two names for the same thing, and disallow names for non-existents.

126 126 We do not disallow two names for the same thing: the necessitations of a  b are not syntactic. But we do disallow names for non-existents, on the grounds that we are Millians/Evansians about proper names (but this not for syntactic amusement) The fact that names must name existents, on our view, does not make any existence facts trivial. We could say that ‘I exist’ is a pragmatic necessity, but really it’s not a necessity at all.

127 127 It may follow from my ability to assert ‘a exists’ using ‘a’ as a genuine rigid name, that a indeed exists. Why does it follow that a necessarily exists?

128 128 Moreover if an entailment like ‘E!a  p’ turns out to be necessary, that is very interesting; it shows that p is true on all worlds where a exists. It may be that for us to make this statement, our world has to be one of them, but that is immaterial. Another way of putting this is: ‘E!(a)  p’ could turn out to be necessary even if p were not necessary.

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