True Stories

True Stories

Barry Smith (IFOMIS/Buffalo)

Jonathan Simon (NYU)

http://ontology.buffalo.edu 2

What is truth?

for contingent judgments

(empirical judgments, judgments not true as a matter of necessity, not judgments about numbers or other abstracta)


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


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?


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’


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


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.


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, ...)


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?


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 existMary is not a cardinal numberMary is not a golden mountainMary is not Cicero


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.


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


But there are also ontologically contentful truth

conditions of the form:

p iff x exists


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


Aristotleend of methodological preamble


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)


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


NecessitationThis 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


Necessitation is a bridge from Reality to Judgment

If reality is such and such a way,

then: necessarily, this judgment is true


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.


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


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


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


Solution

to block the transitivity of entailment in

xNp =: E!x & (E!x p)

impose some factor of relevance between x and p


Portions of reality necessitate judgments

Blanche is shaking hands with Mary


Judgments project on portions of reality



Our goal: understanding correspondence between reality and judgment



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


A Portion of Reality


Cartographic Hooks


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.


A Map

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


Satz und Sachverhalt

a r b

language

world

names

simple objects


Satz und Sachverhalt

a r b

language

world

projection


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)


The Theory of Projection as Dual of Necessitation


Projection: A Bridge from Judgment to Reality

DP xPp := 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.


(John’s death) is part of the projection of (‘John’s funeral occurred’).

But not

(John’s death) necessitates (‘John’s funeral occurred’).


(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


How put projection and necessitation together to define

truthmaking?

x makes p true =: xPp and xNp

xTMp =: p (E!x p)

Barry Smith


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


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’.


E!(John’s funeral) E!(John’s death)


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


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


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.


“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


Logically basic judgments

F(a)R(a,b)S(a,b,c)...

a is colourlesscolourless(a)coloured(a)


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)


Definition

p is ontologically basic = it would have a truthmaker, were it true:

OB(p) := p (p x (E!(x) p))


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.


Truthmaker maximalism

holds, by definition, only for ontologically basic judgments

Armstrong: All judgments are ontologically basic


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


Note: a natural language judgment

is ontologically basic independently of its logical regimentation.


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


Truthmaker MaximalismEvery 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


True storiesSuch 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.


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)


The Ontologically Basic

‘John exists’

‘Socrates is mortal’

‘Socrates is not a cardinal number’.


‘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


(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


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


‘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)


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.


‘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


‘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.


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.)


‘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.


‘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


‘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.


‘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.


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.


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


Some Cases


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.


The true story of ‘John exists’ is:

‘John exists’ has a truthmaker.


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)


The true story of ‘Pegasus does not exist’ is:

‘Pegasus exists’ does not have a truthmaker.


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)


‘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.


The true story for ‘George and Jeb are brothers’ is:

George and Jeb both exist.


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


The true story of ‘John is hungry’ is:

There exists a present state of being hungry on the part of John.


The true story of ‘John is running’ is:

Some process exists, which is a present running on the part of John.


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.


The true story of ‘John is kissing Mary’ is:

Some event exists, which is a present kissing of Mary by John.


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.


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).


The true story of ‘John is not kissing Mary’ is:

There is no event which is a present kissing of Mary by John


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.


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].


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?


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


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.


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.


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.


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.


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).


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


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.


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.


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.


‘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.


The true story of ‘Cicero is Tully’ is:

The entity named by both ‘Cicero’ and ‘Tully’ exists.


The true story of ‘Cicero is not Nero’ is:

Cicero and Nero exist.


‘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.


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.


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.”)


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.)


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.


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 ?)


‘Socrates is human’, ‘All green things are extended’

seem to specify non-trivial features of Socrates and green things


So pick your view

Modal actualism

Combinatorialism

Real potentialities, dispositions, capacities

Etc.


Truthmaker assertionsOne 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.


FIN


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.


in particular, the problems with using token judgmentsand defining true stories as having so much to do withjudgments. Ie a true negative has as its true storythe existence of some other judgment which lacks atruthmaker.... who makes this judgment?For 'grass is not infrared' to be true it doesnt seemthat anyone ever needed to make the judgment 'grass isinfrared'


And that even if we had found a reasonably elegantview, which we didnt.

so thats why im just saying we should look atnecessarily true biconditionals.We surpass deflationists just by saying that you getinteresting ones sometimes, and these may still have agood deal to do with truth, so truth isnt exhausted bythe trivial T schema.

but we arent committed to any specific ontology onthis basis either.


even if we used platonic propositions, theres stillissues here because intuitvely the existence of anyproposition hasnt got much to do with the way theworld is when 'grass is no infrared' is true... thetrue story should involve primarily grass andcolors...

second there are the existence issues, trying to makesense of these things like a doesnt equal b, whathappens when a exists but b doesnt, and all of thatcrap. The details got really messy, and it wasntvery interesting because i think we were already downthe wrong track, so the messiness probably wont leadto any interesting sort of impossibility proof.


then there were the issues with making true storiesfor general truths sound in any way 'built up' out oftrue stories for 'simpler' truths. That turned outalso not to work.

But again, as I said, my skepticism now is thatanything trying to give a specific schema fortruthmakers or true stories, that could force me tomake any ontological decisions (that works in someonotlogical theories and not others) could be for thatreason be rejected modus tollens by someone holding anopposing ontological view.


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.


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


Of course the entailment is not a logical truth.

But there are necessary truths that are not logical truths. (Cf. Husserl, Kripke)


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.


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.


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?


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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