Embed Size (px)
Transcript of True Stories
True StoriesBarry Smith (IFOMIS/Buffalo)Jonathan Simon (NYU)
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 realityStrategy 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 tinkeringThe 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 taskis not conceptual analysis of the notion of truthmaker. Who cares? Its 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 iceany 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 ones ontological theory entails that there are truthmakers even for negative truths about the non-existence of unicorns, then so be it.
But herewe 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 isnt there more mystery, rather than less, when we must explain such relations by means of an extra, gerundive entity?
In particular no negative factsWhy are negative facts so nasty:
Mary is red all the parts exist, we can see how this fact is carved out within realityMary is not green here not all the parts existMary is not a cardinal numberMary is not a golden mountainMary is not Cicero
Against DeflationismThese pessimistic remarks need not lead to deflationism, the view that the meaning of the truth predicate is exhausted by the disquotational schema T.
Against DeflationismThere may be several true biconditionals for any given truthbearer, some more contentful than others.Tarskians are interested in true biconditionals of the formS is true iff p
But there are also ontologically contentful truth conditions of the form:
p iff x exists
Armstrongs rejoinderRejecting truthmaker maximalism implies the need for two theories of truthSince truthmaker maximalism is false we need at least two theories of truth in any case
Aristotleend of methodological preamble
How to understand the relationbetween Amundsens 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 Johns 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 JudgmentIf reality is such and such a way,then: necessarily, this judgment is true
Two difficulties for the identification of truthmaking with necessitation1. Restalls refrigerator If truthmakers are just necessitators,then every contingently existing entity is a truthmaker for every necessary truth Restalls refrigerator, in particular, is a truthmaker for Goldbachs conjecture.
2. Johns funeralEntailment 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. Johns funeral, in particular, is a truthmaker for John is deadBreaks no truthmaking backward in time constraint
There are other malignant necessitatorsGod wills p Gods willing act thereby necessitates p(For Malebranche, all necessitation is of this sort.) But Gods act of willing is typically not a truthmaker for p
Johns funeral and Gods 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
Solutionto 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 judgmentsBlanche is shaking hands with Mary
Judgments project on portions of realityBlanche is shaking hands with Mary
Our goal: understanding correspondence between reality and judgmentBlanche is shaking hands with Mary
ProjectionThink of a judgment as a searchlightEverything that falls within the beam of the searchlight is relevant to the truth of the judgment
A Portion of Reality
Die Projektion3.12 ... der Satz ist das Satzzeichen in seiner projektiven Beziehung zur Welt. 3.13 Zum Satz gehrt alles, was zur Projektion gehrt; aber nicht das Projizierte.
A Map3.13 Zum Satz gehrt alles, was zur Projektion gehrt; aber nicht das Projizierte.
Satz und Sachverhaltarblanguageworldnamessimple objects
Satz und Sachverhaltarblanguageworld
Projectiona 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 RealityDPxPp := 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.
(Johns death) is part of the projection of (Johns funeral occurred).
But not(Johns death) necessitates (Johns funeral occurred).
(Johns funeral) necessitates (Johns death occurred).
But not:(Johns funeral) is part of the projection of (Johns 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 xNpxTMp =: p (E!x p)
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 necessitatorsRestalls refrigerator is not even a candidate truthmaker for Goldbachs conjecture. Gods Necessitating Will is not part of the total projection of John is kissing Mary. Johns funeral is not a truthmaker for (though it is a necessitator of) John is dead.
E!(Johns funeral) E!(Johns death)
If, against the Humeans,there can be dependence relations connecting disjoint individuals, thenIf 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 yThe 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 judgmentsF(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)
Definitionp 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 maximalismholds, 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 j