**Truth Without World**

“In
the natural sciences, when a theory is devised in some idealized domain, we ask
whether the theory is true and try to answer the questions in various ways. Of
course, we expect that the theory is probably false.”

¾
Noam Chomsky, *Rules
and Representations* (p.104)

__The
problem__

(i) *Truth as external
ground*: Truth appears to be concept on which the very notion of rational
thought pivots. The notions of right/wrong, justified/unjustified,
valid/invalid, reliable/unreliable, meaningful/meaningless, etc. all seem to
involve truth as an antecedent notion. In particular, *truth is the external ground to which thought is answerable. The
structure of a thought makes it apt to enter into the ‘space of reasons’, to
stand in truth relevant relations with other thoughts*.

(ii)
Linguistic capacity - the *language
faculty* - is
a species-specific structure of the human brain. For theoretical purposes
(science): a) to be linguistically competent is for one’s brain to realise an abstract function that recursively maps from a
lexicon to an infinite set of structures that pair ‘instructions’ to
phonological systems and intentional-conceptual systems; and b) a language is a
steady state of an individual’s brain. Two consequences: b1) we each have our
own individual language, *qua* brain
state; b2) there are no constitutive external conditions on the language state.

__The
Thesis__

Possession
of the concept of truth is possession of the means to opaquely metarepresent bare phrase structures. A BPS becomes a
representation as an element of a system which can be represented as a
representation.

__Truth:
Deflationism__

__Varieties
of deflationism__

1.
Redundancy theory (Ramsey, Ayer)

2.
Performative theory (Strawson,
Wittgenstein?)

3.
Disquotationism (Tarski?, Quine,

4.
Anaphoric theories (Grover, Brandom)

5.
Propositional deflation theories (Horwich, Soames, M. Williams)

6.
Rich Disquotation? (Frege,
Davidson, McDowell, Wright, McGinn, Hornsby)

__The
Exhaustion Thesis__

The
content (sense/cognitive significance) of the concept of truth is exhausted by
the content of that to which it applies.

Or:

Truths
have no more in common than the adventitious occurrence of the same concepts in
the complex contents to which the concept rightly applies.

__The
Good of Deflationism__

(1)
__The Fundamental Intuition about Truth (FIT)__

The truth of a sentence/proposition/etc.
S depends upon two factors: (i) what it says and (ii)
how the world is. If the world is as S says, then S is true, otherwise false.

Tarski
(1933/36) first showed how FIT can be respected without appeal to (i) an ontology of facts/wordly state of affairs or (ii) an ideology of
correspondence/saying.

(i) ‘Snow is white’ is true iff
‘Snow is white’ says that snow is white & it is a fact that snow is white.

(ii)
(P*p*)(It
is a fact that *p* iff
*p*).

(iii)
(P*p*)(‘*p*’ means that *p*).

(iv)
($*x*)(true(*x*) iff *x* = ‘Snow is white’ and snow is white).

(v)
‘Snow is white’ is true iff ‘Snow is white’ = ‘Snow
is white’ and snow is white.

(vi)
‘Snow is white’ is true iff Snow is white.

*Consequence I*:
The concept of truth is independent of metaphysical/epistemological dispute.

*Consequence II*:
The articulation of the truth of a sentence S involves no metalinguistic
predication over the lexical items of S; the truth conditions of S are
articulated via the predication contained in S itself. But…

*Consequence III*: The concept of truth enshrines a metalinguistic role such that we can sally from
language-talk to world-talk.

(2)
__Generality and Inference__

A
truth concept enables us generalise over clausal position;
in effect, truth provides the service of a predicate for an otherwise stranded
bound variable ranging over some set, all of whose members we wish to assert.

(i) If ‘2+2 = 4’ is a
theorem of PA, then 2+2 = 4.

(ii)
For all *x*, if *x* is a theorem of PA, then *x*.

(iii)
*("*x*)(PA(*x*) → *x*)

(iv)
("*x*)(PA(*x*) → True(*x*))

Pronouns
allow for a similar service in generalising over
nominal position; where, regimented, the pronouns function as variables.

(i) If Bill is over 6ft, then Bill is tall.

(ii)
If one is over 6ft, then one is tall.

(iii)
("*x*)(FT(*x*) → Tall(*x*))

Generalising…

In ND:

1 (1) ("*x*)(F(*x*) → True(*x*)) A

2 (2)
F(*p*) A

1 (3)
F(*p*) → True(*p*) 1UE

1,2(4)
True(*p*) 2,3MPP

1,2(5)
True(*p*) ↔ *p * 4T*df*

1,2(6)
True(*p*) → *p*
↔*df*

1,2(7) *p * 4,5MPP

A
similar derivation for existential generalisation is
obviously invalid (at line (7)):

1(1)
($*x*)(F(*x*) Ù
True(*x*)) A

2(2) F(*p*) Ù
True(*p*) A

2(3) True(*p*) 2ÙE

2(4) True(*p*) ↔ *p * 3T*df*

2(5) True(*p*) → *p* ↔*df*

2(6) *p * 3,5MPP

1(7) *p * 1,2,6EE

The
thought is that the concept of truth plays the functional role of encapsulating
infinite conjunctions/disjunctions. Content-wise, the two generalisations
give way to (1) and (2) respectively, in line with the exhaustion thesis:

(1)
If F(p_{1}),
then p_{1}; and if F(p_{2}),
then p_{2};…

(2)
Either F(p_{1})
and p_{1}; or F(p_{2})
and p_{2};…

__The
Problem with Deflationism: Transparency__

__Transparency
thesis__: Truth is only (at best) syntactically metarepresentational; conceptually, it is *flat* with that to which it applies.

__Problem
I: Incorporation__

(i) ‘Der Schnee
ist weiss’ is true.

(ii)
‘Every semi-stable elliptical curve is a modular form’ is true.

(iii)
The Continuum Hypothesis is true.

__Problem
II: Opaque Generalisation__

*A Triviality*:
To generalise is to relinquish any independent access
to the objects of the domain over which the generalisation
holds.

*Consequence*:
Content-wise, *for* the cognitive agent,
truth generalisations are not flat with that to which
truth is applied.

*To
see this explicitly/formally…*

*Deflationary
assumption I*: Generalisations
are functional bindings of positions in a Boolean structure, e.g., an open
first-order formula.

*Deflationary
assumption II*: QNPs are
incomplete at logical form.

(A)
*All QNP structures are conservative.*

Where
D is a natural language quantifier, and **D** is a function from a nominal set to a
predicate set to a cardinal value:

(CONSERVE)
If *D _{k}*
is a

In
simple terms: if two predicate sets *A*,
*B* have the same intersection with the
same nominal sets, then the D-function defined on the nominals
over the sets takes the same value with predicate *A* as it does with predicate *B*.
So, where *k* = 1, for all sets *X*, *Y*,
(i) holds:

(i) **D**[*X*](*Y*) ↔ **D**[*X*](*X* ∩ *Y*).

(ii)a
Every boy runs ↔ Every boy is a boy that runs.

b Most boys run ↔
Most boys are boys that run.

c Bob’s son runs
↔ Bob’s son is a son that runs.

Consequence:
The truth of a generalisation “lives on” the
character of the members of the nominal set.

Might
non-members be relevant? No…

(B)
*All QNP structures are extended*.

(EXT)
If *D* is a Det
expressing a function *f*
: *P*(*U*) µ
**D**(*U*), for each universe *U*,
then *D* is *extended* iff
"*U*,
*U**, where *X*, *Y* f
*U* and *X*, *Y* f
*U**, **D*** _{U}*[

In
simple terms: the value of every QNP structure is invariant over universes so
long as its argument sets are invariant over the universes.

(C)
*The case of nall*

Consider:

(1)
Everything but boys run ↔ Everything but boys
are boys that run

(2)a
**NALL**[*X*](*Y*) is T iff {*U* - *X*} f Y

b *f*** _{NALL}**[

c Every non-boy
runs ↔ Every non-boy is a non-boy
that runs.

(D)
*QNPs** are not sortally
reducible*

(SR)
If *D* is a Det
defined over *P*(*U*), then **D**[*X*](*Y*) is sortally reducible just if there is

some Boolean
function *f* such that **D**[*X*](*Y*) ↔ D(*U*)*f*(*X*,
*Y*).

In
simple terms, this means that the value of the formula just depends on either
{X ∩ Y} or {X -Y}.
Consequently, the nominal restriction can be canceled by a Boolean compound of
the two sets expressed by some first-order relation between open
sentences. Sortal
reducibility, however, is not a defining semantic characteristic of Det+NP constructions; indeed, it does not even equate with
logicality, for logicality does not equate with being first-order.

*Consequence I*:
QNPs are not LF incomplete

*Consequence II*:
QNP formulae do not give way to their ‘instances’ as a matter of LF syntax.

Moral:
Set theoretical analysis of the structure of QNPs
shows that first-order representation is inadequate - the representation upon
which deflationism is based.

__(Radically)
Bare Phrase Structures__

{{some,
boy}* *{{some, boy} {{likes, *v*} {likes, himself}}}}

Second Phase

{some, boy}* *{{some, boy} {{likes, *v*} {likes, himself}}}

Some
boy {some, boy} {{likes, *v*} {likes, himself}}

<some boy>
likes+*v* {likes, himself}

Copying from the edge of the first phase to [SPEC CP] [SPEC CP]

Copying from V head to incorporation
with

<likes> himself

*v*__
__

__Derivation
by Phase __

A
*phase* of a derivation is a segment of
structure that satisfies interface conditions and so can spell-out to external
systems. Chomsky’s hypothesis is that phases are either

(i) *v**P (an abstract
element that supports all argument roles of a verb)

or

(ii)
CP (a clause that supports a *v**P and
tense and discourse features).

Think
of *v**P as the first phase which, once
constructed, is frozen, but its *edge* is
open to copying higher up to form the second phase. The elements of the first
phase are interpreted conceptually, e.g., compositional event structure. The
elements of the second phase determine morphological form (semantically
irrelevant) and discourse parameters of both phases. Phases iterate.

__The
Architecture of the Language faculty__

LEXICON

__
__

[NUMERATION]

First
Phase Ü
Verb Structure

Discourse
Structure Þ
Second Phase

__The
Role of Truth __

A
hypothesis that might be true: *Truth is
that mechanism that turns structures (RBPSs) into
representations*.

The
mechanism makes available a structure to carry assertoric,
interrogative, imperative, opative, content.

A
structure accessible to truth becomes a representation - it is representational
only as apt to be metarepresented.

TM:
The representation of a representation *as*
a representation.

*as*
a structure.

TM:
Carruthers, Dennett, Recanati,
Grice, Sperber & Wilson, Carston,
(more or less) every deflationist.

Thesis:
TM f

OM
= TM iff the represented structure is transferable.

__Reasons
for Optimism__

1.
Truth is opaque: bare clausal form supports the attribution of truth.

2.
Truth incorporates alien structures, again in bare form.

3.
The disquotational effect drops out for those
structures non-incorporated.

4.
The failure of the deflationary construal of generalisations
is respected: the general

terms are copied high and fix the domain
over which truth may opaquely operate.

5.
Tarski’s ‘truth from meaning platitude’ is respected.

__Further
reading__

__On
internalist methodology__:

Chomsky,
N. 2000: *New Horizons in the Study of
Language and Mind*. Cambridge:

Cambridge University Press.

Collins,
J. 2003: Expressions, sentences, propositions. *Erkenntnis* 59: 233-262.

Collins,
J. forthcoming: Faculty disputes. *Mind
and Language*.

Jackendoff,
N. 2002: *Foundations of Language: Brain, Meaning,
Grammar, Evolution*.

Oxford: Oxford University.

__On
truth__:

Collins,
J. 2002: On the proposed exhaustion of truth. *Dialogue* 41:653-679.

Collins,
J. 2002: Truth: an elevation. *American
Philosophical Quarterly* 39: 325-342.

Tarski,
A. 1933/36: The concept of truth in formalized languages. In A. Tarski 1956:

*Logic,
Semantics, Metamathematics* (2nd edition), ed. J.
Corcoran. Indianapolis:

Hackett.

__On
metarepresentation__:

Sperber,
D. 2000: *Metarepresentation*.
Oxford: Oxford University Press.

__Semantics
of determiners__:

Keenan,
E. and Westerståhl, D. 1999: Generalized quantifiers
in linguistics and logic. In

J. van Bentham and A. ter Meulen (eds.), *Handbook of Language and Logic*.

Holland: Elsevier

Collins,
J. forthcoming: A minimalist perspective: truth and natural language

quantification. *Journal of Philosophical Logic*.

__On
phase derivation__:

Chomsky,
N. 2000: Minimalist inquiries: the framework. In R. Martin, D. Michaels, and

J. Uriagerka
(eds.), *Step by Step: Essays in Honor of
Howard Lasnik*. Cambridge,

MA: MIT Press.

Chomsky,
N. 2001: Derivation by phase. In M. Kenstowicz (ed.),
*Ken Hale: A Life in*

*Language*.
Cambridge, MA: MIT Press.

Chomsky,
N. 2001: Beyond explanatory adequacy. *MIT
Occasional Papers in*

* Linguistics*,
No. 20.

Epstein,
S. D., Groat, E. M., Kawashima, R., and Kitahara, H. 1998: *A
Derivational*

*Approach
to Syntactic Relations*. Oxford: Oxford University Press.

Epstein,
S. D., and Seely, T. D. (eds.) 2002: *Derivation and Explanation in the*

* Minimalist Program*.
Oxford: Blackwell.

Uriagereka,
J. 2002: *Derivations: Exploring the
Dynamics of Syntax*. London: Routledge.

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