This a follow-up to Part
One, which noted that examples (1-2) present a challenge for (D).
(1) Lari is false.
(2) The second numbered example in this post is false.
(D) for each Human Language L, there is a theory of truth
that can serve as the core of an adequate theory of meaning for L
To review, it seems that (2)—a.k.a. Lari—is neither true nor false. So
one might hope for a truth theory that generates (3) rather than (4);
(3) Legit(Lari) --> [True(‘Lari is false.’) ≡ False(Lari)]
(4) True(‘Lari is false.’) ≡ False(Lari)
where ‘Legit(_)’ is some paradox-avoiding restriction. But given “Foster’s Problem,” (D) seems to require truth theories
that don’t generate (3) or (5),
(5) True(‘Ernie snores.’) ≡ Snores(Ernie) & [True(‘Bert yells.’) ≡ Yells(Bert)]
which is true but not meaning-specifying. So one might seek a theory
with a very weak system of deduction, reflecting a hypothesized competence that
lets humans apply semantic axioms—lexical and compositional—only as required to
compute the semantic properties of complex expressions. But can such a theory be
a theory of truth of the sort
required by (D)?
The worry is not that (4) is false. If Lari is neither true nor
false, and in this respect like my dog Bode, then both sides of (4) are false. But
if a true theory specifies a truth condition for sentence S, then in one fine sense, S—unlike
Bode—has a truth condition. So one wonders: what special property does Lari
lack (or have), in contrast with linguistic entities that are allegedly
true-or-false? It’s no answer to say that Lari induces paradox. But following
Davidson, advocates of (D) might say that truth theories for Human Languages
specify truth conditions for utterances,
not expressions relativized to contexts.
And channeling Strawson, they might say that while utterances of (6) are
typically true-or-false, utterances of (7) need not be.
(6) I am hungry. (7)
Vulcan is a rocky planet.
If a user of (7) presupposes that Vulcan exists, in order to say
that it is a rocky planet, that user’s utterance of (7) might fail to be false.
Falsity may well require more than grammaticality and absence of truth; the
world may have to “cooperate with,” or at least not frustrate, certain
communicative intentions. This familiar point extends to at least some
utterances of (8) and (9),
(8) I saw that. (9) He is bald.
since attempts to demonstrate an object can fail, and a speaker can
wrongly assume that someone is not a vague case with respect to ‘bald’ (or ‘hungry’).
So perhaps uses of (1), along with many uses of (2), fail to meet certain conditions
for being true-or-false; where these conditions may themselves be determined in
part by contextual factors (see, e.g., Michael
Glanzberg's work).
I am happy to say that speech acts—in particular, attempts to make
truth-evaluable claims by using sentences—are governed by norms of truth that
go beyond any conditions specified by theories of Human Languages. It would be
nice to have an ideal language whose sentences are themselves true-or-false in
suitable contexts. But if Human Languages are I-languages that generate expressions in a biologically natural
way, why think that theories of meaning
for such languages specify truth conditions for utterances that need not be true-or-false? If truth is downstream
of linguistic meaning—in that acts of
using I-language sentences are candidates
for being true-or-false, subject to review—why think that good theories of meaning
for Human Languages will deploy the predicate ‘True(_)’? If truth is a property
of utterances, it’s hard to see how specifications of truth conditions can be
derived from a specification of a constrained capacity to generate meaningful
expressions. (Saying that meaning is use doesn’t make it so.)
Moreover, Davidson did not discuss quantificational examples
like (10) in detail.
(10) I saw something.
But a Tarski-style theory of truth
is specified in terms of expressions being satisfied
by (or true of) sequences that assign
values to variables. Given (11), T-theorems follow trivially.
(11)
for each sentence S: True(S) ≡ for each
assignment A, Satisfies(A, S)
The trick is to show how “S-theorems,” of the form
indicated in (12), can be derived.
(12) for each assignment A: Satisfies(A, ‘I saw something.’) ≡ F(A)
For example, ‘F(A)’ might replaced
with ‘for some assignment A* that differs from
A at most with
regard to A* what assigns to
the variable x, A*(speaker)
saw A*(x)’; where ‘A*(...)’
stands for whatever A* assigns to ‘...’,
and speaker indexes a dimension of assignments
that is (a la Kaplan) related to
utterance interpretation via some pragmatic constraint—e.g., that assignment A* is germane to a conversational situation s only if A*(speaker)
is the speaker in s.
For today, grant that instances of (12) can be meaning-specifying, despite
the technicalia. The important point here is that a theory of truth for English
will need to have S-theorems like these: Satisfies(A, ‘Lari is false.’) ≡ False(Lari); Satisfies(A, ‘Lari is true.’) ≡ True(Lari); Satisfies(A, ‘Lari is not
true.’) ≡ ~Satisfies(A, ‘Lari is true.’); and Satisfies(A, ‘Lari is not false.’) ≡ ~Satisfies(A, ‘Lari is false.’). Such a theory will imply
that no assignment satisfies (1) or (13),
(1)
Lari is false. (13) Lari is true.
while each assignment satisfies (14) and (15). So (16) must be rejected.
(14)
Lari is not true. (15) Lari is not false.
(16) for each sentence S: False(S) ≡ for each
assignment A, ~Satisfies(A, S).
This is not yet a contradiction. One can say (14-15) are true, along
with (17-18).
(17)
It is not true that Lari is false.
(18)
It is not true that Lari is true.
Drawing on Kleene/Kripke, one can also say that False(S) ≡ True(not-S). But then (19)
(19)
The 19th numbered example in “Liar, Liar, Theory on Fire” is not true.
is true if it isn’t true; so it isn’t true, and hence it is true. That’s not
good. If each assignment satisfies (19) if and only if (19) isn’t true, then since
(19) isn’t true, each assignment satisfies (19); in which case, (19)—a.k.a.
Linus—is true. So it doesn’t help to say that (1) and (13), unlike (14-15) and
(17-18), fail to meet certain conditions on being true-or-false. One can try to
deny (20),
(20)
Satisfies(A, ‘Linus is not true.’) ≡ ~Satisfies(A, ‘Linus is true.’)
or at least offer a theory, perhaps formulated in terms of a
hierarchy of types, that does not imply (20). But even if some such theory avoids
analogous (“revenge”) paradoxes, remember that (D)
(D) for each Human Language L,
there is a theory of truth
that can serve as the core of an adequate theory of meaning for L
requires truth
theories whose theorems are meaning specifying. Moreover, as Parsons and Kripke
remind us, contingent facts can make apparently innocuous claims into
trouble-makers. It can seem that (21) is true in a context if and only if more
than half of the relevant examples are false.
(21) Most of the examples were false.
But imagine twenty-one examples: ten true (e.g., ‘2 >1’, ten false (e.g., ‘1 > 2’), and (21).
Like most things,
many Human
Language sentences are not true-or-false relative to each assignment of
values to variables. So why think that any Human Language sentences have this
remarkable property? I can’t prove
that (10) is like (1) in being unlike Tarskian sentences. Perhaps there is “something
about Lari” that makes it unusually unsatisfiable, and not merely unsatisfied—and
not unsatisfiable in the ways that my dog is. But that hypothesis needs
defense. Prima facie, satisfaction has its place in theories of truth, not in
specifying linguistic meanings. And (D) seems to be a massive simplification: useful
for certain purposes, but not true.
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