4.2.3 |
DEFINITION AND CRITERION |
What are the bearers of truth? There are three main
positions with regard to this philosophical question. Firstly,
there is the view that truth is a property, and the question
is then What is it a property of?
The diverse answers which may be given are:
- declarative sentences or sentence types (which have a
grammatical structure, and which are not interrogative or
imperative, for instance)
- declarative sentence tokens (which are physical objects,
notably series of visual marks or sound waves) —for
example, the sentence token water is transparent and the
sentence token water is transparent are different
inscriptions of the same sentence (type)
- statements (that is, what is said when a declarative sentence
is uttered or inscribed)
- utterances (as speech acts) —compare the 'performative
theory of truth' in which truth is predicated to a sentence
not by uttering a statement but by performing an action
- propositions or meanings of sentences (that is, what is
common to synonymous declarative sentences or sentence types)
It does not follow, of course, that whole theories or beliefs
could not be true or false, but they are true or false because
they consist of elements which are true or false. And it is
these elements which are the primary truth-bearers, whether
propositions, sentence types or something else.
Secondly, there is the view that truth is not a property.
In the redundancy theory of truth and later variants of it, like
the 'simple' theory of truth, the question itself is considered
to be senseless. Closely related to this question is whether
propositions are objects, or whether one does ontologically
commit oneself by quantifying over propositions or sentences. So
long as one sticks to pure substitution this question of
objective entities can easily be evaded, but not when one gives
oneself up to all kinds of quantification without providing a
plausible alternative for the standard interpretations thereof.
(Then the result is something that is neither quantification nor pure
substitution.)
If propositions are 'things', and if they are true or not, this implies
almost automatically that they do have or do not have the property of
truth, even
tho they would only be
imaginary things, and even tho truth would merely be an imaginary
property.
On a third view, the right question to ask is What is the
relationship between formal and informal arguments with respect
to validity and truth?
In this case, the issue of the appropriate constraints on instances of
sentence letters —what can be put for p?— does still
arise, also for those denying that truth is a property.
We have called the primary bearers of truth "propositions" and have
assumed that they are the language-independent meanings of sentences.
It is not important from our point of view whether the primary bearers of
truth are actually something else, such as sentence tokens or speech acts.
It is not important either whether these truth-bearers are 'really'
things or not.
This is a metaphysical pseudoproblem, for if they are 'things', they are
propositional things, and
trivially, these things are entirely different from the things of
nonpropositional reality we have discussed in the first two chapters of
this book.
Similarly, if truth is an attribute, it is a propositional
attribute not at all comparable with the
catenated and noncatenated attributes
we have discussed before in the same chapters.
In short: if propositions are included in the category of 'things', it is
the meaning of thing itself which may change, and if truth is
included in the category of 'properties' or 'attributes', it is the
meaning of property or attribute itself which may change.
More important than the question whether propositions (in the
impartial sense of primary truth-bearers) are 'real' things or
not, is the recognition of a hierarchy of (orders of) propositions
and propositional functions. Such a hierarchy very much
resembles the hierarchy of languages in the semantic theory of
truth, and is needed to solve the problem of semantic paradoxes.
Semantic paradoxes are contradictions derivable in semantics by
apparently valid reasoning with apparently obvious principles
about truth —they are 'beyond belief', so to say. A classical
semantic paradox is the sentence S reading "this sentence is
false". If S is true, then it is false; and if S is false, then
it is true. Another type of paradoxes are the set-theoretical
ones, which involve sets which are members of themselves (in a
purely set-theoretical fashion).
The probably best-known example of such a paradox concerns the set of sets
which are not members of themselves: 'the set of all sets which are not
members of themselves is a member of itself if, and only if, it is not a
member of itself'.
It has been argued that both semantic and set-theoretical
paradoxes are due to one and the same fallacy, namely the
violation of the so-called 'vicious circle principle'. According
to this principle whatever involves all of a collection must not
be one of that collection. As a formal solution to paradoxes
resulting from violation of the vicious circle principle a
theory of types has been developed. It is in the so-called
'ramified theory' that a hierarchy of propositions, and in the
so-called 'simple theory of types' that a hierarchy of (sets of)
individuals were proposed for the first time. The former
hierarchy starts in our ontology with the level of
nonpropositional reality, while the latter hierarchy is present
in every separate domain of the nonpropositional world.
Those who do not accept the vicious circle principle have come with
proposals which closely resemble this principle nevertheless.
A more serious objection is it to claim that a hierarchy such as that of
the semantic theory of truth is not a solution, because paradox might
still arise with respect to any truth ascription if the facts would turn
out badly.
The point made is then that even 'ordinary' ascriptions of truth and
falsity could not even implicitly be assigned levels in a
hierarchy of languages, for example, when A says that all of B's
utterances about S are false, while B says that all of A's
utterances about S are false. The objection is itself erroneous,
however, because it equates utterances about S with utterances
about utterances about S . If A says "all of B's utterances
about S are false", this is an utterance about utterances about
S. And if B says "all of A's utterances about S are false", this
does not involve all of B's utterances about S are false since
that is not an utterance by A about S, but about utterances about S.
The idea that all well-formed sentences must be either true
or false has also been rejected: some of them would just have no
truth-value at all. Those stressing this have been using a
concept of groundedness. A sentence is, then, said to be
'grounded' if it will eventually get a truth-value in a process
in which one starts with a sentence which one is 'entitled to
assert' (like water is transparent) and to which one may add
.. is true (<water is transparent> is true). On such
a construction a sentence like this sentence is true will remain
ungrounded, and in this way paradox can be avoided.
But —as has already been pointed out— this concept of
groundedness still has strong affinities with the idea that what is wrong
with paradoxical sentences is a sort of vicious self-dependence.
A serious objection against the whole intuitive idea of groundedness is
that it puts the cart before the horse.
The reason is that it makes use of a
normative concept, namely the
concept of entitlement.
(Intuitive ideas somehow always seem to implicitly appeal to normative
notions and the evaluative meanings of words.)
If someone is 'entitled' to assert that water is transparent, this is,
firstly, because it is true that water is transparent, and secondly,
because one may tell something that is true and ought not to tell
something that is false.
Therefore, it follows from the truth of both water is transparent
and a principle of truth or truthfulness that one may say,
that is, that one is entitled to say that water is transparent.
The advocate of groundedness, however, suggests that it
would be the other way around, that the truth of a proposition
or utterance would follow from a person's entitlement to assert
that proposition or utterance.
This fallacy is the same as that in the entitlement theory of property in
which it is claimed that something would be someone's property because
'e is entitled to it.
Also this is a hysteron proteron: it is when something is one's property
(in a moral sense) that one is (morally) entitled to it, not the other
way around.
Even if in the relationships between entitlement and truth, and between
entitlement and property, neither term comes before the other,
entitlement alone can never do the groundwork.
