Truth and Lies: Pragmatism and Paradox
By Shaun Malleck,
In the tradition of classical
logic, the existence of semantic paradoxes represent a
challenge to the claim that logic accurately describes truth in relations
between statements. Arguing against the semantic paradoxes such as the Liar
Paradox by modifying the axioms of bivalence and non-contradiction, often does
not lead to final satisfactory solutions. However, an answer to the Liar
Paradox and related semantic paradoxes can be attained through a rethinking of
the truth condition. The truth condition can simply be stated as “A sentence is
true if what is says is the case”. This leaves the condition of “is the case”
not fully determined. In the Liar statement, “This sentence is false,” the case
would seem to consist of the statement’s own truth value and in the cases of
the other semantic paradoxes, the truth value of other sentences. The question
to be put to the Liar is, what does it mean for it “to be the case” for it to
be false? This question and the Liar Paradox itself will be approached through
an analysis of the differing schools of thought on the nature of truth. What
shall be advocated will be the use of an additional logical axiom, the
“Truth-maker Axiom” to disqualify certain paradoxical statements from having
any meaning within logic. Ultimately, this
“Truth-maker Axiom” will be redeveloped within the framework of American
pragmatism to determine a satisfactory meaning of truth free from the problems
presented by semantic paradoxes.
The coherence theory of truth
holds that a statement or belief is true if and only if it is part of a
coherent system of beliefs. The assumption is that there is an absolute
standard of truth existing on its own. This ontologically independent truth
lends truth value to certain statements and not to others. The test for the
truth value of a statement happens by identifying whether or not it is in the
family of statements which posses this absolute and independent quality. The
proof for such a determination is its relation to its fellow family members,
other truth statements. Such a coherence theory is demonstrated in metaphysical
systems like that of Descartes, who utilized his radical doubt to sift through
beliefs to find foundational beliefs in which it was impossible to doubt their
truth. This concept of inherent truth of the rationalist tradition is necessary
to the theory of coherence since there is no other way for truth to be derived
other than it being an essential quality which resists doubt and contradiction.
If the constituent statements are in fact true, then all the statements should
posses a common quality of truth, thus a coherent theory of truth should be
free of contradiction.
The Liar Paradox presents a
particular problem to this theory of truth. If internal coherence is the proof
of the truth of a system, then situations like the Liar Paradox should not
occur. If the statement “This statement is false” is true, then it must be the
case that it is false, so it cannot be true. If it is the case that the
statement “This statement is false” is false, then what it states is the case
and it is in fact true. Each move of fleshing out this paradox is determined by
logical steps. If the contradictions of the Liar Paradox arise from the structure
of logic, this might cast the structure of logic into doubt for accurately
demonstrating how true conclusions can be reached. Traditional deductive logic
relies, like the coherence model of truth, on the relation between premises
rather than on the content of them. In any syllogism “If P then Q, P, therefore
Q” the precise content of Q is inconsequential to the validity of the
syllogism. So long as the antecedent is affirmed, the consequent will follow.
However, in the condition of the Liar statement such logical relations do not
guarantee any conclusion. It is possible that the traditional model of logic
does not accurately describe the relations between statements of truth and
falsity. Traditional logic need not be abandoned though; it is often preserved
through modification of axioms governing what truth and falsity values are
acceptable. Three-valued logics and even more complex multi-valued logics arise
from modification of the axioms of bivalence and non-contradiction. Statements
in such systems can be considered either both true and false or neither true
nor false. These systems prevent “throwing the baby out with the bathwater” in
the face of paradoxes within classical logic, preserving the general and
presumably coherent structure of logic to reveal relations of truth. This
doesn’t, however, save the systems’ coherence. There is exists a “Revenge
Problem” in that for any new system of logic values there can be constructed a
new Liar-like statement which will still result in the same contradictions as
the Liar statement in classical logic. In a statement such as “This sentence is
either false or it’s neither true nor false”, if the statement is false then
what is says must not be the case (it being false or neither) so it would be
true and if that was the case then what it said would be the case but that
would mean it couldn’t be true, only false or true or false. If the statement
was true, then the same contradiction would result, it being that the statement
would be true thus either false or neither and if so, couldn’t be true. The
other possible statement “This sentence is either false or both true and false”
creates a similar situation. What the “Revenge Problem” demonstrates is that
there is no simple modification to logical standards for truth that immediately
alleviate the problem of paradox. If the relations of logic are not coherent as
they stand, they cannot be the standard for uncovering “what is truth” for
statements.
Correspondence theory perhaps can
solve the problem of paradox through changing the way the truth condition is
understood. The truth condition can simply be stated as “A sentence is true if
what is says is the case”. This leaves the condition of “is the case” not fully
determined. In the Liar statement, “This sentence is false,” the case would
seem to consist of the statement’s own truth value, and, in the cases of the
other semantic paradoxes like Yablo’s Paradox, the
truth value of other sentences. The question put to the Liar Paradox was, “what
does it mean for it to “be the case” for it to be false?” According to
correspondence theory for something “to be the case” it should properly match
up with something in the world. Truth is not an inherent property but a value
for judging how accurately what is said matches what is. A correspondence
theory’s understanding of truth does not abandon the axioms of logic but can
preserve them with the addition of an axiom for disqualifying paradoxical
statements that cast the structure of logic into doubt, called the truth-maker.
The “truth-maker axiom” can be simply formulated as, “for all p, if p is true then there exists something s such that s ╞ p”. S represents a truth-maker which is considered something other than
the statement p which determines the
truth value of p, be it a state of
affairs in the world, a fact, a proposition, or whatever. What is important is
that what makes p true is not some
inherent quality about itself. The “truth-maker axiom” arises out of a
distinction made between the correspondence theory of truth and the coherence
theory of truth. The correspondence theory of truth states that a belief is
true if there exists an appropriate entity to which it
corresponds. The entity is considered to be the truth-maker, the source of
truth value for such a belief or statement. The separation between a statement
and the truth-maker entity to which it corresponds is an ontological one. There
actually exists a world independent of human thoughts and statements and the
notion of truth itself is a method of evaluating the consistency to which human
thoughts and statements relate to this ontologically separate world.
According to a correspondence
theory, the statement “This statement is false” should properly match up with
something ontologically separate in the world determining the truth value of
the statement. It seems obvious that the world correlate is the statement
itself. If this is true, then the same reasoning towards contradiction follows.
If the statement “This statement is false” corresponds to what it states to be
true, it must be the case that it is false and if it is false then it must be
the case that it is true. The contradiction is the same with a slight change in
how the problem is framed. If such contradiction exists in the case of
correspondence theory, then how someone can ever fully understand
correspondence with truth is put into question. However, in the case of correspondence
theory this may not actually be a real problem. Once the concept of the
truth-maker is taken into account, truth-maker conditions will discount
statements like the Liar statement from having any real meaning. To restate the
premise of the truth-maker axiom, for every statement p there has to be a truth-maker s which gives it its truth value. In such a statement as the Liar
statement, what is its truth-maker? The truth-maker for the Liar statement is
apparently the product of the statement itself. However the Liar statement
cannot have a truth value without a truth-maker to determine the truth value
through its correlation. The Liar statement operates by conflating the
statement p and its truth-maker s ontologically. This cannot be the
case in a truth-maker based correspondence theory of truth because in such a
system, truth-maker entities have an ontological priority to truth values for
statements. Statements need to correspond to some ontological reality
independent of themselves that is in existence. The
existence of the truth-maker determines the truth value of the statement.
Ontological priority is distinct from temporal relation. A statement like “It
will snow tomorrow” resembles the Liar statement in that it has a truth-maker
that does not yet exist. In the case of “It will snow tomorrow” though the
truth-maker does not yet exist, it still determines the truth value of the
statement. If it does snow tomorrow then the statement will be true according
to its correlation to the truth-maker. If it does not, then the statement will
not correlate to the state of affairs it claims to. The state of affairs, “it
is snowing” must exist before there can be any truth value to the statement “It
will snow”. The same is true for the Liar statement, “This sentence is false”.
There must be something ontologically prior to the statement which determines
its truth or falsity.
What this describes seems to be an
argument against self-referential statements. Any self-referential statement
may be disqualified from having any meaningful truth value simply because of
the ontological union of the statement and its truth-maker. This is, however,
not the case. A statement like “This sentence has five words,” can have a truth
value determined by a truth-maker. The truth-maker in this case is the
grammatical structure of the statement. The existence of five words in the
sentence is the statement’s truth-maker. There is a distinction between the
constituent words of the sentence and the sentence as a statement. The
statement carries a particular meaning which is not contained by any one of the
constituent words which compose it. The statement as a bearer of meaning is
ontologically different from the words which compose it. It is the sentence as
a statement and bearer of meaning that requires a truth-maker to confirm its
truth value and the truth-maker is the sum of the ontologically distinct,
constituent words which compose it. In the case of the Liar statement there is
no such distinction between the bearer of meaning and the truth-maker for the
statement. The statement’s meaning is its truth value and the truth-maker of
the statement is its truth value.
The problem of conflating
ontological priority exists in other semantic paradoxes which must be answered
if the truth-maker is to be accepted as a solution for disqualifying those
truth paradoxes of meaning which could confound the security of logical
systems. In the example of the Open-Pair paradox there are two statements, “S1:
Sentence 2 is false,” and “S2: Sentence 1 is false.” In a circular
argument, superficially each statement in question is ontologically distinct
from its truthmaker. Sentence 1’s truth-maker is
sentence 2’s truth value and sentence 2’s truth-maker is sentence 1’s truth
value. What is sentence 1’s truth value and what is sentence 2’s truth value?
This paradox can be disqualified as a meaningful statement because neither
sentence one nor sentence 2 has any truth value at all. Each sentence requires
the truth value of the other to be settled to determine its own. Again, like
the in the Liar statement, there is a question of ontological priority, in this
paradox there exists no ontological prior statement which can serve as truthmaker for the other. As soon as the first statement is
declared, the second statement is needed to perform a truth-maker function and
the second statement in turn cannot serve such a function without the first
statement first performing a truth-maker function and so on ad infinitum. In such an Open-Pair
statement, there is an infinitely receding appeal to a truth-maker. What is
clear in the truth-maker axiom is that something must exist which generates the
truth value through the relation to the statement and the conditions of the
truth-maker’s existence. Such infinite regressions do not posses this definite
relationship of an actually existent truth-maker to a statement. They are
statements pointing to a truthmaker relationship in
their opposing statement that will never arrive.
The disqualifying of circular
paradoxes of truth like the Open-Pair, allows for the possibility of handling
other, more complex semantic paradoxes involving infinite regression like Yablo’s paradox. Yablo’s paradox
creates an infinitely descending chain of Liar-like statements which are not
self-referential or directly circular. “S1: For any n > 1 Sn is false…S2: For any n > 2, Sn is false…Si: For any n > i, Sn is false”. In
the Yablo paradox there is an infinitely descending
chain of statements which claim the falsity of all those underneath them. If
any sentence in the chain is true, that would imply the falsity of all the
statements afterwards. For any Sk that was
true, the following Sk + 1
would be false but if Sk + 1
were false, then that would imply Sk
+ 2 would be true and this contradicts the original statement Sk which claimed all following sentences
including both Sk + 1 and Sk + 2. This contradiction being
possible in every case of the infinite statements after the first,
makes this a paradox. Yet when the truth-maker axiom is applied, the meaning of
such a paradox as this can be disqualified. What truth-maker s determines whether any statement in
the Yablo sequence is true? It is the truth value of
the following statements in the chain, the truth value of which are determined
by the statements after them in the chain. For S1 to be true,
requires that at least S2 to be false which would require S3
and below to be true and for S3 to be true S4 and below
and so on. The truth-maker axiom demands that there be some existing
ontologically prior s that
determines a sentence’s truth value. In the case of Yablo’s
Paradox it is coherent to say that all the statements in the Yablo chain could be ontologically prior to each other.
However, in order for any one of them to have a truth value there must be one
existing and definite truth-maker. This is what is missing in the Yablo statement chain. The final sentence on the chain
which would be used to judge the previous sentences doesn’t exist since the
number of sentences in the Yablo chain is indefinite.
Existence is the defining quality of a truth-maker which allows it to determine
truth values, “For all p, if p is true then there exists something s such that s ╞ p.” Without a definite ontologically
separate truth-maker, no relation of truth can be established and the Yablo, like the previously considered truth paradoxes,
cannot cast doubt on the conception of truth because with the truth-maker axiom
in place, no paradoxical statements can qualify for any determined truth value.
Curry’s Paradox of absurdity
presents a different problem but one that, like the others, can be solved
through the notion of the truth-maker. Curry’s paradox takes a traditional
formulation that given the truth of one logical premise it follows that a clear
absurdity is true. “If this sentence is true, then Santa Claus exists.”
According to classical logic, conditional statements of the form “if P then Q”
only take a false value when the antecedent is true but the consequent is
false. What is measured by such a truth value is the not the validity of the premises
but the conjunction between them. So according to the traditional truth tables,
a conjunction like “If this sentence is true, then Santa Claus exists,” is only
false when the antecedent “this sentence is true” is true and the consequent
“Santa Claus exists” is false. The consequent “Santa Claus exists,” is false
according to the truthmaker axiom because there is no
actual living entity who delivers presents to every morally upright child in
the world every twenty-fifth of December, thereby violating countless laws of
physics. However, according to the truth tables, for the conjunction to be
false, the antecedent, “this sentence is true,” must be true along with the
false consequent. If this is the case then, according to the modus tollens,
Santa Claus must exist because this follows from the conjunction. If such
absurdity is validly argued through classical rules of logic, again logic is
threatened with accusations of inadequacy in handling truth as humans
understand it as it was confronted with by the liar statement. Yet again, if
the truthmaker axiom is applied to the antecedent of
the conjunction, the entire conjunction can be disqualified as logically
meaningful. In the case of the antecedent, “this sentence is true” a
truth-maker is needed. It is highly mysterious what such a truth-maker could
be. The statement like the Liar statement conflates its truth value with its
truth-maker (which is also its truth value).
Though a correspondence theory of
truth can salvage the functionality of logic in many paradoxical cases by way
of the truth-maker axiom, there still exists problematic
statements. There is the problem of there possibly existing
a “strengthened” form of the Liar statement which could lead the distinction
between meaningful statements corresponding to their truth-makers back to the
contradictions the Liar Paradox presented at the onset of this discussion. The
structure of the “Revenge Problem” is that for any approach that handles the
Liar Paradox adequately, there can be a sentence made that does for the new
approach what the liar did for the original understanding of truth and logic.
There could be a sentence along the lines of “This sentence has no truth-maker”
which seems very problematic. If it is true, it is true by having no truth-maker,
contrary to the truth-maker axiom. If it is false then that implies it does
indeed have a truth-maker since the negation of the sentence would presumably
be true and if that was the case then there would be some truth-maker to
determine a truth value for it. These complexities uncover a sticky point of
truth-maker theory, namely what qualifies as a truth-maker and what a
truth-maker qualifies as true. The problem of this “Strengthened Liar/No
truth-maker” statement lies in its possibility of being false. To say that the
sentence is true, like the traditional Liar statement, conflates truth-maker
and statement with truth value which has already been disqualified as having
any meaningful content. The implication of the statement’s falsity is, that according to the axioms of logic, the negation of
the statement is true. Yet how can anything imply the truth of something else
without being a truth-maker? And if this “strengthened liar/no truth-maker”
statement is the truth-maker for its negation, how can it meaningfully be a
truth-maker since its own truth value is undetermined and its own truth-maker
is unknown?
Related to the “Revenge Problem”
of a “Strengthened Liar-form” statement are statements that assert their own
truth, as “This sentence is true”. If it is true then once again a statement in
need of truth value and a truth-maker are conflated. If it is false then would
this mean that the negation of the statement is true, “This sentence is false”?
Or does this mean that statements that assert their own truth, since there is a
conflation of truth-maker and truth value statement, are disqualified as having
any logical meaning? There is a fear is that if statements that assert their
own truth are disqualified according to the truth-maker axiom and correspondence
understanding of truth, then all truth statements be disqualified with them.
Will the dismissal of self-asserting truth statements from the realm of truth
values infect all truth statements? What lies at the center of this argument is
the notion that each statement, no matter what form it takes, asserts its own
truth. Even the paradoxical Liar statement asserts that what it says is the
case in the same way that the statement “I am telling the truth” asserts its
own truth. The notion of the truth-maker leaves itself open to many ways of
understanding what a truth-maker is. It can be states of affairs, concrete
properties, facts, proofs, or simply what exists that statements can be
formulated about. There is a wide open range of possible interpretations of
what truth-makers could be but no concrete understanding of what a truth-maker
is that could answer the problems presented by truth-teller statements and
“Strengthened Liar/No truth-maker” statements. If such truth-teller statements
like “This sentence is true,” do not posses an ontologically separate
truth-maker, other such truth statements that only perhaps tacitly assert their
truth like “George Washington was the first American President” do so by
asserting that they correspond to a state of affairs ontologically separate
from the statement itself, but according to correspondence theory what
qualifies as a ontologically separate state of affairs is vague and uncertain.
Without such an understanding of what a truth-maker is,
correspondence/truth-maker theory cannot present a theory of truth to properly
answer all of the many semantic paradoxes.
The answer to settling the
unanswered questions of truth-maker theory in a correspondence understanding of
truth is presented in the tradition of the American pragmatists, William James
and John Dewey. The pragmatists set themselves between the two schools of
truth, correspondence and coherence theories, as critics of both. James and
Dewey established a pragmatic framework which understood truth as a process
rather than a static or absolute quality. The truthmaker
axiom seems to be antithetical to such a dynamic notion of truth; it is simply
stated as “For all p, if p is true then there is something s such that s ╞ p”. S represents a truthmaker which is
considered something other than the statement p which determines the truth value of p, be it a state of affairs in the world, a fact, a proposition, or
whatever. For every proposition or statement that can have a truth value, there
is an undefined something separate from the statement which determines the
truth of the statement. The pragmatic framework established by James and Dewey
allows for the incorporation of the notion of truth-makers which define
concretely what qualifies as a truth-maker, how paradoxical statements are
disqualified from having any logical meaning, and how such disqualification of
paradoxical statements preserves all meaningful statements of truth through
defining what a meaningful statement is to human beings.
The problem with the traditional
view of correspondence exists in the nature of the relation of the statement to
the corresponding correlate, the truthmaker. Dewey
states the position of correspondence clearly, “Material truth means that the
consistent idea or judgment states something existing outside its own
existence, in the way that the thing actually is.”1
What is clear is that truth exists primarily in the agreement of statement to
existing thing. This emphasizes that the truth-maker for any given statement is
ontologically distinct, outside the existence of the statement which is not
dependent on the statement itself. What arises is a dualism, which according to
the pragmatists, is as intractable as the Cartesian distinctions between, mind
and materiality. “The difficulty to the ‘truly’ of a proposition is just
shifted to the ‘really’ of the thing…To tell whether a proposition reflects a
thing as it really is we seem to require a third medium in which the original
proposition and its objects surveyed together are compared and their agreement
or disagreement seen.”2
The problem is one of interaction. If the truth-maker of correspondence theory
states “there is something s such
that s ╞ p”, how does s effectively prove that a statement p is true? There must be some causal connections that effectively connects the ontological reality of the truth-maker to the
statement. What this connection has been is something taken for granted in the
correspondence theory.
Dewey suggests that this connection
between truth-maker and statement, “is either a proposition or it is not. If it
is a proposition, it claims to be true or to agree with its object; this object
is beyond itself, and hence another proposition is required for its comparison
and so on ad infinitum.”3
This is a devastating suggestion for the truth-maker axiom. For any truth-maker
to effectively prove the truth value of a given statement, it needs some
connection that may need a truth-maker itself to validate the connection
between the original proposition and original truthmaker.
Like in the truth-teller statement and the “Revenge Problem” statement, such a
truth-maker for another truth-maker is undisclosed and without a way of coming
to understand it completely. Paradoxical statements are able to be disqualified
from possessing any actual meaning because they are without a definite
ontologically separate grounding for determining the truth value. This demand
of ontological priority keeps statements grounded, in reality without falling
into paradoxical loops such as the Liar Paradox. This basic conclusion holds
with the other semantic paradoxes which are paradoxical because they do not
posses one definite truth-maker with a grounded ontological priority. Dewey’s
suggestion that even a grounded ontologically prior truth-maker implies an
ungrounded regress of truth-makers unhinges the very stability of the
truth-maker axiom.
What is at stake for the
pragmatists is an understanding of truth that overcomes the short comings of
the coherence and correspondence views of truth. “Truth of an idea is not a
stagnant property inherent in it. Truth happens to an idea. It becomes true, is
made true, by events. Its verity is in fact an event, a process. Namely the process of verifying itself.”4
This move towards a dynamic understanding of truth in pragmatism certainly
opposes much of the standard tenants of coherence and correspondence. It denies
out rightly the notion in coherence that truth is inherent in statements within
the coherent system. This innateness of truth held in coherence theory is what
opens it to attack by semantic paradoxes. If truth is innate in any statement
which is true, then statements like “this sentence is false” should have some
innate truth property. If a truth property is guaranteed by statements like
this via coherence, then there is no avoiding the contradiction that if the
statement is inherently true it must be false and if it is, then it is
inherently false. It also rejects the given relation of statement to
truth-maker in correspondence theories. The truth-maker axiom, as formulated,
does not hold that a statement is verifiable via a truth-maker but is proven by
a truth-maker. The relationship of each statement to its truth-maker is
absolute and logically necessary. James suggests that there is no way of
concluding the necessity of any truth-maker relation and that contingency is
the very nature of truth in the world. Truth is contingent, in that it is
always in need of verification and is not taken as a necessity or a given.
However, this contingent approach
to truth need not exclude the notion of truth-maker. In statement-to-truthmaker relationships, ontological priority is needed
for such a relationship to produce a truth value. Yet, as the pragmatists have
argued, no such static relationship is tenable. Instead, such ontological
priority can be recast and understood as contingency. This doesn’t seem too
drastic a step to say that in such a statement as “the grass is green” the
truth of such a statement is contingent on the state of the grass. In
statements about universals this works as well. To say “Grass is green” agrees
with the condition of ontological priority in that the truth-maker, the
properties of grass, must exist in order for the statement to have a truth
value, but it is also just as fair to say that the statement is contingent on
the state of affairs of grass universally. Grass must be green in order to
assign the statement a truth value but nothing necessitates the greenness of
the grass corresponding to the content of the statement. In a final step,
logical relationships such as “if P then Q” are contingent upon the content of
P and Q in addition to the relationship between P and Q. This is not to deny
the coherence on the laws of logic but to say that such axioms of logic are
coherent only when they correspond to actual states of the world. Truth-makers
in this sense are always free to either conform to or disconfirm statements.
Contingency does not ruin the truth-maker’s solution to the Liar Paradox
either. The truth statement “This sentence is false,” is contingent upon the
confirmation of its own truth content as a truth-maker which is in turn
contingent upon the truth content it is meant to establish. If the truth-maker
is understood as a contingent principle determining where and when logic
applies, it still can serve the same function of determining truth values in
the process of verification.
To conform
the truth-maker axiom to pragmatic concerns seems unproblematic. As have been
demonstrated earlier, the “Revenge Problem” Strengthened Liar statements and
truth-teller statements of the form, “This sentence is true” which seems to
resist the identification of one clear and distinct truth-maker upon which it
is contingent. This problem need not affect a pragmatic understanding of
truth-makers. “A common assumption of both realistic (correspondence) and
idealistic conceptions is that a statement by its nature implies an assertion
of its own truth…No, replies the pragmatist, a statement, a proposition, in
just the degree in which it has a genuinely intellectual quality, implies a
doubt concerning its own truth and a search
for truth, an inquiry for it.”5
What statements such as “This sentence has no truth-maker” and “This sentence
is true” lack is such an invitation to inquiry. They effectively shut down the
possibility of the further testing of their veracity since they declare their
own truth value and a search for a definite truth-maker in them leads to
nowhere (as previous explication of these paradoxes has shown). The pragmatic
condition of openness to inquiry will ultimately be how such paradoxes can be
disqualified.
It remains to be seen how such an
inquiry occurs with this newly recast pragmatic truth-maker. A deeper
explication of how such a pragmatic inquiry about truth operates is called for.
“Every proposition is a hypothesis referring to an inquiry still to be undertaken, its truth is a matter of its career, of its
history: that it becomes or is made
true (or false) in process of fulfilling or frustration the use of its own
proposal.”6
Human existence cannot be separated out from the actions people take. This is a
fundamental point of the pragmatist position. Thus, statements are seen within
the context of human action in which they are said. Thus James states, “The
practical value of true idea is thus primarily derived from the practical importance
of their objects to us.”7
Statements such as the “It’s pitch black outside” have to have some motivating
force behind their utterance and must have some resulting action in order to be
verified as either true or false. In the case of the statement, “It’s pitch black outside,” it may be verified by one’s
inability to see outside and thus unable to see a rock on the path and trip on
it. Accepting such a truth statement coming from someone else might lead one to
carry flashlight before going out and thus being able to avoid the rock in the
path.
The practical consequences of mundane factual questions seem obvious. The more important distinction pragmatist theory must make is for what counts as truth and what is able to be disqualified of meaning in the more abstract statements, “This sentence is true,” and “This sentence has no truth-maker.” The pragmatic question is under what context could such paradoxical statements have any practical pay-off which is necessary for verification of truth within pragmatism. “True is the name for whatever idea starts the verification process, useful is the name for its completed function in experience. True ideas would never have been singled out as such, would never have acquired a class-name least of all a name suggesting value, unless they had been useful from the outset in this way.”8
The truth-teller statement starts
no such verification process. Its assertion of truth ends the further inquiry
into it. If it is true then it is; there is nothing to verify since the
sentence conflates the claim of its statement and the truth-maker of that
claim. Yet why would the truth value of the truth-teller matter to anyone if it
is context-less as it is in this formulation? Given context the lines of
inquiry are clear, if someone tells one “Really, I am telling you the truth
about the 7000 lb hippopotamus with bad acne. I speak only the truth,” Inquiry
into the statement “I speak only the truth,” will be shaped by the previous
statement asserting the truth of the existence of a 7000 lb hippopotamus with
bad acne and the verification of that statement will in turn inform future
judgments of truth from that individual. The same is true of the Liar Paradox.
Without context, the Liar statement does not provoke further inquiry but, once
put into the context of having been uttered by a particular person,
it suddenly becomes meaningful in judging the potential trustworthiness of that
particular individual given his asserting paradoxical statements. Statements of
the form of the Strengthened Liar, “This statement has no truth-maker,” have no
such pragmatic pay-off or any further inquiry. As demonstrated in previous
analysis of this paradox, inquiry into the truth value of the statement leads
to contradiction and the search for a truth-maker for such a statement leads to
nowhere. Because of this lack of practical meaningfulness to human
understanding, in a pragmatic framework, any strengthened form of the Liar
statement is disqualified.
Truth and the logical laws built to govern it
are particular means to a particular end in pragmatism, especially the school
of thought dubbed instrumentalism that arose from the work of Dewey. Truth is
primarily a tool used to achieve ends within a worldly context. “The point and
reference of the statement is in the use to which the thing is to be put; the
matter of the statement is some existing fact or antecedent. No genuinely
intellectual proposition implies an assertion of its own truth but is only an
anticipation of becoming through the search its own doubtfulness exacts.”9
All statements are thus contingent upon the outcome of their implications for a
truth value. The statements which are true are the ones which have caused some
benefit when human action conformed to them. Survival itself relies upon this
understanding of truth as the propositions that are in the best interest of a
living being to adhere to it also. Though often criticized for being an overly
simple understanding of truth, the pragmatic and instrumentalist understanding
of truth does avoid the pitfalls of coherence theory and correspondence theory
in the face of paradox.
With this understanding of the
pragmatist theory of truth, the notion of the truth-maker axiom can be
revisited and examined from a pragmatic standpoint, not as law for truth but as
a tool discovering truths in the world. A truth-maker is some set of conditions
ontologically prior to a particular truth statement and upon which the truth
statement and its logical implications are contingent. As pragmatist theory
asserts, what a statement is contingent upon for a truth value is the result of
employing such a statement practically in life. Thus, pragmatic truth-makers
are in fact the results of such practical employment of contingent statements
and propositions and the resulting logical relations. If a truth-maker within
correspondence theory is the reality to which statements correspond, in a
pragmatic theory of truth, a truth-maker is the reality of the results of
certain statements and beliefs. “By ‘realities’ or ‘objects’ here, we mean
either things of common sense, sensibility present, or else common-sense
relations, such as dates, places, distances, kinds, activities.”10
Truth-makers are the “real” events of the world which shape human endeavor and
practice. “We so constantly utilize this anticipation as itself a definite
factor in securing a desirable and avoiding and undesirable result that we fail
to note the extraordinary character of its performance – the capacity to make
an unachieved future a present factor in its own determination.”11
What humans do in practice is to perpetually make contingent propositions which
have yet to be bore out by the truth-maker of such propositions, experience.
Such experience determines the truth or falsity of those previously made
contingent statements and the results of that “truth-making” inform the next
propositions which again will be borne out by experience and the pragmatic
truth-maker cycle continues to shape how humans relate to reality.
Now the first criticism that the
pragmatic notion of the truth-maker must answer is the claim that it is simple
subjectivity and, in its removal from the correspondence theory of truth, has
lost the objective reality which it had previously contributed to propositions.
Dewey again anticipates such an argument, “Being itself used as a factor in
reaching the desired end, the way it fits into, or corresponds with other
factors is a matter of prime moment. Were it not a factor at…or were it the
only factor it would not be liable to correction or to verification; there
would be no intelligible sense in which it would correspond.”12
Truth-maker conditions must correspond in some sense to an ontologically
separate reality. People cannot invent what is true about reality, but can only
test what propositions seem to work and from that determine the sense of what
is true. In this sense an external reality does act upon human experience
independent of it, but the extent to which that external reality means
something to human life is a matter as to what practical statements can be
derived from the events of experience. Pragmatic truth-makers are neither
totally objective nor totally subjective and they must be or else they are
meaningless to human experience. “Its own use is the way it corresponds with
the other efficient conditions involved.”13
Now this new truth-maker axiom can
be fully restated in its pragmatic form. “Any given statement p’s truth is contingent upon the events,
results, or states of affairs which result from the adopting of p as a basis for decision”. This is very
different from the original logical formulation but still does its job. In
paradoxical situations, like the Liar statement “This statement is false” what
makes it true? According to the pragmatic model, the truth-maker for such a
statement would be the conditions or states of affairs which would cause the
liar statement to be adopted as a belief or basis for action. Nothing
meaningful would entail from adopting such a statement because it does not
invite further inquiry by asserting its own truth value. The conflation of the
sentence’s actual truth and what that truth would entail is still grounds for
dismissing it as a meaningless statement just as when the truth-maker axiom is
viewed as part of the coherence theory of truth. The practical effects of
accepting the Liar statement would rely first on the determining what it
entails as a belief for human action which cannot be determined until the
practical effects of the liar are understood. Any strengthened form of the Liar
statement must meet the same demand of having some practical effect on human
life to posses any meaning for logic to apply, and no such practical effect is
derivable from “This sentence has no truth-maker”.
This would also resolve the
ambiguities of the truth-teller statement, “This sentence is true” because if
it were true in the pragmatic understanding, then, some state of affairs would
prompt the adoption of it as a basis for action. There is, however, no possible
action or even further line of inquiry for such a statement. It simply is what
it is. Though it asserts its own truth, no truth is totally asserted in
pragmatic understanding. It does not open itself up to external verifiability
through further inquiry. It simply is what it is or isn’t. This however leaves
no mark on the human experience and thus is meaningless to human understanding
and practice. What must be understood is that this does not imply that it is
absurd or false, but simply that no person could understand what a statement
like that would be like if it were in fact true. Rejecting the truth-teller
according to a pragmatic truth-maker principle does not however damage other
truth asserting statements in language, since some truth-maker of events or
states of affairs determining action are implied if the truth-asserting
statement has any contextual meaning in particular human life.
There are still other paradoxes
like Yablo’s and the Ordered-Pair which refer to
infinitely referential truth statements. In the simple Ordered-Pair, the first
sentence claims the second sentence is false and the second sentence claims
that the first is false. This circular argument cannot posses a pragmatic
truth-maker because if the sentences only refer to the truth values of each
other, there is no external reality or state of affairs which could have any
impact on human action which could relate to or settle the issue of the
circular claims. Yablo’s Paradox is one of an
infinitely descending chain of statements claiming the falsity of all those
statements beneath it. Again, such paradox cannot be too problematic since it
does not refer to any external state of affairs except an unending series of
truth values. Truth if it is really truth does not asset itself as such. Only
in statements directly related to the way people’s beliefs directly relate to
events and the state of affairs of the world are these open to truth values.
Even then only after their practical results are borne out, is truth made. Paradoxes
in pragmatism are a pseudo-problem arising from a misguided notion of truth.
The truth-maker axiom is one thing that can be salvaged from correspondence theory for pragmatism. In the framework for pragmatic thought established by James and Dewey, the notion of a truth-maker is there. Pragmatists admit to a necessary correspondence to things people think and say and the way the world is. What pragmatists cannot accept is that such correspondence can be completely and definitively mapped via human propositions. Instead, the correspondence must be more subtle. Propositions about the way the world is must be objective but they must only have truth value according to how well they guide human experience. In such a case the events of experience and state of the world make truth for human minds and such truths can be again applied to guiding human experience. No truth condition can stand on its own in pragmatist theory and once reformulated the pragmatic truth-maker axiom is an appropriate way to formulate how truth does arise in experience. Paradox is a result of taking truth from the world and placing it within systems for determining it. The relations between the human person and the world are what are prior to the systems created to interpret and understand them.□
©Shaun Malleck, 2007
1 John Dewey, “Truth and Consequences,”
Pragmatism, Old & New, ed. Susan
Haack (