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THE PHILOSOPHICAL BASIS OF DIALETHISM?
Jon Cogburn1
Department of Philosophy and Linguistics Program
Louisiana State University
ABSTRACT: In the first half of the paper I show how considerations about the defeasibility
of evidence commit the Dummettian anti-realist to dialethism. Rather than conclude that
Dummettian anti-realism is false, I argue in the second half that such dialethist anti-realism is
a very plausible way to characterize some discourses.
This involves a number of
demonstrations. First, I stand Putnam’s model theoretic argument on its head to motivate a
truth-value glut semantics. Second, I show how this semantics justifies normal use of
classical logic in exactly the same way that successor theories in physics justify continuing
use of earlier false theories. The fact that dialethism actually justifies use of classical logic
undermines what we might take to be the most telling criticism against it. I conclude by
discussing Sartre’s tragic choice and severe intuition clashes in ethics as a test case for the
model, arguing that dialethist anti-realism is a good meta-ethical view.
For Dummettian anti-realists, the claim that meaning is use can be explicated by the
following schema, taken to hold over all meaningful sentences and speakers of language.
Recognition Thesis.
X understands P if, and only if, were X presented with a construction c, then X
could recognize whether c verifies, and whether c refutes, P.
Given that the constructions are assumed to be both necessary and sufficient for truth, the
Recognition Thesis is generally taken to entail that verifiability is both necessary and
sufficient for truth, which can be stated by means of this schema.
e-mail: [email protected]
address: The Department of Philosophy,
106 Coates Hall,
Louisiana State University,
Baton Rouge, LA 70803
Telephone: (225) 578-2220
1
1
Knowability Requirement.
P is true if, and only if, there exists a construction c verifying P.
This requirement lay at the heart of Dummett’s demand that constructivist semantics in
some manner replace the use of classical model theory as part of the architecture of a
natural language grammar. This is because constructivist semantics for intuitionistic
logic and mathematics proceed by recursively correlating conditions for the existence of a
verifying construction (as opposed to classical, bivalent truth conditions) with sentences
of mathematical theories.2 Thus, a revisionary anti-realist such as Dummett who wants to
import the technical apparatus of constructivist mathematics to the realm of natural
language semantics needs to independently motivate the necessity and sufficiency of such
verifying constructions for the truth of non-mathematical sentences.
I will show that the Recognition Thesis only provides evidence for the
Knowability Requirement if dialethism is correct. If there are no true contradictions, then
the Dummettian Recognition Thesis actually undermines the Knowability Requirement.
Establishing this is the dialectical charge of the first part of this paper.
One might say, “Your modus ponens is my modus tollens.”
If the whole
Dummettian package entails the existence of true contradictions, shouldn’t we just give
up the Dummettian package?
A negative answer to these questions requires
independently motivating dialethist anti-realism. This is the charge of the second part of
this paper.
Fax: (225) 578-4897
2
For example, see the discussion in [8].
2
I. IF VERIFICATIONISM IS TRUE (AND DIALETHISM FALSE), THEN TRUTH
ISN’T VERIFIABILITY
Convincing the Dummettian that dialethism is true requires reexamining some old
positivist distinctions in light of Dummett’s dialectic. The ones that concern us are the
verifiability-in-principle/verifiability-in-practice
and
the
strong-verifiability/weak-
verifiability distinctions from A.J. Ayer’s Language,Truth, and Logic.
I.1
First we attend to the distinction between verifiability-in-practice and
verifiability-in-principle. We define verifiability-in-practice as:
A construction c verifiesin-practice P =def c is a warrant for P and c can be
recognized as such by minimally competent people with little or no idealization
of their cognitive capacities or technologies.
For example, I can currently verify the sentence “No dog is on this table.” While the
distinctions between minimally competent people and incompetent people, and between
minimally competent people with idealized capacities and technologies and minimally
competent people without idealized capacities and technologies are surely vague, nothing
here hinges on them being precise.
It is not difficult to show that adopting verifiability-in-practice as the notion of
warrant mentioned in Dummett’s Recognition Thesis leads to absurdity.
Since the
second conjunct in the definition of verifiability-in-practice concerns how much
idealization is required for people to be charged with recognizing a warrant, the
appropriate form of Recognition Thesis would be:
Recognition Thesis'.
3
X understands P if, and only if, were X presented with a construction c (where c
can be appraised by minimally competent people with little or no idealization of
their cognitive capacities or technologies), then X could recognize whether c
verifies, and whether c refutes, P.
The problem is that the condition is trivially satisfied by any sentence whose warrants
(both positive and negative) cannot be recognized by minimally competent people with
little or no idealization of their cognitive capacities or technologies.
For any such
sentence, there is no possible world containing a warrant for or against it which can be
easily recognized. At best, the speaker is able to recognize failed warrants for the claim.
But then the thesis wouldn’t distinguish a speaker’s grasp of any two sentences with
distinct meanings that are both in-practice undecidable.
This result is unacceptable, and should be unacceptable for any clause that is
supposed to provide sufficient conditions for the grasp of a sentence’s meaning. 3 For,
ceteris paribus, if two sentence are different in meaning, and a speaker understands both
sentences, then the speaker should know that they are different in meaning.
The verificationist has to modalize her conception of verifiability. If verifiability
is to serve as a necessary condition on truth, as it was for Ayer, then verifiability must be
in-principle, which can be defined as:
A construction c verifiesin-principle P =def c is a warrant for P and c can be
recognized as such by minimally competent people with arbitrarily large but
finite idealization of their cognitive capacities and technologies.
For example, there are infinitely many simple number-theoretic claims (involving large
numbers) that are unsolvable by human or machine aided computation and which are
3
Some authors (e.g. Neil Tennant in [32]) explicitly state the Recognition Thesis (Tennant calls it the
Manifestation Requirement) as merely a necessary condition on understanding. I present it as both
4
therefore not verifiable-in-practice, yet still verifiable-in-principle.
Paradigmatic
empirical sentences that may be verifiable-in-principle but not in-practice involve
conditions in inaccessible or simply far away regions of space-time.
Clearly, making the Recognition Thesis plausible involves the importing a similar
kind of idealization of the speaker in the antecedent of the counterfactual conditional.
Recognition Thesis''.
X understands P if, and only if, were X ’s cognitive capacities and technologies
finitely extended (in an appropriate manner), and X were then presented with a
construction c, then X could recognize whether c verifies, and whether c refutes,
P.
One might argue that the idealization renders these conditions irrelevant to a speaker’s
understanding of sentences. What does a possible world counterpart who can recognize
huge sums as being correct have to do with a speaker’s understanding of “plus”?
Conclusively resolving this issue takes us too far from our current dialectic, which
involves showing that the Dummettian anti-realist should be dialethist. However, I don’t
think that this worry is particularly damning. As long as the idealization is appropriately
related to a speaker’s actual inferential and evidentiary dispositons as she manifests them,
there should be no problem.
In The Taming of the True, Neil Tennant suggests how such an idealization can be
appropriately limited by the actual behavior of speakers. He gives the constraint in this
manner:
(RF) For a speaker S to be credited with a grasp of the meaning of a sentence ,
we should have good grounds for believing that, if presented with some finite
piece of discourse , S would be able to deliver a correct verdict on any aspect
necessary and sufficient because sufficiency is presupposed in, as far as I’m aware, every anti-realist
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of  that is relevant to arriving at a correct judgement of the form “ is a proof
of ’ or of the form ‘ is a disproof of ’ or of the form ‘ is neither a proof
nor a disproof of ’” that is, for any such aspect , S would, after some time, be
able to judge whether  was as it ought to be, in order for  to have the status
in question. [32, p. 154]
It is to be hoped that by adopting something like Tennant’s (RF) constraint, the
idealization in our final form of the Recognition Thesis can be shown to be nonproblematic. Surely something like Tennant’s constraint is needed. For example, since a
spider’s cognitive capacities could be extended enough for it to be a very good proof
checker of proofs in real analysis we would thus be forced by an unconstrained
Recognition Thesis to say that the spider understands propositions of real analysis.
There are other authorities to whom we can appeal in a further attempt to avoid
this problem. It is exactly the problem generative linguists face in their account of tacit
knowledge of a grammar.4 The grammar discerned by the linguist is a “competence
theory,” known only to the idealized speaker. This idealized speaker is thought to not be
subject to any cognitive shortcomings whatsoever. But then we must wonder what such
an idealized speaker has to do with actual speakers. It is via a “performance theory” that
generative linguists are to specify this. The success of linguistic approaches stemming
out of Chomsky’s earlier work provides some evidence that this problem is solvable in
our context as well.
In the closing section of this paper, we shall see that one of dialethism’s greatest
strengths is that it provides the anti-realist the dialectical wherewithal to answer this
problem much more convincingly than the non-dialethist.
argument for the identification of truth with verifiability (as, for example, in Michael Dummett’s [9]).
4
See [6] for the canonical discussion.
6
I.2
For semantic anti-realists, the satisfiability of the Recognition Thesis by a speaker
and a sentence is supposed to explain the speaker’s understanding of the sentence in
terms of how the speaker uses the sentence. The set of dispositions mentioned in the
Recognition Thesis are the kinds of practical capacities which Dummett argues must be
correlated with the truth conditions generated by a compositional semantics, if we are to
explain linguistic competence by the attribution of tacit knowledge of a compositional
semantics.5
Moreover, the Recognition Thesis is supposed to provide evidence for the
Knowability Requirement. In many writings Dummett, Tennant, and Crispin Wright
discuss issues concerning language acquisition, normativity, and communication to
provide evidence for the Recognition Thesis.6 However, it is exceedingly difficult to
discern a direct argument from the Recognition Thesis to a Knowability Requirment. As
we shall see, the road from one to the other is not at all straight. Most important for our
purposes, however, is how this road leads to dialethism.
To cover this ground we must focus on one half of the biconditional composing
the Knowability Requirement. We can give this principle as:
Verification Constraint.
If P is true, then P is verifiable.
In this section we will be solely concerned with the proper notion of “verifiable”
occurring in the Verification Constraint, given that the Verification Constraint is
supposed to follow from the Recognition Thesis.
5
See especially [10] and [11].
7
Due to the ambiguity of “verifiability” we do well to stipulate some notational
conventions at the outset. “P is verifiable” means it is possible that P be verified. What
is the strength of this possibility? In a sense, it is clearly possible to verify “Cows fly,”
because we would be able to recognize flying cows as verifiers for the sentence.
However, in another sense, it is not possible to verify that cows fly because we’re not
going to run into any flying cows.
We can disambiguate these two modals elegantly by sorting the domain of
quantifiers which range over constructions.
c(VcP) =def In some possible world there exists a construction c that verifies
P.
VP =def P is verifiable in the sense explicated by c(VcP).
c(VcP) =def In the actual world there exists a construction c that verifies P.
VP =def P is verifiable in the sense explicated by c(VcP).
It should be noted that in the Recognition Thesis as given, the constructions in question
are possible constructions, as they are mentioned in the consequent of a counterfactual
conditional.
The anti-realist’s argument for the Recognition Thesis entailing the Verification
Constraint begins with the assumption that there exist absolutely undecidable sentences,
that is, sentences for which no possible verifications or falsifications exist. Then the
worry concerns how to individuate the meanings of such sentences.7 If sentences’
meanings are individuated by the set of possible constructions which succeed and fail to
verify them, then any two undecidable sentences would have the same meaning.
For Dummett’s classical discussion, see [9], for Tennant’s see part 1 of [31], for Wright’s, [40], especially
pp. 1-43.
7
The following discussion concerning the individuation of meanings owes its genesis to personal
communications with and from Neil Tennant and Crispin Wright. I think it is an accurate distillation and
6
8
Unsurprisingly, the anti-realist does use verification conditions to individuate the
meanings of sentences, in a manner that can be represented as:8
Verificationist Canonicity Requirement.
The constructions quantified over in the Recognition Thesis must be such that
two sentences A and B have the same meaning if, and only if, for all
constructions c (from the same domain of constructions quantified over in the
Recognition Thesis) c verifies A if, and only if, c verifies B, and c refutes A if,
and only if, c refutes B.
On the assumption that the Recognition Thesis is correct, we do have some evidence that
verifying and falsifying constructions provide such a canonical manner to individuate the
meanings of sentences. As claimed earlier, if two sentences are different in meaning, and
a speaker understands both sentences, then the speaker should know that they are
different in meaning. However, if the anti-realist’s identity criterion for meanings is
false, then the Recognition Thesis entails that a speaker can understand two sentences
distinct in meaning and still remain unaware that their meanings are distinct. Thus, on
the assumption that grasp of meaning of two sentences different in meaning is sufficient
for recognizing that they are distinct in meaning, we can conclude that criteria for grasp
of meaning ought to individuate meanings as well.
An undecidable sentence is such that no constructions verify or falsify it. But
then any two undecidable sentences have the same set of possible verifiers and falsifiers,
the empty set. So if the Verificationist Canonicity Requirement is correct, then it follows
immediately that any two undecidable sentences have the same meaning. At this point
the anti-realist reasonably asks what possible use for communication such sentences
combination of their considered views about the anti-realist’s dialectic. As such, though, it may not
represent either one of their views.
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could have. Presumably one who believes that there do exist such undecidable sentences
believes we can usefully communicate information with them. But if all such sentences
have the same meaning, then (independent of the fact that they are verification and
falsification transcendent) it is completely unclear how we could possibly communicate
information with them. Thus, pending an answer to this challenge, the anti-realist’s
commitment to the Recognition Thesis and Verificationist Canonicity Requirement also
commit her to the nonexistence of absolutely undecidable sentences.
Given our notational conventions, we can formalize this claim about the nonexistence of an undecidable sentence as P~(~VP  ~V~P). This is classically
equivalent to saying that every claim is either verifiable or falsifiable. Both of these
claims follow logically from verifiability being necessary for truth. However, this may
be irrelevant, since we are trying to discern an argument to the conclusion that
verifiability is a necessary condition for truth. The second claim, P(VP  V~P),
does entail that verifiability is a necessary condition for truth, on the assumption that
verifiability is sufficient.
However, if no such assumption is made about the verifiers mentioned in the
Recognition Thesis being sufficient, we do not yet have an argument for the Verification
Constraint. From the Recognition Thesis and the above train of thought, we have that
either a claim or its negation is verifiable, but this does nothing to prohibit the existence
of a true claim that is falsifiable, and not verifiable, without the assumption of the
sufficiency of such verifiers for truth. Such an assumption is clearly unsatisfactory,
unless we have arguments that show the Recognition Thesis to be plausible with such a
8
For the canonical discussion, see Dummett’s discussion of Fregean senses in the appendix of [10].
10
strong notion of verifiability (i.e. one that is sufficient for truth). Thus, it behooves us to
attempt to find an argument from the Recognition Thesis to the Verification Constraint
which does not rest on the sufficiency claim.9
Dummett’s broader dialectic does propose a manner in which the Recognition
Thesis can provide evidence for the Verification Constraint. Dummett was one of the
first to argue that there are difficulties in subscribing to the Chomskyan assumption that
understanding of a language is in virtue of tacit knowledge of a grammar, where the
semantic component of this grammar is understood to be model theoretic. 10 For
Dummett, the Verification Constraint was an attempt to principly constrain a semantics,
so that it will not violate the Chomskyan assumption. Given this dialectic, the entailment
of P(VP  V~P) by the Verification Constraint can be thought of as providing
evidence for the claim that verifiability is a necessary condition for truth.11
If the notion of truth determined by our semantics is such that verifiability is
plausibly a necessary condition for truth, then we do have assurance that the semantics is
appropriately psycho-linguistically constrained, and will not violate the Recognition
Thesis. Crucially, this is inductive evidence for the truth of the Verification Constraint.
Construed deductively we have just affirmed a consequent (i.e. 1. The Recognition Thesis
9
Tennant (p.c.) thinks that the notion of verifiability proposed in the Recognition Thesis has always been
presupposed to be sufficient for truth by proponents and opponents of Dummettian realism. Given the
discussion presented above, it is clear that this cannot just be assumed without argument. To see this, note
that what is needed to get from (VP v V~P) to (TP  VP), is the assumption (VP  TP). This is the
assumption that if it is possible that there exists a verifier for a claim, then that claim is true. But the mere
possible existence of a verifier is certainly not sufficient for truth.
10
Again, see Dummett’s [10] and [11]. For a very nice discussion of these issues from within empirical
semantics, see the relevant discussion in David Dowty’s [7].
11
It should be clear that this consideration (as well as the following considerations about how the kind of
verifiability in the Verification Constraint should be no more restrictive than that which occurs in the
Recognition Thesis) does not hinge on any intuitionistically unacceptable moves. The moves are still valid,
even if we resolutely present both the Recognition Thesis and the Verification Constraint as entailing the
intuitionistically weaker claim that every sentence is not such that it is both unverifiable and unfalsifiable.
11
implies that every sentence is verifiable or falsifiable. 2. The Verification Constraint
implies that every sentence is verifiable or falsifiable. 3. The Recognition Thesis is true.
Therefore 4. The Verification Constraint is true.)
However, this kind of inductive
evidence for theoretical claims is the norm in empirical matters. So to the extent that
Dummett’s broader dialectic is reasonable, we do have some evidence for verifiability
being a necessary condition upon truth. Moreover, the kind of evidence in question is of
a piece with Dummett’s broader claim that a verificationist semantics can be used in a
psychologically real theory of meaning, while a classical semantics cannot.
Motivating the Verification Constraint in this manner carries a heavy price. If it
is to follow inductively from the Recognition Thesis, then the kind of verifiability in the
Verification Constraint must be no more restrictive than the kind of verifiability
mentioned in the Recognition Thesis. For example, a Recognition Thesis with Ayer’s inprinciple verifiability occurring in it provides no evidence for a Verification Constraint
that forces verifiability-in-practice as a necessary condition upon truth. That is, there
must not be a sentence such that it is verifiable in the sense mentioned in the Recognition
Thesis, and unverifiable in the sense mentioned in the Verification Constraint. If such a
sentence did exist, then we would correctly conclude that the Recognition Thesis did not
provide any inductive evidence for the correctness of the Verification Constraint. In what
follows, “the inductive constraint” shall be the name of the principle that if a sentence is
verifiable in the sense mentioned in the Recognition Thesis, then it is verifiable in the
sense mentioned in the Verification Constraint.
12
This fairly obvious claim, following from reflection on the manner in which the
Recognition Thesis provides evidence for the Verification Constraint, is extraordinarily
important for the dialectic of this paper. From Ayer’s considerations, presented in the
next section, we will have that the verifiability appropriate to the Recognition Thesis is,
at best, sufficient for dialethist truth. But then, by the inductive constraint, we shall have
shown that the kind of verifiability in the Verification Constraint is, at best, sufficient for
dialethist truth. In this manner we shall have established either that the anti-realist’s
Knowability Requirement (which states that verifiability is both necessary and sufficient
for truth) is false, or that dialethism is true. The choice for the Dummettian anti-realist is
then stark. On the one hand she can read this result as holding that if verificationism
(about grasp of meaning) is true, then truth is not verifiability. On the other hand, she can
keep the two main planks of Dummett’s program (the Recognition Thesis and
Knowability Requirement) and embrace dialethism.
Before establishing this, and ultimately urging dialethism on Dummettian
grounds, we must consider one dialectical move that the opponent of the anti-realist
might make at this point.
Given that the Verification Constraint motivated by the
Recognition Thesis only demands that true claims be verified by possible constructions, it
might seem obvious that no evidence has been provided for the claim that verifiability is
sufficient for actual truth. This would strongly motivate the “if verificationism is true,
then truth isn’t verifiability” reading of this paper. Taking the possible existence of a
verifier to be sufficient for truth would yield the following Knowability Requirement.
Knowability Requirement.
P is true if, and only if, it is possible that there exists a construction c verifying
P.
13
(T P  VP , or T P  c(VcP)).
But then, the anti-anti-realist will point out that it is clear that a possible verifier is not
sufficient for truth. Does the anti-realist systematically equivocate?
The passage might be motivated by an epistemic understanding of the modal “is
possible.” If “It is possible that P” were understood as, “P would be discovered true,
were investigation undertaken,” then no equivocation has been committed, but in fact we
would have both that V P  VP, and c(VcP)  c(VcP). Then the Knowability
Requirement would be equivalent to:
Knowability Requirement'.
P is true if, and only if, there exists a (possibly undiscovered) construction c
verifying P.
(T P  VP , or T P  c(VcP)).
As far as I’m aware, nobody has argued that the modals should be so collapsed. I
conjecture that this is because most of the Dummettian discussion thus far has been about
mathematics, where it is not completely implausible to think that if a claim is possibly
true, then it is true, and if a claim is true, then it is necessarily true. If one accepts this,
then the above modals do naturally collapse.
While such a collapse may thus be
motivated for mathematics, it cannot be motivated in the same way for empirical claims,
for it is prima-facie very plausible to hold that “cows fly” is verifiable in another possible
world (one containing flying cows) and not verifiable in this one.
Luckily, the collapse of the epistemic modal in this context can be motivated in
other ways. First, note that the anti-realist really only needs the inference from the claim
that P is true and it is possible that there exists a verifier for P to the conclusion that there
does exist a verifier for P (formally, (T P  VP)  VP ).
14
This is because the bad
scenario is that the Verification Constraint merely states that if a sentence is true, then it
is possible that there exists a verifier for that sentence (TP  VP). Then we want to get
from that to the stronger principle that if a sentence is true, then a (possibly undiscovered)
verifier does exist for that sentence (TP  VP). But it is a short and trivial proof from the
(T P  VP) and needed inference, ((T P  VP)  VP), to the needed conclusion, (T P
 VP).
The needed inference is very plausible, for the notion of verifiability we are
working with has already been modalized by the move to in-principle verifiability in the
last section. By the considerations of the last section, VP merely states that there exists a
warrant such that someone with arbitrarily large extensions of cognitive and
technological resources could correctly assess that warrant as a warrant for P. Now if a
claim is true, and it is the kind of claim that we agree could possess such a warrant, it is
plausible to think that it does indeed possess that warrant. Given that the person for
whom the warrant is accessible can be idealized so much, there’s no reason to think that a
given true claim would, in the actual universe, possess such a warrant.12
As with the issue of idealization in the anti-realist’s dialectic, much more could be
said here, but I hope that we have shifted the burden of proof to the anti-anti-realist, and
if not that much, at least assuaged enough doubts to allow us to move on to the main
claim.
12
The same point could (and ultimately should) be argued by having the warrants be something more
plausibly accessible to less idealized people. Since (as we show in the concluding section of this paper)
one of the advantages of anti-realist dialethism is that the warrants are more accessible than the nondialethist anti-realist’s, this consideration ends up being a strong argument in favor of the dialethist.
However, I don’t want to prejudge any issues in favor of the dialethist at this point.
15
I.3
Here I will show that verifiers in the Recognition Thesis cannot be sufficient for
non-dialethist truth.
This requires attending to another positivistic distinction, that
between strong and weak verifiability. Strong verifiability can be defined in this manner.
A construction c verifiesstrong P =def c is an indefeasible warrant for P, i.e. c
cannot be defeated by future information in any possible extension of our
current state of information.
Ayer held very few propositions to be strongly verifiable.13 While strong verifiability
may be defensible as a characterization of some mathematical sentences, it is not very
plausible anywhere else. This is because warrants for the truth of most of our beliefs
(taken one at a time) can be overturned by future information.
We must note how untenable strong verifiability renders the Recognition Thesis.
For the sake of parsing, we stipulate that “Understands (S,P)” means that speaker S
understands the sentence “P,” “Finitely Extended (S)” means that the speaker S has
sufficiently and reasonably extended cognitive capacities and technologies, “P [ ] Q”
means that if P were the case then Q would be the case, and “Presented with (S,c)” means
that the speaker S is presented with the construction c. Then we would have,
Recognition Thesis (strong).
Understands (S,P) 
(Finitely Extended (S) [ ]
c{indefeasible verifiers}((Presented with (S,c) [ ]
S recognizes whether c verifies, and whether c refutes, P))).
Apart from the question of what S could actually be recognizing in the attitude ascription,
the defeasibility of empirical warrants renders this thesis vacuously able to be fulfilled.
Ayer actually makes the distinction in this manner, “A proposition is said to be verifiable, in the strong
sense of the term, if, and only if, its truth could be conclusively established in experience. But it is
verifiable, in the weak sense, if it is possible for experience to render it probable.” [2, p. 37]
13
16
Thus, for any real warrant P that S is presented with, the rightmost counterfactual
conditional will be satisfied, independently of anything about the agent’s recognitional
behavior.
Ayer was motivated to characterize verifiability in a weaker manner because of
the problem with requiring strong verifiability to be a necessary condition for truth. We
can characterize Ayer’s weak verification as:
A construction c verifiesweak P =def c is a defeasible warrant for P, i.e. c can be
defeated by future information in possible extensions of our current state of
information.
Like all of the other modalities we have been using, the notion of a warrant which “can
be defeated by future information in possible extensions of our current state of
information” is difficult to make precise. In any case, something in the neighborhood of
weak verifiability is at least prima facie plausible as a necessary condition upon truth.
Likewise, something in the neighborhood of a weak Recognition Thesis is not
immediately implausible as a necessary and sufficient condition upon the understanding
of a sentence.
Recognition Thesis (weak).
Understands (S,P) 
(Finitely Extended (S) [ ]
c{defeasible verifiers}((Presented with (S,c) [ ]
S recognizes whether c verifies, and whether c refutes, P))).
With this on the table we can attend to the already established fact that the notion of
verifiability occurring in the Verification Constraint must be no more restrictive than that
which occurs in the Recognition Thesis, if the Recognition Thesis is to provide evidence
17
for the Verification Constraint. Thus, the weak Recognition Thesis at best provides
evidence for the following restriction upon truth.
Verification Constraint (weak).
If P is true, then there exists a construction c such that c is a defeasible warrant
for P
(T P  c{defeasible verifiers}(VcP)).
But then our question is simple. Can such defeasible warrants possibly be sufficient for
non-dialethist truth? They cannot.
It is very clear that some claims will be such that they and their negations are both
weakly verifiable. For example, consider the historical claim that Caesar prosecuted
Gaius Rabirius before Cicero had Cataline’s co-conspirators killed. Cicero writes that he
did, and this does provide some evidence that Caesar did so; however, Cicero’s selfaggrandizing tendencies along with other considerations concerning why Caesar might
have done such a thing provide evidence for the claim that Caesar’s behavior took place
after Cicero prosecuted Gaius Rabirius. Here we have positive evidence both for and
against the claim in question.14 Both considerations qualify as weak verifiers in the sense
we have delineated.
Given that there exist sentences which are both weakly verifiable and weakly
falsifiable, the following argument shows that the verifiers in the Verification Constraint
cannot be sufficient for non-dialethist truth. Here, “VRT” means that P is verifiable in the
14
It should be clear that nothing hinges on this being a completely historically compelling example. What
is of interest to us is just that it illustrates how it is possible to have compelling evidence for and against a
claim. For example, Colleen McCullough argues that if the trial occurred after the executions, then all of
the following make much more sense: (1) the Centuries’ willingness to damn Rabirius, (2) Cicero’s early
fear of Publius Clodius, (3) Cicero’s early hatred of Caesar, and (4) Cicero’s later silence about the trial.
[21, p. 86]
18
sense of verifiability occurring in the Recognition Thesis, and VVC” means that P is
verifiable in the sense of verifiability occurring in the Verification Constraint.
1. P(VRT P  VVCP)
from the inductive constraint
2. VRT P  VRT ~P
from defeasibility considerations (for some P)15
3. P(VVC P  T P)
from the Knowability Requirement
4. (VVC P  VVC ~P)
1,2 universal elimination, modus ponens
5. (T P  T ~P)
3,4 universal elimination, modus ponens
I conclude that, insofar as the anti-realist has offered evidence for the Verification
Constraint, the notion of verifiability occurring in the Verification Constraint at best
sufficient for dialethist truth.
II. DIALETHIST ANTI-REALISM
The natural, perhaps inevitable, reaction of most philosophers (for whom classical logic
is both natural and perhaps inevitable) is to view the above train of reasoning as a modus
tollens. On this reading all I have done is challenge the Dummettian hope of motivating
a verificationist theory of truth via an account of linguistic understanding. I do not think
this is the case.
To buttress my claim that anti-realist dialethism is plausible, I will first attack the
view that dialethism engenders logical revision. This is important because one of the
primary reasons that analytical philosophers eschew dialethism is because they think that
15
One way to block this premiss is to use probability theory to model the verifiers. Perhaps a claim is
weakly verified if its probability is greater than, say, .5. Then, since the probability of a claim and the
probability of that claim’s negation always add up to 1, you could never get that both a claim and it’s
negation were verified. This option is not open to the anti-realist though, because it requires admitting that
such verifiers are not sufficient for truth, as having a probability of greater than .5 is certainly not sufficient
for truth.
19
it is somehow at odds with our normal (classical) inferential practices. I hope to show
that this is false.
I will then argue that anti-realist dialethism is a plausible meta-ethical view. Thus
it will be shown that: (1) some discourses might be such that they should be construed
along Dummettian lines, and (2) when evidence for these discourses is defeasible, it is
very plausible to think that there are indeed true contradictions.
II.1
Is truth in a model a good model of truth? The answer depends on how you
interpret the relevant indefinite descriptions. One of Hilary Putnam’s longest battles has
been against reading the first indefinite as picking out a specific model, or “the intended
interpretation” as we are wont to call it.16 Putnam argues that since isomorphic models
make all of the same sentences true, there is no reason to think that one model is a better
interpretation of language than another one.
Putnam’s argument is controversial. Nothing I say depends upon its validity, for I
seek to stand Putnam’s argument on its head. For Putnam, limitation results about formal
languages motivate his metaphysical positions. We shall see how metaphysical positions
(similar to Putnam’s) motivate a certain formal approach to truth and inference. I raise
the argument simply to show that the correctness of classical inference does not require
us to interpret the assertion, “Truth in a model is a good model of truth,” as meaning,
“Truth in the intended interpretation is a good model of truth.”
For example say that a set  of models (standard classical ones) is admissible if
and only if all of the models in  are isomorphic to one another. Let’s say that a
20
sentence is HP-true in  (THP) if, and only if, some model in  is a model for that
sentence. We can symbolize this as:
(THP)P  (M ( M P) )
Here, truth in a model is our model of truth, but by “truth in a model” we merely mean
true in at least one of the admissible (isomorphic) models in the set .
There are a few interesting things to note about HP-truth. First, the existential
quantifier can be shifted to a universal one without changing the extension of the truth
predicate. We could have given our definition in this manner.
(THP')P  (M ( M P) )
Since all of the models in  are isomorphic, they make all of the same sentences true.
Thus, there exists a model in  for a sentence P if, and only if, every model in  is a
model for P.
Second, note that two quite different ways of defining entailment also end up
being coextensive. Following a distinction Timothy Williamson makes in a discussion of
supervaluational semantics,17 we can say that the set of sentences  locally entails the
sentence  if, and only if, every model for  is a model for . Formally, we write,
 local   M (M   M ).
Given that we are assuming our models to be standard, classical models, local validity is
just the standard Tarskian notion of entailment.
Global entailment, on the other hand, is defined in terms of HP-truth. Here a set of
sentences  entails a sentence  if, and only if, for any set of admissible models , if all
Much of the ensuing discussion comes from meditation upon (the version of) the “model theoretic”
argument presented by Putnam in the appendix of [23] as well as the philosophical discussions throughout
[23] and [24].
16
21
of the sentences in  are HP-true with respect to , then  is HP-true with respect to .
Where “(THP)” means that all of the sentences in  are HP-true with respect to , we
can formalize this as,
 global    ((THP)  (THP))
Again, given that all of the models in  are isomorphic to one another, it is trivial to
show that local and global validity are the same for HP-truth.
Thus, nothing in classical inference relies on truth in the intended interpretation
being a good model of truth, as HP-truth justifies all of the same inferences as truth in the
intended interpretation. In Reason, Truth, and History, Putnam takes this to provide
evidence for the falsity of philosophical realism, which he defines elsewhere as
a bundle of intimately associated philosophical ideas about truth: the ideas that
truth is a matter of Correspondence and that it exhibits Independence (of what
humans do or could find out), Bivalence, and Uniqueness (there cannot be more
than one complete and true description of Reality). [24, p. 107]
Putnam’s “internal realism” characterizes truth in terms of what it is rational to accept,
and hence has strong ties to Dummettian verificationism.
However, for Putnam, metaphysical realism is more than the claim that there are
verification transcendent truths. Putnam himself finds Uniqueness to be one of the more
troubling aspects of metaphysical realism. Though he puts it slightly differently, for
Putnam the coextension of HP-truth and truth in the intended interpretation lends a lot of
evidence to the falsity of Uniqueness. For example, he writes,
For why could it not be surd metaphysical fact that reference is the relation: x
refers to y in at least one admissible model M. Note that all these infinitely
See [35, pp. 142-163] for Williamson’s discussion. For the classic discussions of supervaluational
semantics see Fine’s [15] and Kamp’s [17], as well as Kamp and Partee’s [18].
17
22
many metaphysical theories are compatible with the same sentences being true,
the same “theory of the world,” and the same optimal methodology for
discovering what is true! [23, p. 48]
Again, the validity of this argument needn’t concern us. For our purposes, what is
germane is that Putnam is concluding too little. Once you hold that there is more than
one acceptable description of reality, the restriction that admissible models make all of
the same sentences true, or even be consistent with one another, is completely unfounded.
For example, if you had two consistent descriptions of reality, they could be conjoined to
form one description. The lack of inconsistencies between them would make them
essentially one description.18
Moreover, Putnam’s restriction to isomorphic models requires a hard and fast
distinction between the one empirical theory of the world variously interpreted by
inconsistent metaphysical theories.
Independent of any empiricist qualms about
Putnam’s use of this distinction, the Putnamian should realize that if we are really using
models to model language, then the models ought also to model metaphysical language as
well. But then the Putnamian is confronted with a variety of inconsistent models, each
having an empirical theory in common but containing metaphysical theories that
contradict each other. Therefore, the Putnam’s anti-realist position that there is more
than one acceptable description of reality only really gets teeth if the equally acceptable
descriptions are allowed to be inconsistent with one another.
It would be very easy here to appeal to the thesis of “underdetermination of theory by evidence,” where
in some non-trivial sense it is supposed to be the case that inconsistent yet empirically equivalent physical
theories are possible. Then these two theories would both be thrown into the admissible set of theories. It
should be noted that nothing I say depends upon this thesis. See Mark Wilson’s [36] for powerful
considerations against the thesis.
18
23
What is truly significant (for our purposes) about Putnam’s model theoretic
argument is how it suggests the anti-realist should model true contradictions. The natural
way Putnam should have generalized HP-truth involves realizing that “true-in-anadmissible-model” needn’t carry with it the assumption that the admissible models make
all of the same sentences true. Dropping Putnam’s unwarranted assumption gives us GPtruth, which can be formalized in exactly the same way
(TGP)P  ( M ( M P) ).
This is dialethist, as one can clearly get sets of models such that ((TGP)P  (TGP)~P)
hold. Note that this doesn’t reject classical logic, but rather exploits it. As long as it is
permissible to keep local entailment, classical logic is still validated. However, on this
approach, local equivalent is not equivalent with global entailment. Where we define
global entailment in this manner,
 global    ((TGP)  (TGP)),
we do not have  introduction as unrestrictedly valid. Since there is there is no  such
that TGP(P  ~P) (as no admissible set contains a model for (P  ~P)), a contradiction is
never true. However, as noted above, there are admissible sets of models containing
models for P and models for ~P. Thus, we have
~(P, ~P global (P  ~P)).
Also note that while local and global GP-entailment differ, local logical GP-truth (true in
all models) is the same as global logical GP-truth (true in all of the models of any
admissible set). This is because no admissible set of models will contain a model that
fails to be a model for a classical logical truth.
24
It is also interesting to note that changing the quantifier in the definition of GP
truth also produces a new truth predicate.
In fact, what is produced is a kind of
supervaluational semantics truth predicate. In supervaluational semantics, vagueness is
accounted for in terms of the existence of models where objects are in the extension of
predicates and other models where objects are not in those extensions. So, like our
dialethist, the supervaluationist countenances a set of admissible models, where some of
these models contradict one another. The only difference is that the supervaluationist
defines truth in this manner.
(TSV)P  (M ( M P) )
Given this definition, there is an aesthetically pleasing symmetry between
supervaluational semantics and our dialethism. With dialethist semantics TGP(P  ~P) is
never the case and (TGPP  TGP~P) is sometimes the case.
With supervaluational
semantics TSV(P  ~P) is always the case, and (TSVP  TSV~P) sometimes fails to be the
case.
Things get really interesting when you put the supervaluational approach together
with the dialethist approach, as Achille Varzi does in a recent article. Following standard
presentations of supervaluational semantics, Varzi starts out with a three valued model,
albeit one that contains inconsistencies. For the purpose of exposition, consider the truth
value assignment (call it ) on a propositional language where P is both true and false,
Q is neither, R is true, and S is false. Then you can form the set of consistent three valued
submodels,
{ --{TP, NQ, TR, FS}--,--{FP, NQ, TR, FS}-- }
and then the set composed of sets of these submodels’ classical completions,
25
{ --{ +{TP, TQ, TR, FS}+,+{TP, FQ, TR, FS }+ }--,
--{ +{FP, TQ, TR, FS}+, +{FP, FQ, TR, FS}+ }-- }.
Then, when “--” refers to the immediate subsets, and “+--” refers to the set of + models
in the set surrounded by “--”, you can define truth in this manner
(TAV)P  ( N-- M+-- ( M P) ).
In prose, that is
A sentence A is true (false) in a model M if and only if A is true (false) in every
complete expansion of some consistent contraction of M. [34, p. 9]
Given our initial assignment above, this definition gives us (TAV)P, (TAV)R, (TAV)~P,
and (TAV)~S. Also note that this model does not give us (TAV)(P  Q). In each
contraction set (the sets surrounded by “--”) there is an expansion where the two
sentences have different truth values.
As Varzi realizes, you can also reverse the order, first forming the set of
inconsistent completions
{ +{TP, FP, TQ, TR, FS}+,+{TP, FP, FQ, TR, FS}+ },
and then forming the set composed of sets of these completions’ consistent submodels
{ +{ --{TP, TQ, TR, FS}--,--{FP, TQ, TR, FS }-- }+ ,
+{ --{TP, FQ, TR, FS}--, --{FP, FQ, TR, FS}-- }+ }.
Then truth can be defined in this manner
(TAV')P  (M+  N--+ ( M P) ).
Again, Varzi gives this kind of definition in this manner.
A sentence A is true (false) in a model M if and only if A is true (false) in some
consistent contraction of every complete expansion of M. [34, p. 9]
26
Here we again have (TAV')P, (TAV')R, (TAV')~P, (TAV')~S. However, unlike before,
we do have (TAV') (P  Q).
The differing in extension of the truth predicates is just one of Varzi’s examples
of how pathological the semantic notions get when you add contradictions to the
supervaluational approach. The details of Varzi’s fascinating discussion need not detain
us though. What concerns us is whether the pathologies he describes are evidence
against dialethism. They are not.
All of the truth predicates considered thus far yield classical entailment when
simplifying assumptions are factored in. In this manner they all justify the practice of
classical inference. In showing why this is the case we restrict our discussion to GPtruth, though the moral of the discussion applies, in fact, to the other notions of truth as
well.
One might think that global entailment for GP-truth does not justify our use of
classical inference, since global entailment for GP-truth is inconsistent with classical
inference. Such a thought relies on an incorrect view of justification. For example,
Special Relativity justifies the use of Newton’s theory by space agencies such as NASA,
even though the two are inconsistent with one another.
A successor theory’s justification of the current use of earlier false theories is the
norm in science. In fact, the most common (if not the only) rigorous kind of reduction in
physics is the sense in which a “finer grained” theory is reducible to a “coarser grained”
theory in some limit. Special Relativity is reducible to Newton Dynamics in the limit as
27
(v/c)2 approaches zero.19 This kind of reduction explains why the vast majority of
classical physics applications needed for space flight work just fine when the velocities of
objects are enough below the speed of light. In this manner, the reduction in the limit to a
false theory justifies use of that false theory.
Part of the importance of the dialethist semantics suggested here is the fact that it
reduces to classical semantics as the set of admissible models approaches one. For, when
one restricts the quantifier in the definition of global entailment,
 global    ((TGP)  (TGP)),
to singleton sets of admissible models, the resulting consequence relation is the same as
what we called local entailment,
 local   M (M   M ).
Since local entailment just is the standard Tarksian entailment sound and complete with
respect to classical deduction, we see how our dialethist semantics does reduce to
classical semantics in the exact same manner as theories reduce to one another in physics.
Like the engineers who don’t need to use Special Relativity when plotting space
flights, we are justified in using classical logic for the vast majority of inferential
situations.
For the rhetorical point at hand though, even if we need to invoke
paraconsistent logics for truly difficult inferential situations, the dialaethist semantics
presented here shows why classical reasoning works when true contradictions can be
ignored. Perhaps it also shows how we can safely ignore true contradictions in many of
the contexts and continue to reason classically.
19
In this sense one can reduce Quantum to Classical Mechanics, and Wave to Geometrical Optics.
However, these are more problematic given that the reduction holds at the limit, but in an important sense,
not in the limit. See Batterman’s fascinating discussion of this in [3].
28
There are at least two ways one can think about the correctness of classical
inference even though there are true contradictions. The first is to invoke a Vaihingerian
philosophy of “as-if,” where we engage in the necessary fiction that our theories are
consistent with one another, and can hence be treated as one model, in the manner
suggested by our Putnam discussion. The second is in terms of inferential contexts,
where in a given context we assume there is only one correct model of the way the world
is. In the first case, global entailment is the same as classical entailment; in the second,
local entailment is being utilized. In either case, the practice of using classical inference
has been justified by our dialethist semantics in exactly the same way successor theories
in the science justify the use of earlier false theories.
True contradictions are certainly difficult to reason about in real life, and one
would expect a formal semantics to capture this difficulty. That our dialethist semantics
both captures this difficulty while at the same time justifying the practice of classical
inference, is extraordinarily powerful evidence in its favor. Approaches motivated by
supervaluational semantics provide us with what might be the only successful reduction
in the history of philosophy, and also perhaps the only one attempted with a model of
reducibility that bears some resemblance to reducibility in the natural sciences.20
Moreover, given that we have justified classical deduction, the argument that dialethism
should be abandoned because of the success of classical model theory has no weight.
I realize in putting things this way that I am, as we say in Louisiana, “not putting too fine a point on it,”
but I should be forgiven for thinking this issue merits some bluntness. See Mark Wilson’s [37] for a
compelling argument that things go seriously awry when participants in philosophical debates (in Wilson’s
discussion, debates about mutliple realizability and reductionism in the philosophy of mind) presuppose
false characterizations of notions such as physical law, empirical theory, physical property, and
reducibility.
20
29
II.1
While GP-truth shows that truth in the intended model need not be our model of
truth, nothing we have yet said shows non-Dummettians (and non-Putnamians) that it
should not. Moreover, the example given above involving Caesar should have struck
most readers as extremely implausible. However, it should also be clear that this is just
because most of us are realists about the past. There is, or was, a determinate reality that
(given the meaning of the claim) renders “Caesar prosecuted Gaius Rabirius before
Cicero had Cataline’s co-conspirators killed” true or false, and emphatically not both.
However, once one moves to discourses where anti-realism is more plausible, one
sees that were anti-realism about the past plausible, then dialethism about the past would
be too. Moreover, given that anti-realism is plausible for some discourses, we shall see
that dialethism is too.
Consider intractible intuition clashes in ethics. Take for example, the “tragic
choice” facing Sartre’s friend,21 who can join the Free French Army and avenge his
brother’s death, or stay at home and take care of his mother, but not both.
Pre-
philosophically, most of us would hold that it both is and is not the case that Sartre’s
friend should stay at home and is and is not the case that he should fight the Nazis. Both
are the case in the sense that Sartre’s friend should do them, but are not the case because
doing one precludes doing the other. Non-philosophers describe this as a case of a true
contradiction.
The person on the street’s view is very plausible on Dummettian grounds. For the
Dummettian about ethics cannot envision a notion of truth over and above a sentence’s
possession of warrants for assertion. For those who take moral objectivity seriously (but
21
See the canonical discussion of the tragic choice in [25].
30
still see a difference in kind between ethical judgments and other sorts of judgments, such
as historical ones) this is an extremely plausible view.22 However, as the tragic choice
scenario shows, we often do have extremely strong contradictory warrants concerning
what we ought to do.
The tragic choice scenario is one where a person’s moral obligations are
overdetermined in a given particular situation. However, this sort of overdetermination
is characteristic of kinds of situations as well. The problem with the really difficult moral
controversies is that there are very strong warrants that contradict one another.
I do not want to provide much ammunition to attackers of philosophers like
Singer who show us where consistency about fundamental ethical issues leads (e.g. in
[27]). One would need very good arguments against Singer to defend the inconsistent
views most of us having concerning (for example) our general moral duties to sentient
creatures and our special moral duties to our own pets, families, and friends.
This being said, consequentialists like Singer must admit that some people at least
have conditional obligations to believe inconsistent things.
For example, suppose
someone (call him Fred) consistently responds to Singer’s powerful arguments in Animal
Liberation [26, pp. 1-22] by holding that it is morally permissible to treat human beings
in all of the ways that people currently treat animals. Certainly, the consequences are
better if one is a speciesist than if one is a non-speciesist psychopath.
So the
I think that this view does not fall prey to MacIntyre’s classic criticisms of non-cognitivism in [20], while
still doing justice to the intuitions that motivate non-cognitivism. Patrick Fitzgerald (p.c) has suggested
that there is a strong resonance between the different models approach defended in the previous section and
MacIntyre’s positive views (for example, in [19]) that moral objectivity and warrant are to be found in
traditions. MacIntyre accepts that these traditions will support moral judgments that contradict one
another, but does not view this as undermining moral objectivity. If each tradition is a Putnamian way to
look at the world, equally good as the other yet inconsistent with one another, then our dialethist semantics
does capture the MacIntyrean view well.
22
31
consequentialist is committed to saying that Fred has a moral obligation to have
inconsistent beliefs (conditional upon the fact that, after reading Singer’s work, he is so
strongly disposed to behave in a way we regard as morally wrong).23
Given this, the consequentialist needs an account of how people should reason
with inconsistent moral beliefs. If I am right that the consequentialist needs to provide
such an account, then some of the plausibility of consequentialism does rub off on a
dialethist account of the tragic choice and severe intuition clashes.
This at least raises the spectre of a moral obligation to have inconsistent beliefs
that is not conditional upon other false beliefs. Since most actions are explicable as being
caused by beliefs and desires, for the consequentialist we have a moral duty to believe so
as to produce the best consequences. This suggests that anyone moved by a pragmatist
connection between truth and what is good for us to believe (and it is not wholely
implausible to think there is some such connection for discourses concerning ethics) will
find dialethism attractive.
Given our speciesist’s potential psychotic reaction to Singer’s work, it is better
that he remain unapprised of it and believe that it is obligatory not to eat people who are
severely mentally retarded, yet permissible to eat cows. Arguably (and if I understand
right, according to Sartre), it is better for Sartre’s friend to believe that it is obligatory not
to abandon his mother, yet permissible (indeed obligatory) to go join DeGaul’s forces. In
the case of the speciesist, his duty to believe inconsistent things does not reflect “the way
things are” because his duties are conditional on his pathological tendencies, but nothing
like this is going on in the case of Sartre’s friend. In this case it is sheer anti-dialethist
23
Those who don’t find Singer’s arguments persuasive can use another example. The general schema of
32
prejudice to say that Sartre’s friend is morally and existentially right to believe a
contradiction, yet somehow radically mistaken both logically and in appraising the ethical
facts. In the case of Sartre’s friend, the pragmatic identification of what is good for him
to believe and what is true seem to come together.
This being established, it should be noted that dialethist needn’t rely on such
(perhaps vulgar) pragmatism. To illustrate, let us suppose the really basic ethical issues
can and ought to be thought about consistently. It would still be the case that there are
very good arguments both for and against the morality of specific kinds of ethical issues.
It is a common experience to begin an introductory ethics course by teaching
consequentialism, deontological ethics, and perhaps virtue ethics in the first part, and
then to completely (or all but) ignore those fundamental views when turning to practical
ethics. For many of the pressing issues of the day there are usually very plausible
arguments both for and against whatever issue is being addressed, and usually these
arguments are independent of the truth of one’s favorite normative ethics.
One might respond to this by saying that a better way to describe the aporia at the
end of a well taught ethics class, and Sartre’s tragic choice for that matter, in terms of
lack of truth values rather than in terms of contradictory truth values.24 I hope that in the
case of ethics at least, our considerations about conditional obligation undermine this
somewhat. Again, any model of how people ought to reason given their conditional
moral obligation to believe inconsistent things provides a model of how people ought to
reason given an epistemic obligation to believe inconsistent things (due to the existence
of claims that are both true and false).
my argument can clearly be applied to any bit of convincing moral argumentation.
33
In any case, the three value strategy is not without serious problems. If we
identified truth with possession of a good warrant, we would naturally say that a sentence
lacked a truth value when neither it nor its negation possessed a good warrant. This is
quite different from what’s happening in the case of Sartre’s friend and in the case of the
normative ethics seminar. The advocate of three values collapses underdetermination of
truth value by warrant with its overdetermination.
In addition, describing the tragic choice and intractable disagreements as cases of
sentences that lack a truth value involves not identifying ethical truth with possession of a
good warrant. The non-dialethist must say that a sentence P is true if and only if there
exists a good warrant for it and does not exist a good warrant for its negation. Then the
tragic choice case would be a case where it is not true that someone has a given
obligation and also not true that they do not have that obligation. Finally, if we no longer
define falsity as not-being-true (accepting a third value), we are then free to say the tragic
choice is a case of neither true nor false, rather than a case of a true contradiction.
Once we realize this, we see that there are yet more problems for the antidialethist. The reason we are anti-realists about ethics is because we cannot make sense
of the truth of a claim outstripping our abilities to recognize that truth. But with the three
valued anti-dialethist maneuver all of the metaphysical problems that motivate
Dummettian anti-realism raise their head again with a vengeance. For (on the antidialethist strategy) to determine that a sentence is true, a speaker must not only assess
evidence for the truth of the sentence, but also assess the lack of evidence against the
sentence.
24
One might be motivated to respond in this manner because of the thought that it can never be rational to
34
To see how epistemically intractable the anti-dialethist’s truth predicate really is,
let us turn briefly to what is in essence Crispin Wright’s formulation of it.
A statement is superassertible, then, if and only if it is, or can be, warranted and
some warrant for it would survive arbitrarily close scrutiny of its pedigree and
arbitrarily extensive increments to or other forms of improvement of our
information. [39, p. 48]
One would have to be a god to have recognitional capacity vis a vis superassertibility.
There are just too many ways that warrants for claims can be overthrown. While Wright,
of course, countenances logical revision of the intuitionistic sort, he does not see that the
dialethist needn’t make the superassertiblist’s concession to realism. For the anti-realist
who wants to claim that all truths are knowable, dialethism involves quite a bit of
epistemic gain. It is certainly a much more plausible requirement on speakers that they
know that a claim is warranted than it is for them know that a claim is superwarranted.25
Thus, if I am right, dialethist anti-realism has a number of things going for it.
First, unlike the intuitionist, the dialethist can not only avail herself of classical inference,
but can also provide a compelling account of why that inference is justified. Second,
dialethism avoids collapsing the distinction between not enough evidence either way
(underdetermination of warrant), and too much evidence both ways (overdetermination of
warrant). Third, dialethism has more phenomenological validity, in that normal speakers
are likely to describe overdetermination of warrant in discourses such as ethics as
accept and reject the same proposition. For a strong critique of this thought see Goodship’s [16].
25
This point gets a real bite when you consider the initial problems concerning idealization faced by the
Dummettian dialectic. See footnote 11 and the discussion at the end of section I.2 of this paper.
Superassertibility makes both of these problems much worse, and dialethist assertibility makes them both
much better. Though dialethist assertibility is better for the Dummettian, it is not clear without much more
argumentation how this affects Wright’s project. The dialectical situation in which Wright offers
superassertibility is not the same as the one here. In [36] Wright characterizes different properties a truth
35
involving true contradictions.
Finally, a dialethist truth predicate is more plausibly
something grasp of which can be attributed to competent speakers. In addition, as a
consequence of our discussion, arguments for a Dummettian, Putnamian, or pragmatist
construal of a given discourse also motivate a dialethist construal of that discourse. 26
predicate might be thought to have for different discourses. In the context of this project, Wright presents
superassertibility as a characterization of a “minimal” truth predicate with the least realistic properties.
26
I would like to thank J.C. Beall for encouragement, Robert Kraut for provocation, and Neil Tennant for a
mixture of both. I also need to thank Robert Batterman, Stewart Shapiro, William Taschek, and Crispin
Wright for helpful comments on an earlier draft of the first half of this paper, presented at the first Ohio
State University Symposium for Crispin Wright. “Why shouldn’t your modus ponens be my modus
tollens?” and, “you still have to explain why truth in a model is such a good model of truth,” were
Stewart’s challenges. For challenging discussions about the tragic choice and severe intuition clashes in
ethics I need to thank Emily Beck Cogburn, Patrick Fitzgerald, David Merli, Mary Sirridge, John
Whittaker, and Ken Zagaki.
36
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39