The Meaning-Inconsistency View on the Semantic Paradoxes
Matti Eklund
(matti.eklund@filosofi.uu.se )
Unfinished work in progress – comments welcome
1. Introduction: the inconsistency view of the semantic paradoxes
Consider the liar paradox: the paradox of what to say about a sentence which says of itself that it is
not true. (I turn straight off to what is sometimes called the “strengthened liar”.) It seems no matter
what we attempt to say of this sentence we land in contradiction. Suppose that the liar sentence is
not true. Then what it says is the case is indeed the case. But then it is after all true. Hence the
supposition leads to contradiction. So contrary to the supposition the liar sentence is true. But then
what it says is the case is indeed the case. So it is not true (for it says that it is not true).
Contradiction. This time we assert a contradiction. The reasoning relies only on widely accepted
logical principles and principles about truth.
The literature abounds with different purported solutions to the liar paradox, but each of
them in turn has radically counterintuitive consequences – and not just counterintuitive
consequences but consequences that seem to be at odds with what we arrive at by reflection on the
meanings of the key expressions involved. One may naturally suspect that the same will be true of
any purported solution.
One reaction to this – my own reaction – is to want to defend an inconsistency view on the
semantic paradoxes: to say that when we go through the paradoxical reasoning we correctly follow the
rules for the key expressions, the truth predicate and the logical expressions, so that when we
conclude the absurdity that we conclude, that just shows that there is an incoherence among the
rules. Most straightforwardly, we may think of the rule for ‘true’ as being the T-schema, and the rules
for the logical expressions as being the classical logical principles.1 Of course the real story may be
more complicated than this. An immediate question regarding any inconsistency theory concerns
what the talk of ‘rules’ amounts to. There are several different ways of cashing it out. I have my own
1
Where by the T-schema I shall mean the schema
‘p’ is T if and only if p.
A predicate satisfies this schema just in case a valid schema results when we substitute this predicate for the
schematic letter ‘T’.
1
preferred way. When speaking of my own preferred inconsistency view, I will refer to it as the
meaning-inconsistency view.2
Briefly, here is what the meaning-inconsistency view says about the matter (more details will
follow in later sections). It is a common view that particular sentences or inferences are meaningconstitutive: that it is part of competence with ‘bachelor’ and ‘unmarried’ to prepared to accept ‘all
bachelors are unmarried’ or to accept the inference from ‘___ is a bachelor’ to ‘___ is unmarried’.
The talk of rules in connection with the inconsistency view should, according to the meaninginconsistency view, be understood on this model: we can say that in the relevant sense of rule, what
has just been stated are rules for ‘bachelor’. There certainly are problems with the view as thus briefly
explained. I will return to them later and discuss what revisions are necessary.
A second immediate question is whether not an inconsistency view absurdly implies either
that every sentence of the language is true (for they all follow from the rules) or that none is true (for
‘true’ is incoherent and nothing falls under an incoherent predicate). In response let me again say
what my preferred meaning-inconsistency view says: Distinguish between the rules governing an
expression (e.g. the introduction and elimination rules for ‘and’) and the semantic value of that
expression (e.g. the truth function that ‘and’ expresses). It is standardly held that if some rules are
meaning-constitutive for an expression, then the semantic value of an expression is such as to make
the rules true and truth-preserving. For example, given that the standard rules for conjunction are the
rules for ‘and’, the semantic value of ‘and’ is what makes these rules correct: the standard semantic
value for ‘and’, which renders these rules truth-preserving. If we apply this picture wholesale then we
shall have to say that ‘true’ fails to have a semantic value: for no semantic value can render the rules
for ‘true’ correct. But there is a possible straightforward revision. Compare David Lewis’s wellknown view on the reference of theoretical terms.3 Lewis (following Carnap) held theoretical terms
to be somehow implicitly defined by the theories in which they occur. In the simplest case, the
referent of a theoretical term is whatever makes true the sentences of the theory wherein the term
occurs. But we certainly want to say that theoretical terms occurring in false theories can refer, so we
can’t always say exactly that. What Lewis does is to allow that the term refers to what comes closest
to making true the relevant sentences of the theory; where closeness here is not just a matter of what,
quantitatively, makes true the most sentences. Overall best fit is what is at issue; qualitative
considerations enter in as well. And if it turned out that a given theory was inconsistent, the same
would apply. We might still want to allow that theoretical terms introduced in the theory refer, and
we can get to say this in the same way as in the case of an, as it were, merely false theory. It is
The label “meaning-inconsistency view” for the view I defend is due to Brian Weatherson.
See, e.g., Azzouni (2006, 2007), Burgess & Burgess (2011), Ludwig (2002), Patterson (2007, 2008,
2009), and Scharp (2007, 2008, 2013a, 2013b) for alternative inconsistency views.
3 See e.g. Lewis (1970), (1972) and (1997).
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presumably obvious where I am going with this: the relationship between the semantic value of ‘true’
(and of the logical expressions) and the rules, in the sense gestured at, which govern them is, I
suggest, the same as that between the semantic value of a theoretical term introduced by an
inconsistent theory and the sentences of that theory.
The semantic values of the expressions employed in the liar reasoning are then not such as
to make all premises in the reasoning true and all steps truth-preserving. While the rules, or meaningconstitutive principles, are inconsistent, the actual truth conditions are not. So somewhere in the liar
reasoning there is an untrue premise or a non-truthpreserving step. One thing I would add, however,
is that it is likely, on the picture sketched, that it will be indeterminate what the semantic value of the
truth predicate is, and what the semantic values of the logical expressions are. This is because it will
be reasonable to speculate that there will be no unique assignment of semantic values that comes
closest to making true the meaning-constitutive principles. I will elaborate on this point below.
The above summarizes what, in general, an inconsistency view on the semantic paradoxes of
the kind I want to focus on is, and also what my favored version of it is. In what follows I will
discuss various complications and consequences.
One possible virtue of an inconsistency view is that it explains the appearance that the liar
paradox simply lacks a solution: that whatever purported solution we come up with has absolutely
unacceptable consequences. The inconsistency view’s explanation is that whatever we say, we end up
in violation of some rules. (I wouldn’t put any theoretical weight on the following way of describing
the situation, but it is evocative: Think of using a term with a particular meaning as taking on certain
semantic obligations – obligations regarding how to use the term. When a language is inconsistent,
the semantic obligations speakers take on are inconsistent. There will then be certain situations where
whatever the speaker tries to say, she will end up violating some semantic obligation.4)
In section 2, I will defend the meaning-inconsistency view against objections according to
which it relies on mistaken assumptions about meaning. Section 3 will devoted to describing some
fallback positions if the meaning-inconsistency view cannot be defended: views sharing many of its
virtues but not committed to the controversial views on meaning that the meaning-inconsistency
views rely on. In section 4, I discuss the type of indeterminacy naturally seen as bound up with the
meaning-inconsistency view and compare other views on indeterminacy in the literature on the
semantic paradoxes. Sections 5 through 7 deal with the significance of the inconsistency view,
responding to skepticism concerning whether the questions it seeks to answer are worth asking. In
One virtue of this way of putting it this way (though again I wouldn’t put any weight on it) is that it helps
characterize what distinguishes the general kind of inconsistency here discussed from dialetheism – the view
that there are true contradictions – which also can be regarded as an inconsistency view. Dialetheism doesn’t
yield that there is no way that a speaker can satisfy her semantic obligations. It is only that sometimes doing so
involves accepting both a sentence and its negation as true.
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section 8 I compare the view Tim Maudlin (2004) has defended. The reason for singling out
Maudlin’s view for special consideration is that on the face of it, it is about as removed in spirit from
any kind of inconsistency view as can be, but closer examination brings out more complexity. Section
8 compares other inconsistency views.
2. Making room for the meaning-inconsistency view
To subscribe to the meaning-inconsistency view is obviously to buy into a picture of meaning that
many theorists would reject; a picture of meaning according to which there are specific principles
constitutive of the meaning of an expression. This would be rejected both by theorists who reject
questions about what is part of meaning as opposed to just part of theory as ill-defined and by
staunchly referentialist theorists who think the meaning of an expression just is its reference. In other
words, it is to take a stand on highly contested issues in theorizing about meaning. One reaction to
this is to seek to argue that these other theories are inadequate. However, I will not attempt to do
that. Rather, what I will do, in the next section, is to indicate how some main points I want to make
can be replicated within these other frameworks.
But that is the next section. In this section I will instead focus on the class of views on
meaning and content that are the most amenable to an inconsistency view: views on which some but
not all of the different principles involving a given expression that we are inclined to accept are
genuinely meaning-constitutive, and their being so is somehow a matter of what cognitive relation to
them competence with the constitutive expression involves. Call such views SCR-views, for selective
conceptual-role views.5 One might in principle be attracted to an SCR-view while holding that meaningconstitutive principles cannot be inconsistent. Indeed, most friends of the SCR-view would deny the
possibility of such inconsistency. What I will argue, however, is that any reasonable SCR-view should
allow for the possibility of meaning-inconsistency of the kind I hold that we see in the case of the liar
paradox. (It is of course a further question whether this possibility is actualized in our language. But I
suspect that all resistance to whether our language is inconsistent derives from resistance to the idea
that any non-trivial well-functioning language could be inconsistent)
Let me begin the argument for this point in what may seem a rather roundabout way, by
considering objections to my preferred meaning-inconsistency view. In a critical discussion of my
work on these matters, Beall and Priest (2007) say,
How are sc-dispositions [competence-constituting dispositions] to be distinguished from
dispositions that hold in virtue of mere belief. People, after all, are disposed to accept many
‘Selective’ to distinguish them from holistic conceptual role views, according to which all inferences in which
an expression partakes are meaning-constitutive.
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claims that would seem to have little to do with semantic competence. Consider the disposition
to accept that the world is older than 1 minute. All competent speakers of the language—barring
some malfunction that hinders competency—have that disposition. Why is that not an scdisposition? There would seem to be no principled reason for claiming that it is not.6
It is a bit odd to raise this specifically as a problem for my view. For this is an argument against any
SCR-view – not just SCR-views which leave room for meaning-inconsistency – and surely Beall and
Priest must recognize that they cannot thus simply dispose of that whole tradition. There are many
things that a defender of an SCR-view can say; and I do not see that the specific features of my view
bars me from taking over any of these responses. For example, a friend of the SCR-view can,
following Christopher Peacocke (1992), elucidate the idea of meaning-constitutivity by appeal to the
notion of what is “primitively compelling” where, roughly, for a thinker to find it compelling and to
regard it as not standing in need, even in principle, of further justification. This promises to
distinguish what is genuinely meaning-constitutive from examples like that which Beall and Priest
provide. And it does not rule out a meaning-inconsistency view, since the principles that lead to
trouble in the case of the liar can all be primitively compelling despite the fact that they lead to
absurdity. (To stress, I do not mean to subscribe to Peacocke’s view. I use it only as a model.)
A general problem for any SCR-view that aims to leave room for meanings to be
inconsistent is that anyone who realizes that some set of principles lead to inconsistency – for
example a philosopher studying the liar paradox – will plausibly thereby be led to be disinclined to
accept all of these principles. And we don’t want to say that this philosopher thereby loses her
semantic competence. As with Beall and Priest’s problem case, what we have here is a problem that
arises for SCR-views generally. The problem arises for any SCR-view given when the cognitive
relation between a competent thinker and the meaning-constitutive principles is something like
belief. But already independent considerations show that such an identification is too simple-minded.
If anything has the status of a meaning-constitutive principle, the sentences expressing basic logical
laws surely do. But for pretty much any basic logical law, one can find logicians and philosophers
rejecting it.7 Hence it is somewhat trickier than might have been expected to identify the cognitive
relation in question. But given that the simple-minded suggestions regarding the nature of the
cognitive relation do not work, the path to inconsistent meaning-constitutive principles lies open in a
way it would not do if the simple-minded suggestion were correct.
What else might the cognitive relation be? Any discussion here will perforce be brief. But one
suggestion is that it is something like taking it to be the default position that [...]. It is striking that
6
7
Beall and Priest (2007), p. 76.
See Williamson, e.g. (2007), for discussion.
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counterexamples to taking the cognitive relation to be something like (dispositions to) belief or
acceptance always involves someone having a special reason to deny the supposed analyticity. Timothy
Williamson has prominently called attention to Vann McGee’s rejection of modus ponens when
criticizing the notion of epistemic analyticity, and he has also called attention to how speakers can for
theoretical reasons reject instances of the schema “every F is an F”. But strikingly, the examples
involve thinkers armed with specific reasons to reject the epistemic analyticities. If one imagines
someone rejecting modus ponens or instances of “every F is an F” without special reason to do so, it
becomes considerably more doubtful that this thinker – social externalism aside – uses these terms
with their standard meanings.8
What this means is that the problems that arise for the picture of meaning that the meaninginconsistency view relies on arises for SCR-views generally. This point does not immediately show
that the friend of an SCR-view ought to allow that meanings can be inconsistent in the way I claim
comes to light in the liar paradox. But that more general conclusion is not far away. The most
straightforward way that the friend of an SCR-view can rule out the possibility that a meaninginconsistency view could be correct is by insisting that the cognitive relation in question is such that a
competent thinker cannot stand in that cognitive relation to inconsistent principles. If the cognitive
relation was belief maybe that could be so. But once we have arrived at the conclusion that we must
say something more subtle about what the cognitive relation is, the path lies open to a meaninginconsistency view.
If the meaning-inconsistency view couldn’t be combined with a plausible view on referencedetermination – if, say, the meaning-inconsistency view had the consequence that the semantic value
of ‘true’ was undefined or empty – then there could be reason for a friend of an SCR-view to reject
the possibility of a meaning-inconsistency view at least for philosophically significant cases. But I
argued above that the Lewisian picture of reference-determination straightforwardly allows that
‘true’, even if inconsistent in the way outlined, has a non-empty extension.
I have gone through general reasons for why a friend of an SCR-view should not have
anything against the possibility of a meaning-inconsistency view. Let me now turn to the arguments
of individual theorists who are broadly sympathetic to SCR-views but who explicitly distance
themselves from meaning-inconsistency views: Paul Horwich, Ralph Wedgwood and Crispin Wright.
First, the arguments of Horwich. Horwich prominently discusses Arthur Prior’s ‘tonk’,
characterized by the inference rules: from p to infer p tonk q; from p tonk q to infer q. It being thus
characterized means that a speaker competent with ‘tonk’ would have to stand in the right cognitive
See Williamson (2007), and, for discussion, Eklund (2007) and (2010a). Williamson uses these examples to
criticize SCR-views; what I hold is that the examples only puts pressure on how SCR-views are best
formulated. Wright (2004), p. 169f, gestures toward the sort of idea I am describing here.
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relation to these rules. Horwich’s initial gloss is that a competent speaker would have to have an
‘underived disposition to infer in accordance with’ these rules. He then argues it would be impossible
to have the meaning-constituting inferential dispositions in question:
…since any ‘q’ could be trivially derived from any ‘p’, we would have to be disposed to accept
every sentence—which is inconsistent with the very nature of acceptance (specifically, with the
role of acceptance in decision making).9
In a footnote, Horwich elaborates, saying that “since a person cannot decide to perform every one of
the alternative actions open to him, he cannot have every one of the beliefs that would motivate
those decisions”.10
There is an important slide in Horwich’s discussion. From talking about ‘underived
dispositions to accept’, he goes on to talk about ‘dispositions to accept’, and in the passage quoted
from the footnote, it seems he must be thinking about plain acceptance. The last point is, in the
context of the discussion of ‘tonk’, the most important. While what Horwich actually says in the
footnote is correct, the following amended version would not be: “since a person cannot decide to
perform every one of the alternative actions open to him, he cannot have every one of the dispositions
to believe that would motivate those decisions”. For it can well be that some dispositions trump others,
and that is why some decisions rather than others are made.
Another example Horwich discusses is ‘pom’, characterized as follows: from ‘x is English’ to
infer ‘x is a pom’ and from ‘x is a pom’ to infer ‘x is pretentious’.11 Again Horwich’s view is that it is
impossible to have the requisite meaning-constituting dispositions. His point here is: “insofar as the
above rules for ‘pom’ are taken to be fundamental…we would have to be arbitrarily imposing a new
condition for accepting ‘x is pretentious’—one that is inconsistent with either its present meaning or
with that of ‘x is English’. What Horwich is relying on here is an assumption to the effect that if the
elimination-rule for ‘pom’ is meaning-constitutive for ‘pom’ it is also meaning-constitutive for
‘pretentious’. While there are views on when meaning-dispositions are constitutive that have that
consequence, such views are not mandatory. Nor do they seem natural: accepting an instance of
Horwich (2008), p. 457f.
Horwich (2008), p. 458fn11. It cannot be inconsistent with the nature of acceptance that a speaker should be
disposed to accept every sentence of a given language. There can after all be languages where all sentences express
trivial truths. What might potentially be inconsistent with the nature of acceptance is that a speaker should be
disposed to accept every proposition. One reason this is relevant is that one can potentially see the introduction
of ‘tonk’ into a language as having the effect that all sentences of the language come to express trivial truths.
However, I do not want to press this point, for I would not want to commit to this view of what is effected by
the introduction of ‘tonk’. What is more, for all this first point shows, Horwich’s point can just be reformulated
in terms of concepts and propositions.
11 [page reference]
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conjunction elimination, from a is red and b is green to infer a is red, may be constitutive of competence
with conjunction, but is only doubtfully constitutive of competence with the concept red.
In chapter 6 of his (2005), Horwich also briefly discusses the supposed rule to accept all
instances of ‘if it is true that p then p’, which by his lights leads to contradiction. His view is that for
this be a meaning-constitutive rule for our ‘true’, our conformity to it must amount to an ‘ideal law’:
we would have to “(ideally) conform to it in counterfactual circumstances”.12 But this rule governing
‘true’ does not amount to an ‘ideal law’: for when properly apprised to the liar paradox we would not
accept all instances. Note that if this argument is good, Horwich in one fell swoop does away with all
meaning-inconsistency views. For no rule that leads to contradiction is one we would follow in ideal
circumstances, apprised of all the facts. But the obvious question to ask is on what basis Horwich
imposes his requirement for counting as a meaning-constitutive rule. The answer is given earlier in
the same chapter. Horwich wants to distance himself from a view on which rule-following has to
involve “explicit formulation of, and causal response to, the rule”, and for that reason understands
rule-following in terms of what a thinker would do in counterfactual circumstances.13 That is the full
motivation for the move. But crucially, in the context of discussion of the possibility of a meaninginconsistency view, this motivation, even if good, does not speak at all to the issue of what form the
characterization of the appeal to counterfactual circumstances should take. But that means that
Horwich has no argument for the specific conception that rules out a meaning-inconsistency view.
Turn next to Wedgwood. Wedgwood (2011) says,
How can these capacities—our possession of concepts and our capacities for all of the various
types of attitude—essentially require a disposition to engage in a belief-forming process that has
no [essential] connection with the truth? These capacities are cognitive powers, not cognitive foibles
or liabilities.14
The argument comes in the last sentence. But I don’t see why it should be regarded as compelling.
Even if we find it natural to think of these capacities as ‘powers’, it is doubtful how seriously we are
to take that. And more importantly, even if it is right to conceive of them as powers, we should think
of them as powers to think thoughts involving such-and-such a concept. It is consistent that such a power
should have an essential connection to liabilities. Here is an illustration. Among concepts of the kind
Wedgwood seeks to rule out, there can be a concept such that competence with it involves a
disposition to infer in a way which sometimes but only in very special cases fails to be truth[page reference]
[page reference]
14 Wedgwood (2011), p. 198; my emphases.
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preserving and whose possession brings cognitive advantages to its possessor – e.g. it makes for
quick-but-dirty reasoning, making reasoning simpler, and in a vast range of cases the reasoning
preserves truth. Having this concept in one’s arsenal is certainly a cognitive power, even if it carries
with it a certain liability.15
Wedgwood goes on, saying “We can dramatize this point by considering the idea of a
perfectly rational being. It seems plausible to me that every concept that we possess could also be
possessed by this perfectly rational being”.16 Wedgwood talks about what “seems plausible” to him,
suggesting that he is here relying on intuition. But can we really rely on intuition when it comes to
questions about what possible concepts a perfectly rational being could possess?
Next, turn to Wright’s important discussions of the matter, in his classic (1975) as well as in
his later articles. Wright’s focus is on an inconsistency view on vagueness but the considerations clearly
generalize. Roughly, an inconsistency view on vagueness is one where a vague predicate F is
governed among other things by a tolerance rule which yields that a small enough difference in F’s
parameter of application (e.g. age for ‘old’) never matters at all to the justice with which F is applied.
One objection Wright appears to raise in (1975) is that meaning-constitutive rules cannot be
inconsistent while sufficing, by themselves, to confer meaning upon an expression: since any use of
the expression can be made to fit with the meaning-constitutive rules, these rules do not rule out
anything.17 This objection, while raised specifically in the context of a discussion of vagueness, can be
raised against any philosophically interesting inconsistency view. However, this reasoning is
unpersuasive.
Suppose the meaning-inconsistency view is true, and consider two different speakers, Wrong
and Wronger, both rather peculiar. They are both happy to assertively utter any sentence of the
language. However, only one of them, Wrong, is able, when queried, to justify his assertions by what
appears to follow logically from inconsistent meaning-constitutive principles. What Wrong does is to
use the inconsistency to arrive at a contradiction, and then he uses the principle that from a
contradiction anything follows. Wronger, by contrast, simply produces his utterances willy-nilly, or
else appeals to principles that are not meaning-constitutive to justify his assertions. The friend of the
meaning-inconsistency view can fault Wronger on the ground that he is not using the relevant
expressions correctly. Already this suffices to show that Wright’s objection is too swift. Some uses can
be deemed incompetent. This said, however, it may be thought that Wrong still indicates an
embarrassment for the meaning-inconsistency view. For clearly Wrong too uses the expressions of
his language wrongly: but he would, the envisaged objection goes, be classed by the meaningCompare Cherniak (1984).
Wedgwood (2011), p. 198.
17 See Wright (1975), pp. 361ff.
15
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inconsistency view as using the expressions of his language correctly. In response, it should first be
stressed that on the meaning-inconsistency view sketched above, the actual truth conditions of the
sentences concerned are not such as to make the sentences that Wrong utters true, and one ought to
assert only what is true. So there is one way in which Wrong too clearly goes wrong: he is wrong
about the truth conditions. Given this first point, there are two ways one might go with respect to
Wrong. One might say that since all the steps in his reasoning are underwritten by meaningconstitutive principles, he cannot be faulted on the score of semantic competence, although he does
get truth conditions wrong. Or one might say that since Wrong gets truth conditions wrong, he does
display lack of semantic competence. Though it may be an interesting issue which alternative should
be preferred, I see no pressing need to decide between them.
One concern which may underlie Wright’s objection is that inconsistent rules cannot by
themselves rule out any potential usage of the expressions concerned. But I can be brief about this. For
surely the view that meaning-constitutive principles can be inconsistent does not carry with it a
commitment to the view that our competence can be exhaustively described by appeal to a mere list of
these inconsistent rules.18
Further, Wright emphasizes that we “have not the slightest inclination” to regard the verdict
reached by the sorites chain as correct.19 This, he says, an inconsistency view is powerless to explain,
and he thinks that for this reason such a view must be rejected as misguided. Two replies are worth
making to this, corresponding to points I have already made above. First, there is a distinction
between on the one hand saying that the rules governing some expression are inconsistent and on the
other hand saying that the meaning of the expression is exhausted by a mere list of such rules. The
meaning-inconsistency view only involves commitment to the former claim. Consider the following
simple ‘model’: the rules concerning how paradigmatic Fs and non-Fs are to be classified are simply
weighed more heavily than the tolerance rule to the effect that sufficiently similar cases should be
classified the same way. This is consistent with an inconsistency view, and would explain the
phenomenon to which Wright points. (In case the consistency with such a view should be doubted,
consider this: if A has promised B to do one thing and has promised C to do another, then, all else
equal, A is under inconsistent obligations, and cannot possibly fulfil her obligations. Compatibly with
this there can be features of one of the promises which makes that promise determinately take
precedence.) Already the availability of this model, crude as it is, serves to deflect Wright’s objection.
Second, as I said above in connection with Wrong, I am not certain that we should regard Wrong as
semantically incompetent; his mistake can receive a different diagnosis. But if indeed we should not so
Thus, Wright says e.g. that “[t]he rules of [a game supposed to be governed by inconsistent rules] do not
provide an account of how the game is played, for it is possible that someone might grasp them yet be unable
to participate” (1975, p. 362).
19 Wright (2007), p. 426. Compare (1975), p. 362, and (1987), p. 236.
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regard him, then the fact about inclinations to which Wright points is not something which should be
explained by appeal to semantic competence alone.
3. Alternative egalitarian views
Call the untrue premises and invalid inferences in the liar reasoning the culprits, and call the premises
and steps that are reasonable candidates for being culprits suspects. One general feature of the
inconsistency view is that it accords all the suspects what we may call the same meaning status: the
suspects have equal claim to be meaning-constitutive. Specifically, the suspects are on this account all
meaning-constitutive in the way indicated. Let us call any account of the liar given which the suspects
all have the same meaning status an egalitarian account. It is because the meaning-inconsistency view
is egalitarian that it is reasonable to speculate that it is indeterminate what the semantic values of key
expressions in the liar reasoning are: since the jointly inconsistent suspects all have the same meaning
status, they all have at least roughly the same claim to be respected in an assignment of semantic
values. There are egalitarian accounts different from the meaning-inconsistency view and in some
cases without the attendant commitment to an SCR-view on competence. Let me briefly outline
three.
Consider first holists, who hold that there is no distinction between what is meaningconstitutive and what is not so, and replace this distinction with the picture, familiar from Quine, of
our belief system as a network, with some beliefs closer to the ‘core’ and some beliefs closer to the
‘periphery’. The holist, like other theorists, faces the question of how the semantic values of
expressions are determined. (For example, she must be able to provide an answer to questions like:
how come ‘cow’, as we use it, is true of cows but not of horses?) A natural way of doing so would
seem to be to say that the semantic values of our expressions are such as to make our belief system,
as a whole, as correct as possible (given the way the world is); and to this end, it is more crucial that
core beliefs come out true than that beliefs near the periphery do.
This picture immediately suggests a natural story to tell about why seemingly intractable
paradoxes like the liar can arise. On her view, the liar arises because beliefs all close to the core are
jointly inconsistent. All of these beliefs are therefore among those that the semantic values of our
expressions crucially ought to make true. There is no reason to think that one of these beliefs is
determinately farther away from the core than the rest are. There will then be no determinate fact of
the matter as to which belief is not in fact true. It is then indeterminate what the semantic values are,
and what the culprit in the liar reasoning is.
This holistic account shares some important features with the inconsistency view. The
beliefs that are reference-determining (all of our beliefs, according to her) are jointly inconsistent.
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The inconsistency that comes to light in the liar likely gives rise to considerable indeterminacy. And
the suspects in the liar all have the same kind of meaning status: they are all core beliefs.20
I anticipate the objection that insofar as the holist is a Quinean, she will be a
disquotationalist about truth, and as such reject any claim to the effect that she must provide a story
about how semantic values are determined. But holism doesn’t entail disquotationalism, and
whatever the consequences of disquotationalism, holism alone does not allow one to sidestep
questions about the determination of semantic values.21
A third egalitarian view, in addition to the meaning-indeterminacy view and the Quinean
view, is best explained as follows. Some theorists, notably David Lewis and Frank Jackson22, hold
that folk theories implicitly define (many) ordinary expressions, in roughly the same way that scientific
theories are sometimes held to implicitly define theoretical terms. On this kind of view, the way to
study ordinary concepts is to figure out what the folk theories for the concepts are; the reference of
the concept will be what satisfies the folk theory. It is possible that an expression-defining folk theory
is untrue. The semantic value of the expression defined is then what comes closest to satisfying the
theoretical claims in which the expression occurs, provided anything comes sufficiently close
(otherwise the expression simply does not refer).23
Given this kind of view, the following account of the liar paradox suggests itself naturally. It
is part of the folk theory defining the predicate ‘true’ that this predicate satisfies the T-schema. It is
part of the folk theory defining the logical expressions that they satisfy the logical principles that
jointly characterize classical logic. What the liar reasoning shows is that these folk theories cannot be
jointly true. The expressions implicitly defined by these folk theories – the truth predicate and the
logical expressions – then refer to what come closest to satisfying these folk theories.
On the theory of reference-determination we are now discussing, folk theories play one of
the roles traditionally assigned to meanings: they determine reference. (They do not play other roles
assigned to meanings. For example, it is not necessarily part of semantic competence to know them.)
It is also clear that given the analysis of the liar suggested given this theory of referencedetermination, the suspects all have pretty much the same meaning status. They are all part of
reference-determining folk theories.
About this last remark: Insofar as she is a Quinean, the holist may reject all talk of meaning and accordingly
she would also reject the notion of “meaning status”. But the talk of meaning status can be avoided. The main
point is just that for the holist, the suspects all have roughly equal claim to be made true by the semantic values
of the expressions concerned.
21 I also have doubts about exactly what consequences disquotationalism, even if acceptable, would have. But
that is a separate issue.
22 See e.g. Lewis (1970, 1972, 1997) and Jackson (1998).
23 Of Lewis and Jackson, Lewis is the most explicit regarding what to say when nothing exactly satisfies the folk
theory’s claims – see e.g. his (1997).
20
12
As with the other egalitarian views, we will likely have indeterminacy given this view. Given
that the semantic values of the expressions concerned cannot actually make the relevant folk theories
true, the semantic values will be what makes them as near true as possible. There is no reason to
think that there is a determinate, unique winner here.
While I have described this third egalitarian view with reference specifically to Lewis and
Jackson, the point is more general. Even someone who is reluctant to say that inconsistent principles
are in any sense part of meaning can agree that such principles are an important part of the
metasemantics in that they play a crucial role in reference-determination.
Both the Quinean view and the Lewis-Jackson view are open to those who reject SCR-views.
So even if indeed one should reject SCR-views – certainly a live possibility for all that I wish to
commit myself to – there are clearly related views, and views with similar consequences as far as the
liar problematic is concerned, that one could accept.
There is also a fourth egalitarian view I should mention. One might hold, as against the
Quinean holist, that there is a distinction between what is meaning-constitutive and what is not so,
while holding also that it is very often a indeterminate matter whether a given principle is meaningconstitutive. One might then hold that the suspects in the liar reasoning are all borderline cases of
being meaning-constitutive of the expressions employed. The suspects then all have the same
meaning-status, as on the other views just considered. And again we likely have the same widespread
indeterminacy as on these other views. It will again likely be indeterminate which suspects are made
true by the semantic values of the expressions concerned.24
4. Indeterminacy
I have stressed that on the egalitarian accounts, it is likely to be an indeterminate matter what the
semantic values of key expressions employed in the paradoxical reasoning are. Some prominent
accounts of the semantic paradoxes, like that of Field (2008), centrally claim that paradoxical
sentences are indeterminate in truth value. It may seem that such an account thereby is a natural ally
of an egalitarian account. But I think such a conclusion would be badly mistaken, and it is instructive
to see why.
There are, in principle, two fundamentally different ways in which a sentence can be,
somehow, indeterminate in truth-value. First, there can be a determinately best way of assigning a
semantic value to the sentence, but the semantic value in question is not a determinate classical truth
value. This is the standard treatment of indeterminacy, as seen in, for example, traditional
supervaluationist and fuzzy approaches to vagueness. Second, there can fail to be a determinately
In (1992), Mark Johnston defends this kind of view with respect to color, and in (1989) he defends this kind
of view with respect to personal identity.
24
13
best way of assigning a semantic value to the sentence. There can be several acceptable assignments,
and the sentence can have different semantic values under the different acceptable assignments.
Introducing some terminology, let us say that the distinction just drawn is between first-level and
second-level indeterminacy. A sentence is second-level indeterminate just in case it has different truthvalues under different acceptable assignments of semantic values. A sentence is first-level
indeterminate just in case there are acceptable assignments under which the sentence lacks a classical,
determinate truth-value. Analogously, we can define first-level and second-level indeterminacy for
subsentential expressions. Of course, not all cases of lack of classical determinate truth-values need
be strictly cases of indeterminacy (consider e.g. presupposition failure and reference failure). But let us
stick with these labels, for here the focus will be on varieties of indeterminacy.25
Given the distinction between levels of indeterminacy one can make the following
observation. An account like Field’s postulates first-level indeterminacy while the kind of
indeterminacy plausibly implied by an egalitarian account is second-level.
An objection to what I just said is that second-level indeterminacy in a way collapses into
first-level indeterminacy. Suppose we arrive at the theoretical view that a certain sentence is secondlevel indeterminate: it has different semantic values under different assignments. One can think we
can then reflect on this and conclude: this sentence is not determinately true or determinately false,
but indeterminate. So, the sentence is (first-level) indeterminate.
Such reasoning should not be ruled out immediately. But nor should it be immediately
accepted. What we arrive at by the further reflection is a new candidate assignment of semantic
values. And then we should simply compare this candidate assignment to others, by whatever
theoretical criteria should be employed. Is it better than others? Or as good as the best? It is by no
means obvious that this new candidate assignment should be reckoned the unique winner.
Moreover, even if second-level indeterminacy should always carry first-level indeterminacy in
its wake – and even if it by chance should so happen that an account like Field’s should, so to speak,
be extensionally equivalent with what a given egalitarian view would say – it is one thing to postulate
first-level indeterminacy as part of a view which is not an inconsistency view; and another to hold
that there is first-level indeterminacy as a consequence of a fragment of our language being
inconsistent. While the accounts would have some consequences in common, the routes to these
consequences are importantly different.
5. Philosophies and theories
I discuss the distinction between first-level indeterminacy and second-level indeterminacy at some length in
my (2010b), and broach the issue earlier in my (2002) and (2005).
25
14
Let me turn next to some questions that may be raised about the interest of an inconsistency view
(or, generally, of an egalitarian account).
We should distinguish between what we might call philosophies (or perhaps metatheories) of the
liar paradox and theories of the liar paradox – a theory of the liar paradox being an account of what the
semantic values of key expressions are and a philosophy of the liar paradox being an account of why
the semantic values are what they are. The egalitarian accounts presented are all philosophies of the liar
paradox. Accounts of the kind one typically finds in the literature may be viewed either as theories or
as philosophies, in the way indicated. Consider for example contextualist theories, like that of Burge
(1982), which centrally appeal to context-sensitivity in their accounts of what goes on in the liar
reasoning. A theory according to which truth is context-sensitive is simply an account according to
which the semantic value of the predicate varies with context. A standard philosophy according to which
truth is context-sensitive is a philosophy according to which a context-sensitivity theory of truth is
true because it really is part of the meaning of the predicate ‘true’ – part of what, so to speak, we aim
to express by this predicate – that this predicate is context-sensitive. This characterization may seem
utterly unhelpful: surely, one may think, this is the philosophy that must accompany the theory. But
contrast this with a philosophy of truth according to which the context-sensitivity theory of truth is
not correct for this reason, but because, say, the best way to satisfy the jointly inconsistent meaningconstitutive principles for our language involves taking our truth predicate to have different semantic
values as used in different contexts.
Since an egalitarian philosophy of the liar paradox is in principle compatible with a theory – in
fact, any theory – of the kind prominently discussed in the literature, the metalevel discussion
concerning whether an egalitarian or a standard account of the liar paradox is correct does not have
any immediate consequences for the search for a satisfactory account of what is going on: it does not
have any immediate consequences regarding what semantic and logical principles are actually satisfied
by the key expressions used in the paradoxical reasoning. This is a source of skepticism about the
significance of the metalevel issues I have been concerned with here. (“If metalevel discussions won’t
help us solve the paradox, what’s the point? Let’s get to the real issue, that of trying to solve the
paradox.”)
This skepticism about metalevel discussions assumes that what is of fundamental importance
about the liar is a solution, properly so called – where this is conceived of as a theory, in the
terminology introduced. But why should we be interested in a solution in the first place? To address
this question, let me pause on a prior one: What kind of problem is the liar paradox? The liar paradox
can be thought of as merely a problem concerning the expressive limitations of various possible languages.
Tarski’s theorem, the classic result here, says that in no language which can talk freely about its own
expressions are both the property of being true, conceived as satisfying the T-schema, and the
15
classical truth functions expressible. This theorem serves as a starting point for much work on the
liar: much formal work on the liar has in effect been devoted to the question of how close we can get
to expressing these things. For example: taking a language which can talk freely about its own
expressions and in which the classical truth-functions can be expressed, how close can a predicate of
this language come to satisfying the T-schema?
What purely formal work by itself cannot show, and cannot seriously be meant to show, is
what actually is expressed in English: what can settle that, if anything, is attention to the details about
how English is used. This simple point raises a few issues.
It is an open question whether the thoughts and practices of speakers of English – where I
mean ‘thoughts and practices’ to be a cover-all phrase standing for whatever exactly it is that
determines the meanings of expressions of English26 – determine exactly what properties and
relations really are expressed by the relevant expressions. In fact, it would seem rather miraculous if
they did – and not just because semantic indeterminacy is generally ubiquitous. Speakers not aware of
the liar reasoning would presumably take all the relevant properties and operations to be expressible.
But then we cannot assume that the thoughts and practices of speakers of English also determine
exactly which assumption it is that does not in fact hold true, and which property or operation turns
out not to be expressible, if it turns out that not all expressions can express what we thought they
express.
Suppose further that there is something about the thoughts and practices of speakers of
English that does determine exactly what are the semantic values of the key expressions employed. So
what? The dispositions of speakers could have been somewhat different from what they are, and that
they are what they happen to be doesn’t seem to be of great philosophical interest.27 What is the
philosophical interest of the fact that the thoughts and practices of English speakers are just what
they happen to be?
Some may wish to protest here that if we were just interested in any old expression of
English, then what the exact semantic value of that expression is would not be a matter of great
interest; but we are dealing with the workings of the expression ‘true’ and hence we are dealing with
the concept of truth, one of the most central theoretical concepts in philosophy. According to many
theorists, the concept of truth has a significant role to play both in the philosophy of language and
thought and in metaphysics and epistemology.
The phrase “thoughts and practices” is from McGee (1993).
Perhaps, say, the French respond differently to some of the puzzle cases. A point often raised against the
minimal fixed point there is that it assigns the wrong status to “no sentence is both true and false” and “every
sentence is either true or false”: these sentences are both true, not truth-valueless as the fixed point theory
insists. What if it turned out that the French speakers’ intuitions about the French counterparts of these
sentences accorded with what the fixed point theory says?
26
27
16
There are however general reasons for thinking that the protest is mistaken, even apart from
deflationist doubts about the significance of truth, and it is important to see why. The technical
concept of truth – the concept of truth employed in various theoretical enterprises – need not be
coextensive with the ordinary concept. Technical concepts may well differ in their extensions from
their ordinary language counterparts. So for the purpose of investigating the technical concept of
truth and its uses, finer points regarding the extension of the ordinary language predicate ‘true’ are
beside the point.28
6. Field on change in meaning
In his recent book (2008), Hartry Field brings up the possible objection that the departures from
classical logic he proposes involve a change of meaning. In response he asks, “why make a fetish
about whether these things involve a change of meaning?”, and goes on,
…these linguistic questions [concerning what does and does not amount to change of meaning],
even if deemed clear, strike me as of very little interest. The paradoxes show that there’s
something wrong with firmly held patterns of reasoning, whether or not these patterns are
meaning-constituting. What’s of interest is to figure out how best to modify this reasoning: to
find a new way of reasoning that we can convince ourselves is intuitively acceptable, and which
avoids plainly unacceptable conclusions.29
Field’s remarks have immediate implications for the question of the significance of the inconsistency
view on the semantic paradoxes. Everyone agrees that the liar paradox arises because our naïve
theory of truth is inconsistent. The inconsistency view further insists that the principles that give rise
to inconsistency have the status of semantic rules. A friend of this theory thereby, by Field’s lights,
makes a fetish of change of meaning. Have we not said all that is of interest already when we have
said that the naïve theory of truth is inconsistent?
However, it is one thing to insist that there is some way of dealing with the semantic
paradoxes (I am not saying ‘solving’, for reasons to be made clear – there are good questions about
what a solution, properly so called, must involve) such that questions about whether it is faithful to
So with respect to deflationism, the really interesting deflationist thesis is not the thesis that the ordinary
language truth predicate only has an expressive function – the interesting deflationist thesis would be that there
couldn’t be a truth predicate with a more theoretically involved role than this.
29 Field (2008), p. 17. In earlier work, Field seemed friendly toward an inconsistency view. In his (2005), he said
“…in earlier days if not now, the principles of the naive theory of truth were probably central to the meaning
of the term ‘true’ and the principles of classical logic central to the meaning of the connectives; but we know
now that we can't consistently maintain both naive truth theory and classical logic, so at least some of the
meanings we attached to our terms must have been bound up with error” (p. 85f).
28
17
the actual meanings of the expressions employed are beside the point; it is another to insist that such
questions are moot, full stop. The first of these two claims seems to me clearly right. Of course there is
a worthwhile project of coming up with a formal system with a number of nice features, without
worrying about whether the expressions employed are synonymous with expressions in common use.
Tarski showed that we cannot have everything we might have wanted; one project is that of figuring
out how close one can come to the unattainable ideal. Call the project just described the constructive
project. However, the second claim is much stronger, and much more debatable. Notice that success
in the constructive project doesn’t in any immediate sense help solve the paradoxes. Whatever solving
a paradox exactly involves, it involves explaining what goes wrong in the intuitively compelling
reasoning from intuitively acceptable premises to paradoxical conclusion. One doesn’t explain this
simply by showing how a piece of reasoning wherein expressions with different meanings are
employed fails to be sound. If one holds that the constructive project is the only worthwhile project
one can engage in when dealing with the paradoxes, one is in effect insisting that a solution, properly
so called, cannot be had.
Note too that the fact that we are dealing with a paradox is really incidental to the
constructive project. Even if it weren’t for the semantic paradoxes we could ask questions about
whether the actual semantic notions we have and the actual logical expressions we have could be
improved upon: questions about whether there are other possible expressions that could better serve
the purposes to which the semantic and logical expressions are put.
A general point Field makes is this. We know that our naïve theory of truth is inconsistent.
Somehow changes must be made to the theory. But why bother about whether these are also changes
in the meanings of the expressions concerned? I have just given a straightforward reply to this
concern: if our proposal involves a change in meaning would mean that we do not actually solve the
paradox in question. But there is a deeper worry that underlies Field’s remarks: that questions about
what does and does not belong to the meaning of an expression are not well-defined. A certain kind
of Quineanism informs what Field says. Given this Quineanism, questions about whether a
purported solution really involves a change in meaning are moot. But this means that the Quinean
problematizes the search for a solution to the paradox of the kind gestured at in the above paragraph.
The question of what exactly holds of our language appears to be moot. This is not immediately an
objection to the Quinean view; the Quinean may be perfectly fine with this consequence. But it is
important to keep in mind what the consequences of this Quinean view are.
These remarks concerning Field may seem to be in some tension with what I said in the
previous section: there I downplayed the significance of finding a solution, properly so called, to the
liar; but when discussing Field I emphasized the significance of finding a solution. However, the
tension is only apparent. What I find less significant are finer points about the extension of the truth
18
predicate; what is significant is an explanation of how the paradox arises. The meaning-inconsistency
view offers the latter but doesn’t speak to the former. There would be a tension between the
different things I say if the explanation of how the paradox arises turned on finer points about the
extension of the truth predicate, but on my view it is not so.
7. What is a solution?
Close to the surface here are questions about what it is to solve the semantic paradoxes. Above I
mentioned a necessary condition on a solution: one must not simply get rid of the key expressions
used in the paradoxical reasoning but somehow give an account of what is going on in the reasoning
that uses these very expressions. There is also more to be said, of relevance to how to understand an
inconsistency view. One unusually explicit statement of what is normally expected of a solution is in
Martin (1970a). Martin says that to solve the liar paradox is to “uncover” some “rulelike features of
our language” such that they “have the effect of blocking at least one of the assumptions of the
argument”.30
Martin’s statement is in a crucial respect ambiguous. Let me try to display the ambiguity.
Here is the strong reading, which I suspect is the intended one. We tend to think of each of the
suspects in the liar paradox that it is justified by the rules of our language. The liar reasoning proves
us wrong. Closer attention to the liar reasoning would yield that (at least) one suspect was not to have
been trusted in the first place: there was actually no linguistic rule justifying it. To solve the liar
paradox would be to identify the odd guy out, to identify the suspect that was not after all justified by
the rules. I suspect that as a statement of what a solution is normally expected to involve, this is right.
But important to see is that if this is what we expect of a solution, it cannot be expected that all
paradoxes should have solutions. In effect, if this is what we expect of a solution, then the liar
paradox has a solution only if a standard philosophy is right. But if, for instance, something like the
inconsistency view on the liar is right, then all the suspects can be justified by appeal to the rules of
the language, for they are all meaning-constitutive principles. (It is only because Martin employs the
terminology of “rules of language” that I use this terminology here. To talk of ‘rules’ here at least
carries some false implications. Notice incidentally that if we take Martin’s talk of rules seriously, the
liar paradox may lack a solution in Martin’s sense because there are not really any such things as rules
of language.)
On a different, weaker reading of Martin’s statement, the liar paradox has a solution even if
the inconsistency view is right. It is still true, given this view, that it is by attention to what the rules
of language are that we arrive at the semantic values of the expressions employed in the liar
30
Martin (1970a), p. 91.
19
reasoning, and the semantic values are not such as to make the liar reasoning sound. On this view, we
figure out what the “rules of language” (say, meaning-constitutive principles) are. Then, noting their
inconsistency, we will have to weigh them, and at least in principle we can then arrive at the semantic
values of the expressions employed – and since the conclusion of the liar reasoning is absurd, one of
the suspects will in fact not be true. We have again, to use Martin’s formulation, uncovered rulelike
features of our language, and through investigation of them we have found out how the liar
reasoning leads us astray. On the weaker understanding, all that a solution has to involve is some
theory, in the sense earlier characterized.31
8. Tim Maudlin on truth
In his (2004), Tim Maudlin defends the idea that the truth and falsity predicates have the extensions
they are assigned in the minimal fixed point of a Kripke-style fixed point theory of truth. The liar
sentence and generally all ungrounded sentences are there neither true nor false. This has
consequences that are widely regarded as unacceptable, such as that “x~(T(x)&~T(x))” is neither
true nor false rather than simply false, and that “x(T(x)T(x))” is neither true nor false rather than
simply true.
Maudlin, however, defends his outlook as follows:
…truth and falsity are always ultimately rooted in the state of the world. That is: if a sentence is
either true or false, then either it is a boundary sentence, made true or false by the world of nonsemantic facts, or it is semantically connected to at least one boundary sentence, from which its
truth value can be traced.32
(A boundary sentence is one that does not have its truth value in virtue of other sentences.)
Maudlin’s point also serves to respond to another common objection to a Kripke-style
theory. Strong negation cannot be expressible in Kripke’s language by any means, for if it were then
31
Compare also Haack (1978) on what a solution should achieve:
…it should…indicate which apparently unexceptionable premise or principle of inference must be
disallowed…; and that it should, in addition, supply some explanation of why that premise or principle is,
despite appearances, exceptionable. It is hard to make precise just what is required of such an explanation,
but roughly what is intended is that it should be shown that the rejected premise or principle is of a kind to
which there are independent objections – objections independent of its leading to paradox, that is. It is
important, though difficult, to avoid supposed ‘solutions’ which simply label the offending sentences in a
way that seems, but isn’t really, explanatory. (p. 139)
Can the liar paradox be ‘solved’ given an inconsistency view, given that Haack is right? Arguably not, since the
paradox provides the only reason for rejecting whichever “premise or principle” must be rejected.
32 Maudlin (2004), p. 49.
20
the liar paradox could be reinstated: we need only consider a sentence which says of itself that it is
not true, where the ‘not’ is understood to express strong negation. One can feel that it is ad hoc to
say that strong negation is not expressible in our language. But given his outlook, Maudlin can say:
The absence of Strong negation from this language, rather than being ad hoc, is a direct
consequence of the fundamental postulate. Strong negation is ruled out by the global constraint
that all completely unsafe sentences be ungrounded, and the demand that all connectives be
truth-functional. Classical truth-values cannot simply be conjured out of thin air: they must
originate always at the boundary of a language, where the language meets the world.33
The spirit of Maudin’s discussion is very different in spirit from what I want to say about the liar. He
wants to defuse the paradox by appeal to a deep fact about the metaphysics of truth; I think that, in a
sense, the paradox cannot be defused. Discussion of how Maudlin argues will be instructive, also
because I will argue that even by his own lights, Maudlin ought to be rather amenable to an
inconsistency view.
Here is one question regarding what Maudlin says. Either (i) he is concerned only with our
language and his ‘fundamental postulate’, the point about truth and falsity quoted above, speaks only
to what predicates and operators we have in our language, or (ii) he is talking about all possible
languages, and is denying that there strong negation is there to be expressed in any language – it is an
illusion that there is any such operation. If the idea only is (i), then, even by Maudlin’s lights, there
can be relevantly different possible languages, where strong negation can be expressed. The question
whether we speak a language of the kind Maudlin himself describes at length or whether we speak a
language where the expressions behave differently must then be resolved empirically. Suppose
instead that the idea is (ii), which also certainly seems to fit Maudlin’s discussion better. Then one
might be inclined to want to appeal to a “thus I refute Maudlin”-argument: whatever the case may be
with our language surely one could by fiat resolve to speak a language with strong negation.
While I am sympathetic to this argument against Maudin, I will not press it. Surely the
natural response for Maudlin is to challenge what is being urged concerning option (ii). But I will go
on to press a problem in the general vicinity.
As Maudlin is upfront about, some consequences of his theory, and some things he wants to
assert, are by the lights of the theory he defends not true. Partly in response to this, Maudlin
introduces a notion of permissibility distinct from truth, and he wants to classify the untrue things he
wants to affirm as permissible. As a result, Maudlin devotes some time to the immediate worry that
33
Maudlin (2004), p. 51.
21
problems regarding truth can be reinstated but now as problems regarding permissibility. For
example, there is a revenge problem focusing on sentences like
This sentence cannot be permissibly [assertively uttered] according to the normative rules
governing discourse in English.34
The discussion of this problem gets complex. Here is a brief summary. There is a number of
important desiderata concerning rules of permissibility.35 Because of paradox, a given permissibility
predicate cannot satisfy all these desiderata.36 As a result, Maudlin says, there will not be a unique,
absolute notion of permissibility, but only relative notions – permissibility relative to some set of rules
– none satisfying all the desiderata. Maudlin attempts to use this to deal with the revenge problem,
saying
….the practical advice one is likely to offer with respect to rules of permissibility is this: simply
try to avoid conversational contexts which lead into problematic areas… There are many rules of
permissibility…that can nearly meet the ideals outside of these contexts… And there is no need
to even consider problematic sentences unless one is engaged in some useless pursuit like
philosophy.37
I think what Maudlin says is problematic, in several ways. First, if no ungrounded sentences can be
true, why should they be able to have the other property of being permissibly assertively uttered?
Maybe Maudlin’s idea is that permissibility, unlike truth, is not a semantic property. But permissibility
would seem to be as much a semantic notion as truth is, and whatever motivation there is for
Maudlin’s fundamental postulate concerning truth and falsity there ought to be equal motivation for
a parallel fundamental postulate concerning permissibility and impermissibility – a postulate
according to which permissibility and impermissibility are always ‘rooted in the state of the world’.
But by Maudlin’s own lights this parallel postulate concerning permissibility should not be accepted.
If Maudlin were to deny that permissibility is a properly semantic notion on the ground that it is not
fundamentally a language-world relation, he faces the objection that it is not a given that truth is a
semantic notion in that sense. Second, relatedly, even if there is a notion, call it M(audlin)-truth, that
works as Maudlin says truth does, there’s also, by Maudlin’s own lights, a distinct notion, that which
he calls permissibility (or rather several ‘relative’ notions of permissibility). It is then an empirical
Maudlin (2004), p. 174.
Maudlin (2004), p. 171f.
36 Maudlin (2004), pp. 170 and 172.
37 Maudlin (2004), p. 175f.
34
35
22
question whether ‘true’ expresses M-truth or some notion of permissibility, and intuitive judgments
like those mentioned as standard problems with the minimal fixed-point theory speak in favor of the
view that ‘true’ expresses permissibility rather than M-truth. Third, focusing now on permissibility
itself, why should we conclude from the fact that there’s no perfect satisfier of the desiderata for a
permissibility predicate that permissibility is always relative, rather than that it may in some sense be an
indeterminate matter what is permissible? Compare: if ‘t’ is introduced by empirical theory T and there
is nothing that satisfies everything in T’s implicit characterization of ‘t’ but only some near-enough
satisfiers, one doesn’t conclude that ‘t’ is relative (that there is no content to the question of what t is)
but rather that it is indeterminate what ‘t’ refers to.38 Fourth, in the context of a discussion of the
meaning-inconsistency view it is probably not hard to see what the previous point leads up to: what
Maudlin in effect suggests regarding permissibility strikingly similar to inconsistency view. He takes
an ‘absolute’ permissibility predicate to have to satisfy all the desiderata; and when the desiderata
aren’t all jointly satisfiable, he doesn’t conclude that the notion of permissibility is empty or
meaningless. Instead, the claim is that its reference is relative.
Maudlin does not himself seriously discuss the possibility of an inconsistency view. He
discusses Tarski’s view that natural language is inconsistent. But the way he, without much
discussion, chooses to understand the claim that natural language is inconsistent in such a way that a
language is inconsistent for some speakers if it is possible to construct arguments in that language, that
are “accepted by the speakers as valid [sic] yet which have contradictory conclusions”.39 That is of
course an exceedingly weak understanding, and does not respect any intuitive notion of a language
being inconsistent. Presumably, Maudlin’s underlying assumption is that this is the best one can do
with the idea of an inconsistent language or language-fragment. It is then especially striking that
Maudlin’s own view on the notion of permissibility is a kind of inconsistency view not far removed
from that which I defend in the case of truth. And if Maudlin is in general hospitable to some kind of
inconsistency view – or perhaps generally some kind of egalitarian view – why not directly give such
an account when talking about truth, rather than arriving at such a view via an epicycle?
References
Azzouni, Jody: 2006, Tracking Reason: Proof, Consequence, and Truth, Oxford University Press, Oxford..
Azzouni, Jody: 2007, “The Inconsistency of Natural Languages: How We Live With It”, Inquiry 50:
590-605.
Beall, Jc and Graham Priest: 2007, “Not So Deep Inconsistency”, Australasian Journal of Logic 5.
Burgess, Alexis and John Burgess: 2011, Truth, Princeton University Press, Princeton.
38
39
[Lewis reference]
Maudlin (2004), p. 19.
23
Cherniak, Christopher: 1984, “Computational Complexity and the Universal Acceptance of Logic”,
Journal of Philosophy 81: 739-58.
Eklund, Matti: 2002, “Inconsistent Languages”, Philosophy and Phenomenological Research 64: 251-75.
Eklund, Matti: 2005, “What Vagueness Consists in”, Philosophical Studies 125: 27-60.
Eklund, Matti: 2007, “Meaning-Constitutivity”, Inquiry 50: 559-74.
Eklund, Matti: 2010a, “Review of Timothy Williamson, The Philosophy of Philosophy”, Australasian
Journal of Philosophy 88: 752-4.
Eklund, Matti: 2010b, “Vagueness and Second-Level Indeterminacy”, in Richard Dietz and
Sebastiano Moruzzi (eds.), Cuts and Clouds, Oxford University Press.
Field, Hartry: 2005, “Recent Debates About the A Priori”, in Tamar Gendler and John Hawthorne
(eds.), Oxford Studies in Epistemology, Oxford University Press, Oxford.
Field, Hartry: 2008, Saving Truth from Paradox, Oxford University Press, Oxford.
Haack, Susan: 1978, Philosophy of Logics, Cambridge University Press, Cambridge.
Horwich, Paul: 2008, “Ungrounded Reason”, Journal of Philosophy 105: 453-71.
Jackson, Frank: 1998, From Metaphysics to Ethics: A Defence of Conceptual Analysis, Oxford: Clarendon
Press.
Johnston, Mark: 1989, “Fission and the Facts”, Philosophical Perspectives 3: Mind and Action Theory, pp.
369-97.
Johnston, Mark: 1992, “How to Speak of the Colors”, Philosophical Studies 68: 221-63.
Lewis, David: 1970, “How to Define Theoretical Terms”, Journal of Philosophy, 67: 427-46.
Lewis, David: 1972, “Psychophysical and Theoretical Identifications”, Australasian Journal of Philosophy
50: 249-58.
Lewis, David: 1997, “Naming the Colours”, Australasian Journal of Philosophy 75: 325-42.
Ludwig, Kirk: 2002, “What is the Role of a Truth Theory in a Meaning Theory?”, in Joseph
Campbell, Michael O’Rourke and David Shier (eds.), Meaning and Truth: Investigations in Philosophical
Semantics, Seven Bridges Press, New York.
Martin, Robert L.: 1970a, “A Category Solution to the Liar”, in Martin (1970b), pp. 91-112.
Martin, Robert L. (ed.): 1970b, The Paradox of the Liar, New Haven and London: Yale University
Press.
Maudlin, Tim: 2004, Truth and Paradox: Solving the Riddles, Clarendon Press, Oxford.
McGee, Vann: 2003, “A Semantic Conception of Truth?”, Philosophical Topics 21: 83-111.
Patterson, Douglas: 2007, “Inconsistency Theories: The Significance of Semantic Ascent”, Inquiry 50:
575-89.
Patterson, Douglas: 2008, “Understanding the Liar”, in Beall (2008).
Patterson, Douglas: 2009, “Inconsistency Theories of Semantic Paradox”, Philosophy and
24
Phenomenological Research 79: 387-422.
Peacocke, Christopher: 1992, A Study of Concepts, MIT Press, Cambridge, Massachusetts.
Scharp, Kevin: 2007, “Replacing Truth”, Inquiry 50: 606-21.
Scharp, Kevin: 2008, “Aletheic Vengeance”, in Beall (2008).
Scharp, Kevin: 2013a, “Truth, the Liar and Relativism”, Philosophical Review 122: 427-510.
Scharp, Kevin: 2013b, Replacing Truth, Oxford University Press, Oxford.
Wedgwood, Ralph: 2011, “Primitively Rational Belief-Forming Practices”, in Andrew Reisner and
Asbjorn Steglich-Pedersen (eds.), Reasons for Belief, Cambridge University Press, Cambridge.
Williamson, Timothy: 2007, The Philosophy of Philosophy, Blackwell, Oxford.
Wright, Crispin: 1975, “On the Coherenc of Vague Predicates”, Synthèse 30: 325-65.
Wright, Crispin: 2004, “Intuition, Entitlement and the Epistemology of Logical Laws”, Dialectica 58:
155-75.
Wright, Crispin: 2007, “Wang’s Paradox”, in Randall Auxier and Lewis Edwin Hahn, The Philosophy of
Michael Dummett, Open Court, La Salle, Illinois.
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