## 1. Characterizing Category Mistakes




One might have expected this entry to start with a definition of
'category mistake'. However, giving an explicit
informative definition of category mistakes is no easy task. A typical
dictionary definition looks like this: "The error of assigning
to something a quality or action which can only properly be assigned
to things of another category, for example treating abstract concepts
as though they had a physical location" (Stevenson 2010). But
such definitions are at best too vague to be useful, and at worst
simply incorrect. For example, if 'properly assigned' is
interpreted as meaning
*truly assigned*, then the definition massively over-generates:
the sentence 'Two is odd' assigns to something (the number
two) a quality (being odd) that can only be truly assigned to things of
another category (odd numbers), but the sentence clearly isn't a
category mistake. Alternatively, if 'properly assigned' is
understood as 'grammatically assigned', then we risk
classifying obviously ungrammatical strings such as 'the boys
eats' as category mistakes.




Other definitions suffer from not being sufficiently theoretically
neutral, relying on specific controversial accounts of category
mistakes. For example, one might try to define category mistakes as
sentences that are syntactically well-formed but meaningless. But as
we shall see both parts of this proposed definition depend on
controversial assumptions about the nature of category mistakes: that
they are syntactically well-formed (cf. SS3.1) and that they are
meaningless (cf. SS3.2.1). Moreover, even if we are willing to
eschew theoretical neutrality, note that most of the accounts
discussed do not offer an obvious way to distinguish category mistakes
from other linguistic phenomena. For example, according to the
truthvaluelessness view (SS3.2.3) category mistakes are contentful
but truth-valueless but, at least according to many philosophers, so
are some instances of vague sentences such as 'John is
tall'. And according to the presuppositional approach
(SS3.4), category mistakes suffer from a presupposition failure,
but then so do sentences that are not category mistakes such as
'The king of France is bald'.




Perhaps the question of how to define category mistakes will receive a
more satisfactory answer in the future or perhaps (following a general
trend in analytic philosophy against conceptual analysis) we should
eschew the project of defining category mistakes altogether. At any
rate, extant debates on the topic of category mistakes have focused
largely on the question of how to account for their infelicity rather
than on the question of how to define the concept or distinguish
category mistakes from other phenomena. The remainder of this entry
will follow suit.




Even without offering an explicit definition, there is a
phenomenological way of characterizing category mistakes. As noted at
the outset, there seems to be a distinctive kind of infelicity which
we can recognize by example: the sort of infelicity present in
paradigmatic category mistakes such as 'The number two is
blue'. We can thus characterize category mistakes as sentences
that are infelicitous in a similar manner to these paradigmatic
examples. While this kind of phenomenological characterization may not
seem theoretically informative, on reflection it reveals several
interesting features of category mistakes. First, category mistakes
can be created using a wide range of syntactic types: for example,
adjectives ('Two is green'); adverbs ('John sleeps
furiously'); or prepositional phrases ('The theory of
relativity is under the table'). Second, the infelicity
characteristic of category mistakes seems to occur in a range of
complex constructions (for example, 'The number two isn't
blue' or 'Either the number two is blue or it is
prime'). Third, whether the sort of infelicity in question is
present can depend on context, in various different ways. For example,
an utterance of 'That is green' seems infelicitous in a
context where the demonstrative refers (or appears to refer) to the
number two, but entirely innocuous in a context in which it refers to
a pen. And an utterance of 'The priest is pregnant' can be
infelicitous in a context where speakers assume that all priests are
male, but entirely innocuous in a context where it is assumed that
there are female priests. As we shall see, these features play a role
in the ensuing debate.


## 2. A Brief History of the Topic




Philosophers seem to have been interested in the phenomenon of
category mistakes at least since Aristotle, even if the phenomenon was
not explicitly labelled. For example, In Metaphysics Zeta 5, Aristotle
raises an interesting puzzle concerning the attribute
'snub': on the one hand, 'snub nose' seems to
mean exactly the same thing as 'concave nose' which
suggests that 'snub' simply means the same as
'concave'. On the other hand, this cannot be the entire
story because, unlike 'concave', 'snub' can
only be felicitously attributed to noses: 'concave bowl',
for example, is entirely felicitous while 'snub bowl' is a
 kind of category
 mistake.[1]




However, it seems fair to trace the contemporary debate on category
mistakes to the first half of the 20th century, and most
notably to the work of Gilbert Ryle (who also coined the term
'category mistake'). Influenced by the work of Edmund
Husserl, Ryle argued that category mistakes were the key to delineating
ontological categories: the fact that 'Saturday is in bed'
is a category mistake while 'Gilbert Ryle is in bed' is
not, shows that Saturday and Ryle belong to different
 ontological
 categories.[2]
 Moreover, Ryle
maintained that distinguishing between categories was *the*
central task of philosophy: "The matter is of some importance,
for not only is it the case that category-propositions (namely
assertions that terms belong to certain categories or types), are
always philosopher's propositions, but, I believe, the converse
is also true. So we are in the dark about the nature of philosophical
problems and methods if we are in the dark about types and
categories" (Ryle 1938, 189). Section 3.2.1 below
treats developments of the view that Ryle's held, namely, 
that category mistakes are grammatical but meaningless.




To see why category distinctions were so important to Ryle, we need
to look at another major influence: Bertrand Russell. Russell argued
that a range of paradoxes (including his famous set-theoretic paradox
and the Liar paradox) can be solved by restrictions of type. For
example, the famous set-theoretic paradox requires considering sets
that are (/ are not) members of themselves. However, if 'is a
member of \(s\)' is a predicate that can only meaningfully
be predicated of objects of a certain type which does not include
\(s\) itself, then '\(s\) is (/ is not) a member of
\(s\)' is simply a meaningless sentence, and the paradox
cannot even be properly expressed. This inspired two related ideas,
which gained further support from the work of Wittgenstein and the
logical positivists: first, due to some kind of type confusion,
apparently grammatical sentences might nevertheless be meaningless;
second, apparent philosophical puzzles might be resolved by exposing
type confusions and declaring the sentences allegedly stating the
puzzle meaningless.




Ryle argued that these ideas should be applied much more widely than
Russell's discussion of the paradoxes suggested. The thought was
that by recognizing some philosophically puzzling assertions as
category mistakes, one would expose them as meaningless, thus
dissolving these puzzles altogether. This philosophical methodology saw
its culmination in *The Concept of Mind*, in which Ryle declared
that the dualistic position and the mind-body problem that it gives
rise to is "one big mistake and a mistake of a special kind. It
 is, namely, a category
 mistake".[3]
 The exact relation between these philosophical
problems and more paradigmatic cases of category mistakes (sentences
such as 'Saturday is in bed' which Ryle discussed in his
earlier work) is not entirely clear, but even putting Ryle's own
application of the concept aside, his work on category mistakes
generated a lasting philosophical interest in the phenomenon.




Some of the ensuing debates continued the project of attempting to
 demarcate ontological categories using category
 mistakes[4],
 while others focused more directly on
the semantic status of category mistakes. In the 1940s and 50s the
orthodox view seems to have accepted Ryle's claim that category
 mistakes are
 meaningless[5],
 so
much so that in his 1954 paper 'Entities' Arthur Prior
complained that anyone who takes category mistakes to be false rather
than meaningless "must nowadays count themselves among the
heretics" (Prior 1954, 160). Even in that period, this
orthodoxy had its dissenters (Prior 1954; Ewing 1937; and Quine
1960). For example, in *Word and Object*, Quine criticized the
view that took category mistakes to be meaningless as "just a
spontaneous revulsion against silly sentences" (Quine 1960,
229). These objectors were primarily focused on refuting the claim that
category mistakes are meaningless and the alleged applications of this
claim to metaphysical debates, rather than in offering any positive
account of why category mistakes are nevertheless infelicitous.




The 1960s saw a more direct interest in category mistakes as an
independently interesting linguistic phenomenon. In 1966 Drange
published an entire monograph devoted to the topic (Drange 1966), and
a lively exchange in the *Australasian Journal of Philosophy*
focused on the question of whether category mistakes are truth-valued,
with Lambert and Haack supporting the view (labelled 'no
type' or 'falsidal') that category mistakes are
truth-valued and Brady, Goddard, and Routley arguing that they
 are
 not.[6]
 The period between the
late 1960s and the early 1980s saw a series of papers attempting to
account for category mistakes using a range of tools from formal logic,
culminating with the publication of the second monograph devoted to
 category mistakes: Lappin
 (1981).[7] 
 However, by the mid-1980s the topic of
category mistakes seemed to have fallen out of fashion: for over twenty
years it was by and large neglected in the philosophical literature, at
least as a self-standing issue.




Almost entirely divorced from the philosophical debate, category
mistakes were also extensively discussed in the linguistics literature
(though almost never under that label--terms used in the
linguistic literature for various aspects of the phenomenon include
'selectional violations', 'selectional
restrictions', 'semantic anomaly' 'sortal
presuppositions'). Here the driving figure of the debate was Noam
Chomsky. In his 1957 monograph *Syntactic Structures*, Chomsky
maintained that the now-famous category mistake 'Colorless green
ideas sleep furiously' is grammatical but meaningless, using this
claim to support his contention that syntax is an autonomous field from
semantics. The claim was further developed in Fodor & Katz's
influential paper 'The structure of semantic theory' (Fodor
& Katz 1963), where they claimed that the ability to recognize
which sentences are 'semantically anomalous' (their term
for category mistakes) was a crucial component of linguistic
competence. Moreover, they developed a semantic framework which
predicted that category mistakes are (grammatical but) meaningless.
However, in his 1965 book *Aspects of the Theory of Syntax*
Chomsky revised his view of category mistakes, now arguing that they
are *un*grammatical, and offering a syntactic theory which
rendered them syntactically ill-formed (cf. SS3.1). The theory
followed many of the technical details of Fodor and Katz's
theory, but this time treating features they took to be semantic as
syntactic.




In the late 1960s category mistakes played a central role in the
chasm between the followers of Chomsky (whose view was labelled
'Interpretative Semantics'), and proponents of a new
movement in linguistics labelled 'Generative Semantics',
whose key proponents were Lakoff, McCawley, Ross, and Postal.
Interpretative semanticists claimed that sentences were assigned a
syntactic structure by an autonomous syntactic module, a structure
which could then be provided as input for semantic interpretation. By
contrast, generative semanticists eschewed the sharp distinction
between syntax and semantics, maintaining that the structure of a
sentence was determined by a combination of so-called syntactic,
semantic, and pragmatic considerations. In particular, they labelled
infelicitous sentences such as category mistakes as simply
'ill-formed', resisting the attempt to pin down the precise
 source of the
 ill-formedness.[8]




As in philosophy, by the 1980s dedicated discussions of the
phenomenon of category mistakes seemed to have died out, although the
concept is still routinely mentioned in passing, especially in
introductory text-books. The standard view seems to be that category
mistakes are 'semantically anomalous' or
'semantically ill-formed'. It is not entirely clear what
these labels amount to, but most likely they indicate the view, which
seems to be accepted by the majority of linguists these days, that
category mistakes are grammatical but meaningless.




However, since the early 2000s, the topic of category mistakes has
been experiencing a small revival in both philosophy and linguistics
(with the division between those two fields no longer
 being
 sharp).[9]


## 3. Accounts of the Infelicity of Category Mistakes


### 3.1 The Syntactic Approach




One way to account for the infelicity of category mistakes is to
maintain that they are syntactically ill-formed. The most substantial
defense of this approach appeared in Chomsky's 1965 monograph
*Aspects of the Theory of
 Syntax*.[10]
 Chomsky's account proceeds roughly as
follows. In addition to assignments of general grammatical categories
such as 'noun' and 'verb', lexical items also
receive what Chomsky calls 'selectional features'. For
example, even though 'boy' and 'sincerity' are
both nouns, the former receives the selectional features
'+animate', and '-abstract', while the latter
receives the features '-animate', and
'+abstract'. Verbs and adjectives are also marked with
selectional features, representing, for each argument place, the kinds
of argument they accept. For example, the verb 'admire'
expects a '+animate' for its subject argument, thus
predicting that 'The boy admires sincerity' is grammatical,
while the category mistake 'Sincerity admires the boy' is
not.
 




Chomsky's key argument in favor of the syntactic approach is
that the use of selectional features as part of syntax is independently
motivated (Chomsky 1965, SS4.1). Thus consider the following
strings:



(1)
The boy who is next to the table is unusual.
(2)
\* The book who is next to the table is unusual.
(3)
The book which is next to the table is unusual.
(4)
\* The boy which is next to the table is unusual.



According to Chomsky, while (1) and (3) are grammatical, (2) and
(4) are not. But in order to account for this difference, it looks like
we need to incorporate something like the selectional features
'+/-animate' into syntax. And, the argument goes, once such
features have already been incorporated into syntax, a natural account
of the infelicity of category mistakes follows.




However, even if Chomsky's who/which argument succeeds in
showing that syntax should be sensitive to the animate/inanimate
distinction, it is not clear that this is sufficient to account for
 category mistakes in
 general.[11]
 For example, Hebrew has a special verb to
denote picking grapes (rather than other sorts of fruit), and a special
verb to denote putting on socks (rather than other kinds of clothing).
The following are both category mistakes in Hebrew:



(5)
\* Ani botzer et ha-tamrim.

I am grape-picking the dates.
(6)
\* Ani gorev et ha-kfafot.

I am sock-putting-on the gloves.



The problem is that in order to extend Chomsky's syntactic
approach to account for such category mistakes, one would need very
specific selectional features such as '+/-grape' and
'+/-sock'. Of course, this is not a decisive argument
against the syntactic approach--perhaps syntax really should be
enriched with such a wide array of sectional features. However, it
does undermine the claim that the syntactic approach can be executed
using independently motivated syntactic machinery, as clearly no
(other) syntactic phenomenon requires sensitivity to whether an
argument denotes a grape.




There are also some more direct objections to the syntactic
approach. One issue concerns the fact that one can felicitously embed
category mistakes in other environments. Thus consider the following
examples:



(7)
\* John said that rides boy the on.
(8)
John said that the number two is green.
(9)
\* John dreamt that rides boy the on.
(10)
John dreamt that the number two is green.



While embedding the ungrammatical string 'rides boy the
on' in the context of propositional attitude reports results in
ungrammatical sentences ((7) and (9)), embedding the category mistake
'the number two is green' in the same environment arguably
 results in felicitous, grammatical sentences ((8) and
 (10)).[12]




Another potential problem for the syntactic approach has to do with
the context sensitivity of category mistakes. Consider the following
examples:



(11)
The thing I am thinking about is green.
(12)
That is green.
(13)
The number two has the property I've just
 mentioned.



Whether or not these sentences exhibit the kind of infelicity
associated with category mistakes depends on context: (11) and (12)
are perfectly felicitous in a context where it is clear that the thing
I am thinking about/referring to is a pen, but not so in a context
where it is the number two. Similarly, (13) is felicitous in a context
where it is clear that the property I've just mentioned the
property of being prime, but not so if it was the property of being
green. This is a problem for the syntactic approach, because whether a
sentence is syntactically well-formed or not is a context-invariant
property: it cannot vary according to context in this manner.


### 3.2 Semantic Approaches




A second way of accounting for the infelicity of category mistakes is
to maintain that they are syntactically well-formed but semantically
defective. This general approach encompasses several different views.
To see why, note that there are various kinds of semantic values that
are assigned to a single sentence token. First, a sentence is assigned
a general *meaning*. Without going into too much theory, we can
think of the meaning of a sentence as the result of combining the
definitions of each of the words it contains, and also as what the
sentence shares with its translations into other languages. Thus the
meaning of the English sentence 'I am tall' is a property
it shares with the French sentence 'Je suis grande'.
Second, when a sentence is uttered in a particular context, it
expresses a particular *content*. For example, in a context
where Sophie utters the sentence 'I am tall' it expresses
the proposition that Sophie is tall, and in a context where Jim utters
this sentence it expresses the proposition that Jim is tall. Third,
particular tokens of the sentence receive
a *truth-value*--for example, when Sophie utters 'I
am tall', her (token) sentence is true if she is indeed tall,
and false otherwise.




Corresponding to these three kinds of semantic values are three
different semantic accounts of category mistakes: according to the
first ('the meaninglessness view'), category mistakes are
syntactically well-formed but meaningless; according to the second
('the contentlessness view') they are meaningful but lack
content; according to the third ('the truthvaluelessness
view'), they are meaningful and have a content, but lack a
truth-value (or at least lack one of the two standard truth-values,
*true* and *false*).


#### 3.2.1 The Meaninglessness View




The meaninglessness view has been the most popular account of category
mistakes throughout the history of the debate, and still receives
considerable support from both linguists and philosophers. For
example, Beall and van Fraassen (2003, 125) say that "there are
different ways in which a (declarative) sentence might properly be
called 'meaningless'. Perhaps the best example involves
so-called category mistakes" and Sauerland and von
Stechow (2001, 15413) describe sentences such as Chomsky's
famous 'Colorless green ideas sleep furiously' as ones
 which "are syntactically well formed but do not make any
 sense".[13]




The meaninglessness view is highly intuitive: category mistakes are
extremely infelicitous and often generate the feeling that they simply
do not make any sense. Another advantage of the meaninglessness view is
that it arguably has the best chance of providing a clean answer to the
question of how to characterize category mistakes (cf. SS1). This
is so because if category mistakes are grammatical but meaningless,
then plausibly, they also constitute the *only* kind of sentence
that have these two features. By contrast, the same does not seem to be
true of any of the other accounts discussed: for example, even if
category mistakes are syntactically ill-formed (SS3.1) or suffer
from presupposition failures (SS3.4) they are clearly not the only
kind of strings to have these features. The meaninglessness view might
also be motivated by a commitment to a particular favored theory of
meaning. For example, a proponent of conceptual role semantics might
maintain that category mistakes play no conceptual role, and thus are
 predicted by the theory to be
 meaningless.[14]




However, the meaninglessness view also faces several serious
challenges. First, note that some of the observations raised against
the syntactic approach (SS3.1) also pose a problem for the
meaninglessness view. For example, consider the context sensitivity of
category mistakes. Since in some contexts 'The thing I am
thinking about is green' is entirely innocuous the sentence is
clearly meaningful. But as with being syntactically well-formed, being
meaningful is a context invariant property of a sentence so the
sentence must be meaningful even in those contexts where the thing I
am thinking of is the number two.




Similarly, the fact that category mistakes embed felicitously in
propositional attitude reports presents at least a challenge to the
meaninglessness view: since 'John said that the number two is
green', or 'Jane dreamt that her toothbrush is
pregnant' are themselves felicitous reports, these reports are
not (even by the lights of the meaninglessness view) meaningless. This
leaves the question of whether it is possible that the report as a
whole is meaningful, even though the embedded category mistake is not.
Note that in the case of the syntactic approach, we were able to test
how such embeddings behave using clear examples of syntactically
ill-formed strings, ones which are not themselves category mistakes
(e.g. 'John said that rides boy the on'). In this case,
however, matters are much trickier as we do not have any clear examples
of grammatical but meaningless sentences that are not category mistakes
which we can use to test the behavior of such embeddings. Nevertheless,
more theoretical arguments concerning the semantics of attitude reports
might bear on the question. For example, if we accept that the meaning
of a sentence is composed out of the meaning of its constituents and
that the relevant 'that'-clause is a constituent of the
 attitude
 report,[15]
 it follows that the attitude report as a whole cannot be meaningful 
if its constituent category mistake is meaningless.




Considerations of compositionality (the principle that the meaning of
a sentence is composed of the meaning of its parts), can also be
brought to bear more directly on the question of whether category
mistakes are meaningful. One might be tempted to think that the mere
fact that a category mistake such as 'Two is green' is
composed out of meaningful words arranged in a grammatical way is
sufficient to trivially entail, given compositionality, that the
sentence is meaningful. This temptation ought to be resisted, though:
for all we have said, the principle of compositionality merely shows
that when a sentence *has* a meaning then that meaning is
composed out of the meaning of its parts. This is not the same as
saying that any (grammatical) combination of meaningful parts always
 successfully results in a sentence
 meaning.[16]
 It is thus open to defenders of the meaninglessness view to accept
that meaning is compositional, but deny that category mistakes are
meaningful.




Nevertheless, considerations of compositionality might still pose a
significant challenge to the meaninglessness view. This is so because
defenders of the meaninglessness view need to provide a compositional
semantic theory that accounts for the meaning of those sentences that
they *do* deem to be meaningful. The problem is that once such a
theory provides a systematic recipe for how to assign meanings to
benign sentences, there is a risk that an assignment of meanings to
categorically mistaken combinations will automatically fall out. To
illustrate the point, suppose that the semantic theory assigns objects
to the names 'Two' and 'Desky' (the number two
and a particular desk respectively), and the ordinary functions from
objects to truth-values to the predicates 'is green' and
'is prime'. Suppose further that the recursive
specification of the theory say that the meaning of any sentence of the
form '\(a\) is \(P\)' is the claim that
\(f(o)=\)true, where \(f\) is the function denoted by
'\(P\)' and \(o\) is the object denoted by
'\(a\)'. Note that even if this theory was only
designed to account for the meaning of standard combinations such as
'Desky is green' and 'Two is prime', it also
inadvertently assigns a meaning to the category mistakes 'Two is
green' and 'Desky is prime'. Of course, one can try
to amend the semantic theory so that it avoids this consequence, but
the question is whether a semantic theory can be constructed that
succeeds in assigning meanings to precisely all and only
non-categorically mistaken sentences.




A completely different set of challenges to the meaninglessness view
stems from the fact that while category mistakes are rarely used in
literal discourse, they are highly prevalent in figurative speech.
Consider for example a metaphorical use of 'The poem is
pregnant' (by a critic, wanting to describe the richness of the
poem); a metonymic use of 'The ham sandwich left without
paying' (uttered by a waiter in reference the customer who
ordered the ham sandwich); or uses of category mistakes in fiction (a
story containing the sentence 'The tree forgave the boy'
or even 'The number two was happy'). Indeed, the very fact
that the sentences in question are category mistakes often serves as
 in indication that the sentence is used figuratively rather than
 literally.[17]




The very fact that category mistakes have such figurative uses is
not in itself a problem for the meaninglessness view: prima facie,
there is no contradiction between the claims that, when taken
literally, category mistakes are meaningless while when used
figuratively, they can be meaningful. However, figurative uses of
speech clearly have *some* connection to their literal meanings,
with different theories offering different accounts of this connection.
The question then becomes, for each such account of figurative uses,
whether it requires the relevant sentence to also be literally
meaningful.




Consider the case of metaphor. According to one central view of
metaphor, the metaphorical meaning of a sentence is communicated via the
mechanism of conversational implicature: when one utters a metaphor,
the proposition literally expressed by the metaphor blatantly violates
one of Grice's maxims of conversation (typically the maxims of
quality or relevance) thus giving rise to an implicated content which
constitutes the metaphorical meaning. There is more to say about the
details of the view, but the crucial point for our purposes is that on
the Gricean account of metaphor, metaphorical meanings are generated
indirectly, using the literal content of the sentence. But then in
order for a sentence to receive a metaphorical interpretation, it must
also have a literal meaning, and in particular successful metaphors
that are category mistakes are also literally meaningful, *pace*
the meaninglessness view.




A better hope for the meaninglessness view are accounts of metaphor
on which the metaphorical meaning does not depend on the literal
meaning of the entire metaphorical sentence, but merely on the meaning
of some sub-sentential phrases. For example according to Joseph
Stern's account (Stern 2000), when a sentence is used
metaphorically, some of its sub-sentential phrases are embedded under a
special operator called 'Mthat', which delivers as an
output a new (contextually determined) metaphorical meaning for that
phrase. Thus on Stern's view, when used metaphorically the
sentence 'The poem is pregnant' has the deeper structure
'The poem is Mthat(pregnant)', where
'Mthat(pregnant)' can be interpreted in context as, for
example, the property of containing many ideas. When we consider such
syntactically simple metaphors, Stern's view seems entirely
consistent with the meaninglessness view: at no stage in this
interpretation are we required to assign a (literal) meaning to the
entire categorically mistaken sentence. However, things become more
difficult once we consider metaphors with a more complex structure.
Thus consider the following conversation, discussing Jane's
research:



Jill:
So, I heard that Jane ended up giving up her
 idea for the thesis?
Sally:
Oh, she didn't just give it up. She dropkicked
 the idea noisily off the nearest cliff!



Sally's second sentence 'She dropkicked the idea noisily
off the cliff' is a metaphor, so on Stern's view, some
syntactic phrase within that sentence should be read as falling within
the scope of an 'Mthat' operator. Magidor (2017, 70) argues
that Mthat must apply here to the entire verb phase ('dropkicked
the idea nosily off the nearest cliff'). But note that Stern
requires Mthat to apply to meaningful
 phrases,[18]
so the entire verb phrase needs to be meaningful.
Interestingly, however, once one has conceded that the verb phrase is
literally meaningful, there is no reason not to take the entire
sentence to be meaningful as well: the introduction of the subject term
is entirely innocuous, and if there were any problem arising from
category mistakes being meaningless it should have already arisen at
 the stage where one talks of an idea being dropkicked off a
 cliff.[19]




Another more general problem for reconciling the meaninglessness view
with an account of metaphor is raised by Camp (2004, 225). Camp points
out that not all metaphors are category mistakes, and indeed some are
obviously literally meaningful and even true. (Consider for example a
metaphorical use of 'Anchorage is a cold city'.) This
posits a dilemma for the meaninglessness view. Either even in such
cases, the metaphorical meaning is accounted for without making use of
the literal meaning of the sentence in which case the account deprives
itself of some helpful resources in interpreting the metaphor. Or
else, the account of metaphor becomes bifurcated--offering one
account for metaphors that are also category mistakes and another one
for those that are not.


#### 3.2.2 The Contentlessness View




According to the contentlessness view, category mistakes are
meaningful but fail to express a proposition. An attractive feature of
the contentlessness view is that it addresses one of the most pressing
objections against the previous two accounts: namely, accommodating the
context sensitivity of category mistakes. Unlike grammaticality and
meaningfulness, what content (if any) is assigned to a sentence is not
a context-invariant property. So one can coherently maintain that
'This is green' is perfectly acceptable in contexts where
the demonstrative refers to a pen, while lacking content in contexts
where the demonstrative refers to the number two.




The contentlessness view can be developed in two rather different
ways. The first way to develop the view is particularly attractive to
those who accept some kind of radical contextualism about natural
language: the view that every (or nearly every) expression of natural
language is context sensitive. Suppose one accepted, for example, that
the content of the predicate 'is green' is extremely
sensitive to context (dimensions of sensitivity might include which set
of shades are being picked by the predicate or which parts of the
object need to exhibit the color in order to satisfy it). One might
then maintain that in the case of category mistakes such as 'Two
is green', the sentence is so artificial that there simply
isn't enough material in the context to determine which property
'is green' denotes, and hence some words in the sentence
 (and ipso facto the sentence as a whole) cannot be assigned a
 content.[20]
 A second, very different way to develop the view assumes that in
category mistakes such as 'Two is green', each word
succeeds in picking out a content but these contents fail to compose
together to form a unified proposition.




A way to put pressure on the contentlessness view on either of its
versions is by constructing examples of apparent category mistakes (or
category mistake-like utterances) that are designed specifically to
ensure there should be a content in place. With respect to the first,
contextualist proposal we can consider the following sequence, uttered
in a particular context:



(14)
This pen is green. So is the number two.



The first sentence in the sequence uses 'is green' in a
perfectly ordinary context so it is assigned a content in the usual
manner (a particular color property). This property is then
anaphorically referred to in the second sentence. This ensures that
the second sentence in the sequence doesn't suffer from the kind
of content failure due to insufficient contextual information, despite
attempting to attribute a color to the number two.




Of course (14) does not pose any problems for the second version of
the contentlessness view, which locates the problem with category
mistakes in the composition of contents (presumably, according this
version, the number wouldn't be able to compose with the color
property referred to anaphorically). However, consider an utterance of
the following sentence, in a context where the thing I am thinking
about is a table (and where the description is interpreted as
non-rigid):



(15)
The thing I am thinking about is green.



As uttered in this context the sentence is entirely innocuous, and
hence clearly expresses a proposition (call this proposition
'\(p\)'). The problem, however, arises when we evaluate
\(p\) relative to a possible world \(w\) in which the thing I am
thinking about is the number two. (Crucially, note that we are
evaluating the very same proposition \(p\), not the proposition that
would have been expressed by (15) had it been uttered in
\(w\)). Relative to \(w\), \(p\) is a proposition which effectively
ascribes to the number two the property of being green. The example
does not quite provide us with an example of a contentful category
mistake (arguably, since (15) is actually uttered in the innocuous
context, it is not itself a category mistake), but it does suggest
that some propositions succeed in ascribing colour properties to
numbers, and hence this kind of predication shouldn't in general
be an obstacle to generating contents.




In addition to these worries, note that while the contentlessness view
is well-equipped to address some of the objections against the
meaninglessness view (such as the context sensitivity objection), it
nevertheless shares some of the problems that the meaninglessness view
faces. For example, successful embeddings under propositional attitude
reports present a challenge for the contentlessness view if one
maintains that the report as a whole is contentful, and that the
content of the embedded category mistake is a constituent of the
content expressed by the report as a whole. And many views of the
semantics of figurative language conflict with the contentlessness
view as well: for example, the Gricean view of metaphor discussed
above requires that category mistakes are not only meaningful but also
contentful.


#### 3.2.3 The Truthvaluelessness View




The third semantic account of category mistakes is one according to
which category mistakes are meaningful, contentful, but lack a
truth-value ('the truthvaluelessness view'). This gets
around many of the issues raised against previous semantic accounts.
For example, in the case of (14) or (15) defenders of the
truthvaluelessness view need not deny that there is a proposition
\(p\) which predicates greenness to the number two. They can simply
maintain that in such cases the proposition is truth-valueless. The
truthvaluelessness view also seems to be better equipped to deal with
the embedding problem (there doesn't seem any obvious issue with
a contentful or even true report that embeds a truth-valueless
sentence) or the problems to do with figurative language (even if the
figurative meaning depends on a literal meaning or content, it does
not seem to depend on any literal *truth-values*).




Shaw (2015) proposes another interesting argument in favor of the
 truthvaluelessness
 view.[21]
 Shaw maintains that there is a special mechanism for restricting the
domain of quantifiers so as to avoid categorically mistaken statements
in their scope. Suppose for example that Bob's yard contains
several planted trees and also a pile of wooden planks lying on the
ground. Now consider the contrast between the following two
sentences:



(16)
Bob uprooted everything in his yard and burned it.
(17)
Bob burned everything in his yard.



In (16), we seem to be quantifying only over the trees in the yard,
while in (17) we are quantifying over (at least) both the trees and
the planks. Shaw argues that this observation cannot be accounted for
by typical mechanisms of contextual domain restriction, or by
pragmatic considerations such as providing a charitable
interpretation. Instead, he proposes, this kind of restriction can be
explained by the following two hypotheses: first, language users
attempt to interpret statements so as to maximize truth-evaluability
(namely, as having some truth value or other); second, category
mistakes are truth-valueless. The thought is that if the quantifier
in (16) is allowed to range over some of the planks, then the open
sentence 'Bob uprooted \(x\)' will be a truth-valueless
category mistake relative to assignments where the variable is
assigned a plank and this will entail the universally quantified
sentence as a whole is truth-valueless. In order to avoid this
consequence and maximize the truth-evaluability of the statement,
interpreters restrict the quantifier so as to range only over the
trees.




Shaw's argument, however, is not decisive. One issue is that the
restriction data is not entirely systematic, in the sense that other
examples with exactly the same structure seem to elicit different
intuitions. For example, consider a context involving a long column of
letters and numbers randomly mixed together. Suppose John multiplied
all the numbers in the column by three. The following seems at best
false, possibly infelicitous:



(18)
John multiplied everything written on the page
 by three.



Note that Shaw's analysis predicts that the quantifier in (18)
would be restricted to only the numbers on the page, and thus that the
utterance should be felicitous and true. Second, even assuming that
Shaw is right that we do systematically restrict domains of
quantification so to avoid categorically mistaken predications, it is
not clear that the claim that category mistakes are truth-valueless is
essential for this mechanism of domain restriction. Consider any
theory that systematically tracks the status of category mistakes as
infelicitous (e.g., a presuppositional view, as discussed in
SS3.4). On the face of it, one could equally well explain
Shaw's data using the alternative hypothesis that the
categorically mistaken status of sentences projects into quantified
statements in precisely the way that Shaw predicts, and that speakers
have a strategy of maximizing the
*felicity* (rather than truth-evaluability) of their
utterances.




The truthvaluelessness view also faces some unique challenges. One
such challenge arises from its commitment to the claim that there are
sentences which express a proposition but are nevertheless
truth-valueless. Two widely accepted principles governing the notions
of truth and falsity are Tarski's truth-schemas, which can be
stated thus:



(T)
The proposition that \(p\) is true if and only
 if \(p\).
(F)
The proposition that \(p\) is false if and only
 if not \(p\).



But as Williamson (1994, 187-198) argues, these principles are
inconsistent with the claim that there is a truth-valueless
proposition: For suppose that the proposition that \(p\) is neither
true nor false. From (T), since it is not true that \(p\), then
not \(p\). From (F), since it is not false that \(p\), then not
not \(p\). We have now arrived at a direct contradiction:
*not*-\(p\) and *not*-*not*-\(p\).




Note that this is an objection that neither of the previous two
semantic accounts of category mistakes face: the Tarskian truth schema
do not apply to cases where '\(p\)' does not express a
proposition at all (either because it is meaningless or because it is
meaningful but contentless).




Of course, a natural response for defenders of the
 truthvaluelessness view is to reject the Tarskian
 truth-schema.[22] 
 Indeed, arguably, the semantic paradoxes such as the Liar already
motivate the rejection of the schema for reasons entirely independent
of category mistakes. Against this, defenders of the schema have
suggested that the semantic paradoxes might be addressed in a way that
does not require a commitment to truth-valueless propositions. One
potential assessment of the dialectical situation is this: perhaps
accounting for the infelicity of category mistakes is not on its own
sufficient to ground a rejection of the truth schema, which is
often thought to be fundamental to our concepts of truth and
falsity. However, if the schema ought to be rejected on independent
grounds, then applying the apparatus of truth-valueless propositions
to the case of category mistakes looks attractive. If we accept this
assessment, then the issue of whether one should accept the
truthvaluelessness view turns on the much wider issue of our response
to the semantic paradoxes.




As noted at the outset of this subsection, one of the key advantages
of the truthvaluelessness view over the previous two semantic views is
that it does not automatically deem any sentence in which a category
mistake is embedded to be infelicitous. How does, then, the
truthvaluelessness view treat embeddings of category mistake in more
complex sentences, and in particular those involving logical
connectives such as disjunction, conjunction, or conditionals?




A range of logics have been developed for determining the truth-values
of complex sentences in the presence of truth-value gaps. One option
is to use Weak Kleene logic (WK), on which a complex sentence which
has a truth-valueless constituent will always be truth-valueless as
well. But assuming the truthvaluelessness view takes a sentence to be
infelicitous if and only if it is truth-valueless (at least where the
lack of truth-value is due to the occurrence of some category
mistake), this approach will over-predict infelicity. Consider for
example the following:



(19)
If numbers have colors, then the number two is green.



While the sentence is perhaps surprising, it seems significantly more
felicitous than typical category mistakes, but on the WK treatment it
will be deemed truth-valueless and hence predicted to be
infelicitous. Other problems occur when we consider how WK treats
quantified sentences. Consider for example the following:



(20)
Something is green.



Suppose the domain contains several concrete objects (including some
green ones), as well as some abstract objects. Intuitively, (20) is
felicitous and true (after all, there are some green objects in the
domain). However, according to the WK treatment of category mistakes
the sentence ought to be truth-valueless. This is so because the
existential quantifier scopes over the open formula '\(x\) is
green' which is truth-valueless relative to some assignments
 (e.g. ones where \(x\) is assigned a
 number).[23]




Both of these problems are avoided by using Strong Kleene logic (SK)
instead. According SK, a sentence with a truth-valueless constituent
isn't automatically deemed truth-valueless. Specifically, a
sentence of the form 'If \(A\) then \(B\)' (with the
conditional interpreted as material) is true if \(A\) is false and
\(B\) is truth-valueless, and an existentially quantified sentence is
true if it has one true instance (even if some other instances are
truth-valueless), and thus neither (19) nor (20) would be deemed
truth-valueless. However, the SK treatment of category mistakes
possibly errs in the other direction, namely by under-predicting
infelicity. Consider for example the following:



(21)
? Either the number two is green or the number
 five is prime.
(22)
? The number two is green and Lisbon is the
 capital of France.



On a SK treatment of category mistakes, the fact that (21) has one
true disjunct (the second) is sufficient to render it true, and the
fact that (22) has one false conjunct (the second) is sufficient to
render it false. Both sentences are thus predicted by the account to
be felicitous. The judgements might not be as clear in these cases,
but insofar as one judges these sentences to be infelicitous that is a
challenge for the SK approach.




One additional worry that has been raised against both the WK and the
SK treatment of category mistakes (Thomason 1972, 231) is that not all
classical tautologies are deemed true on these logics. For example,
both logics render the following truth-valueless:



(23)
Either the number two is green or the number two
 isn't green.



While this is only to be expected on views which maintain that
'the number two is green' is meaningless or at least
contentless, it is arguably a less palatable consequence for the
truthvaluelessness view. An alternative view which avoids this
consequence is an account of category mistakes using supervaluationist
logic. The view is developed in detail in Thomason (1972), but in
broad terms it proceeds as follows: a valuation is an assignment of
the values true/false to each atomic sentence, where unproblematic
instances receive truth values as usual and category mistakes are
assigned an arbitrary truth value. Complex sentences receive a truth
value relative to each valuation in the standard recursive manner, and
finally a sentence is considered *true* if it is true relative
to every valuation; *false* if it is false relative to every
valuation; and *truth-valueless* if it is true relative to some
valuations and false relative to others. This ensures that (23) is
deemed true because it is true relative to every valuation (one can
prove that the same holds for all other classical
tautologies). Moreover, it also deems existential quantifications such
as (20) true and hence correctly predicts that they are felicitous.
However, as with the SK approach, the supervaluationist treatment of
category mistakes renders both (21) and (22) to be truth-valued, and
hence (incorrectly?) predicts that they are felicitous.




In SS3.4 we will see yet another version of the truthvaluelessness
view, which offers a different way of addressing the embedding of
category mistakes in complex sentences.


### 3.3 Pragmatic Approach




A third approach to accounting for the infelicity of category mistakes
is to maintain that they are syntactically well-formed, meaningful,
and truth-valued but pragmatically inappropriate.




The most natural way to develop a pragmatic account of category
mistakes is to appeal to Grice's maxims of conversation.
According to Grice's maxim of quality, one ought not to assert
what one believes to be false. Since atomic category mistakes are
 arguably trivially
 false[24],
 it seems obvious to participants in the conversation that the speaker is
uttering something that they do not believe, violating the maxim. Thus
unless the speaker is interpreted as attempting to communicate
something other than the literal content of the sentence (e.g. a
metaphorical meaning), the utterance would be infelicitous.




One problem for this approach is that while trivially false sentences
such as \(2 + 2 = 5\) are conversationally inappropriate at some
level, they don't seem to suffer from the kind of severe
infelicity that we see with category mistakes. (Indeed, an indication
of this difference is that, unlike the case of category mistakes,
there is no temptation to classify '\(2 + 2 = 5\)' as
meaningless or even truth-valueless.) Another difficulty for the
account as we sketched it is that not all category mistakes are
trivially false. Consider the following:



(24)
The number two isn't green.



This sentence seems just as infelicitous as its non-negated
counterpart, and yet it is not trivially false (if anything, it seems
trivially true). This is not yet a serious problem for the Gricean account
of category mistakes. The account can be easily extended to address
this example as well: according to Grice's maxim of quantity,
one should make their contribution as informative as required. But
trivially true sentences (such as, it is claimed, (24)) are clearly
not informative, thus violating the maxim of quantity. There are
trickier cases, however, ones of category mistakes that are neither
trivially true nor trivially false. Consider for example the
following:



(25)
Either the temperature in London is green, or the temperature in London is zero degrees.



This sentence is arguably also infelicitous in the way which is
typical of category mistakes, but (assuming category mistakes are
truth-valued, as per the pragmatic approach) whether (25) is true or
false depends entirely on the truth value of the second
disjunct--which is itself neither trivially true nor trivially
false.




In the next section (SS3.4) we will see a different pragmatic (or
at least semi-pragmatic) approach.


### 3.4 The Presuppositional Approach




The fourth account of the infelicity of category mistakes is one
that places this in the context of a broader phenomenon--that of
*presupposition failures*. This account comes in several
different versions, some more semantic and some more pragmatic in
nature. While each version can be seen as an instance of one of the
accounts discussed above, it is instructive to discuss these various
 presuppositional accounts in
 tandem.[25]




A widely recognized phenomenon in the study of language is that of
*presupposition*. Consider the following sentences:



(26)
The king of France is bald.
(27)
George stopped smoking.
(28)
It is Jill who murdered Jack.



It is standardly accepted that these sentences generate, respectively,
the presuppositions that France has a king; that George used to smoke;
and that someone murdered Jack. What precisely this amounts to is a
matter of controversy in the theory of presupposition, but as a first
pass we can say that when these sentences are uttered in conversation,
the presupposed material is not the main point of the speaker's
assertion and that participants in the conversation are expected to
already have accepted it. Moreover, when such sentences are uttered in
contexts where speakers do not already accept the presupposition, the
utterance suffers from presupposition failure, and is consequently
infelicitous. For example, in current context, an utterance of (26)
seems infelicitous because we all know France does not have a king,
and an utterance of (28) is infelicitous in a context where it was not
 already commonly believed that Jack was
 murdered.[26]




A particularly notable feature of presuppositions is that they project
into embedded contexts in predictable patterns. For example, it is
standardly accepted that if \(s\) presupposes \(p\) then not-\(s\)
also presupposes \(p\). Thus (29) also generates the presupposition
that France has a king, and is therefore equally infelicitous in
current context:



(29)
The king of France isn't bald.



More interestingly, it is standardly accepted that if \(s\)
presupposes \(p\) (which itself is presupposition free) then both
'\(p\) and \(s\)' and 'If \(p\) then
\(s\)' are presupposition-free. This prediction accounts for
why, even in contexts where participants in the conversations do not
accept in advance that Jack was murdered, the following no longer
suffer from presupposition failure: 



(30)
Jack was murdered, and it was Jill that murdered him.
(31)
If Jack was murdered, then it was Jill that
 murdered him.



The presuppositional account of category mistakes maintains that
category mistakes are infelicitous because they suffer from
presupposition failure. Suppose, for example, that the predicate
'is green' triggers the presupposition that its subject has
a color. This means that 'The number two is green'
generates the presupposition that the number two has a color, a
presupposition which is assumed to be false in nearly all contexts. A
key way to test this presuppositional hypothesis is to check it against
the various projection properties for presupposition, and indeed this
test seems to lend support to the hypothesis:



(32)
\* The number two isn't green.
(33)
Numbers have colors, and the the number two is
 green.
(34)
If numbers have colors then the number two is
 green.



Note that (32) is just as odd as the original category mistake. By
contrast, while (33) and (34) may be unusual or false assertions, they
do not seem infelicitous in a similar manner. These projection
properties point to a key advantage of presuppositional accounts: they
seem to predict a range of data on how category mistakes behave when
embedded in complex environments. Unlike the WK account (SS3.2.3),
the presuppositional approach does not assume that every complex
sentence with a category mistake as a constituent is infelicitous (for
example, it predicts that (34) is not infelicitous despite the
embedded category mistake). On the other hand, unlike the SK and the
supervaluationist accounts (SS3.2.3), it predicts that sentences
such as the following are infelicitous, given that the standard
projection rules for presupposition are that a conjunction inherits
all the presuppositions of its first conjunct):



(35)
\* The number two is green and Lisbon is the
 capital of France.



So far, we have sketched the presuppositional account in very general
terms. However, there are a variety of different ways to develop the
account. A first key question is how presupposition failure affects
the truth-value of a sentence. Category mistakes aside, the literature
on presupposition is split between views which maintain that sentences
suffering from presupposition failure are truth-valueless, and those
that maintain that while presupposition failure leads to infelicity,
such sentences are nevertheless truth-valued. The former approach
maintains that 'The king of France is bald' is
truth-valueless, while the latter deems it to be infelicitous but
false.




As applied to category mistakes, the former approach yields either a
version of the contentlessness view or of the truthvaluelessness
view--depending on whether one takes presuppositional failure to
lead to a failure to express content or merely a failure to have a
truth-value. (From now on we will assume that this presuppositional
account is understood as a version of the truthvaluelessness view.) An
important advantage of this version of the truth-valueless approach
over the ones discussed previously is that it seems to correctly
account for the behavior of category mistakes embedded in complex
sentences. However, note that the view still predicts that contentful
sentences can lack truth-value, and more specifically that contentful
instances of logical tautologies (e.g. 'It's not the case
that two is green and two isn't green') can fail to be
true.




When we apply the latter approach - the claim that presupposition
failures do not lead to truth-value gaps--to the case of
 category mistakes, we get a version of the pragmatic
 approach.[27]
 How does this account compare to the Gricean pragmatic account
discussed above? As with other versions of the presuppositional view,
this account seems to fare better than the Gricean account in terms of
predicting the behavior of category mistakes embedded in complex
sentences. On the other hand, a significant disadvantage of the
presuppositional account over the Gricean one is that, depending how
 the account is developed, it might require far more linguistic
 stipulations.[28]




A second question which separates different versions of the
presuppositional account is what kind of presuppositions are involved
in the case of category mistakes. A natural hypothesis (endorsed by
Asher (2011)) is that these are *type* presuppositions. For
example, we might suggest that 'is green' triggers the
presupposition that its subject is a concrete object; that 'is
prime' triggers the presupposition that its subject is a number;
and that 'is pregnant' triggers the presupposition that
its subject is a female. This has the advantage of supporting the
intuition (borne in their name) that category mistakes have something
to do with a misclassification of *kinds* or
categories. However, Magidor (2013, 139-146) argues that the
presuppositions involved are more specific that this: for example,
that the subject has a color in the case of 'is green', or
that it is either prime or composite in the case of
'prime'. Her argument relies on discourses such as
these:



(36)
Mathematician: you know, not only numbers, but
 also polynomials are prime or composite. This polynomial, for
 example, is prime.
(37)
Doctor: you know, we've developed a method
 that allows males to be pregnant too. This male, for example, is
 pregnant.



These discourses seem entirely felicitous even though the final
sentence in each discourse violates the proposed type presupposition.
In response a proponent of the type-presuppositional hypothesis might
suggest reverting to a different type-based hypothesis. For example, in
response to (36) they might suggest that the presupposition generated
is that the subject-term is a *mathematical object*. However,
this new proposal might be too liberal and because it fails to account
for why '2.145 is prime' is a category mistake and it might
also be too restrictive because it fails to account for other versions
of the argument, where an expert suggests that a non-mathematical
 object can be prime as
 well.[29]
 So the question remains whether we can find a suitable kind to play the
relevant role here.




A final question which separates different versions of the
presuppositional account is the issue of what determines whether the
presupposition is satisfied or not on a particular occasion. According
to Asher (2011), the lexicon encodes the type that each lexical item
belongs to, and this in turn determines whether the relevant
presupposition--a type presupposition on his view--is
satisfied. This lexical approach, however, faces similar problems to
those which we have seen with the meaninglessness view. The lexicon
cannot predict that the following subject terms are of the wrong type
in those contexts where the definite description or the demonstrative
pick out the number two:



(38)
The thing I am thinking about is green.
(39)
That is green.



One feature of the lexical approach which is worth highlighting is
that it sets apart the case of category mistakes from other instances
of presupposition failures: clearly, it is not the lexicon that tells
us whether John used to smoke, and hence whether 'John stopped
smoking' suffers from presupposition failure. This can be seen
either as a disadvantage of the approach (because it does not
assimilate category mistakes smoothly into the more general theory of
presupposition) or as an advantage (because it might help explain what
is distinctive about the infelicity associated with category
mistakes).




An alternative approach, one that is applicable to presuppositions
more generally, is to maintain that it is worldly facts which
determine whether the presupposition is satisfied or not. Thus for
example, 'John stopped smoking' suffers from
presuppositional failure if and only if John in fact used not to smoke and
similarly 'The thing Jill is thinking about is green'
suffers from presupposition failure if Jill is thinking about the
number two, but not if she is thinking about a table. According to a
third proposal, one in the spirit of Stalnaker (1973), what matters
aren't the actual facts, but rather which propositions
are *taken for granted* by the participants in conversation. To
see how this differs from the 'worldly' approach, note
that on this Stalnakerian approach to presupposition, 'John
stopped smoking' would suffer from presupposition failure in a
context where participants take it for granted that John never did
smoke, even if they are wrong and John in fact used to smoke.




In so far as our primary aim is to account for the infelicity of
category mistakes, this might point to an advantage of using the
Stalnakerian approach to presupposition over the worldly one. Consider
for example, an utterance of:



(40)
The thing Jill is thinking about is green.



This utterance would be infelicitous in a context where participants
take for granted that Jill is thinking about the number two (even if
in fact she is thinking about a table), and felicitous in a context
where it is taken for granted that Jill is thinking about a table (even if in fact she is thinking about a the number two), so the
Stalnakerian view predicts that presupposition failure patterns
exactly with the infelicity characteristic of category
mistakes. Moreover, the Stalnakerian approach seems to be particularly
well-suited for explaining why the infelicity of category mistakes
varies across a range of contextual settings. Consider, for example,
the following:



(41)
The priest is pregnant.



In contexts where it is taken for granted that priests are male, (41)
arguably functions as a category mistake. However, in other
contexts--ones where speakers are aware of churches that ordain
female priests--the sentence can be entirely felicitous. And
indeed, the Stalnakerian approach predicts that whether the sentence
suffers from the relevant presupposition failure depends precisely on
what is taken for granted in conversation.




It is worth noting, however, that a presuppositional account of
category mistakes which relies on the 'worldly' conception
can also account for these infelicity patterns, albeit in a more
indirect way. The account can maintain that infelicity depends not on
actual presupposition failure, but on being believed (perhaps falsely)
to suffer from presupposition failure. 




We have seen that there are various choice points for how to develop a
presuppositional account of category mistakes. It might be thought to
be an advantage of the presuppositional account of category mistakes
(on any of its versions) that it utilizes an independently motivated
linguistic theory. However, a significant disadvantage of utilizing
such a theory is that it makes it harder for the presuppositional
approach to account for what is distinctive about the infelicity of
category mistakes, i.e., what distinguishes their infelicity from other
cases of presupposition failure and explains why category mistakes
 form a distinctive and unified phenomenon (cf.
 SS1).[30]


## 4. Implications for Other Debates




In addition to the intrinsic interest in the phenomenon of category
mistakes, which account of category mistakes is adopted also has a
range of implications for other debates. In this section we will
survey a few of these (this survey is not intended to be
exhaustive).


### 4.1 Implications for the Philosophy of Language




Debates about category mistakes have substantial implications for some
foundational questions in philosophy of language and linguistics.
Consider the question of how to formulate the principle of
compositionality. It is widely accepted that meaning is in some sense
compositional, but there are many non-equivalent ways to elaborate
what precisely this amounts to. One hypothesis which originates in the
work of Richard Montague but has been substantially developed by
Pauline Jacobson (and others), is the idea of *direct
 compositionality*[31]:
 "the hypothesis that the syntax and the semantics work 
'in tandem'. The syntax builds expressions and the
semantics works to assign meanings to the representations as they are
built in the syntax" (Jacobson 2012, 109). As Jacobson argues,
the hypothesis of direct compositionality is attractive for a number
of reasons: it is theoretically parsimonious, unifying the
compositional theories of syntax and semantics, and it explains why
semantic composition seem to proceed in a *local* fashion: the
meaning of each sub-sentential expression is computed using only the
meanings of its syntactic constituents rather than using material in
other parts of the sentence. But as Jacobson remarks, "Direct
Compositionality entails that there are no syntactic expressions of
any sort, which do not have a meaning" (Jacobson 2012,
110). Note that this entails that the direct compositionality
hypothesis is inconsistent with the meaninglessness view of category
mistakes and thus the question of how to account for the infelicity of
category mistakes interacts with the question of which formulation of
the principle of compositionality ought to be adopted.




Other accounts of category mistakes have implications for different
foundational issues. For example, we have seen that the
truthvaluelessness view is committed to the existence of
truth-valueless propositions, which in turn conflicts with the
Tarskian truth-schema. For another example, consider the
presuppositional account of category mistakes (on any of its
versions). If the presuppositional account is correct, then the set
of presupposition triggers is much wider than has previously been
assumed: presupposition triggers are not restricted to a small number
of special words like 'know' or 'the', but
rather encompass at least most adverbs and adjectives in natural
language. This in turn has a variety of implications for
the *triggering problem*: the question of why particular
lexical items trigger their respective presuppositions, and the issue
of whether this question can be answered based on general pragmatic
principles, or rather by maintaining that presupposition triggers are
 simply a conventionally encoded aspect of
 language.[32]




One's account of category mistakes also has implications for
more specific questions in the philosophy of language. We have seen
(SS3.2.1) that the meaninglessness view of category mistakes is
arguably incompatible with a range of accounts for the semantics of
metaphor. This means that one should either reject the meaninglessness
view, or else offer a theory of metaphor that is compatible with the
view. Another area where the debate on category mistakes is important
is the semantics of fictional discourse. Consider a sentence such as
'A famous detective lives in 221b Baker Street'. There is
a sense in which the sentence seems true (contrast it with 'The
famous detective was called 'Watson'' which seems
false). However, the sentence isn't true on its most
straightforward literal reading. One popular view on how a true
reading of such sentences can be generated (see, e.g., Lewis 1978), is
to assume that the fictional sentence is within the scope of an
(unpronounced) operator, so the sentence is taken to express a claim
of the form: 'According to the Sherlock Homes stories, a famous
detective lives in 221b Baker Street', a claim which is
straightforwardly true. Recall, however that fictions can often
contain categorically mistaken sentences; for example, "Once
there was a tree and she loved a little boy" (Silverstein
1964). But if the fictional sentence \(s\) is either meaningless or
even contentless, then arguably, even after embedding it in the
propositional operator 'according to the story', we will
get a contentless ascription (cf. Friend 2007, 143). The upshot is
that the operator view of fictional discourse is incompatible with
both the meaninglessness view and the contentlessness view of category
mistakes.




Even if one accepts that category mistakes are contentful, uses of
category mistakes in fiction have significant implications for the
philosophy of language. For example, Nolan (2015) argues that
fictions involving personified abstract entities (e.g., fiction in
which Death is a character) entail that fictions routinely feature
substantive impossible contents. This observation is important because
it presents a challenge for accounts of contents which take them to be
as coarse grained as possible worlds, as on such accounts there is
 only one impossible
 proposition.[33]


### 4.2 Implications for Metaphysics




We have seen (SS2) that the interest in category mistakes in the
1930s was fueled by the thought that category mistakes reveal some
deep facts about ontological categories. While the project of using
category mistakes to define ontological categories is no longer being
actively pursued, category mistakes still play an important role in
other debates in metaphysics.




Consider the debate about the relationship between a material thing
and its matter. A lump of clay is molded into a statue. According to
monists, the lump is identical to the statue. According to pluralists,
they are two distinct objects which occupy the same space. A key
argument in favor of pluralism proceeds as follows:



(42)
The statue is Romanesque.
(43)
The lump is not Romanesque.



Therefore,



(44)
The statue is not identical to the lump.



An interesting feature of this argument is that (43) is, at least
arguably, a category mistake. This fact can be exploited by both
pluralist and monists in a variety of ways.




First, assume that category mistakes are truth-valueless (either
because they are meaningless, or because they are meaningful but
truth-valueless). This poses a problem for the pluralist's
argument because if (43) is a truth-valueless category mistake, the
 argument is unsound (one of its premises isn't
 true).[34]
 The pluralist might respond by arguing that the negation in (43)
isn't ordinary descriptive negation but rather an instance
of *meta-linguistic negation*, that is the kind of negation
that is present in utterances like this:



(45)
I am not happy, I am *elated*!



While this might account for why (43) is a felicitous utterance it is
not clear that it helps the pluralist: if the negation in (43)
isn't standard, then the premise isn't sufficient to show
that the statue and lump genuinely have conflicting properties, and
are thus distinct. Almotahari (2014) pushes this line even further,
arguing that the sequence 'The lump is not Romanesque, but the
statue is' indeed involves meta-linguistic negation, but also
that a necessary condition on the occurrence of meta-linguistic
negation in such contexts is precisely that, if read with ordinary
negation, the first clause ('I am not happy'/'The
lump is not Romanesque') is semantically incompatible with the
second clause ('I am elated'/'The statue is
Romanesque'). This conclusion, claims Almotahari, is
detrimental for the pluralist: in order to involve meta-linguistic
negation the two clauses must be (when taken literally) incompatible,
but they can only be incompatible if the statue is identical to the
lump, which is precisely the monist's contention. Interestingly,
the claim that category mistakes are truth-valueless offers the
pluralist a rejoinder to Almotahari's argument: if we assume
that two statements are semantically incompatible just in case they
cannot be simultaneously true, then the two clauses might be
incompatible not because the statue is identical to the lump, but
simply because one of the two claims is a
 truth-valueless category mistake and hence in itself never
 true.[35]




The claim that (43) is a category mistake can play a role in this
debate even if one assumes that category mistakes are truth-valued but
pragmatically infelicitous. Consider a monist who accepts that the
lump and the statue are identical and reads the negation in (43) as
ordinary descriptive negation. This would render the pluralist's
argument to be simply unsound: if the statue is Romanesque and lump is
identical to it, then the lump is Romanesque as well and (43) is
false. However, there is still a burden on the monist to explain why
(43) *seems* to many to be true. This is where an account of category
mistakes might come into play. Speakers often confuse pragmatic
infelicity with falsity. So if 'The lump of clay is
Romanesque' is pragmatically infelicitous (because it is a
category mistake), speakers might mistakenly take it to be false
(rather than true and infelicitous) and hence assume its negation
 is
 true.[36]




Finally, irrespective of the semantic status of category mistakes,
the pluralist can present a somewhat different challenge to monism: if,
as the monist claims, the statue is identical to the lump, how can the
monist account for the fact that 'The lump is Romanesque'
is a category mistake, while 'The statue is Romanesque' is
not? Whether the monist can respond to this challenge depends on the
precise details of one's account of category mistakes, and to
what extent substituting co-referential terms preserves the relevant
kind of infelicity.




Next, consider a different debate at the intersection of philosophy of
language and metaphysics, one concerning the phenomenon of
copredication. Imagine a context where three copies of *War and
Peace* are on the shelf. Each of the following seems to have a
true reading:



(46)
(Exactly) three books are on the shelf.
(47)
(Exactly) one book is on the shelf.



A natural way to account for these diverging readings is to posit
two respective readings of 'book': one on which it is used
to pick out physical books (of which we have three), and one on which
it is used to pick out "informational" books (of which we
have one). However, on further reflection this still leaves a puzzle
concerning (47): if 'book' in this sentence picks out an
informational book (arguably a kind of abstract entity), how can this
kind of object have the physical property of being on the shelf? These
kind of apparently 'mixed' reading are referred to in the
literature as instances of *copredication*.




Some solutions to this puzzle involve constructing non-standard
semantic and syntactic structures for copredicational sentences (e.g.,
Asher 2011; Gotham 2017), but Liebesman and Magidor (2017) argue that
sentences such as (47) should be taken at face-value: the sentence is
about informational books, but on their view, informational books can
have physical properties such as being on shelves.




A central challenge for this view is that it requires us to
distinguish between (47) and clearly infelicitous category mistakes
such as:



(48)
\* One prime number is on the shelf.



To sharpen the problem, consider any theory of category mistakes which
accounts for the infelicity of (48) by maintaining that locational
properties such as 'on the shelf' are restricted so as to
only apply to physical objects (whether the nature of the restriction
is syntactic, semantic, or pragmatic). This predicts that if (47) has
the structure Liebesman and Magidor attribute to it (namely, a
straightforward predication of the locational property to an
informational book), the sentence should have resulted in an
infelicitous category mistake. Liebesman and Magidor (2017,
148-9) respond to this worry by arguing that the restriction
placed by 'on the shelf' is not a type restriction such as
'is a physical object', but rather a more specific
restriction, such as 'has a location' (we have seen this
idea in SS3.4 in the context of the presuppositional approach,
though it could in principle be adopted by proponents of any of the
semantic accounts as well). This more specific restriction allows them
to account for how (48) can be a category mistake even if (47) is not:
while neither a number nor an informational book are physical objects,
the latter but not the former satisfies (so they claim) the property
of having a location. Whether or not this account of copredication is
accepted, we see once again how which theory of category mistakes is
adopted has substantial implications for debates in metaphysics.