Metasemantics of Complex
Expressions
Michael Johnson
Hong Kong University
0. OUTLINE
Outline
0. Outline
1. Natural Language
2. The Language of Thought
3. The ‘Direct’ Theory
4. Arguments for DT
5. Arguments against DT
6. Conclusion
1. NATURAL LANGUAGE
Compositionality
Natural languages are compositional.
What does that mean?
Why should we care?
Computability
I think those two questions are related:
Natural languages are compositional in the
sense that the meanings of complex NL
expressions are computable from the meanings
of their parts and the way that those parts are
syntactically combined.
Understandability
I think those two questions are related:
We care about this claim regarding the
compositionality of NLs, because only it (as
opposed to other readings of ‘compositional’)
explains how we can understand a potential
infinitude of novel utterances, given our finite
means (brains).
Note for the Savvy
(Yes, I know computability ≠ compositionality,
but you get the point…)
Interpretation (Finite Case)
To understand a NL expression is to assign it a
mental representation that shares its content.
For the (finite) set of simple NL expressions we
can understand them (assign them contents) via
a lookup table that pairs each NL expression
with a mental equivalent.
Interpretation: Infinite Case
To understand a NL expression is to assign it a
mental representation that shares its content.
For the (infinite) set of complex NL expressions,
we can understand them (assign them contents)
by computing their contents from the contents
assigned to their parts (& from their syntax), on
the assumption that they’re compositional.
Example
Psychological Reality of Formal
Semantics
The general idea is that the sorts of ways we
have of computing the meanings on paper are
the same sorts of ways the mind goes about
computing those things.
2. THE LANGUAGE OF THOUGHT
Interpreting Thoughts
To understand a NL expression is to assign it a
mental representation that shares its content.
But this is not what it is to understand a thought
(a mental representation).
Interpreting Thoughts
We don’t compute the meanings of our
thoughts.
We don’t have to work out what we’re thinking.
There are no ‘garden path’ thoughts.
We can’t misinterpret our thoughts (wrong
quantifier order, wrong meaning of BANK).
To have a thought is to understand it.
The Infinite Regress
If to understand a thought (mental
representation) was to pair it with a distinct
thought (mental representation) that had the
same content as it, then either we wouldn’t
understand half our thoughts (the ones that
interpreted the other half) or we’d have an
infinite number of thoughts (each of the
interpreters would themselves be interpreted,
and so on).
Understanding = Having
To understand a thought is to think it, to have it,
to token it.
You needn’t interpret it, translate it, or assign it
a meaning.
No Regress
And so even if LOT were ‘compositional’ in the
‘computational’ sense:
That wouldn’t be required by our ability to
‘understand’ a potential infinitude of thoughts.
If to understand a thought is to have it, then our
ability to understand an infinite number of
thoughts is explained by our ability to have an
infinite number of them.
No Regress
And so even if LOT were ‘compositional’ in the
‘computational’ sense:
A recursive syntax gives us all we need to explain
how we can have an infinite number of
thoughts.
Compositionality
New claim: LOT is compositional.
What does that claim mean?
Why should we care?
Metasemantics
Here’s a suggestion.
Everyone agrees that an expression’s having a
meaning is not beyond the bounds of
explanation.
Expressions have meanings in virtue of certain
facts that hold of them.
Compositionality as Metasemantics
LOT is compositional = complex expressions of
LOT have the contents they do in virtue of the
contents their parts have, and the way those
parts are syntactically combined.
Compositionality, for LOT, solves “the essence
problem for the meaning relation” (Carnap,
Aufbau).
CMT
Let’s call the thesis that LOT is compositional in
this sense “compositionality as a metasemantic
thesis.”
And let’s also abbreviate “compositionality as a
metasemantic thesis” to “CMT”.
3. THE ‘DIRECT’ THEORY
Metasemantics
But CMT is only one possible solution to the
essence problem for the meaning relation (i.e.
it’s only one possible metasemantic theory).
That is, there are other possible answers to the
question ‘In virtue of what does a complex
expression mean what it does, rather than
something else, or nothing at all?’
The ‘Direct’ Approach
For example, you might think that complex
expressions get their meanings in the same way
that simple ones do, however that is. Maybe the
story is causal, or informational, or teleological,
or inferential role-y, or real patterns-y, or
whatever.
Contrast
The contrast is this. CMT requires that complex
expressions get their meanings in a different
way from simple ones. They inherit their
meanings from their constituents
(“compositionally”), whereas simple expressions
can’t do this because, being simple, they have
no constituents.
The ‘Direct’ Theory
For the purposes of this talk, I’m going to
assume that the correct metasemantic story for
simple expressions is a “broadly causal” one
(Stampe, Dretske, and Fodor are paradigm
examples).
For simplicity’s sake, I’ll often state the view as
‘x means y in virtue of the fact that y
appropriately causes x.’
The ‘Direct’ Theory
And I’m going to defend the claim that the same
story applies to complex expressions. I’ll call this
claim “the direct theory” or DT, to contrast it
with CMT, “the inheritance theory,” where
complex expressions don’t get their meanings
directly, but inherit them from simple
expressions that do.
4. ARGUMENTS FOR DT
Arguments For
There are 4 basic considerations that tell in favor
of DT:
It’s intuitively correct
It’s ontologically safe by virtue of its neutrality
It’s theoretically beautiful (uniform)
It’s non-arbitrary in an important way
Intuitive Correctness
Suppose an agent has three mental
representations A, B, and C.
A is caused, appropriately, by artistic things
B is caused, appropriately, by brown things
C is caused, appropriately, by cow things
Intuitive Correctness
Further suppose, though, that the complex
expression ABC in the agent is caused, normally,
not by artistic brown cow things, but by brown
cow things of any aesthetic ability.
We’re inclined to think that ABC means “brown
cow,” rather than “artistic brown cow.”
Intuitive Correctness
CMT demands that ABC mean “artistic brown
cow.” That’s what its parts, jointly, mean, and it
inherits its meaning from its parts, jointly.
DT gets the right answer. It says that ABC means
what causes it, appropriately, which is in this
instance brown cows. So it means “brown cow.”
Ontological Neutrality
Suppose Krayzie Bone tells
you he shot your
homeboy “foe tha sake of
money.”
Ontological Neutrality
A lot of philosophers don’t believe in ‘sakes,’
they think they’re non-existent. But if that’s
true, ‘sake’ means nothing; and so ‘I shot x foe
tha sake of money’ means nothing, if we hold to
CMT.
Ontological Neutrality
But if we endorse DT, we can say that the
meaning of ‘x shot y foe tha sake of money’ is
true whenever the situations that appropriately
cause tokenings of that expression obtain.
Ontological Neutrality
This is so even if we assign
‘sake’ a null content.
Local Uniformity
Causal theories, in general, have a problem with
causally isolated things, like numbers and
numerical functions, abstract objects, logical
relations, etc.
If you think ‘or’ means what causes ‘or’
appropriately, then ‘or’ doesn’t mean
disjunction, for disjunction causes nothing.
Local Uniformity
However, you can maintain a causal theory for
simple expressions by endorsing DT.
If complex expressions get their meanings
“directly,” then even if ‘or’ does not mean
disjunction, ‘P or Q’ might still mean P or Q, in
particular, if ‘P or Q’ is appropriately caused by
states where either P or Q obtain.
Local Uniformity
Any non-standard meaning for the simple
expression ‘or’ doesn’t “percolate up” to
complex expressions involving it, because DT is a
direct theory, not an inheritance theory.
So long as dogs or cats appropriately cause ‘dogs
or cats’ the latter means the former, even if ‘or’
means nothing, or something other than or.
Global Uniformity
Also, if DT is true then (by definition) complex
expressions get their meanings in the same way
as simple expressions. There is only one theory
of how expressions get their meanings.
CMT is decidedly non-uniform: if it’s true, then
complex expressions inherit their meanings,
whereas simple expressions, obviously, don’t.
Theoretical Beauty
I think this is significant.
If you’re inclined towards a causal theory for
some simple expressions (natural kind terms, for
example), you have to have a different
metasemantic theory for other simple
expressions (‘or,’ for instance) unless you deny
CMT.
Theoretical Beauty
I think this is significant.
And if you accept DT, you not only get to treat all
simple expressions in the same way, you get to
treat all complex expressions in the way you
treat the simple ones. That’s true theoretical
beauty if ever there was any.
Hocceity
If you’re a compositionalist, you have to decide
how to compose meanings.
For example, if ‘brown’ means B = {x: x is brown}
and ‘cow’ means C = {x: x is a cow}, does ‘brown
cow’ mean the intersection of B and C, the
union of them, the complement, the
complement of the union…?
Hocceity
If you’re a compositionalist about language, you
can just say that convention determines how
syntactic combination relates to composition.
Hocceity
But how does this work in the case of the mind?
What your mental states mean is in no way
conventional. We’re inclined to say that ‘brown
cow’ means the intersection of B and C, because
that’s what causes ‘brown cow.’
The extra degree of freedom is only resolved
non-ad-hocly by assuming DT!
Summary
DT gets the right intuitive results in cases of
under- or overarticulation of constituents, as
compared with CMT. It’s intuitively correct.
DT is ontologically neutral: it doesn’t commit us
to the parts of meaningful things themselves
having meaning. As such, it’s ontologically safe,
when compared with CMT.
Summary
Causal theorists who deny DT have an unified
metasemantics. They are even forced to deny
that all simple expressions are causal. Accepting
DT, on the other hand, is theoretically beautiful.
Finally, composition rules for the mind are ad
hoc, and a compositionalist can only discover
them by assuming DT! DT is pro hoc.
ARGUMENTS AGAINST DT
Arguments Against
There are three concerns I imagine you might
have about accepting DT and rejecting CMT:
Productivity
Systematicity
Intuitive incorrectness
Productivity
If compositionality is false (for LOT) how do we
produce and understand a potential infinitude
of thoughts?
Productivity
Production is easy. If you believe in LOT,
thoughts are a type of sentences. How do you
produce, potentially, infinitely many of them? By
having a recursive syntax for LOT.
Understandability
Understanding is easy too. As I noted before, to
have a thought is to understand it. So how do
you understand infinitely many thoughts? By
producing infinitely many thoughts. And again,
you do that with a recursive syntax for LOT.
Systematicity
A language is systematic when expressions that
have similar constituents in the language have
similar meanings in that language.
For example, in English, ‘John loves Mary’ and
‘Mary loves John’ have similar (identical even!)
constituents and also have similar meanings
(each meaning involves John, Mary, and loving).
Systematicity
Fodor and Lepore (both jointly and separately)
think that systematicity entails or at least
guarantees in a very strong way
compositionality.
Systematicity
There are fancy things I can say, but I’ll just say
this one unfancy thing. The facts are that ‘John
loves Mary’ and ‘Mary loves John’ have similar
meanings. If DT assigns the correct meanings to
those expressions, then it explains those facts. If
it doesn’t, then systematicity is not the issue:
incorrectness is. If DT assigns radically unrelated
meanings to ‘M loves J’ and ‘J loves M’ then it
assigns the wrong meanings to them.
Systematicity
But give me a case! Show me where DT violates
systematicity!
Intuitive Incorrectness
I argued previously that DT was intuitively
correct whereas CMT was intuitively incorrect.
But some data seems to go the other way.
Intuitive Incorrectness
There are cases where we have some complex
expression CE and the intuitive content (IC) of
CE can’t cause CE:
IC is in the future of CE’s tokening.
IC is causally isolated.
Tokeners of CE are insensitive to IC.
Etc.
Examples
IC = the world will end tomorrow.
CE = ‘the world will end tomorrow.’
IC = something is red and blue all over.
CE = ‘something is red and blue all over.’
IC = my son likes the Lakers.
CE = ‘my son likes the Lakers.’
Intuitive Incorrectness
But this has really nothing to do with DT vs. CMT
(unlike, I should note, the cases I gave of CMT’s
intuitive incorrectness).
These are just problems with causal theories of
content. And they arise, identically, for causal
theories of simple expressions.
Examples
IC = futurity
Simple expression = ‘future’
IC = impossibility
Simple expression = ‘impossible’
IC = untokenability
Simple expression = ‘untokenable’
Summary
DT has no problem explaining how we produce
and understand an infinite number of thoughts,
given the equivalence of producing and
understanding thoughts.
And while it might have a problem with
systematicity, this would really just amount to
getting things wrong. But there’s no evidence DT
gets things wrong.
Summary
OK, well maybe there’s evidence that it gets
things wrong, but it’s the same sort of evidence
that causal theories of simple expressions get
things wrong.
We may have to fix our theories, but this isn’t a
motivation to abandon the ‘direct’ approach.
CONCLUSION
Conclusion
The main motivation for compositionality is
learnability concerns. These don’t exist for LOT.
When ‘compositionality’ is reinterpreted along
the lines of CMT, we can see that other concerns
like productivity, systematicity, etc. also have no
tooth.
Conclusion
DT is intuitively correct, ontologically safe,
theoretically beautiful, and pro hoc.
So I’m right.