Metasemantics of Complex Expressions Michael Johnson Hong Kong University.

Metasemantics of Complex Expressions

Michael JohnsonHong Kong University

0. OUTLINE

Outline

0. Outline1. Natural Language2. The Language of Thought3. The ‘Direct’ Theory4. Arguments for DT5. Arguments against DT6. 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


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


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 correctIt’s ontologically safe by virtue of its neutralityIt’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 thingsB is caused, appropriately, by brown thingsC is caused, appropriately, by cow things


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.”


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.”


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.


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.


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:

ProductivitySystematicityIntuitive 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.


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.’


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 = futuritySimple expression = ‘future’IC = impossibilitySimple expression = ‘impossible’IC = untokenabilitySimple 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.

Metasemantics of Complex Expressions Michael Johnson Hong Kong University.

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