Metasemantics of Complex Expressions

1. Metasemantics of Complex Expressions Michael Johnson Hong Kong University

2. 0. outline

3. Outline 0. Outline • Natural Language • The Language of Thought • The ‘Direct’ Theory • Arguments for DT • Arguments against DT • Conclusion

4. 1. Natural language

5. Compositionality Natural languages are compositional. What does that mean? Why should we care?

6. 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.

7. 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).

8. Note for the Savvy (Yes, I know computability ≠ compositionality, but you get the point…)

9. 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.

10. 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.

11. Example

12. 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.

13. 2. The language of thought

14. 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).

15. 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.

16. 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).

18. 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.

19. 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.

20. 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.

21. Compositionality New claim: LOT is compositional. What does that claim mean? Why should we care?

22. 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.

23. 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).

24. 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”.

25. 3. The ‘direct’ theory

26. 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?’

27. 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.

28. 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.

29. 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.’

30. 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.

31. 4. Arguments for dt

32. 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

33. 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

34. 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.”

35. 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.”

36. Ontological Neutrality Suppose Krayzie Bone tells you he shot your homeboy “foe tha sake of money.”

37. 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.

38. 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.

39. Ontological Neutrality This is so even if we assign ‘sake’ a null content.

40. 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.

41. 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.

42. 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.

43. 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.

44. 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.

45. 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.

46. 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…?

47. Hocceity If you’re a compositionalist about language, you can just say that convention determines how syntactic combination relates to composition.

48. 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!

49. 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.

50. 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.