## Piraha Exceptionality: a Reassessment

The PirahÃ£ were discussed here a couple of times, in the context of the linguistic relativity hypothesis (Sapir-Whorf). One of the controversial claims about the PirahÃ£ language was that it lacked recursion (which is found in all human languages, and is seen as an essential feature of human language).

This paper by Andrew Ira Nevins, David Pesetsky, and Cilene Rodrigues attempts to refute many of the fantastic claims about PirahÃ£, and includes a detailed argument against the claims about the lack of syntactic recursion and embedding (to get to the full text, click on the title at the top of the page).

## Comment viewing options

### Recursion in natural languages

One can also argue that no natural languages have "true" recursion since the level of nesting in all but the most contrived cases is always bounded (presumably due to cognitive limitations). There's been some work on the subject hereabouts. AFAIK, no papers are out yet, but here is an abstract of a talk regarding this. In summary, with true nesting there seems to be a maximum "stack depth" of about two in natural languages, but right-branching ("tail recursion") is less limited.

### Kenning

This page is a wonderful collection of deeply nested kennings, Nordic circumlocations. They were actually used! And people were supposed to understand them, real time, in oral recitation.

Example:
SÃ³knrÃ½rir vann sextÃ¡n herÃ°imeiÃ°a hrÃ­Ã°ar mÃ¡na viÃ°ar hauÃ°rmens sÃ¡ra.
The destroyer of attackers wounded sixteen increasers of storm of moon of tree of land-necklace.

land-necklace = ocean
tree of ocean = ship
moon of ship = shield
storm of shield = battle
increaser of battle = warrior

### Not a counter-example

The destroyer of attackers wounded sixteen increasers of storm of moon of tree of land-necklace

There are still only a small number of recursions there, and I believe the slight stretching of comprehensibilty both recursively and through the transitive generation of poetic tropes is an intentional part of the poetic device, meant to display eloquence.

The extra opacity we perceive is because we are unfamiliar with the poetic tradition: the constituent images would have been as familiar to their intended audience as scene cuts in film and TV are to us.

### diminisher of harm-path of ness of sword

An interesting example nonetheless. I notice that as Lauri predicted, these deeper recursions are tail recursions.

This one demonstrates a kind of mutual recursion between "sword" and "shield", where shield is expressed in terms of sword in terms of shield in terms of sword. It's a sort of multi-level eta expansion (not quite the right term but I can't think of a better one). In OCaml:

type shield = Shield
type sword = Sword

let ness (x:sword) = Shield;;
let harmer (x:shield) = Sword;;
let path (x:sword) = Shield;;

let f x = path (harmer (ness x));;


Type inference tells us that f is a function from sword to shield:

val f : sword -> shield = <fun>


So assuming that all phrases which denote 'shield' are equivalent, we can just insert the shortest one, replacing "lÃ¦braut eiÃ°s lÃ¶gÃ°is" with, perhaps, "hlÃ­far", if we're willing to risk the wrath of a group of people who spend an inordinate amount of time inventing complex recursive synonyms intended to glorify words like "warrior"...

### An LtU record

Type inference tells us that f is a function from sword to shield:

I think you just set a new record for PLT nerdiness with that one, Anton.
;-)

Quite!

### Not quite

The idea of using type systems for analysing natural language is not actually very exotic. Look up e.g. Montague grammars for a concrete example.

### And everyone knows

And everyone knows computational linguists aren't nerdy at all...

Marc's just nervous because he realizes I might finally be onto a mathematical proof of Sapir-Whorf!

### I can't heeeear you...

And everyone knows computational linguists aren't nerdy at all...

Hey... I resemble that remark!

Marc's just nervous because he realizes I might finally be onto a mathematical proof of Sapir-Whorf!

If anyone needs me I'll be cowering under my desk...

(See what happens when we start discussing linguistics on LtU...)

### Harmer of the diminisher of nerdiness of PLT

Not to be outdone on the nerdiness scale, it just struck me that what we have going on here is actually unification:

A = B of C
C = D of E
E = F of G

therefore B of D of F of G = A

So I guess we actually need to write an Oz or Prolog program to handle this more naturally...

### This statement is false

"This statement is false." Depending on evaluation strategy, isn't that an infinite recursion?

### Maybe not...

Since I assume you must currently be in an infinitely loop thinking about this sentence, I won't interrupt you by responding. ;-)

### I'm fine. There are benefits

No problemo! There are benefits to being of above-Turing intelligence. Or maybe that's being presumptuous... :-)

### I find it much simpler just

I find it much simpler just to not bother with consistency... or soundness for that matter.

### "This statement is false."

"This statement is false." Depending on evaluation strategy, isn't that an infinite recursion?

There is no syntactic recursion in that sentence. The issue at hand is whether all languages have syntactic recursion.