Abstract
We argue in this paper that there is no recursion in language. Recursion is a mathematical self-calling function, and clearly there is no such thing in language. What Chomsky introduced as recursion in his Syntactic Structures (1957: pp. 23–24) was clearly a loop, and this means that Chomsky’s recursion was at first iteration. The presence or absence of recursion in language is therefore a matter of definition, as is obvious from the various characterisations proposed at the Mons conference. Recursion is generally thought of as a loop, a feedback loop or embedded structures.
The question remains of why recursion in language managed to gain such widespread support in various scientific communities. We offer a number of reasons, one of them inspired by Wittgenstein’s claim that “It is what human beings say that is true and false; and they agree in the language they use. That is not agreement in opinions but in form of life”. Even in the sciences.
“Then Shem Macnamara had been very poor, only too ready for a free meal and a quiet sneer at the success of a fellow poet. Then, instead of expensive mouthwash, he had breathed on Hogg-Enderby, bafflingly (for no banquet would serve, because of the known redolence of onions, onions) onions.
“Onions”, said Hogg. He was frowned on in puzzlement. Cocktail onions, he offered. Well just imagine. Shem Macnamara deepened his frown. Something in that voice saying Onions? He did not take any onions.”
“Enderby outside”
Anthony Burgess (Penguin, 1982, p. 224).
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Notes
- 1.
For an introduction to “dénomination”, see Kleiber’s Nominales (1994).
- 2.
See my papers and some of Kleiber’s recent ones on http://www.res-per-nomen.org.
- 3.
See also Peirce, who thought that ontologies were only as strong as their foundations, i.e. not at all because all foundations are hypotheses (1868, Fr. tr. 1984: 197).
- 4.
See the beginning of his Philosophical Investigations (PI).
- 5.
On the notion of interpretant, see, for example, §5.473, 5.253 and 2.303, in Peirce’s collected works. French translation in Peirce (1978).
- 6.
The alternative view is a nominalist one: integers are the names of sets.
- 7.
Many thanks to Olga Frath for her patient explanations.
- 8.
Tractatus Logico-Philosophicus (TLP): 5.62.
- 9.
This is why dualism is so resilient. Philosophers, such as Dennett, Chalmers, Popper, Crick, the Churchlands and many more, develop basically dualistic theories, even though some of them (e.g. Dennett) think they do not.
- 10.
See Frath (2012).
- 11.
As was, for example, Jacques Benvéniste’s water memory, the notion that water may retain a “memory” of substances previously dissolved in it.
- 12.
As happened to aether, the nineteenth century notion that space was filled with some physical medium.
- 13.
PI§24. Italics is Wittgenstein’s. Bold is mine.
- 14.
For example, the Fibonacci series can be programmed recursively. By definition, the first two numbers in the Fibonacci sequence are 0 and 1, and each subsequent number is the sum of the previous two. In mathematical terms, the sequence F n of Fibonacci numbers is defined by the recurrence relation:
F = F n−1 + F n−2, with seed values F 0 = 0, F 1 = 1 (adapted from Wikipedia).
Please note that recurrence can also be achieved by iteration, i.e. a loop. Iteration and recursion are very close and achieve similar results. Both iterative and recursive programmes necessitate a stopping condition to terminate the computing process. If not, computing goes on until the computer is switched off (in the case of iteration) or until the memory is full (in the case of recursion).
- 15.
See Fig. 14.2.
- 16.
“Philosophy is a battle against the bewitchment of our intelligence by means of language” (PI§109).
- 17.
PI§109.
- 18.
PI§98, TLP§5.563, P§I1.
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Frath, P. (2014). There Is No Recursion in Language. In: Lowenthal, F., Lefebvre, L. (eds) Language and Recursion. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9414-0_14
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