On "On Recursion"

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doi: 10.6084/m9.figshare.5097691

Background

In rejecting Merge Is Not Recursion, they wrote: "Moreover, one could say that the 'recursion dispute' has been settled for good with Watumull et al.'s (2014) Frontiers in Psychology article". So I took "On Recursion" by Watumull et al. (2014) as the position of linguistics on recursion, and I compared it against recursion in mathematics.

In mathematics, Turing (1937) proved that every recursive function is computable and every computable function is recursive. In linguistics, recursion by Watumull et al. (2014) is more stringent, because for them every recursive function is computable, but not every computable function is recursive.

Given the difference, my question is: Should linguistics deviate from mathematics on recursion? And my answer is no. No, it should not, because Watumull et al. (2014) are modifying the mathematical definition of recursive function to discriminate human language from other animal communication systems, and mathematical recursion already does that discrimination.

This paper was a forerunner for A Complete Hierarchy of Languages.

References

Link to the page of "On 'On Recursion'" in figshare, and direct link to the pdf file.

The external references mentioned in this page are:

• Turing (1937): "Computability and λ-Definability"; doi: 10.2307/2268280.
• Watumull et al. (2014): "On Recursion"; doi: 10.3389/fpsyg.2013.01017.

Versions:

• f1 20170609
• f2 20170630
• f3 20190531