Towards a Philosophical Grounding of Universal Statistical Properties
Underlying Human Language: Mirroring Nature and Rule-Following
Kumiko Tanaka-Ishii
Research Center for Advanced Science and Technology
kumiko@rcast.u-tokyo.ac.jp
May 28, 2018
Big data has revealed new understandings of natural language, namely, that humanlanguage universally follows certain statistical properties. These properties appear aspower laws, in which the logarithms of two statistical variables are related linearly andthe phenomenon is only observable with a certain minimum amount of data. Only afew such power laws are known, but they hold for texts without exception and evenbeyond texts: daily utterances, including those of child-directed speech, music pieces,and programming language sources all exhibit the same properties, such as shown in(Kobayashi and Tanaka-Ishii 2018). Various cases of human semiosis therefore seem tofollow some kind of identical characteristic, or rule.
Curiously, we never conduct linguistic actions intending to produce such properties,
yet the accumulation of such actions inevitably leads to these properties. Therefore, areason these properties hold must exist. In the scientific domain, the reason remains
unrevealed and will likely remain so without a significant leap in neuroscience. Hence,the subject for now remains a philosophical discussion. This talk attempts to comprehend
what these universal properties might signify, from two different perspectives.
The first perspective is the classical viewpoint of “mirroring nature.” Power laws havebeen abundantly reported for natural and social systems, which are studied as complex
systems in the physics domain. If we live within such a system, then our representational
system of language must be able to accommodate the target structure. In the talk, somescientific explanations (Mandelbrot 1952; Heidelberger and Klohr 2004) of the universal
properties, which take such a mirroring approach, will be summarized.
The mirroring approach does not, however, provide any understanding on how exactly
universal properties emerge. As mentioned before, each such property is global and observable with a certain amount of data, but this occurs through accumulation of individualacts. In other words, we cannot be consciously generating these properties; instead, wesimply use language word after word, possibly following some rules as Wittgenstein (1953)
demonstrated, and the consequence inevitably leads to universal statistical properties. If
the origin of these properties lies in individual acts, then what stipulates every act of rule
following? Or, what is the nature of the rules?
The origin of universal properties is thus considered from this second perspective of1

rule following. Specifically, recent mathematical formulations to explain the emergenceof statistical properties by generative processes have a strong relation with philosophicaldebates on rule following (McGinn 1984; Kripke 1982; Miller and Wright 2014; Kusch
2006). A generative process stipulates the following event (word) according to somerule, given a past sequence of generated events. The emphasis of generative processes
differs, however, between mathematics and philosophy. In philosophy, the central issue is
how a repeated event possibly possesses the same meaning as the past events, whereas
in mathematics, the main issue lies in the rules for introducing new events. Regarding
this introduction of new events, there is a debate by McGinn (1984) in relation to thepassage (Wittgenstein 1953)[199], but the argument within the themes of rule following
and private language is deemed to remain few.
In the talk, I will discuss how a new word is initiated within private language inorder to present a new meaning. Such introduction of new words within a context of
repeated words gradually extends the communication sphere to form a complex system.
The complex structure that emerges through the accumulation of such rule-following acts
is the source of the statistical laws of language, forming one basis of our language game.

References
Heidelberger, M. and Klohr, C. (2004). Nature from Within: Gustav Theodor Fechnerand His Psychophysical Worldview. University of Pittburg Press.
Kobayashi, T. and Tanaka-Ishii, K. (2018). Taylor’s law for human linguistic sequences.
In Proceedings of Annual Conference on Computational Linguistics. arXiv:1804.07893.
Kripke, S. (1982). Wittgenstein on Rules and Private Language. Harvard University Press.
Reprint in 1984.
Kusch, M. (2006). A sceptical guide to mearning and rules: Defending Kripke’s Wittgenstein. McGill Queens University Press.
Mandelbrot, B. (1952). An informational theory of the statistical structure of language.
Proceedings of SYmposium of Applications of Communication theory, pages 486–500.
McGinn, C. (1984). Wittgenstein on Meaning: An Interpretation and Evaluation. BasilBlackwell.
Miller, A. and Wright, C. (2014). Rule-Following and Meaning. Routledge.
Wittgenstein, L. (1953). Philosophical Investigations. Willey-Blackwell. 4th reprint 2009.

2