The Emergence of the Unmarked without constraint interaction
The Correspondence Theory of Faithfulness predicts the existence of languages in which markedness constraints, e.g., *COMPLEX, NOCODA, are active in a reduplicant but not in the corresponding base. This scenario, referred to as The Emergence of The Unmarked (TETU), provides a key argument for constraint violability in Optimality Theory (OT). It arises from the following language-specific ranking schema: IO-faithfulness Markedness constraint
BR-faithfulness (McCarthy & Prince, 1995). A canonical example from Sanskrit (Parker, 2002:35) involving *COMPLEX is given in (1). The underlined segment in the base does not surface in the reduplicant prefix.
(1) Sanskrit reduplication
pa-psa: PERFECTIVE ‘devour’ du-druw PERFECTIVE ‘run’ pa-pračh PERFECTIVE ‘ask’ sa-swar PERFECTIVE ‘sound’ tu-s̥tu PERFECTIVE ‘praise’ ta-stha: PERFECTIVE ‘stand’
In this paper, we derive TETU in reduplicants from a general theory of information transfer without recourse to constraint interaction. Our approach is inspired distally by information theory (Shannon, 1948) and more proximally by Message-Based Phonology (Hall, Hume, Jaeger, & Wedel, 2016).
There are two central tenets. The first is an application of Bayes’ Law to message transmission, given in (2). The formulation captures an aspect of Shannon’s fundamental theorem for information transfer in a discrete channel with noise (Shannon, 1948: 22). Shannon provides a proof that errorless transfer can be obtained by modifying the signal as a function of the predictability of the message.
(2) ! "#$$%&# $'&(%), +,(-#.- = ! "#$$%&#|+,(-#.- ∗ !($'&(%)|"#$$%&#) The law in (2) states that the posterior probability of a message given a phonological form (signal) in context, ! "#$$%&# $'&(%), +,(-#.- , is a linear function of the prior probability of the message in that context, ! "#$$%&#|+,(-#.- , and how clearly the speech signal differentiates the intended message from competitors, referred to as signal specificity,
!($'&(%)|"#$$%&#).
The second tenet is the principle of effective information transfer, stated in (3):
(3) Human language deployed as a system of information transfer maintains consistently high ! "#$$%&# $'&(%), +,(-#.-
Taken together, (2) and (3) dictate that phonological form (signal) changes as a function of message predictability. Moreover, the direction of change is also predicted. Phonological form will change such that signal specificity, the degree to which the phonological form differentiates the message from competitors, will go down as message predictability goes up.
Reduplication patterns provide a convenient domain to test these claims since they involve two messages, the message conveyed by the base and the message conveyed by the reduplicant, expressed by similar signals in environments likely to differ in predictability. In many cases of reduplication, the message conveyed by the reduplicant, e.g., perfective aspect in (1), will be more predictable than the message conveyed by the base. This is because affixes tend to be syntactically restricted to occur in positions with fewer competitors than for bases (cf. the FAITHrootFAITHaffix meta-ranking: McCarthy & Prince 1995: 118; though see Ussishkin & Wedel, 2002). According to (3), increased predictability of reduplicants over bases entails that signal specificity will decrease in the reduplicant relative to the base. Thus, any change in phonological form occurring in the reduplicant must make the reduplicant form more like competitors, i.e., less specific.
Consider cluster simplification in (1). Amongst 788,993 unique words of Sanskrit, [pa] sequences occur 31,146 times; [pra] sequences occur just 15,310 times (queries of sanskritdictionary.com on 06/21/2016). The same goes for other consonant clusters, e.g., 540 instances of [dru], c.f. 6932 of [ru]; 245 instances of [swa], c.f. 31,132 of [sa]; 966 instances of [stha], c.f., 43,528 of [ta], etc. Reducing the cluster to a singleton onset makes the reduplicant more similar to other words in the lexicon, decreasing signal specificity. That this type of change occurs in an environment of increased predictability follows from the Bayesian law in (2) and the principle of effective information transfer in (3). It seems that reducing signal specificity may also explain which of the two onset consonants in the base surfaces in the reduplicant. In [tu-s̥tu] ‘stand’ and [ta-stha:] ‘praise’, for example, [t] instead of [s] surfaces in the reduplicant. This fact has been attributed in past work to a preference for low sonority onsets (Parker, 2002), but given that there are more [t]-initial words than [s]- initial words, it is also consistent with increasing lexical competition in high predictability environments. We surmise that the sonority preferences identified in past work have, over time, biased the Sanskrit lexicon towards high sonority onsets (c.f., Martin, 2007).
In sum, TETU in reduplicants, a key argument for language-specific constraint rankings and constraint violability, can also be derived from core properties of language as a system of information transmission; a general law of such systems (2) coupled with a fundamental property of human language (3) correctly predicts TETU in languages, such as Sanskrit, in which reduplicants are more predictable than bases and clusters provide a higher degree of signal specificity than singletons. A broader implication of the proposal is that TETU can be modelled with domain-general principles, i.e., Bayes Law in (2) and the principle of effective information transfer in (3).
References
Hall, K. C., Hume, E., Jaeger, F., & Wedel, A. (2016). The Message Shapes Phonology. Martin, A. T. (2007). The evolving lexicon. (PhD), University of California Los Angeles.
McCarthy, J. J., & Prince, A. (1995). Faithfulness and Reduplicative Identity. In J. Beckman, L. Walsh Dickey, & S. Urbanczyk (Eds.), University of Massachusetts Occasional Papers in Linguistics 18 (pp. 249-384). Amherst, Mass.: GLSA Publications.
Parker, S. (2002). Quantifying the Sonority Hierarchy. (Ph.D.. Dissertation), University of Massachusetts, Amherst, Amherst. Shannon, C. E. (1948). A Mathematical Theory of Communication. The Bell System Technical Journal, 27, 379-423.
Ussishkin, A., & Wedel, A. (2002). Neighborhood density and the root-affix distinction. In M. Hirotani (Ed.), Proceedings of NELS 32 (pp. 539-549). Amherst, MA: GLSA.
