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Applied linguistics and Tesol

Applied linguistics and Tesol

Natural Order Hypothesis

Central to many aspects of second language acquisition (SLA) theory is the work of Krashen (e.g. 1985, 2003). Of particular relevance to the topic of the current paper are his Input Hypothesis (1985 passim) and the claimed Natural Order of Acquisition, which he also refers to as the Natural Order Hypothesis. The Input Hypothesis states that language acquisition results from the learner's having received 'comprehensible input'. In his treatment of the Natural Order Hypothesis, Krashen describes the stages of language learning in terms of the purported acquisition of morphosyntactic features (2003:1-2) such as copula, present progressive, and passive voice. In his scheme, any given stage is referred to as T and the next stage as 'i + 1.

1. All language learning is impossible, episode one. Given Krashen's conception, the duration which a learner will require to advance from stage i to stage i + 1 is the time ti. For the sake of simplicity in the following argument, let us assume a constant rate of change from the moment the learner's grammar is at state to the moment it has reached state i + 1, recognizing that the reality is, of course, more complex (see Figure 1, overleaf, in which I represent the learner as a tortoise).

After the period ti/2 has elapsed, the learner will be halfway from i to i + 1. Assume that in each additional step of our analysis, the learner progresses halfway from the current point to the goal. Thus on the second step he will have progressed three quarters of the way from the starting point i to the goal of i + 1. From the three-quarter point, the learner will progress only one-eighth of the way to the goal of i + 1 in half of the time remaining, and so on. Only after an infinite number of such steps will the learner finally reach i + 1. Thus, since learners do not have an infinite amount of time to proceed from i to i + 1, it is logically proven that All Language Learning Is Impossible. I call this 'The Tortoise's Paradox.

2. The relevance (and irrelevance) of (il)logical proofs. Some readers will recognize in the above a fairly transparent variant of Xeno's Paradox (see, for example, Hofstadter 1989:29-32), the ancient proof of the philosopher Xeno which purports to show that All Motion Is Impossible. The problem with this sort of proof, as Hofstadter demonstrates, is that it confuses properties of the external world and what are really irrelevant features of a particular way of describing the world: the infinitude of the chosen mode of calculation of the time for a learner to get from i to i +1, for example, does not reflect any aspect of external reality. The reader probably felt a twinge of suspicion when I stated that we should assume constant rate of change from i to i + i. Indeed, such suspicion is warranted. The above proof that ...

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