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Vortrag: Discrete mathematics as the tool for linguists

Linguistics certainly benefits from many different fields of knowledge, be it science or humanities or… whatever else there is, but, as for any science, none of them is as crucial as the metascience of mathematics. However, additional specifications are needed.

Many linguists use statistic machinery to find correlations and otherwise make predictions about language and/or its use, but, as Agricola Moroz once said (p. c.), “Statistics is to check hypotheses not to create them”, which seems to be easily forgotten by many of those linguists who benefit from using statistics, N-grams, Markov models and such things.

Discrete mathematics, on the other hand, actually provides us with a workable metaframework able to generate large parts of frameworks from itself, the most obvious examples being, first of all, theory of formal languages (created, by no accident, by none other than linguist Noam Chomsky, (Chomsky, 1956)) and then lambda calculus and model theory, both of the latter lying in the heart of formal semantics (see, for example, (Heim, et al., 1998)).

Given such a metaframework, we can create frameworks which by their very design make certain predictions about the data, be it binary branching and endocentricity of Minimalist Merge (Chomsky, 2000) or regularity (again, in the sense of the theory of formal language) of phonology.

That being said, even those who indirectly benefit from discrete mathematics (and that embodies most of formal linguists) often fail to directly describe their deeds in terms of its relevant subfield. For some frameworks it is not directly needed because they provide a translation of its terms to the terms of discrete mathematics; for others it is much more problematic because a relevant translation is either not full (or even non-existing) or misleading. That leads us to the main point of this abstract: every new framework (even if it is a modification of an existing one if the modification is drastic enough) has to provide its formal equivalent in discrete mathematics (probably in either first-order logic or monadic second-order logic, as most other areas, such as graph theory, are, in turn, expressible through one of those) to be used interchangeably by other linguists.

Following that, I am going to write my thesis on generative phonology and morphology (on Ancient Greek material) providing a formal description for most of the notions used (such as phonological segment, boundary segment, or all postsyntactic operations) relying on first-order logic and, where relevant, graph theory.

References

Chomsky Noam Minimalist inquiries: The framework // Step by Step: Essays on Minimalist Syntax in Honor of Howard Lasnik / ed. Martin Roger, Michaels David and Uriagereka Juan. - Cambridge, MA : MIT Press, 2000.
Chomsky Noam Three models for the description of language // IRE Transactions on information theory. - 1956. - 3 : Vol. 2. - pp. 113–124.
Heim Irene and Kratzer Angelika Semantics in Generative Grammar. - Malden : Blackwell Publishers, 1998.

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Tag: 25.09.2021
Anfangszeit: 11:10
Dauer: 00:40
Raum: Don Giovanni

Sprache: en

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