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Symmetry Breaking and Symmetry Restoration

Evidence from English Syntax of Coordination

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Szymon J. Napierała

This book treats the faculty of language as part of the Universe subject to physical laws. It presents phenomena from syntax and semantics in the interdisciplinary context. The author analyses the origin of syntax and semantics as autonomous modules (asymmetry), even though they display parallelisms (symmetry). He presents linguistic phenomena in the interdisciplinary context where spontaneous symmetry breaking has a central explanatory role, as it is the case in the physical world.

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Chapter 1: Symmetry and asymmetry – background

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1.1    Introduction1

The term symmetry stems from Greek and corresponds to the English word commensurability. In fact, the two terms may be regarded as synonymous. The former originates from Ancient Greek συμμετρία, which consists of σύν (‘with’) and μέτρον (‘measure’), whereas the latter from Latin con (‘with’) and mensura (‘measure’). Although both terms have the same meaning, the Greek term gained more popularity both in scientific and general usage. Its importance cannot be underestimated: appeal to symmetry is of vital importance in philosophy, mathematics, physics, chemistry, biology, linguistics, as well as in various extra-scientific contexts A closely related notion is the reverse one, namely asymmetry, whose meaning implies some departure from symmetry, or symmetry breaking in more formal terms.

1.2    Definitions

The most natural definition of symmetry may be derived from its etymology of a notion synonymous to commensurability. It denotes some state of proportion, equivalence, balance or invariance. This is how symmetry is understood in mathematics and physics: invariance under some transformations that affect a given system (e.g. cf. Wigner 1967:3–13). However, symmetry has also a broader meaning linked to unity, beauty, and harmony, and it was conceived as such in the early scientific thought.

Plotinus, expressing a somewhat different view, states that the idea that symmetry/proportion relation is a sine qua non condition for beauty is almost universally recognized. Similar views were further expounded in medieval times since Pseudo-Dionisius the Aeropagite2. For Thomas Aquinas proportion (i.e. symmetry), along with...

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