Symmetry Breaking and Symmetry Restoration

Evidence from English Syntax of Coordination

by Szymon J. Napierała (Author)
©2017 Monographs 170 Pages


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.

Table Of Contents

  • Cover
  • Title
  • Copyright
  • About the author
  • About the book
  • This eBook can be cited
  • Table of Contents
  • Acknowledgements
  • Abbreviations
  • Introduction
  • Chapter 1: Symmetry and asymmetry – background
  • 1.1 Introduction
  • 1.2 Definitions
  • 1.3 Interdisciplinary background
  • 1.3.1 Symmetry in mathematics
  • 1.3.2 Symmetry in physics
  • 1.4 Linguistic background
  • 1.4.1 The third factor of language design and symmetry considerations
  • 1.4.2 Selected examples of symmetry and asymmetry in syntax
  • 1.4.3 Symmetry sensu stricto and symmetry sensu largo
  • 1.5 Areas of symmetry and asymmetry to be examined
  • 1.5.1 In syntactic relations
  • Merge
  • Syntactic categories
  • Coordination, subordination and related phenomena
  • 1.5.2 In descriptive domains
  • Syntax and other modules of grammar
  • NS – LF – PF
  • Chapter 2: The operation Merge
  • 2.1 Background
  • 2.2 Merge, Concatenate and Label in the context of symmetry considerations
  • 2.3 Merge and the catastrophic theory of the origin of FLN
  • 2.3.1 Concatenate
  • 2.3.2 Label / Projection
  • 2.3.3 Concatenate, Label and the catastrophic emergence of syntax
  • 2.3.4 Adjunction – some loose ends
  • 2.4 Initial symmetry of Merge and its breaking in Boeckx (2008)
  • 2.5 Top-down derivations in Zwart (2009)
  • 2.6 Symmetry and asymmetry in the Parallel Merge approach (Citko 2005)
  • 2.7 Some empirical and theoretical problems
  • 2.7.1 Background
  • 2.7.2 Binary Merge – empirical and theoretical counterevidence
  • Empirical counterevidence
  • Theoretical counterevidence
  • 2.7.3 An attempt to overcome the theoretical impasse (Leung 2007)
  • 2.7.4 NS – LF – PF symmetry considerations
  • 2.8 Alternative solutions
  • 2.8.1 Jackendoff’s (2011) Parallel Architecture model
  • 2.8.2 Hornstein and Pietroski’s (2009) Basic Operations unifying model
  • 2.9 The approach advocated in this book
  • 2.9.1 Preliminary issues
  • 2.9.2 SSB, symmetry restoration and Merge
  • 2.9.3 Psychological reality and Merge-based derivations
  • 2.9.4 Summary
  • 2.10 Conclusion
  • Chapter 3: SSB, symmetry restoration and syntactic categories
  • 3.1 Introduction
  • 3.2 SSB, Label and syntactic categories
  • 3.3 Distinction and parallelism among syntactic categories
  • 3.4 Empirical evidence from Boeckx (2008)
  • 3.4.1 Commensurability
  • 3.4.2 Permutability (interchangeability)
  • Projection by movement
  • Reprojection (projection in situ)
  • 3.4.3 Further arguments for EM/IM symmetry
  • 3.4.4 Conclusions: SSB, symmetry restoration, projection by movement and reprojection
  • 3.5 Lack of categorial distinctions – selected examples
  • 3.5.1 Protolanguage
  • 3.5.2 Al-Sayyid Bedouin Sign Language
  • 3.5.3 Pirahã
  • 3.5.4 Riau Indonesian
  • 3.5.5 The foregoing issues and the SSB approach – conclusions
  • 3.6 General conclusions about the nature of FL
  • 3.7 Controversies and areas for future research
  • 3.8 Summary and some further issues
  • Chapter 4: Empirical evidence: coordination
  • 4.1 Coordination – introduction
  • 4.2 Coordination and symmetry restoration
  • 4.3 Culicover and Jackendoff’s (1997) “syntactic coordination despite semantic subordination” – evidence
  • 4.3.1 Background
  • 4.3.2 Binding
  • 4.3.3 Islandhood
  • 4.3.4 LSand, LS(?)or and remaining issues
  • 4.3.5 The clasification of LSand and LS(?) or revisited
  • 4.4 Parataxis/adjunction
  • 4.5 More general conclusions: autonomy of syntax in light of SSB
  • Conclusions
  • Appendix – response to some criticism
  • References

← 14 | 15 →

Chapter 1: Symmetry and asymmetry – background

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 actuality, radiance and integrity is one of the four major prerequisites for beauty. ← 15 | 16 →

As Brading and Castellani (2003) summarize this broader meaning of symmetry, it is

(…) that of a proportion relation, grounded on (integer) numbers, with the function of harmonizing the different elements into a unitary whole: “The most beautiful of all links is that which makes, of itself and of the things it connects, the greatest unity possible; and it is the proportion (summetria) which realizes it in the most beautiful way” (Plato, Timaeus, 31c). From the outset, then, symmetry was closely related to harmony, beauty and unity, and this was decisive for its roles in theories of nature.

(Brading and Castellani 2003:2–3)

Asymmetry is defined in contradistinction to the above, as some deviation from symmetry, some lack thereof. The process of changing symmetry to asymmetry is called symmetry breaking, whereas the reverse process will be named symmetry restoration in this work.

(1)a)symmetryasymmetry(symmetry breaking)
b)asymmetrysymmetry(symmetry restoration)

As will be presented later, symmetry breaking may have various levels, and so the symmetries and asymmetries may also have various levels. This is a significant conclusion that will be pursued later in this book (in Chapter 4) where an analysis based on the symmetry axis will be proposed to account for various syntactic phenomena, ranging from the symmetric to the asymmetric edge.

Discussing the problems of imprecise nomenclature as regards symmetry considerations in physics, Castellani (2003:322) distinguishes the following levels of symmetry breaking (or levels of asymmetry):

(2)Various levels of asymmetry according to Castellani (2003:322)
a)Dissymmetry or non-symmetry – lack of a single symmetry out of many possible symmetries in a given system (in the context of a given phenomenon)
b)Asymmetry – lack of any (>1) of numerous possible symmetries in a given system (in the context of a given phenomenon).
c)Broken symmetry – a result of symmetry breaking (i.e. (a) and/or (b))

In this book symmetry breaking will be regarded as a process, while asymmetry /dissymmetry as a result of this process. In many contexts, the distinction between asymmetry and dissymmetry is not considered necessary in this work, so both terms will be treated equally. The distinction will only be mentioned when it is clearer that the asymmetry under consideration is a result of a process of symmetry breaking involving one out of many possible symmetries in a given ← 16 | 17 → system under analysis, or when reference will be made to Pierre Curie’s (1884) conclusion that “Dissymmetry is what creates the phenomenon” (the claim I will explain in more detail in section 1.3.2).3

Below is a summary of how the foregoing two meanings of symmetry, narrow and broad, are applied in various disciplines of science with respect to the three kinds of symmetry: exact, approximate and broken. Before doing so, however, it is necessary to explain these notions, which will be done with reference to another classification thereof, as summarized in Castellani (2003).


ISBN (Hardcover)
Publication date
2017 (May)
Spontaneous symmetry breaking Symmetry restoring Coordination Subordination Syntactic categories Reprojection
Frankfurt am Main, Bern, Bruxelles, New York, Oxford, Warszawa, Wien, 2017. 170 pp.

Biographical notes

Szymon J. Napierała (Author)

Szymon J. Napierała has studied English and Psychology and received his doctorate degree in English at the Adam Mickiewicz University in Poznań, Poland.


Title: Symmetry Breaking and Symmetry Restoration