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Article published In:
Cognitive Linguistic Studies
Vol. 6:2 (2019) ► pp.354–369

An algebraic perspective on abstract and concrete domains

| Chabahar Maritime University
| Shahid Chamran University of Ahvaz
| Chabahar Maritime University
| Shahid Chamran University of Ahvaz
| Chabahar Maritime University

Looking at isomorphic constructs from an algebraic perspective, this article suggests that every concrete construct is understood by reference to an underlying abstract schema in the mind of comprehender. The complex form of every abstract schema is created by the gradual development of its elementary form. Throughout the process of cognitive development, new features are added to the elementary form of abstract schema, which leads to gradual formation of a fully-developed abstract schema. Every developed abstract schema is the underlying source for understanding an infinite number of concrete isomorphic constructs. It is suggested that the process of the mapping of base domain (base construct) unto target domain (target construct) is conducted and mediated by an abstract domain. This abstract domain, which is free from concrete features of base and target, is isomorphic to both base and target domains. To describe the mediatory role of this abstract domain, it might be argued that the chain process of understanding a less familiar domain in terms of a relatively more familiar domain (salience imbalance model) cannot continue infinitely. This chain must stop at some point. This point is the abstract domain, which is isomorphic to base and target domains.

Keywords: isomorphic constructs, conceptual metaphor theory, base domain, target domain
Article outline
  • 1.Introduction
  • 2.Isomorphic constructs
  • 3.Isomorphic constructs in mathematics
  • 4.Concrete and abstract domains
  • 5.Conceptual metaphor theory and chain of domains
  • 6.Concrete realization of abstract domains
  • 7.Pairs of domains throughout the chains
  • 8.Conclusion
  • Acknowledgements
  • Note
  • References
Published online: 4 February 2020
DOI logo
https://doi.org/10.1075/cogls.00036.kha
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