Mathematical Neuroinformatics Group, Human Technology Research Institute, National Institute of Advanced Industrial Science and Technology, Tsukuba, Ibaraki, Japan.
PLoS Comput Biol. 2010 Jul 22;6(7):e1000858. doi: 10.1371/journal.pcbi.1000858.
Classical and Connectionist theories of cognitive architecture seek to explain systematicity (i.e., the property of human cognition whereby cognitive capacity comes in groups of related behaviours) as a consequence of syntactically and functionally compositional representations, respectively. However, both theories depend on ad hoc assumptions to exclude specific instances of these forms of compositionality (e.g. grammars, networks) that do not account for systematicity. By analogy with the Ptolemaic (i.e. geocentric) theory of planetary motion, although either theory can be made to be consistent with the data, both nonetheless fail to fully explain it. Category theory, a branch of mathematics, provides an alternative explanation based on the formal concept of adjunction, which relates a pair of structure-preserving maps, called functors. A functor generalizes the notion of a map between representational states to include a map between state transformations (or processes). In a formal sense, systematicity is a necessary consequence of a higher-order theory of cognitive architecture, in contrast to the first-order theories derived from Classicism or Connectionism. Category theory offers a re-conceptualization for cognitive science, analogous to the one that Copernicus provided for astronomy, where representational states are no longer the center of the cognitive universe--replaced by the relationships between the maps that transform them.
经典和连接主义认知架构理论分别试图将系统性（即人类认知的属性，即认知能力来自相关行为的群体）解释为语法和功能组合表示的结果。然而，这两种理论都依赖于特定的假设来排除这些组合形式（例如语法、网络）的特定实例，这些实例无法解释系统性。类比于托勒密（即地心说）行星运动理论，尽管这两种理论都可以与数据一致，但都未能完全解释它。范畴论是数学的一个分支，它提供了一种基于附加形式概念的替代解释，该概念涉及一对保持结构的映射，称为函子。函子将表示状态之间的映射的概念推广到包括状态变换（或过程）之间的映射。从形式意义上讲，与从古典主义或连接主义推导而来的一阶理论相比，认知架构的高阶理论是系统性的必然结果。范畴论为认知科学提供了一种重新概念化的方法，类似于哥白尼为天文学提供的方法，其中表示状态不再是认知宇宙的中心——而是代表它们的映射之间的关系。
