Systematicity and a Categorical Theory of Cognitive Architecture: Universal Construction in Context.
Systematicity and a Categorical Theory of Cognitive Architecture: Universal Construction in Context.
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DOI：
10.3389/fpsyg.2016.01139
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发表时间：
2016
影响因子：
3.8
通讯作者：
Wilson WH
中科院分区：
文献类型：
--
作者：
Phillips S;Wilson WH
为什么思考某些想法的能力意味着思考某些其他结构相关的想法的能力？尽管经过数十年的激烈争论，认知科学家尚未就认知结构这一属性（共同提供认知能力的基本过程和构成模式）的解释达成共识，即系统性。系统性通常被认为涉及表示/处理同等可认知实体之间的共同结构关系的能力。然而，解决系统性问题的主要理论方法，即经典（符号）和联结主义（子符号），需要任意（特别）假设来得出系统性。也就是说，它们的核心原则和假设没有提供因果理论所要求的系统性的必要和充分条件。因此，这些方法无法充分解释为什么系统性是人类认知的（接近）普遍属性，尽管是在有限的背景下。我们回顾了解决系统性问题的另一种类别论方法。作为一种结构的数学理论，范畴论以普遍建构的形式为系统性提供了充分必要条件：每一个系统相关的认知能力都由共同成分和独特成分组成。此外，每个通用结构都可以被视为给定上下文（类别）中的最佳结构。从这个角度来看，通用结构是从学习中衍生出来的，是一种优化。那么，最终的挑战是解释上下文的决定因素。如果上下文是一个范畴，那么解决这个问题的自然延伸就是高阶范畴论，其中范畴本身就是构造的对象。
Why does the capacity to think certain thoughts imply the capacity to think certain other, structurally related, thoughts? Despite decades of intensive debate, cognitive scientists have yet to reach a consensus on an explanation for this property of cognitive architecture—the basic processes and modes of composition that together afford cognitive capacity—called systematicity. Systematicity is generally considered to involve a capacity to represent/process common structural relations among the equivalently cognizable entities. However, the predominant theoretical approaches to the systematicity problem, i.e., classical (symbolic) and connectionist (subsymbolic), require arbitrary (ad hoc) assumptions to derive systematicity. That is, their core principles and assumptions do not provide the necessary and sufficient conditions from which systematicity follows, as required of a causal theory. Hence, these approaches fail to fully explain why systematicity is a (near) universal property of human cognition, albeit in restricted contexts. We review an alternative, category theory approach to the systematicity problem. As a mathematical theory of structure, category theory provides necessary and sufficient conditions for systematicity in the form of universal construction: each systematically related cognitive capacity is composed of a common component and a unique component. Moreover, every universal construction can be viewed as the optimal construction in the given context (category). From this view, universal constructions are derived from learning, as an optimization. The ultimate challenge, then, is to explain the determination of context. If context is a category, then a natural extension toward addressing this question is higher-order category theory, where categories themselves are the objects of construction.