Systematicity and a categorical theory of cognitive architecture: universal construction in context
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 m...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2016-07-01
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| Series: | Frontiers in Psychology |
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| Online Access: | http://journal.frontiersin.org/Journal/10.3389/fpsyg.2016.01139/full |
| _version_ | 1818986925018578944 |
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| author | Steven Phillips William Wilson |
| author_facet | Steven Phillips William Wilson |
| author_sort | Steven Phillips |
| collection | DOAJ |
| description | 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 towards addressing this question is higher-order category theory, where categories themselves are the objects of construction. |
| first_indexed | 2024-12-20T18:58:32Z |
| format | Article |
| id | doaj.art-f10c68b4529e4303ad9647c93cde2790 |
| institution | Directory Open Access Journal |
| issn | 1664-1078 |
| language | English |
| last_indexed | 2024-12-20T18:58:32Z |
| publishDate | 2016-07-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Psychology |
| spelling | doaj.art-f10c68b4529e4303ad9647c93cde27902022-12-21T19:29:27ZengFrontiers Media S.A.Frontiers in Psychology1664-10782016-07-01710.3389/fpsyg.2016.01139160578Systematicity and a categorical theory of cognitive architecture: universal construction in contextSteven Phillips0William Wilson1National Institute of Advanced Industrial Science and TechnologyUniversity of New South WalesWhy 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 towards addressing this question is higher-order category theory, where categories themselves are the objects of construction.http://journal.frontiersin.org/Journal/10.3389/fpsyg.2016.01139/fullconnectionismcompositionalitysystematicitycategory theoryUniversal constructionClassicism |
| spellingShingle | Steven Phillips William Wilson Systematicity and a categorical theory of cognitive architecture: universal construction in context Frontiers in Psychology connectionism compositionality systematicity category theory Universal construction Classicism |
| title | Systematicity and a categorical theory of cognitive architecture: universal construction in context |
| title_full | Systematicity and a categorical theory of cognitive architecture: universal construction in context |
| title_fullStr | Systematicity and a categorical theory of cognitive architecture: universal construction in context |
| title_full_unstemmed | Systematicity and a categorical theory of cognitive architecture: universal construction in context |
| title_short | Systematicity and a categorical theory of cognitive architecture: universal construction in context |
| title_sort | systematicity and a categorical theory of cognitive architecture universal construction in context |
| topic | connectionism compositionality systematicity category theory Universal construction Classicism |
| url | http://journal.frontiersin.org/Journal/10.3389/fpsyg.2016.01139/full |
| work_keys_str_mv | AT stevenphillips systematicityandacategoricaltheoryofcognitivearchitectureuniversalconstructionincontext AT williamwilson systematicityandacategoricaltheoryofcognitivearchitectureuniversalconstructionincontext |