Ultrametric Model of Mind, I: Review
arXiv Preprint Archive January 13, 2012 via arXiv
Summary
An ultrametric topology mathematically models Ignacio Matte Blanco's principles of symmetric and asymmetric being, as described in his 1975 book. This model corresponds to hierarchical clustering in empirical data, such as text. The ultrametric structure captures the logic of symmetric being, which underlies reasoning that lacks self-awareness or consciousness, as well as conscious reasoning. A companion paper examines how symmetric reasoning can be identified within narrative text that contains both symmetric and asymmetric reasoning.
Study at a glance
| Characteristics | Theoretical or philosophical paper Peer reviewed |
|---|---|
| Topics | Cs.ai 68t01 I.2.0; i.2.3; j.4 Cognitive-science |
| Key finding | An ultrametric topology can mathematically model the structure of logic reflecting Matte Blanco's symmetric being and the reasoning processes involved in conscious or unconscious thought. |
Abstract
We mathematically model Ignacio Matte Blanco's principles of symmetric and asymmetric being through use of an ultrametric topology. We use for this the highly regarded 1975 book of this Chilean psychiatrist and pyschoanalyst (born 1908, died 1995). Such an ultrametric model corresponds to hierarchical clustering in the empirical data, e.g. text. We show how an ultrametric topology can be used as a mathematical model for the structure of the logic that reflects or expresses Matte Blanco's symmetric being, and hence of the reasoning and thought processes involved in conscious reasoning or in reasoning that is lacking, perhaps entirely, in consciousness or awareness of itself. In a companion paper we study how symmetric (in the sense of Matte Blanco's) reasoning can be demarcated in a context of symmetric and asymmetric reasoning provided by narrative text.