A Note on the Categorical Nature of Causality (III)

 

A Note on the Categorical Nature of Causality (III)

Karin Verelst
FUND-CLEA
Vrije Universiteit Brussel
Pleinlaan 2, B-1050 Brussels
kverelst@vub.ac.be

 

Abstract:

Discussions on causality abound, but rare are the attempts at precise definition of what is meant. The reason might be that the concept in itself is intrinsically pluriform, but even then theories enclosing some kind of causation should exhibit certain common structural characteristics, otherwise the use of the common term would be absolutely pointless. I show that a fairly straightforward categorical characterisation of causation is possible when one takes both the history of the concept and Meyerson’s careful analysis of the relation between causation and time into account. Historically it has been seen (by Aristotle) that a causal relation between events is never simply straightforward, but always implies — explicitly or not — a connection between a universal (global) and a particular (local) level. This is why the idea of causecan be linked to the idea of lawfulness. But there is a difference between a law and a cause because of the asymmetry between space and time: space is actual everywhere but time only at this moment. Laws definethe identical, but identity as well is only unproblematic at this moment. Meyerson shows that causality  therefore somehow implies the conservation of identity through time. The idea of conservation is essential here. Now when causal connections are interpreted as order relations (as is the case in, e.g., relativistic theories), then causation appears as the Galois adjoint to identity, and causality will be aequivalent to the idea of physical law. This allows to formally characterise causality in this type of theories, without having to “explain” it any further. Given the functoriality of the derivative and the interconnection between symmetry and conservation, this approach might be generalisable to other physically viable notions of causation through the use of Noether’s Theorem.

 

References:

[1]  F. Borceux, Handbook of Categorical Algebra I, Cambridge University Press, Cambridge, 1994.

[2]  E. Meyerson, Identit´e et R´ealit´e, F´elix Alcan, Paris, 1932.

[3]  E. Noether, “Invariante Variationsprobleme”, Nachr. d. K¨onig. Gesellsch. d. Wiss. zu G¨ottingen, Math-phys. Klasse, pp. 235–257, 1918.

[4]  K. Verelst, “On what Ontology Is and not-Is”, Foundations of Science, 13, 3, 2008.