Causa Efficiens versus Causa Formalis: origens da discuss\~ao moderna sobre a dimensionalidade do espa\c{c}o

TL;DR

This paper explores the historical and philosophical foundations of space dimensionality, highlighting how different causal explanations from Aristotle, Kant, and Ehrenfest have shaped modern scientific perspectives, especially emphasizing the role of formal causes.

Contribution

It analyzes the evolution of causal explanations in the context of space dimensionality, emphasizing the increasing importance of formal causes in contemporary physics.

Findings

Historical causal frameworks influence modern space theories.

Ehrenfest combined efficient and formal causes in space dimensionality.

Formal causes are increasingly central in modern physical explanations.

Abstract

Metascientific criteria used for explaining or constraining physical space dimensionality and their historical relationship to prevailing causal systems are discussed. The important contributions by Aristotle, Kant and Ehrenfest to the dimensionality of space problem are considered and shown to be grounded on different causal explanations: {\it causa materialis} for Aristotle, {\it causa efficiens} for young Kant and an ingenious combination of {\it causa efficiens} and {\it causa formalis} for Ehrenfest. The prominent and growing r\^ole played by {\it causa formalis} in modern physical approaches to this problem is emphasized.