Vectors on Curved Space

Dialectica 63 (4):491-501 (2009)
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Abstract

In this paper I provide an ontology for the co‐variant vectors, contra‐variant vectors and tensors that are familiar from General Relativity. This ontology is developed in response to a problem that Timothy Maudlin uses to argue against universals in the interpretation of physics. The problem is that if vector quantities are universals then there should be a way of identifying the same vector quantity at two different places, but there is no absolute identification of vector quantities, merely a path‐relative one.My solution to the problem is to use the mathematical characterization of vectors as differential operators on scalar fields. On the proposed hypothesis a scalar field is a conjunctive state of affairs, and vector and tensor fields are relations instantiated by scalar fields

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Citations of this work

How to Be a Spacetime Substantivalist.Trevor Teitel - 2022 - Journal of Philosophy 119 (5):233-278.
Quantitative Properties.M. Eddon - 2013 - Philosophy Compass 8 (7):633-645.

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References found in this work

The metaphysics within physics.Tim Maudlin - 2007 - New York: Oxford University Press.
The Metaphysics within Physics.[author unknown] - 2007 - Tijdschrift Voor Filosofie 69 (3):610-611.
On universals.Nicholas Wolterstorff - 1970 - Chicago,: University of Chicago Press.

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