Mathematical Vectors and Physical Vectors

Dialectica 63 (4):433-447 (2009)
From a metaphysical point of view, it is important clearly to see the ontological difference between what is studied in mathematics and mathematical physics, respectively. In this respect, the paper is concerned with the vectors of classical physics. Vectors have both a scalar magnitude and a direction, and it is argued that neither conventionalism nor wholesale anti‐conventionalism holds true of either of these components of classical physical vectors. A quantification of a physical dimension requires the discovery of ontological order relations among all the determinate properties of this dimension, as well as a conventional definition that connects the number one and mathematical unit vectors to determinate spatiotemporal physical entities. One might say that mathematics deals with numbers and vectors, but mathematical physics with scalar quantities and vector quantities, respectively. The International System of Units distinguishes between basic and derived scalar quantities; if a similar distinction should be introduced for the vector quantities of classical physics, then duration in directed time ought to be chosen as the basic vector quantity. The metaphysics of physical vectors is intimately connected with the metaphysics of time. From a philosophical‐historical point of view, the paper revives W. E. Johnson's distinction ‘determinates‐determinables’ and Hans Reichenbach's notion of ‘coordinative definition’
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1111/j.1746-8361.2009.01215.x
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 35,527
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Ontological Dependence.Tuomas E. Tahko & E. J. Lowe - 2015 - Stanford Encyclopedia of Philosophy.
Ontological Dependency.E. J. Lowe - 1994 - Philosophical Papers 23 (1):31-48.
Determinables as Universals.Ingvar Johansson - 2000 - The Monist 83 (1):101-121.

View all 11 references / Add more references

Citations of this work BETA

Add more citations

Similar books and articles


Added to PP index

Total downloads
22 ( #280,668 of 2,287,732 )

Recent downloads (6 months)
1 ( #393,085 of 2,287,732 )

How can I increase my downloads?

Monthly downloads

My notes

Sign in to use this feature